&EPA
                  EPA 600 7 78 1 72a
                  August 1 978

Premixed
One-dimensional
Flame (PROF) Code
User's Manual

Interagency
Energy/Environment
R&D Program Report

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                  RESEARCH REPORTING SERIES


Research reports of the Office of Research and Development. U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional  grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:

    1.  Environmental Health Effects Research

    2.  Environmental Protection Technology

    3.  Ecological Research

    4.  Environmental Monitoring

    5.  Socioeconomic Environmental Studies

    6.  Scientific and Technical Assessment Reports  (STAR)

    7.  Interagency  Energy-Environment Research and Development

    8.  "Special" Reports

    9.  Miscellaneous Reports

This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort  funded  under the 17-agency  Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems.  The  goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
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effects; assessments  of, and development of, control technologies for energy
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                       EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
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This document is available to the public through the National Technical Informa-
tion Service. Springfield, Virginia 22161.

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                                      EPA-600/7-78-172a

                                             August 1978
Premixed  One-dimensional  Flame
    (PROF) Code User's  Manual
                           by


                  Robert M. Kendall and John T. Kelly


             Acurex Corporation/Energy and Environmental Division
                       485 Clyde Avenue
                   Mountain View, California 94042
                     Contract No. 68-02-2611
                         Task No. ,7
                   Program Element No. EHE624A
                  EPA Project Officer: W. Steven Lanier

               Industrial Environmental Research Laboratory
                  Office of Research and Development
                  Research Triangle Park, NC 27711
                        Prepared for

               U.S. ENVIRONMENTAL PROTECTION AGENCY
                 Office of Research and Development
                     Washington, DC 20460

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                                  ABSTRACT

       The Prenrixed One-dimensional Flame (PROF) code numerically models com-
plex chemistry and diffusion processes in premixed laminar flames.  Since this
code Includes diffusion, it gives realistic solutions of coupled combustion
and pollutant formation processes in the flame zone, as well as downstream
in the post-flame region.  Experience has shown that the code can be a valu-
able aid when interpreting experimental flame data.
       In addition to flames, the PROF code can also treat problems involving
well-stirred reactors, plug-flow reactors, and time-evolution chemical kine-
tics.  A wide variety of conventional and experimental combustion systems can
be treated by the code's flame and reactor options.
       This PROF code user's manual describes the problems that can be treated
by the code.  It also describes the mathematical models and solution procedures
applied to these problems.  Complete input instructions and a description of
output are given.  Several sample problem input and output listings are pre-
sented to demonstrate code options.  A program listing and code Fortran vari-
able definitions are included in the manual.
                                      ii

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                             TABLE OF CONTENTS

Section                                                               Page

   1    INTRODUCTION 	 1-1

   2    PROBLEM DESCRIPTION  	 2-1

   3    MATHEMATICAL MODELS  	 3-1

        3.1  Flame Model	3-1

        3.1.1  Species Axial Diffusional Flux  	 3-2
        3.1.2  Species Production Terms  	 3-5
        3.1.3  Species Flux at the Wall	3-6
        3.1.4  Bulk Gas Volumetric Heat Loss	3-7
        3.1.5  Axial Diffusional Heat Flux	3-11
        3.1.6  Wall Heat Flux	3-13
        3.1.7  Specialized Boundary Conditions 	 3-14

        3.2  Plug-Flow Reactor Model 	 3-16
        3.3  Time-Evolution Chemistry Problem  	 3-17
        3.4  Well-Stirred Reactor Model  	 3-17

   4    SOLUTION PROCEDURES

        4.1  Flame Solution Procedure  	 4-1

        4.1.1  Finite Difference Form of the Flame Conservation
               Equations	4-1
        4.1.2  Chemistry Solution Procedure  	 4-6
        4.1.3  Linearized Predictor - Corrector Procedure   	 4-9

        4.2  Plug-Flow Reactor Solution Procedure  	 4-12
        4.3  Well-Stirred Reactor Solution Procedure 	 4-13

   5    CODE INPUT INSTRUCTIONS  	 5-1

        5.1  Card Input Deck	5-1
        5.2  Thermochemical Input Data Format	5-12
        5.3  PROF Thermochemical Data Update Program (TCUP)   	 5-15

        5.3.1  List Option	5-15
        5.3.2  Update Option	5-15

   6    OUTPUT	6-1

        6.1  Integral and Nonintegral Input Parameters 	 6-1
        6.2  Species Names and Concentrations  	 6-1
        6.3  Thermochemical Data	6-2
        6.4  Kinetic Reaction Data	6-2
        6.5  First Guess Alphas  	 6-2
                                    iii

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Section                                                               Page

         6.6  Chemistry Solutions  at  Grid  Points	6-2
         6.7  Condensed Output for Each  Iteration	6-3
         6.8  Mole Flux at Grid Points	6-3
         6.9  Grid Information Summary Table  	  6-4
         6.10 Kinetic Reaction Summary Information  	  6-5

    7    SAMPLE CASES

         7.1   Sample Case 1  -  Free Methane/Air  Flame	7-1
         7.2  Sample Case 2 -  Methane/Air  Flame Attached to
              a Flameholder  	  7-23
         7.3  Sample Case 3 -  Methane/Air  Chemical  Evolution
              in an Internal Combustion  Engine  	  7-36
         7.4  Sample Case 4 -  Methane/Air  Well-Stirred Reactor  ....  7-47
         7.5  Sample Problem 5 - Catalytic Combustor  Fuel
              Conversion Efficiency 	   7-55

    8    DEBUG OUTPUT AND PROBLEMS AND PITFALLS 	   8-1

         8.1   Debug Output Description	   8-1
         8.2  Flame Solution,  Problems and Pitfalls 	   8-5
         8.3  Well-Stirred,  Plug-Flow and  Time-Evolution Chemical
              Kinetic Solution Problems  and Pitfalls  	   8-7

    9    PROGRAM FORTRAN VARIABLES LIST  AND DEFINITIONS 	   9-1

   10    PROGRAM AND SUBROUTINES	10-1

         10.1   ACEF Main Program	10-1
         10.2  READIN Subroutine   	  10-2
         10.3  OBTAIN Subroutine   	  10-2
         10.4  GETDAT Subroutine   	  10-2
         10.5  KINKIN Subroutine   	  10-2
         10.6  EPROP Subroutine 	  10-2
         10.7  FLAME Subroutine 	  10-3
         10.8  RDFLX Subroutine 	  10-4
         10.9  RERAY Subroutine 	  10-4

    11    PROGRAM SOURCE DECK LISTING  AND SYSTEM REQUIREMENTS	11-1

    12    REFERENCES	  12-1

    Appendix A  Brief Development and Demonstration of Bifur-
                 cation Approximations  to Diffusion- Coefficients  .   .  A-l
                                     iv

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                             LIST OF FIGURES
Figure                                                                Page
   1     Schematic of Unconfined Flame 	  2-2
   2     Schematic of Confined Flame 	  2-3
   3     Schematic of Well-Stirred and Plug-Flow Reactor Problems   .  .  2-5
   4     Planck Mean Absorption Coefficients at One Atmosphere
        Total Pressure	3-10
   5     Schematic of Flameholder Processes  	  3-15

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                                LIST OF SYMBOLS




A         cross sectional area




B ,        monochromatic radiation intensity
C.        J factor constant coefficient
 \J




C         specific heat





C         weighted specific heat defined by Equation (25)





C         circumference of bounding tube
 W
CV        denotes control volume




D-.       binary diffusion coefficient
  ' J



H        diffusion constant defined by Equation (6)




E         activation energy for kinetic reaction




F..        diffusion factor of species i




h         enthalpy of bulk gas




i         denotes species when used as subcript




J         J factor in wall transport expression




J.        flux of species i in axial direction

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                        LIST OF SYMBOLS (Continued)


Jw        flux of species i at bounding tube wall
 wi

k         thermal conductivity of bulk gas


          spectral absorption coefficient


K         Planck mean absorption coefficient


K         equilibrium constant for reaction m
 pm

L         characteristic dimension of flame for radiation properties


m         mass rate of gas


M         molecular weight


p         pressure


q         axial heat transport
q..        heat transport at the bounding tube wall
 Inf
Q         volumetric heat loss


qn        radiative flux
r,        radius of bounding tube
 W
R         gas constant



S         distance along flame axis



S_        Schmidt number
 \f




                                    vii

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                       LIST OF SYMBOLS (Continued)




3"         normalized distance defined by Equation (33)




T         temperature




V         volume of well-stirred reactor or radiation integration volume




W..        chemical production rate of species i




X.j        mole fraction of species i




Y..        mass fraction of species i




o.        species concentrations in moles per gram




6         flame zone length scale




e         emissivity of gas
 7



vj        third body efficiency of species i in reaction m

  m


 ij       integral expression which depends upon the particular inter-

          molecular potential function which is utilized




p         density




a         Stefan-Boltzmann constant




aref      collision cross section for reference species

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                         LIST OF SYMBOLS (Concluded)





Superscripts





P         reaction products





R         reaction reactants
                                     IX

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                                 SECTION 1
                                INTRODUCTION

       This User's Manual fully describes and provides instructions for using
the Premixed One-dimensional Flame (PROF) computer code *
       The PROF code can be used to predict the detailed chemical kinetic
combustion and/or pollutant formation events which occur in a wide variety
of experimental and practical combustion devices.  Both steady, free and
confined premixed flames, where gaseous diffusion is important, can be
treated by the code.  Also, well-stirred reactor, plug-flow reactor, and
fixed mass time-evolution chemical kinetic problems, where diffusion is not
explicitly treated, can be modeled by the code.  References 1 and 2, as well
as Section 7 of this report, present some examples of problems which can be
treated by the PROF code.
       The key program element in the PROF code is a stable and reliable
kinetic chemistry routine.  This routine can be applied to any chemical
system for which kinetic reaction data is available.  To model flame and
reactor-type problems, appropriate driver routines are linked to the general
chemistry routine.  The flame model includes axial gas phase diffusion and
is, mathematically, a multivariable boundary value problem.  This problem
requires a coupled grid solution procedure for all variables.  This grid
problem is solved in PROF by using a predictor - linearized corrector itera-
tive matrix procedure.  The reactor type models do not have explicit diffu-
sion terms.  These models are initial value problems solved by simple time
or space marching in the PROF code.
*
 Program is coded in Fortran V.

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       The PROF code was developed to accurately model the detailed combustion
and pollutant formation processes occurring in premixed one-dimensional
flames.  Previous plug-flow models applied to premixed flame combustion and
pollutant formation processes did not incorporate axial diffusion in the
formulation.  Since ignition processes require upstream diffusion, these
plug-flow models could not be directly applied to flames without making
some gross assumptions as to the upstream ignition zone starting conditions.
In addition, the accuracy of these nondiffusive models is very poor in the
flame zone, where diffusion is important.  Since the PROF code Includes
axial diffusion, predictions of combustion and pollutant formation processes
can be achieved in the flame zone as well as downstream of this zone.  The
accuracy of these predictions is dependent only on the adequacy of elementary
kinetic reaction and transport data.  Thus, PROF predictions, combined with
experimental data, can provide valuable insights into the complex chemical
events taking place within as well as downstream of the flame zone.
       Although the PROF code was developed to treat, primarily, the premixed
one-dimensional flame problem, the PROF code formulation has been expanded
to include reactor-type problems which do not explicitly include axial diffusion,
This single code can now be applied to a wide variety of practical and experi-
mental combustion problems.
       A brief description of the problems that can be treated by the PROF
code appears in Section 2.  Section 3 presents the mathematical models and
boundary conditions for the flame and reactor type problems.  Appropriate
solution procedures for the mathematical models are given in Section 4.  A
full set of code  input instructions are  given in Section 5, and the standard
output format is  described in Section 6.  Listings of  input data  and
selected sections of output for several  sample problems are given in
                                    1-2

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       Section 7.  Descriptions of debug output and a short discussion of
potential problem areas appears in Section 8.   Code Fortran variables  and
definitions are given in Section 9.  Summary descriptions of the program
and subroutines are presented in Section 10.  A complete listing of the
program appears in Section 11.
                                     1-3

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                                 SECTION 2
                            PROBLEM DESCRIPTION

       The PROF code is applied primarily to premixed one-dimensional  lami-
nar, laterally unconfined, flame problems.  Figure 1 illustrates schemati-
cally an unconfined flame which is anchored to a flat flame burner by a
flameholder.  The flameholder provides a sink for the flame's "excess" heat
and reactive species.
       The PROF code models axial diffusion of heat, q, and species, Jn-,
as well as chemical kinetics within the flame.  The calculations can also
include radiative heat loss to the surroundings and heat and reactive
species losses to the flameholder.  Very general chemical systems can be
treated by the code.  Molecular heat and mass transport modeling incorporate
accurate approximations for unequal species diffusion and nonunity Lewis
number effects.
       The PROF code unconfined flame option can be applied to a number of
experimental and practical flame problems.  For example, it can be used to
analyze coupled combustion and pollutant formation processes, such as fuel-
nitrogen conversion, in experimental flat flames.  Also, practical problems
such as determining premixed flame speeds and flamability limits of coal
or oil-derived gaseous fuel mixtures can be solved with this option.
       To augment the PROF unconfined flame predictive capability, models
for the thermal and chemical effect of confining walls on bulk gas properties
are included in the code.  Figure 2 illustrates schematically the confined
flame problem treated by the PROF code.  In this case both axial and radial
heat and mass transport are considered.  Transfer coefficients are used to
                                    2-1

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                                              Post flame zone
                                           Luminous zone
qf         Jf1
                                      Preflame zone





                                       flameholder
Figure 1.  Schematic of unconfined flame.
                   2-2

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ro
co
             Post-flame
             zone
             Luminous
             zone
             Preflame
             zone

                              !   f!    f
L
VI
r
                                     m
                               Figure 2.  Schematic of confined flame.

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model heat and mass tranfer to the confining walls in terms of bulk and
wall gas conditions so that the efficient one-dimensional calculation scheme
can be applied to this problem.  The details of radial  variation of composi-
tion and chemical reaction are lost in this method, but this approach
is useful to assess the impact of wall effects on bulk  gas properties.
       For the confined flame problem, the state of the gas at the tube wall
is assigned as a boundary condition along with the initial bulk species
fluxes and temperatures.   The wall gases may be in equilibrium or any arbi-
trary kinetic state.  Given the boundary conditions, the code determines
bulk gas properties as a function of distance along the tube axis.
       A variety of experimental and practical combustion and pollutant
formation problems can be treated by this option.  Some examples are tubular
reactors, surface combustors, and catalytic combustors.
       Besides flame problems, where axial gas phase diffusion is important,
the PROF code can also treat fully-mixed, well-stirred  reactor and one-
dimensional nondiffusive plug-flow reactor and time-evolution chemical
kinetic problems.  Figure 3 illustrates schematically some possible appli-
cations of the well-stirred reactor and plug-flow reactor PROF code options.
The schematic of the jet-stirred combustor illustrates  an application of
the well-stirred reactor option.  In this problem, a specified mass of
reactants and products flows continuously through a fixed-volume chamber.
Intense mixing of the reactants occurs within the combustor and chemical
reaction takes place uniformly throughout the chamber.   Depending on the
gas and wall temperatures, heat may or may not be lost  through the walls
                                     2-4

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m
                                                              water
                                                       A-16159
                                                              water
                WATER-COOLED SAMPLING PROBE
                    (Plug-Flow Reactor)
                                                   m
                    JET-STIRRED  REACTOR
                  (Well-Stirred Reactor)
         Figure 3.  Schematic of well-stirred and plug-flow
                   reactor problems.
                                2-5

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of the chamber.  In this well-stirred reactor case a steady-state fixed
volume of fluid is reacting with a mean residence time defined by the con-
stant mass flowrate through the reactor.
       The schematic of a water-cooled sampling probe in Figure 3 illus-
trates an application of the plug-flow reactor option.  In this problem,
a chemically reacting sample is introduced into a tube whose walls are
cooled much below the entering gas temperature.  The cooling effect of the
wall quenches the gas phase reactions, allowing the sample to pass through
the probe unaltered by these reactions.   Besides cooling the gases, the
wall might also provide sites for heterogeneous gas phase reactions which
will alter the sample composition.  Only radial diffusive heat and mass
transfer are considered in this option.
       Besides the problems illustrated in Figure 2, the plug and well-
stirred reactor options can also be applied to a variety of gas turbine,
furnace and catalytic combustion and pollutant formation problems.  The
PROF code can also treat the reaction of a fixed mass of gas in time as the
pressure and temperature change.  Chemical evolution inside internal com-
bustion engines, combustion bombs and other time-dependent combustion
systems can be predicted by this option.  Of course the option assumes
uniformly mixed and reacting mixtures within the system.  Therefore, apply-
ing this option to spatially nonuniform systems represents only an approxi-
mate modeling of the system.
       The following section describes the assumptions, equations and solu-
tion procedures utilized in the PROF code.  The solution procedure has been
optimized for predicting premixed one-dimensional flames.  The following
                                     2-6

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discussion will emphasize the development of the flame equations.   Well-
stirred and plug-flow reactor equations are subsets of the flame equations
and the reduction of flame equations to these cases will  be only briefly
discussed.
                                    2-7

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                                 SECTION 3
                            MATHEMATICAL MODELS

       In this section the flame model is discussed first.  This is followed
by discussions of the plug-flow reactor, time-evolution chemical kinetic
and well-stirred reactor models.
3.1    Flame Model
       The flame option governing equations are developed by integrating the
steady two-dimensional species, mass and energy equations across a plane
perpendicular to the axis.  This results in a set of one-dimensional flame
equations in terms of bulk gas properties.  These properties vary along the
flame axis as a result of fluxes of heat and mass at the edge of the flame
and chemical reaction and axial diffusive fluxes within the bulk gases.  For
a large diameter/height ratio free flame with an initially uniform flow,
the edge fluxes are relatively small and the bulk properties are equivalent
to local conditions across the flame.  For a flame confined in a tube (e.g.,
catalytic combustor) the edge fluxes can be significant.  In this case, the
edge fluxes are approximately treated by a transfer coefficient approach
where the fluxes are assumed to be directly proportional to bulk and wall  gas
states.  Using transfer coefficients permits one-dimensional solution procedures
to be applied to an essentially two-dimensional problem.
       The quasi-one-dimensional flame conservation equations can be written
as:
       Species
                            dY.         d(AJ,)
                          *-ars "1 --TIT-- V                    (1)
                                     3-1

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       Energy
                                   i
where global continuity has been incorporated into the above equations.
The momentum equation has been replaced by assigning pressure.  Assigning
a fixed pressure is a valid approximation for the low-velocity flame cases
of primary interest.  The species conservation expression, Equation (1),
shows that the species mass fraction along the flame axis is altered by
species bulk gas phase chemical production, W. , axial  diffusive flux, J.,
and wall diffusive flux, J.. .   In the energy conservation expression,
                          W1
Equation (2), the enthalpy along the flame axis is altered by the bulk gas
heat loss rate, Q, axial diffusive heat flux,S J-h. + k dT/ds, and wall
                                              i  1 '
heat loss, q .  Expressions for  W^ , J., Jw>, Q, K and q , along with
boundary conditions, complete the definition of the flame problem.
3.1.1  Species Axial Diffusional Flux
       Utilizing binary coefficient data, the rigorous expression for species
multi component diffusional flux can be obtained by implicitly solving the
Stefan-Maxwell relations.  This involves a level of effort which, in most
practical flame cases, is beyond that consistent with the quality of the
transport data input into the code.  For the PROF code the simple, yet
adequate, bifurcation approximation for the binary diffusion coefficients is
use'd with the Stefan-Maxwell relations to develop an explicit expression
for species flux.
       The approximation, which is fully developed in Reference 3 and summarized
in Appendix A,assumes that the contributions of species i and j to the diffusion
coefficients, V..t can be separated in the following manner:
                 J
                                    3-2

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where I) is a reference self-diffusion coefficient and  F.  and  F. are diffu-



sion factors.  For binary and ternary systems,  Equation  (3) is exact.  The



pressure and temperature dependence of V^  is absorbed into U so that F.



and Fj are independent of temperature and pressure.  For more complex
     J


systems, equation (3) may be considered as  a good correlating function of



diffusion data.  The primary advantage of this  approximation  is that it



permits an explicit formulation for diffusional  mass flux J.  in terms of



gradients of species i to be developed from the Stefan-Maxwell relations.



Neglecting thermal diffusion effects, the flux  can be  written in the follow-



ing form (see Appendix A):
                               rar -\M7\dT   **^n                (*)
where


                             F   and
where X1 and Yi are the mole and mass fractions,  respectively.  Computations



that consider this formulation are considerably more  efficient than those



that use arbitrary expressions for the Pi .  and apply  either the Stefan-Maxwell



implicit equations or develop the concentration dependent multi component
 

diffusion coefficients.
                                    3-3

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       In Equation (4),  D is  typically  taken as the self-diffusion coeffi-

cient of some reference  species,  e.g.,  (L.  The F^ are taken as constants

independent of temperature and pressure.   From Reference 4:
                                    ,  T(T/M^y'      ?
                     D = 2.628 x  io"J 2ej\ ^  (cmVsec)          (6)

                                     Pa ref"ij'


                                                                 o
with T in K, P in atmospheres, and collision cross section, a in A.  For
                                                 o
$2 as tne reference species,  a is equal to  3.467  A.  From Appendix A the

integral expression for transport properties is approximated by:



                    o(5'1)*1.07  [T/(E/k)]--159                      (7)
                      J

where the maximum energy of attraction function,  e/k, for Og is 106.7 and

thus:


                 D = 0.172 x  10'4 T1'659/?  (cm2/sec)                   (8)

                   = 5 T1.659
                                   3-4

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       Introducing Equation (8) into Equation (4) gives the axial species
diffusional flux expression:
                  J| - - TTTF1""" br + hH( - F, ^))             (9)
3.1.2  Species Production Terms
       Each W. in the species conservation equation represents a summation
of contributions from all reactions which include that species.  For reac-
tions of the type:
                                 ZR  D
                                    BI
where y are the stoichiometric coefficients on species B^ .  W. can be written
as:
where
                             Ey? In pi    EuJ  In p^ln K
                                m            flfl            H   ._.
                                                                     Pi
                         m
and vl  denotes third body efficiency of species i.  The forward reaction
     1m
rate coefficient, k^ , has the Arrhenius form:
                    m
                           kf  =aT"e-(E/RT'
                             m
                                     3-5

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The backward reaction rate coefficient is taken to be equal to the forward
reaction rate coefficient divided by the equilibrium constant.
       As discussed in detail in Reference 5 the solution of these equations
is subject to several pitfalls which need to be carefully circumvented.  The
most discussed problem is associated with k^r  becoming very large, forcing
                                            m
the bracketed term in Equation (11) to zero to maintain a finite net contri-
bution of the term to the species conservation equation.   Forcing the
bracketed term toward zero is equivalent to imposing equilibrium.  Because
the term appears in several species equations, it is necessary to combine
these equations in such a way that this equilibrium relation effectively
replaces only one mass balance relation.
       Even with the rearrangement of equations, the iterative Newton-Raphson
procedure used to solve the simultaneous equation set can be defeated if a
significant change has occurred in the character of the equations.  In the
PROF chemical kinetics package a combination of gradual recharacterization
of equations and damping has proved highly successful in determining a
solution.  This is very important if an efficient grid-type coupled diffusion/
kinetics boundary value solution is to be achieved.
3.1.3  Species Flux at the Wall
       For a flame situated in a bounding tube with reactive walls, a net
species flux to the wall develops which is rigorously a function of the
detailed radial distribution of species concentration at the wall.  For
efficient computations, the PROF formulation utilizes a transfer coefficient
approach to establish the species flux at the wall.  In this approach, the
species flux is assumed to be directly proportional to the difference
between the bulk and wall gas composition.  Since it is not necessary to
                                     3-6

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know the detailed radial species concentration distribution, this formula-
tion allows an efficient axial -direction, one-dimensional computational
scheme to be retained.  For consistency, the wall flux proportionality
factor is developed in a manner similar to the axial species diffusion case.
Analogous to the axial diffusion expression, the wall species flux is
written as:
Wi - pu [0]  se- =-L (v. - y
                                                                        (13)
with the J factor being represented by a simple Reynold's number relation,
C,  Re"m.  The Schmidt number, u/pU, adjusts the J factor to a transfer
 J
coefficient appropriate to the reference species; the y-jF^ corrects it
further for the specific species in question.  Consistent with the accuracy
of typical J-factor correlations (see Reference 6) the molecular weight and
]iy gradients (as in Equation 9) have been neglected in the driving potential
formulation.
3.1.4  Bulk Gas Volumetric Heat Loss
       The term Q in the energy equation is a bulk gas phase volumetric heat
source, or sink term.  If desired, Q can be assigned as a constant or as a
function of distance along the flame axis.  However, most often Q, for uncon-
fined flames, is the volumetric heat loss due to radiation.  The PROF code
formulation includes logic to model heat loss due to radiation for nonsooting
f 1 ames .
       The radiation heat loss, is written as:
                            /QA ds = -/($  q) dV                     (14)
                                     3-7

-------
where V  q is the divergence of the radiative flux.  For conditions where
the flame radius is small compared to all absorption coefficients at all
frequencies (i.e., /fw 1C dr  1  for all v), and where radiation back from
                    O
the environment can be neglected, Qr becomes (Reference 7):

                          Qr = -4KpaT4                                  (15)

where 1C is the Planck mean absorption coefficient given by:
This is the emission-dominated or optically thin limit approximation which
is valid for typical nonsooting laboratory flames.  To complete the defini-
tion of radiative heat loss, K  values are now defined.
       The major radiating species in hydrocarbon flames are C(L, 1^0, and
CO.  For each of these species, there are roughly one to four important
radiation bands scattered through the 1 to 15 micron wavelength range of
interest.*  Each band typically occupies a relatively narrow region of the
spectrum and can be separated from adjacent bands by a region which neither
absorbs nor emits thermal radiation.  The properties of the band systems are
required to properly calculate emission losses.
       Rigorously, the spectral absorption coefficient, K^, is available
only for the individual line spectra and applying this property requires
much effort.  Therefore, its usefulness is limited in applications requiring
 Approximately 2 to 20 percent of the energy released in combustion becomes
 infrared radiation, whereas only 0.4 percent becomes visible or ultraviolet
 radiation  (Reference 8).  Therefore, only infrared radiation need be
 considered.
                                    3-8

-------
just heat loss from combustion products.  An alternate (and simpler)
approach is to use a wide band absorption model.  In the PROF code the
wide band model correlation parameters of Edwards and Balakrishnan
(Reference 9) are utilized to determine the emissivity of COgj H^O, and
CO.  The Planck mean absorption coefficient is determined from the gas
emissivity by using the optically thin limit expression (Reference 10):
                                     -
                                   2  L
where e  is the gas emissivity and L is the characteristic dimension of the
system.  Calculated Planck mean absorption coefficients for temperatures
between 400K and 2600K are given in Figure 4 for the pure gaseous com-
ponents COp. 1^0 and CO at a total pressure of 1 atm.  For all cases, the
path length, L, is taken as 0.001 feet, a number which is small enough to
ensure recovery of optically thin data.  As shown, COg is a strong radiator
at high temperatures compared to 1^0 and CO.  The emissivities, from which
the K  values were obtained, have been compared to available data (Refer-
ence 11).  For an assumed pressure-pathlength product of 0.01 atm-foot at a
total pressure of 1 atm, the calculated results were within 10 percent of
the reported data.  This agreement lends confidence to the use of the IC's
given in Figure 4.
       To establish 1C for a mixture of gases at any pressure, a simple
summation scheme was derived which considers radiatively noninteracting
gases.  This expression has the form:
                              KP -
                                    3-9

-------
     16  
     14
     12
 I

4->
 C
X   10 
at
o
o
o
I/)
.O
IB

C
10
Q)
 O
 C
 
-------
and is valid as long as the optically thin approximation is valid.  Applying
data given in Figure 4, Equation (17) and the heat loss relationship,
Equation (15), the radiation heat loss in flames is established.
3.1.5  Axial Diffusional Heat Flux
       The axial diffusional heat flux consists of a species enthalpy trans-
port term, A J-jn-j  antl  a conduction  transport term,  AkdT/ds.   The  species
 flux  Ji  has  been  defined  in Section  3.1.1.   To  fully  define the axial  diffu-
 sional  heat  flux,  an  expression  for  mixture thermal conductivity, k, must
 be  developed.
        As  mentioned previously,  accurate multicomponent transport properties
 for all  flame  conditions  are not available  and  approximations  are in order
 to  provide simple, yet adequate, transport  coefficient data for practical
 flame calculations.   In this spirit, the code thermal  conductivity expression
 is  developed from approximate relationships and some  diffusion factor con-
 cepts which  were  used in  Section 3.1.1.
        The thermal conductivity  of a mixture of polyatomic molecules can be
 written  (Reference 4)  as:

                          kmix =  kmono-mix * kint                        ^18'
 where 'cmono_mi-x is the mixture thermal conductivity computed neglecting  all
 internal energy modes and k.  .is  the  contribution of the internal energy
 modes of the molecules to the mixture  conductivity.   An approximate
 relationship for  l
-------
                              I
                  mono-mix  ^7
                             i
                                            mono
                                                     X.
                                                     r:
                                                     1J
                                                                         (19)
 where kj     is the thermal conductivity of the pure species i, neglecting
 all internal degrees of freedom, and u.  is the viscosity of species i.
 Expressions for k^,^ and UT can be written (Reference 4)  as:
                                mono
                                          -
                                       4  Mj
                                                                        (20)
                                    5
                                 ~
6A*7piPii
                                                                        (21)
where At. is a ratio of collision integrals.  Based on a Lennard-Jones inter-
molecular potential the value of this parameter will be between 1.10 and 1.14.
A value of 1.12 has been chosen here and the 1.385 adjusted to 1.344  to allow
the elimination of additional terms.  Introducing k^     and u. , Equations
                                                    mono
(20) and (21), respectively, and t?.., defined in Equation (3), into Equation (19)
                                  ' J
the expression for
                              becomes:
                 k
                 mono-
                         .
                       mi x
                                           _
                                           Fi  4 M
                                            1.344
                                                                        (22)
To complete the definition of k, the expression for the internal energy mode
contribution to thermal conductivity must be added to Equation  (22).
*A value  of 1.385  x  1.065 was actually  used in Reference 4, but subsequent
  papers co-authored  by Mason dropped the 1.065.
                                      3-12

-------
 From Equations  (59)  and (77)  of  Reference 13, the following relation can
 be obtained:
                                      Mi ,     5   R
                     K.  .
                      int
 which with Equations (3)  and (5)  yields:
                            p^iil
k1nt
The  value of  k  used  in  PROF is then:
               k =
     Cp + 0.29 R
 where

                                                 .
                                                                        (23)
(24)
                                                                        (25)
3.1.6  Wall Heat Flux
       A flame situated in a nonreactive tube at a fixed wall  temperature
will either lose or gain heat through the wall depending on the  bulk  gas
temperature.  If the wall is reactive, then an additional  heat loss or gain
comes into play depending on wall  and bulk gas composition.  As  in the wall
species flux, the PROF code formulation treats the wall  heat flux by  assum-
ing that, for the nonreactive wall  case, heat flux is  proportional to the
difference between bulk and wall  gas temperatures.   For  the reactive  wall
case, a more general expression is  used to account for the heat  released by
chemical  reactions which occur between the bulk  gas and  wall.  The completely
general  expression for wall  heat  flux is then:
                                    3-13

-------
                           .-" _L
                              vi
h   ~ \ /      \
ITCP)(T-T)
'ky1
                          (26)
where, again, the J factor introduced  in Equation (13) is used.  With h
defined by:
It is noted that the driving potential  reduces to the temperature difference
for constant composition.
3.1.7  Specialized Boundary Conditions
       For flames propagating in  free space,  the upstream boundary conditions
are the unburnt gas temperature and  composition and the downstream boundary
condition is that of negligible diffusion of  species and heat.  In the
laboratory, flames are typically  anchored to  their burners by the use of
flameholder grids.  These  grids stabilize the flame by providing a sink for
the flames "excess" heat or reactive species.  While stabilizing the flame,
these grids also alter the flame  properties from those that would be
achieved in free space. For accurate prediction of laboratory burner flames,
the effects of flameholder processes on flame properties must be included
in the code modeling.
       Figure 5 illustrates schematically the heat and species balances
which develop around a flameholder grid.  Of  primary importance is the
absence of heat or reactive species  diffusion upstream of the grid.  The
amounts of heat or reactive species  which diffuse from the downstream
region to the flameholder  grid depend on the  ratio of burner flow speed to
                                     3-14

-------
             Flameholder
            Heat Balance at Flameholder
mY.
             Flameholder
           Mass Balance at Flameholder
 Figure 5.  Schematic of flameholder processes.
                     3-15

-------
free space flame speed.  For some laboratory burners, flow speeds are
adjusted such that little heat or reactive species are lost to the flame-
holder.  Under these circumstances, heat loss from the flameholder, terms
-q-   + q~    and heterogeneous reaction terms, Ww., shown in Figure 5,
  rin    rout                                      n
may be neglected in the formulation.  In these cases, the only effect of the
flameholder on flame properties is to prevent upstream diffusion of heat or
species to the burner face.
       When the burner speed is low compared to the free flame speed, signifi-
cant amounts of heat and reactive species diffuse to the flameholder.  For
these cases, the PROF code models flameholder heat loss by assigning a
fixed temperature to the gas at the flameholder.  In addition to the heat
loss, heterogeneous recombination of reactive species which diffuse to the
flameholder are modeled by locally increasing the homogeneous recombination
reaction rates to very high values.
3.2    Plug-Flow Reactor Model
       As indicated previously, the plug-flow reactor conservation equations
are subsets of the flame equations.  The primary difference between the plug-
flow reactor and the flame equations is the absence of axial diffusion
effects for the plug-flow reactor.  Deleting axial diffusion terms from
Equations (1) and (2), the plug-flow reactor equations are:
       Species
                        " ~ar   ft"i   vw"w1
                    .      .  - C-J-                             (28)
Energy
                         * ar  A - cw"w                               <29>
                                     3-16

-------
The expressions for W. , Jw., Q and q^ remain the same as in the flame case
(see Sections 3.1.2, 3.1.3, 3.1.4 and 3.1.6).  Since axial diffusion is not
present, only upstream and wall composition and temperature values are needed
as boundary conditions.
3.3    Time-Evolution Chemistry Problem
       For the reaction of a fixed mass of gas in time as the pressure and
temperature change, Equation (28) must be reinterpreted.  Dropping wall
effects, Jw., and combining ds, m and A, Equation (28) becomes:
       Species
                                                                       (30)
For the time-dependent problems, the parameter (Ads/m) is now interpreted
as a time differential divided by the density of the fixed mass of the gas,
or:
                               dt E Ads_
                               P     m

Only the initial mixture composition and assigned pressure and temperature
                                   i
are needed as boundary conditions  for this  problem.
3.4    Well -Stirred Reactor Model
       The well-stirred reactor problem is  different from the flame case in
several respects.  In a well -stirred reactor, gas composition and temperature
are assumed to be uniform  in both time and  space within the reactor.  The
spatial uniformity is a result of intense mixing and the time uniformity is
due to the specification of steady and equal mass fluxes into and out of the
                                     3-17

-------
reactor.  Unlike the flame and plug-flow reactor cases, algebraic equations
rather than differential equations define the well-stirred reactor problem
These equations can be written:
       Species
                                      m
       Energy
                         hout - hin ' T  1                               (32)
where V is the reactor volume and all other quantities are the same as those
defined in Equations (1) and (2).  If reactor volume is associated with the
product, A ds and differentials replace the differences in Equations (30)
and (31), then the well-stirred reactor problem is seen to be equivalent to
a single step in the plug-flow reactor problem.  Since the solution "time
step", V/ih, is typically very large in well-stirred reactor problems, it is
essential that a stable-and reliable kinetic chemistry solver be employed.
Fortunately, the chemistry solver developed for predicting flame problems is
ideally suited for solving well-stirred reactor problems.
       The boundary conditions applied in the well-stirred reactor case
are the assignment of inlet species concentrations and enthalpy.
                                    3-18

-------
                                 SECTION 4
                            SOLUTION PROCEDURES
       The solution procedures adopted for the treatment of the set of
equations developed in Section 3 are presented in this section.  The highly
coupled nature of the equations requires a careful solution formulation
if an efficient and reliable procedure is to be realized.  The principal
focus of this section is on the various aspects of the flame solution
procedure with lesser emphasis on the plug-flow and well-stirred reactor
solution procedures.
4.1    Flame Solution Procedure
       The flame solution procedure is treated in three subsections.  The
first describes the finite difference treatment of the conservation equa-
tions, the second the chemistry solution procedure and the third the
linearized predictor-corrector iteration-scheme for the overall solution.
4.1.1  Finite Difference Form of the Flame Conservation Equations
       The governing differential equations (Equations (1) and (2)) are
cast into algebraic form by applying simple linear finite differences.  The
resulting set of algebraic equations are then solved utilizing matrix
procedures.
       The following schematic illustrates the control volumes from which
the finite difference forms of the equations are developed.
                                    4-1

-------
                                              Constant properties
                                              assumed In control
                                              volumes bounded by
                                 n-1
       Introducing the normalized distance coordinate s  defined by:
                           ds  =
                                 AQds
                               ApT
                                  1.659
       (33)
and applying simple linear finite differencing, the species equation becomes:

Species
             TAW'659]/
''. - v,= HHJ
Y.    -  Y.
 _n+l    _i
      -  S
                            rY   - Y
                                       '-Yi.
                                              n+1     n
                            n     n-1     n    n-
                                                           FiVl,n
                                   4-2

-------
             n+1
         1    ^T  If    r?~AMn+l.n + Fiyn,n+l)
          n+1     n  \ n+1    n / \               /
             'n-1
        y,    + y,
         ]        '
                                           M.
                                            n-l,n
                                                              (34)
                               ApT
                                  1-659
            m
where
      M.-M.
M.. =  I. 3 and
                                                                       (35)
 Dividing through by molecular weight,  M., and utilizing the composite quanti

 ties:
                                     4-3

-------
            BP
            = FT
           (36)
the final form of the species equation is given by:
    i  -rO.659

a,- - a.- - |PM a TT  r.

        i., " ui >
        n+1  n
                 4.1
                 n+1  n
      a- - a.
          -a.
)'

    i /

    an\n,n+l

    n
   n  n-1
                       (37)
            4-4

-------
            + a.
                                                                        (37)
                      V  gn * Vl  _A_ rl-659    wi
                               5      An pl         ~MT
                       m
The energy equation is developed  in a  similar manner and  leads  to


                      2b  AT      L    /          \   ~   /          \

        *  -  hn-l  = y,  P * y.    K+l  (' + Vl.) ' "n  (" * Mn,n+l)
                     ILi    ',  t
                     'n+1    'n
                                             - Tn)]
   2bn/a  !      L   /          \   -      /
-    P+^      hn  (l + ^ - Vl   I1 + Vl.n
   'n    'n-1    L




+ hn Vl,n - Vl^.n-1 + Vl  (Tn '  Vl)J
                              1.659
                            ->T
 where
                         + CPn^,n^l  +  Cpnyn+1'n)
                                     4-5
                                                                         08)

-------
       If guesses are inserted into Equations 37 and 38 for a^ , T, h and h
at the downstream station, n + 1, the equations can then be rearranged to
give the unknown variables 
-------
the functions, g-, were linear.  The correction to V. needed to drive e-
                J                                    i                  j


to zero is based on the current values of the unknown variables and the



corresponding array of values of the partial derivatives Bg^/SV^ .   This can



be written as:
This relation can be inverted to yield
which when integrated, presuming the partial derivatives constant, yields




                                         ,-1


                                             Ag,                       (41)
                                               j





But Ag. represents the desired change in g. which is simply -g..  Successive
      J                                   J                   J


iterations, if properly constrained and/or linearized, will drive g. to zero.
                                                                   \J


In the PROF code chemistry solution, the partial derivatives use the vari-



ables, AnPi, UnJ and fcnPM and (41) yields, for example:
                                                                        ,   %

                                                                        (42)
which  if  taken  as  linear  all  the way to solution  gives:
                                     4-7

-------
                  /    \   _    n.   /   x
                  K) -E Uf;  W                            (43>
                            j      J
       When the initial  guesses, V., are close to the solution  and  the
equations are fairly linear, the straightforward application of the above
Newton-Raphson iterative solution procedure is rarely defeated.  With sub-
stantial  chemical  kinetics  neither of these two conditions can  be expected
and achieving a solution by straightforward application of the  method is
not assured.   In the PROF code a procedure has been implemented which has
greatly increased the reliability of the above Newton-Raphson solution
procedure when applied to problems with substantial kinetics.  This proce-
dure consists of:
       1.  Ordering all  kinetic reactions by the magnitude of the gross
           forward or reverse reaction  rate
       2.  For each reaction seek the species equation in which it  is
           most important
       3.  If its gross  effect on the equation exceeds some fraction of
           the other terms  in the equation, combine all equations affected
           by that reaction so as to introduce it into only one equation
       4.  Restructure that one equation so that the error is linear about
           the equilibrium  state of the reaction
       5.  If a saddle point in the error equation is identified, alter
           the guesses to permit the procedure to search for a  solution
           in a more likely solution domain
       6   Utilize a damping scheme that constrains the corrections, AV.,
           from oscillating and also from overcorrecting the variables,  V..
                                     4-8

-------
This procedure has proven highly successful.  It is difficult to sufficiently
emphasize the importance of this reliability for coupled calculations  within
a grid structured problem.
4.1.3  Linearized Predictor - Corrector Procedure
       For well-stirred or plug-flow reactor problems, which do not explicitly
include diffusion, solution by the chemistry solver routine constitutes the
final step in achieving an answer.  For flame type problems, where axial
diffusion is considered, the equations are still in error due to utilizing
guessed values for the variables at downstream stations, n + 1.  For these
problems, a corrector step is added to the solution procedure to reduce to
zero the error caused by using downstream guessed values for the variables
in the equations.
       At convergence, the chemistry solver iterative Newton-Raphson solution
procedure has available a full set of derivatives of all of the variables
with respect to the errors in the equations.  Knowing explicitly the varia-
tion of the equation errors with respect to input variables, a matrix of
derivatives of variables with respect to input variables (which include the
guessed downstream quantities) can be constructed.  Using the species expres-
sion, Equation (37), as an example, a linearized representation of the con-
servation equation about the current solution estimate, can be written in
the following form.
                                      fact A i  o      o  ,                  (44)
where subscripts p and c refer to the predictor and corrector values respec-
tively and the repeated j index implies summation.  The superscript 0
                                     4-9

-------
defines a composite species concentration term which includes the guessed
downstream species concentration plus the known upstream initial  species
concentration and various multiplying factors*  Equations 44 and a similar
equation for h, h and T are constructed for the entire grid.  In matrix form,
the resulting set of simultaneous equations covers a large sparse matrix in
a block tridiagonal form.  These equations are solved for the predictor
values a.jp, hp, hp and Tp at all of the grid locations.   If equations 37
and 38 are truly linear about the current solution estimate, the predictor
values would satisfy all the equations and the final answer would be achieved.
However, the equations are not linear and several  iterations of the corrector
step are required before a solution is found.  Also, due to nonlinearties,
it has been found that during the initial iterations, when the solution
estimates are far from the answer, corrections to the variables must be
limited to prevent overcorrections.  The PROF procedure, which limits the
variable corrections at each iteration, has proven to be adequate for all
problems calculated.
       Although flame solutions have been achieved by simply repeating the
predictor step, the addition of the corrector step has been found to reduce
the required number of iterations by factors of 2 to 10.  Since Step 5 takes
only 10 to 15 percent of the total computation time, it is a very effective
method for reducing total computer run time.  In addition to increasing
computational speed, the corrector step allows the prediction of flame speed
through the application of constraints on the grid variables.  The flame
speed, or mass flowrate, m, is obtained by assigning a species concentration
or temperature which is between the inlet and final equilibrium value, to
*
 Specifically it equals all a.    and a.    terms in Equation 37 divided by
                             Vl      Vl
 the coefficient on the a.  term.
                          n
                                     4-10

-------
a grid point removed from the inlet.  The species constraint value may be
assigned to any stable species which monotonically increases or decreases
through the flame.  The corrector step then updates the mass flowrate at
each iteration until the assigned variable constraint is achieved at the
specified grid point.
       Summarizing the complete flame solution procedure, the set of alge-
braic equations found from the finite difference form of the species and
energy equation are solved by the following steps:
       1.  Guessed initial values are selected for a^, T, h and h at grid
           points downstream of the first station.  These are available as
           output from a prior run or are generated internally from a linear
           interpolation between initial and guessed final values.
       2.  Applying known upstream conditions and the initial guessed values,
           current grid point values for a., T and h, are found through
           matrix solution of the equation set in the chemistry solver
           routine.
       3.  When the downstream boundary is reached the no diffusion boundary
           condition is applied.
       4.  Utilizing the derivatives of a and T obtained from chemistry
           solutions at all grid points, the rate of change of all a^'s,
           h's, h's and T's with respect to initially guessed a^'s, h's and
           T's at each grid point are constructed.
       5.  The block tridiagonal matrix developed from Equation 44 and
           step 4 is solved simultaneously for all ct.c, hc, hc, Tc in
           terms of mc.
                                    4-11

-------
       6.  A constraint condition is then introduced to determine mc and
           all other corrected variables.  Using the corrected ct^'s, h's,
           h's and T's, as new guesses steps 2 through 6 are repeated until
           a converged solution is found.
4.2    Plug-Flow Reactor Solution Procedure
       The plug-flow reactor algebraic equations are derived from the differ-
ential equations, Equations 28 and 29, utilizing the same linear finite
differencing as was applied in the flame case (see Section 4.1.1).   However,
the distance, s, remains untransformed in the plug-flow reactor case.  The
finite difference plug-flow reactor governing equations are:
Species
                      Y.  - Y.
                       'n    Vl
                                     AW.
. m.
                                                                         (45)
                         m  "i\     -    /
Energy
                         - V,
       As indicated previously, these equations do not require any guesses
for downstream species concentrations or enthalpy.  Solution of this simple
initial value problem is then found once the chemistry solver step, described
in Section 4.1.2, is completed.  Calculations over substantial lengths are
carried out by repeating the above described step for either fixed or
variable distance increments.
                                       4-12

-------
       The time-evolution chemical kinetic problem is solved in a manner
similar to the plug-flow reactor problem.  However, in the time-evolution
problem, the last term in Equation (45) is dropped and the parameter
   S    - S
jjj"  	2       is ^Placed by a time increment divided by density, or
  ,j/l ~ t^ n
               In the time-evolution problem p is carried implicitly in

the calculations.
4.3    Well -Stirred Reactor Solution Procedure
       The well-stirred reactor solution procedure is equivalent to a single
distance step of the plug-flow reactor procedure with V/m replacing the
parameter Ads/m in equations (45) and (46).  Typically the "time step"
parameter V/m for the well-stirred reactor problem can be quite large
relative to that typically employed for plug-flow reactor problems.  This
presents no special difficulty for the chemistry solution procedure.
Sufficient convergence and rescue procedures have been incorporated into
this routine to minimize nonconvergences due to starting with poor first
guesses for the variables.
                                    4-13

-------
                                 SECTION 5
                                                  *
                          CODE  INPUT  INSTRUCTIONS

       This section fully describes the punched card input needed to  activate
the PROF code flame, well-stirred, plug-flow and time-evolution  reactor
options.  A number of comments are included in this section to help guide
the user in setting up input card decks.  Comments specific to individual
sample problems are given in Section 7.

5.1    Card Input Deck
                    (Format 20A4)
                    Title of Run
                    (Format 1613)  Integral  Parameters
               IS   Number of species conservation equations
       4-6   KR6   Flag on type of solution to be obtained
               -1   Well-stirred reactor with assigned temperature of
                    entering reactants
                0   Plug-flow reactor problem with distance as scale
                    and assigned temperature of initial reactants
                1   Chemically reacting mixture with assigned temperature
                    and pressure as a function of time
                2   Premixed flame problem with mean Lewis number of
                    unity i.e. h = constant through flame for no
                    radiation or specified heat loss (see ITC parameter
                    description for heat loss option)
                3   Premixed flame problem, including nonunity Lewis
                    number effects
       7 - 9 N      Number of species (currently set N = IS)
      10 - 12 NL    Number of axial grid points
                                     5-1

-------
13 - 15 NIT  Number of grid solution corrector step iterations
16 - 18 INA  Control on solution cycle
         0   No effect
         1   Punch a., etc. for subsequent input (see card set 9)
         2   Read a.j, etc. (card set 9)
         3   Punch and read a^, etc.
         4   Recycle calculation - stacked runs
         5   Recycle and punch a.., etc.
         6   Recycle and read a., etc.
         7   Recycle, read and punch a.., etc.
19-21 IALF For first input deck IALF must be 1 or 2; but if IALF = 2,
             INA must = 2, 3, 6 or 7.
         0   Do not read card set 7
         1   Read card set 7 and set up interpolated a^ first guesses
         2   Read card set 7 but do not set up subsequent first
             guesses
22  - 24 IAP
         0   Do not read nonintegral parameters
        >0   Read nonintegral parameters (card set 3)
25  - 27 ITC
         0   Do not read in thermochemical data
        >0   Read in  linear fitted  thermochemical data
        <0   Read in  curve fitted thermochemical data
             If ITC is nonzero, thermochemical data is read from a
             mass storage  file designated as unit 12 for linear fit
             data and unit 11 curve  fit data.  The formats for this
             data are given in Section 5.2.  Besides indicating what
                               5-2

-------
             kind of thermochemical  data is to be read, this
             parameter also identifies what kind of heat loss model
             is to be applied in the calculations.
        1   No heat loss downstream of flameholder
        2   Volumetric heat loss input as function of distance (card
             set 6)
        3   Radiative volumetric heat loss
        4   Convective heat loss to bounding walls (card set 6)
28 - 30 IFV
         0   Do not apply constraint condition
         1   Flame calculation with constraint
31 - 33 IKN
         0   Do not read in kinetic data.  If this is the first of a
             stacked set of decks, no kinetics will be considered,
             otherwise previously read data will be used.
        >0   Read in kinetic data (card set 8)
34 - 36 IKAP Variable to which constraint is applied.  Used only in
             flame calculations i.e. IFV ? 0.  0 assigns a constraint
             on temperature; 1 to IS assigns a constraint on the
             corresponding species concentration (See card set 7 for
             order of species).
37 - 39 KAP  Grid point at which constraint is applied
40 - 42 KR7  Output control
         0   Final summary table and flame speed
         1   Detailed kinetics, molar fluxes of species, plus all of
             the above.
         2   Flame subroutine summary information, predictor/corrector
             matrix procedure information, and all  of the above.
         3   All the above plus kinetic debug information
        >3   Complete debug printout
                            5-3

-------
43 - 45 NFH  Flameholder flag
         0   No flameholder
         1   Read and assign flameholder temperature at second grid
             point
         2   Same as in NFH = 1 plus third body reactions are
             equilibrated at flameholder
46 - 48 MOOT Assigned mass flowrate flag
         0   Flame speed calculation
         1   Assign a fixed mass flowrate flame problem with a con-
             straint condition
Card Set 3   Nonintegral Parameters
Card 1       (Format 8E10.5)
1 - 10 APR   Composite "time scale" parameter
             Well-stirred reactor (KR6 = -1):
                        APR = (-5.)   Volume of reactor divided
                               .m/   by the mass rate through
                                     the reactor (cm3sec/gm)
             Plug-flow reactor (KR6 = 0):
                              A
                        APR = -J--     Inverse of mass velocity
                               m     (cm2sec/gm)
             Time-evolution problem (KR6 =1):

                        APR = AtQ    Reference time step (sec)
                             5-4

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             Flame option (KR6 = 2 or 3):
                 For APR > 0 and MOOT = 0
                           6A
                     APR = -T2-      (See Section 4.1.1 for defini-
                            ng       tions of these terms.  Section 7
                                    gives instruction on how to
                                    construct this parameter).
                 For APR < 0 and MOOT = 0
                     The APR in storage from previous run is used
                     in present run.
                 For APR > 0 and MOOT = 1
                                  
                           APR = /-    Mass flux (gm/cm2sec)
                                 Mo
                     This is only for an assigned mass flux
                     problem.  Internally, APR reverts to
                     MOOT = 0 definition after input sequence.
11 - 20 BP   Composite diffusion parameter
             Well-stirred reactor (KR6 = -1):  BP = 0.
             Plug-flow reactor (KR6 =0):  BP = 0.
             Time-evolution problem (KR6 =1):  BP = 0.
             Flame option (KR6 = 2 or 3):  BP = A0D/m6 (See Sec-
             tion 4.1.1 for definition of these terms.  Section 7
             gives instructions on how to construct this parameter).
21 - 30 P    Pressure (atm) (This value is replaced in assigned P
             and T time-evolution problem by PPB input.  (See card
             set 5)).
31 - 40 T    Initial temperature (K). (This value is replaced in
             assigned P and T time-evolution problem by TTB input.
             (See card set 5)).
                               5-5

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41 - 50 TKAP    Value of constraint variable.  Can be temperature, in
                K degrees, or any monotonically increasing or decreas-
                ing major species concentration, in mole/gm units.
                This constraint condition is only used with flame
                calculations.  The code will adjust the flame speed
                or grid spacing until the constraint variable is
                achieved at grid point KAP.
51 - 60 TFLAME  Assigned flameholder and gas temperature in K at
                the second grid point.  For well-stirred reactor
                calculations TFLAME is used as the first guess for
                reactor temperature.
Card Set 4      Spatial or Temporal Grid Parameters for points N = 1,
                NL
Card(s) 1       (Format 8E10.4)
1 - 10,
11 - 20,..AP(N) Time or area parameter
                Well-stirred option (KR6 = -1)
                Ratio of reactor volumes, V/VQ.  AP(1) is not used,
                start with AP (2)
                Time-evolution problem (KR6 = 1)
                Ratio of grid point time step to the reference time
                step, At/AtQ, AP(1) is not used, start with AP(2).
                Plug-flow option (KR6 = 0) and flame option (KR6 = 2
                or 3)
                Area ratio A/AQ at each grid point.
Card(s) 2       (Format 8E10.4)
1 - 10,
11 - 20,..DS(N) Space step parameter
                Plug-flow option (KR6 = 0)
                Relative grid spacing along flow axis in cm.
                                5-6

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                Time-evolution (KR6 = 1)  and well-stirred option
                (KR6 = -1)
                Set equal to 1.
                Flame option (KR6 = 2 or 3)
                Relative normalized grid spacing along flow axis.
                (See Section 4.1.1 for definition of DS(N)).
Card Set 5      Assigned Temperatures and Pressures for Fixed Mass
                Time-Evolution Problems (KR6 = 1)
Card(s) 1       (Format 8E10.5)
1 - 10,
11 - 20,TTB(N)  Temperature in K at station N for NL stations
Card(s) 2       (Format 8E10.5)
1 - 10,
11 - 20,PPB(N)  Pressure in atm. at station N for NL stations
Card Set 6      Heat Loss Options
Option I - Volumetric heat loss (ITC 2)
Card(s) 1       (Format 14, 6X, E10.5)
1 - 4    INS    Number of heat loss entries to be specified as a
                function of axial distance.
11-20  QLS    Volumetric heat loss (cal/cm3 sec)
                If INS is greater than one then local Q values
                referenced to the QLS above will be input as a
                function of axial distance.
Card(s) 2       (Format 8E10.5)
1 - 10,
11 - 20,SSS(N)  Only for INS > 1.  Distances in cm which Q local
                to QLS ratios are specified; 1 to INS ratios are
                required.
                              5-7

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Card(s) 3
(Format 8E10.5)
1 - 10,
11 - 20, Q/Q(N) Local Q to QLS ratios specified as a function of
                axial distance.  1 to INS entries required.
Option II - Convective transfer coefficient input (ITC 4)
Card 1
1-4    INS
11-20  Cj

Card(s) 2
(Format 14, 6X, E10.5)
Number of heat transfer factor entries
Transfer coefficient constant for J factor
(see Section 3.1.3).
(Format 8E10.5)
1 - 10,
11 - 20, SSN(N) Distances in cm at which transfer coefficient values
Card(s) 3
1 - 10,
11 - 20, Q
Card(s) 4
1-4    IH
          1
          2
are specified.
(Format 8E10.5)
                         m
Local values of Q = l/DhL  at SSS, consisting of the
hydraulic diameter, Dh, and the Reynolds number
reference length, L used in Equation 13.  For well-
stirred reactors D.  is four times volume/surface area
and for plug-flow reactors and flames D.  is four times
sectional area/perimeter.
In addition to the general formulation of Equation 13,
two limiting cases of specific interest are:
     Assigned J factor as a function of distance:
     let Cj = reference J factor, m = 0 and
     Q = J/(DhCp
     Assigned Nusselt Number:  let C, = reference
                                    j
     Nusselt number, m = n = 1, and Q = Nu/D.2'Nu).
(Format 14, 6X, 3E10.5)
Wall reactivity parameter
Noncatalytic wall
Reactive wall - composition to be specified
                              5-8

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11 - 20 TW
21 - 30 EXM
31 - 40 EXN
Card(s) 5
1 - 10,
11 - 20, PW(N)
Card Set 7
Card(s) 1 to IS
1 - 8   NAMA
11-20 ALPHF
21 - 30 ALPHE
31 - 40 BPA
Same as 2 but adiabatlc wall
Wall temperature (K)
Exponent m of Equation 13
Exponent n of Equation 13
(Format 8E10.5)

Wall species relative mole concentrations (should
yield same elemental composition as the bulk gas
phase).  Species order is the same as on card set 7.
This input is not needed when IH=1.
Initial species concentrations, downstream species
concentration guesses, species diffusion factor's and
equivalent species names.
(Format 2A4, 12, 2E10.3, F10.4)
Species name utilized in kinetic reaction input.
(These names must also be compatible with or equiva-
lent to (see card(s) IS2 in this card set) the names
on the thermochemical input data tape).  See Sec-
tion 5.2 for a description of thermochemical data.
Initial species concentration in relative mole
concentrations.
Estimate of terminal species concentrations in
relative mole concentrations.  Input should approxi-
mate maximum value achieved in flame for initial
trace quantities.  This input is overridden if first
guesses are input from prior run.  (See card set 9
for a description of this input).
Bifurcation diffusion factors, l/Fi, for each species.
See Section 3.1.1 for the definition of these factors.
These are not needed for nonflame and nonwall loss
calculations.  For these cases a value of one may be
input.
                               5-9

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      Card IS + 1     (Format 2A4)
      1  - 3           Input of END signifies the end of the species input
                      set
      9-10 KNY      Number of equivalent species name cards to follow
      Card(s) IS + 2  (Format 2A4, 2X)
(Col)  1  - 8,   NAMA   Species name used in thermochemical  input data file
      21 - 28,
      41 - 48,
   or 61 - 68
(Col)  11 - 18, NAMC   Species name equivalenced to NAMA.  Can be name on
      31   38
      g-j _ go'        species or reaction input which does not match thermo-
      71 - 78         chemical input data file name.
                      Four equivalenced sets of names may appear on each
                      card with a maximum of four cards being read.  No
                      species name can occur in more than one equivalence
                      set.
      Card Set 8      Kinetic Data
                      If IKN > 0 this data must be present.  For IKN = 0,
                      the reaction data stored during previous input is
                      used in calculations.  Reactions and their associated
                      rates are given in the form:
                                      A+B+M+c+D
                      where M denotes a general third body.
                      The forward rate coefficient is given by:
                                        Ea
                                     h
                              kf = AT e    (mole-cm-sec units)

                      The reverse rate is obtained through use of the
                      equilibrium constant and the forward rate.  (The
                      species names must be compatible with or equivalent
                      to those on the thermochemical input data tape and
                      initial species concentration input data).
                                     5-10

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 Card 1           (Format 13)
 1-3      MT   The  number of reactions  and  rate coefficients to be
                 input
 Card(s)  2       (Format 5  (A4,  IX),  5X,  3E10.  4, 2(A4,  F6.1))
 1  -  4,
 6-9     NAMA  Name of reactants  (e.g.  H, 0,  H2, 02 etc.)
 11-14     M    General third body (Enter M) or specific  third body
                 (e.g.  H, 0,  H2, 02,  etc.)
 16 - 19,
 21 - 24    NAMA  Name of products (e.g. H, 0, H2, 02, etc.)
 26 - 30         '-^in ^o'  wnere A is pre-exponential  factor  in
                 mole-cm sec units
 31 - 40   A/A0  Pre-exponential factor
                 Note log,Q of this value added to  entry  in col. 26-30.
                 For A  = 1.0 no entry is required  in  columns 26-30.
 41-50    b    Temperature exponent
 51 - 60   Ea    Activation energy in Kcal/gm mole  units
 61 - 64,
 71 - 74   NT    Individual third body name (e.g. H,0  etc.)
 65 - 70,
 75 - 80   TB    Individual third body efficiencies (i.e.  rate with
                 specific third body is TB times the rate associated
                 with the general third body.   TB should  be one  less
                 than the specific third body rate  since  M already
                 includes the individual third body).
-Card Set  9      Initial  guesses for flame species  concentrations and
                 velocity (INA = 2, 3, 6, 7).   If present, these
                 guesses  replace those obtained from card set 7.
 Card 1           (Format  20A4)
 1  -  80           Title run  in which the following input data  was
                 generated
                               5-11

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       Card 2          (Format 213,  3E10.5)
       1-3     NS    Number of grid points  in  first  guess  input
       4-6     NIS   Number of species  in first guess  input.  The order  of
                       species must  be the same  as in  card set  7.
       7-16    APRR  If nonzero and MOOT =  0,  this entry overrides  the APR
                       value input in card set 3 and becomes  the first  guess
                       for the flame speed parameter (see Section  4.1.1 for
                       the definition of  this term.)
       17-26   BPR   If nonzero, this entry becomes  the value for BP
                       and overrides entry in card set 3.  (See Section 4.1.1
                       for the definition of  this term).
       Card(s) 4       (Format 10E8.4)
       1  - 8,
       9  - 16,
       17 - 24 DSS(N)  Normalized grid spacing parameter for species  input
                       (NS values input). Same  definition as given in  card
                       set 4.
       Card(s) 6       (Format 10E8.4)
       1  - 8,
       9-16   HI(N)  Grid enthalpies in (cal/gm) units.  NS-1 values  must
                       be input covering  stations 2 through  NS.
       Card(s) 7       (Format 10E8.4)
       1  - 8,
       9-16 ALA(I,N) Grid species concentrations in  (mole/gm) units.  NS-1
                       values must be input  covering stations 2 through NS.
                       NIS number of species  input.
5.2    Thermochemical Input Data Format
       For program operation, thermochemical  data (i.e.  specific heat,
enthalpy and entropy) for all species included in card set 7 (given in
Section 5.1) must be present on mass storage devices designated by unit 12
                                     5-12

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for tabular format and unit 11 for curve fit format.   The order of this  data
on the storage device is not important.   However, it  is important that the
species names input on card set 7 match identically with or are equivalenced
to the species names on the thermochemical  data files and the kinetic reac-
tion input data, card set 8.  The thermochemical data files can be full
libraries of data, from which only a limited number of species will  be
selected for each problem of interest.  Revisions or additions to this
library can be made utilizing the TCUP program which is described in
Section 5.3.
       As indicated in Section 5.1, either tabular or curve fit thermochemi-
cal data can be utilized by the code.  If ITC is greater than zero on card  2
(see Section 5.1) then tabular data is required by the code.  For each
species of interest the following 31 data cards must be present on unit  12.
       Card 1          (Format 10X, 2A4, 2X, 2F10.1)
       11 - 18  NAMA   Species name utilized in initial concentration and
                       reaction input
       21-30  MW     Molecular weight of species
       31 - 40  HRF    Heat of formation of species at 298K (Cal/mole)
       Cards 2-11    (Format 5 (IX, E12.5))
       2 - 10,
       12 - 20, ...CP  Specific heat every 100K from 100K to 5000K
                       (cal/moleK)
      - Cards 12-21   (Format 5 (IX, E12.5))
       2 - 10,
       12 - 20,        Enthalpy difference referenced to 298K every 100K
                       fron) 100oK to 5oooK (Kcal/mole)
                                     5-13

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       Cards 22 - 31   (Format 5 (IX, E12.5))
       2 - 10,
       12 - 20,.F = (G-H2g8o)/T.  Function related to free energy every
                       100K from 100K to 5000K (cal/moleK).
       If ITC is less than zero on card 2 (see Section 5.1) then curve fit
data is required by the code.  For each species of interest the  following
3 data cards must be present on unit 11.
       Curve fits of data are in the form Cp = F3 + F4T + F5/T2  and cover
a lower and upper temperature range.
       Card 1          (Format 10X, 2A4, 2X, 2F10.0)
       11-18  NAMA   Species name utilized in initial concentration and
                       reaction input
       21-30   MW    Molecular weight of species
       Card 2          (Format 6E9.6, 6X, F6.0, 6X, A4)
                       Low temperature curve fit.
       1-9     FI    Heat of formation at 298K (cal/mole)
       10-18   F2    Change in enthalpy from 298K to 3000K (cal/mole)
       19-27   F.J    Coefficient in above Cp expression
       28 - 36   F^    Coefficient in above Cp expression
       36 - 45   Fg    Coefficient in above Cp expression
       46 - 54   Fg    Entropy constant at 3000K (cal/mole)
       61 - 66   TU    Upper temperature limit of low temperature range
                       curve fit  (K)
       73 - 76  NAMA   Name of species used in reaction set
       Card 3          (Same format  as above)
                       High temperature range curve fit.  Same data as above
                       for temperatures beginning at the maximum of the
                       above data.
                                     5-14

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5.3    PROF Thermochemical Data Update Program (TCUP)
       The TCUP program, described in this section, updates  and expands  the
PROF code curve fit or tabular thermochemical  data files.  Another option
lists the complete thermochemical data file.
       The program accepts only a list or update directive and checks  to
see if the CURVE FIT or TABULAR data master file is assigned.   The program
terminates if the directive is not correct or the data file  is not found.
5.3.1  List Option
       The program gives a complete listing of the contents  of the master
file and indicates the number of species present.  The master file should be
assigned to unit 11.  Only one card is required for a list.
       Card 1          (Format A2, 8X, 2A4)
  Col. 1 - 10          (Starting in Col. 1)   LIST or LI
  Col. 11 - 18         (Starting in Col. 11)   CURVE FIT or CU, TABULAR or TA
                       for type of data to be listed
5.3.2  Update Option
       The program adds, changes, and deletes whole records, (i.e. 3 cards  of
curve-fit data and 31 cards of tabular data for each species).
       Three files must be assigned.
           1)  The old master file on unit 11
           2)  The new master file on unit 12
           3)  A scratch file on unit 10
       An update directive is established by the following card.
       Card 1          (Format A2, 8X, 2A4)
  Col. 1-2           (Starting in Col. 1)   UPDATE or UP
  Col. 11 - 18         (Starting in Col. 11)   CURVE FIT or CU, TABULAR or TA
                       for type of data to be updated
                                    5-15

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       Update Control Cards
       One card is required for each set of species data being updated.   Only
one update to a species can be made in each run.   If there is more than  one
update to a species, only the first update will  be carried out.
       Additions to the file are activated by the following control  card:
                       (Format A2, 8X, 2A4)
                       *ADD or *A
                       Program adds following species data to the current
                       data file.  The program checks to see if the species
                       already exists and if so, no additions are made.   The
                       new species data is added onto the end of the master
                       file.
       Card Set 3      Thermochemical Input Data
                       Species identification and data card
       Card 3          (Format 10X, 2A4, 2X, 2F10.0)
  Col. 11 - 14   NAMA  Species name utilized in reaction input
  Col. 21-30   MW    Molecular weight of species
  Col. 31 - 40   HRF   Heat of formation of species at 298K (cal/mole)
       For tabular data, the thermochemical information must be entered  in
the following form:
       Cards (4 - 13)  (Format 5 (IX, E12.5))
  Col. 2 - 10,
       12-20   CP    Specific heat every 100K from 100K to 5000K
                       (cal/moleK)
       Cards (14 - 23) (Format 5 (IX, E12.5))
  Col. 2 - 10,
       12 - 20, H-H298oK every 100K from  100K to 5000K (Kcal/mole)
       Cards (24 - 33) (Format 5 (IX, E12.5))
  Col. 2 - 10,
       12 - 20, F =  (G-H2g8o)/T.   Function related to free energy every
                       100K from  100K to 5000K  (cal/moleK)
                                    5-16

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       For curve fit data, the thermochemical information must be entered in
the following form, where CP = F3 + F.T + Fc/T2:
       Card 4          (Format 6E9.6, 6X, F6.0, 6X, A4)
                       Low temperature range curve fit
  Col. 1 - 9           F] Heat of formation at 298K (cal/mole)
  Col. 10 - 18         F2 change in enthalpy from 298K to 3000K (cal/mole)
  Col. 19 - 27         F3 Coefficient in above Cp expression
  Col. 28 - 36         F. Coefficient in above Cp expression
  Col. 37 - 45         Fg Coefficient in above Cp expression
  Col. 46 - 54         F6 Entropy constant at 3000K (cal/moleK)
  Col. 61 - 66         TU upper temperature limit of low temperature range
                       curve fit (K)
  Col. 73 - 76   NAMA  Name of species used in reaction set
       Card 5          (Format 6E9.6, 6X, F6.0, 6X, A4)
                       High temperature range curve fit.  Same data as above
                       for temperatures beginning at the maximum of the
                       above data.
       The following instructions must be present to replace current species
data on the file with new data:
                       (Format A2, 8X, 2A4)
                       (Starting in Column 1) *CHANGE or *C
                       The change instruction must be followed by curve fit
                       or tabular data in the same format as given under the
                       add option described above.
                                    5-17

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       The following instruction must be present to delete current species
data on the file:
                       (Format A2, 8X, 2A4)
                       (Starting in Column 1) *DELETE or *D
                       (Starting in Column 11) NAMA species -  name which  is
                       to be deleted.  This name must match that used on  the
                       file.  If no name is given then the delete command
                       is not carried out.
       Last card       (Format A2, 8X, 2A4)
  Col.  1  - 2           (Starting in Column 1) *END or *E.   This  card ends
                       the update process.
                                   5-18

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                                  SECTION 6
                                    OUTPUT

       The  PROF code output gives complete summary information for flame,
well-stirred  and plug-flow reactor and time-evolution chemical kinetic prob-
lems.  If called for,  it can also provide information on intermediate itera-
tions and chemistry routine solutions.  For each iteration during a flame
solution the  code always prints out a line of output which gives the flame
speed parameter, its error, the maximum error in concentration and the
constraint  (i.e. damping) applied to the corrector step correction vector.
In addition,  all of the input data is output along with the title of the
run.
       Debug  output can be activated by assigning KR7 equal to or greater
than three.   The meaning of this output is discussed in Section 8.  The
following subsections  describe a typical nondebug output.
6.1    Integral and Nom'ntegral Input Parameters
       The  first (or more) page of output lists the run title, integral
parameters, nonintegral grid parameters, assigned pressures and temperatures
and wall heat loss data.  This output is listed in the same order in which it
is read in on card input, and is simply a printing of the input information
with notations to clearly indicate what has been read.   Examples of this
output for several sample problems are given in Section 7.
6.2    Species Names and Concentrations
       The next page of output lists the species names, initial mole fractions,
guesses of final  mole fractions and the diffusion factors for the individual
species.   This output is clearly labeled and is simply  a listing of output.
                                     6-1

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6.3    Thermochemical Data
       The next page(s) of output is a listing of the thermochemical  curve
fit or tabular data obtained from the thermochemical  data file for each
species.  If curve fit data is specified, three lines of output giving the
species name and molecular weight, curve fit and other constants appears
for each species.   For tabular data, 31 lines of output giving specific
heat, enthalpy and free energy for each species appears.   This information,
which is clearly labeled, is completely described in  Section 5.2.
6.4    Kinetic Reaction Data
       On this page of output a completely labeled listing of kinetic reac-
tion input data is given along with the associated reaction rates.
6.5    First Guess Alphas
       If punched card output from a prior run is used as first guesses, the
values read in will be output in this section.  Information given includes,
the normalized distance coordinate used in the prior  run and the enthalpy
and species concentration distributions obtained in the prior run.   In addi-
tion to this listing of input data, the enthalpy and species concentrations
scaled from the input to the problem being calculated are also output.  These
values are assigned to the grid points as first guesses.
6.6    Chemistry Solutions at Grid Points
       If KR7 is 2 or greater chemistry solution output is printed at each
grid point.  Information given in this output includes, the number of intera-
tions required to achieve a converged chemistry, the  grid point index, pres-
sure mixture molecular weight product, temperature in degrees K, and partial
                                      6-2

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pressures of the IS species in atmospheres.  Output corresponding to the NL
grid points are given in this section of output.
6.7    Condensed Output for Each Iteration
       For flame problems where KR7 is 2 or greater, values of alpha (species
concentrations, enthalpy and for problems where KR6 = 3, temperature and
enthalpy tilda) as predicted in the chemistry routine are output followed by
values of alpha determined in the corrector step.  Descriptions of the proce-
dures used to obtain these values are given in Sections 4.1.2 and 4.1.3.  The
degree of convergence of the flame solution is indicated by the relative dif-
ference between the predictor and corrector alphas at each grid point.  When
the predicted alphas equal the corrected alphas the solution is converged.
       Following the predictor and corrector alphas is a single line of out-
put giving the flame speed parameter, APR, the predicted correction in this
parameter, DAPR, the maximum alpha error found for the entire grid, and
the constraint on the corrector step correction vector.  This constraint
multiplies the correction vector and prevents over corrections from being
made to the variables.
6.8    Mole flux at grid points
       On the final iteration of a flame solution problem, the code prints
out the reaction creation, diffusion flux out and convective flux out for
each species at all grid points.  These appear underneath one another and
are in units of mole/cm2/sec.  The grid point number at each station is printed
out along with the nodal width in centimeters for that station.  The
creation and sum of the flux terms at each end point will only balance
if the solution is converged.
                                      6-3

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6.9    Grid Information Summary Table
       This section of output always appears and provides final information
for flame, well-stirred reactor, plug-flow reactor and time-evolution chemical
kinetic problems.  The first line of output gives the number of iterations
and how many grid points are being calculated.  For flame calculations, the
flame speed parameter, APR, is printed out along with the associated flame
speed in cm/sec.  It should be noted that for a flame problem which is not
yet converged (i.e. DAPR is a considerable fraction of APR and maximum
relative alpha error is greater than 0.001 in final output described in
Section 6.7), these parameters, plus all subsequent output, only represent
intermediate values and have no physical significance.  The grid coordinates
output for NL grid points are the distances, in cm, between nodes defined
by s on page 4-2.  These are the coordinates which can be used in plotting
gas properties.  For time-evolution and well-stirred reactor problems
this output does not apply.  The nondimensional grid coordinates are the
nodal widths used to develop the grid coordinates and time.  These are
Input parameters.  Like the grid coordinate output, the time output is
the time  in seconds between nodes.  For well-stirred reactor problems
this output gives the residence time in reactor for each reactor
calculation.  Following the coordinate information is gas enthalpy (cal/gm),
temperature (K), density  (gm/cm3), system molecular weight and species
concentration for the NL  grid points.  This information is strung out
eight grid points to a line until NL grid points are covered.
                                     6-4

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6.10   Kinetic Reaction Summary Information
       If KR7 is greater than zero, detailed information on the kinetic reac-
tion rates are output in this section.   The first block of output gives the
forward kinetic production rate of each reaction in mole/cm3/sec at each
grid point.  This information is strung out eight grid points to a line until
NL grid points are covered.  The second block of output gives the ratio of
the forward to backward rate of each reaction.  A value near one indicates
that the reaction is approaching equilibrium.  This output is also strung
out eight grid points to a line until NL grid points are covered.  The third
block of output lists, for each grid point, the reactions and rates, in
mole/cm3/sec units which contribute to the formation of the individual
species.  This output can be used to assess the importance of various reac-
tions to the chemical evolution of the problem.  If a reaction does not con-
tribute significantly to any species formation or depletion over the entire
grid, then this reaction can be extracted from the calculation without sig-
nificantly affecting the results.
                                     6-5

-------
                                  SECTION 7
                                 SAMPLE  CASES

       A total of five sample cases are discussed in this section.  These
cases illustrate how the flame, well-stirred reactor, plug-flow reactor and
time-evolution chemical kinetic problem input decks are set up and what type
of output is to be expected when these problems are run.  Listings of the
input cards along with selected sections of output are given for each case.
7.1    Sample Case 1 - Free Methane/Air Flame
       The free flame case, described presently, and the attached flame
problem, which will be discussed subsequently (Section 7.2), are the
primary options of the PROF code.  As mentioned previously for the free
flame case, the elementary chemical kinetic and transport data input into
the code along with the initial conditions define flame speed.  Within the
bounds of flammability, the code will always determine a flame speed consistent
with the input data.  In the case of the attached flame problem, mass flowrate
of reactants is assigned.  In some instances, the assigned flowrate is
inconsistent with the chemical kinetic and transport data input into the
code.  Under these conditions no stationary nontrivial flame solution will
exist and the code will fail.  To avoid this problem, a free flame calculation
should be performed prior to an attached flame calculation.  The mass flowrate
corresponding to the predicted flame speed can then be compared to the
potential assigned flowrates.  If the former flowrate is less than an
assigned mass flow, no stationary solution exists and the flame will be
"blown off."  For these cases, either the assigned flowrate or the kinetic
and transport data must be adjusted before a nontrivial attached flame
                                     7-1

-------
SAMPLE PROBLEM 7.1
1.
2.
;.
i.
5.
6.
7.
a.
9.
10.
11.
12.
13.
11.
19.
16.
17.
ia.
19.
20.
21.
22.
23.
21.
29.
St.
27.
28.
29.
30.
31.
32.
3!.
31.
39.
36.
37.
38.
39.
10.
11.
12.
13.
11.
1!.
16.
17.
1C.
19.
90.
91.
52.
93.
91.
CHI/AIR
16 3 16
.036671
1.
1.
1.
1.
.9
.09
.2
1.0
CHI
02
C02
H20
H2
CO
CH3
CH20
CHO
H02
H
0
HO
N2
CH
CH2
END
37
CHI
CHI HO
CHI H
CHI 0
CHS 0
CHS 02
CH20
CH20 HO
CH20 0
CH20 H
CHO 02
CHO HO
CHO 0
CHO
CO HO
CO 0
H02 0
H02 HO
H02 H
H02 H
H 02
H 02
0 H2
HO H2
HO HO
SAROFIM P=1ATM
29 8 3 1 1
.29 1.0
1. 1.
1. 1.
1. 1.
1. 1.
.3 .2
.09 .09
.5 .5

.091
.191
1.-9.1
.-9.06
.-9
.-9
.-9
.-9
.-9
.-9
 -
. 
. 
.718 .718
. 
 -


H CH3 H
CH3 H20
CHS H2
CHS HO
CH20 H
CH20 HO
M CO H2
CHO H20
CHO HO
CHO H2
CO H02
CO H20
CO HO
H CO H
C02 H
M C02
02 HO
02 H20
HO HO
02 H2
M H02
HO 0
HO H
M20 H
M20 0
T=298 PHT=.952
-3 1 I 1 12 2
298.
1. 1.
1. 1.
1. 1.
1. 1.
.1
.05
1.0 1

1. -31. 0523
1. -31. 0168
.8
1.2980
1. -33. 5333
.-3 .9830
.-31.3257
.-31.2980
.-3 .9601
.3 .9016
.-35.1557
.-31.1158
.-31.3175
.9732
.-31.13
.-31.37


1.50*18
1.00*13
2.00*11
2.00*13
3.50*13
1.00*12
2.00*16
2.50*13
3.00*13
1.70*13
3.00*13
1.00*11
5.10*11
2.00*12
5.50*11
3.60+1A
2.50*13
2.50*13
2.50*11
2.50*13
2.00+15
2.20+11
1.70+13
2.20+13
6.00+12


002




05
05
.0




















0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.5
0.5
0.0
-1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0



1. 1. 1.
1. 1. 1.
1. 1. 1.
1. 1. 1.
.05 .05 .05
.05 .1 .1
2.0 2.0 1.0



















0. 100.0
6.000
11.900
6.900
3.300
15.000
35.000
1.000
0.
3.000
0.
0.
0.
28.800
1.080
2.500
0.
0.
2.000
.000
.870 H20 20.
16.800
.160
5.200
.780

-------
-4
I
CO
55.
56.
57.
56.
99.
60.
61.
62.
63.
64.
65.
66.
67.
66.
69.
70.
71.
72.
73.
74.
75.
76.
77.
76.
79.
60.
81.
A2.
63.
84.
85.
86.
87.
66.
69.
90.
91.
92.
92.
94.
95.
96.
97.
96.
99.
100.
101.
102.
103.
104.
105.
106.
107.
10".
109.
110.
111.
H
0
H
0
CHS
CH2
CH2
CH
CH2
CH
CH
CH2
HO
H
H
0
HO
HO
02
02
0
HO
0
H
CH4/AIR
M
M
M
H





4


H20
HO
H2
02
CH2
CH
CH20
CHO
CHO
CHO
CO
CH




H20
H20
0
0
H
H
H
H2
SAROFIH P=1A
7
4
2
4
6
5
5
5
5
5
5
3











t
00 + 19
00+18
00+19
00+18
00+09
00 + 11
00+11
00+11
00+11
00+11
00+11
00+11
-1
-1
-1
-1








.
.
.
.




.
.
.
.
0
0
0
0




5
5
5
7




.7
.5
.5
.5




0
0
0
0











t




4.
10.
4.
26




2
6
7
6
0
0
0
.0




.0
.0
.
.0




PHIs. 952
                           TS298
 25 16 .40331-01 .25000+00
.5      .3      .2      .1      .05     .05     .05
.5000-01.5000-01.5000-01.5000-01.1000+00.1000+00.2000+00.
.1000+01.2000+01.2000+01.4000+01.4000+01
-.604+02-.604+02-.594+02-.580+02-.569+02-.555+02-.539+02-
-.446+02-.419+0?-.396+02-.381+02-.400+02-.497+02-.639+02-
-.591+02-.589+02-.568+02-.587+02
.3211.02.3130-02.3018.02.2920.02.2650-02.2765.02.2663.02.
.2000-02.1749-02.1459.02.1139.02.5332.03.1403.03.6115.05.
.2185-10.6520-12.2643-13.7919-15
.6779-02.6655-02.6467-02.6341-02.6239-02.6116-02.5970-02.
.5053.02.4709.02.4305.02.3840.02.2837.02.1871.02.1065.02.
.5256-03.4612-03.4503-03.4309-03
.1153-04.2690-04.5796-04.6712-04.1090-03.1363-03.170*3-03.
.4140.03.5151-03.6389.03.7894.03.1141.02.1560.02.2204-02,
.2941-02.3009-02.3056.02.3067.02
.2189-03.4226-03.6649-03.6977.03.1037.02.1197-02.1363-02.
.2449.02.2615-02.3225.02.3675-02.4585.02.5341-02.5840.02.
.6314.02.6365-02,6401-02.6422.02
.1495.03.2009.03.2473.03.2760.03.2920.03.3086.03.3267.03.
.4091.03.4324.03.4558.03.4780.03.5083.03.4855.03.3734.03.
.1457-03.1147-03.9449-04.6167-04
.2435-04.5410-04.9601-04.1376.03.1653-03.1984.03.2383.03.
.4944.03.5922-03.7075.03.8410-03.1123-02.1304-02.1030.02.
.3444-03.2772-03.2303.03.1999-03
.1134.04.2196-04.3609.04.4649.04.5762-04.6921-04.8393-04.
.1857.03.2229-03.2609.03.2919.03.2690-03.1606.03.1601-04.
.6629.10.2345-11.7027.13.1799.14
.1033.05.2046-05.3443.05.4609.05.5367-05.6217-05.7159.05.
.1230.04.1406-04.1572.04.1659-04.1329.04.6032-05.4928-06.
.1066-11.5619-12.3625.12.2874-12
.1466.11.9261.11.3293.10.6421.10.5694-10.2605.10.2149.10.
.4844-08.1327-07.3565.07.8995.07.3312-06.4929.06.9734-07.
.5414-09.3769-09.2656-09.2354-09
.2175.06.7213-06.1661.05.2430.05.2801-05.3070-05.3202-05.
.3065.05.3187.05.3411-05.3608.05.3064.05.1462-05.2763.06.
.4599-07.3301-07.2529-07.2093-07
.4782-11.3798.10.3956.09.2107-08.4409.08.7727.08.1206.07.
.4276-05.7723-05.1349.04.2319-04.6039-04.1236-03.1885-03.
.3229-04.2114-04.1509-04.1178-04
.1880-09.6446-09.1717-08.3000-08.332B-0A.3034-08.2407-08.
. 3738.06.9750-06.2434.05.5819.05.?402-04.6672-04.1154-03.
. 2797-04.2011-04.154V-04.1283-04
.3575-09.1073-OP.2A 09-Ofl.5?95-08.6660-08.7641-06.6406-08.
05     .05
5000+00.5000+00

.519+02-.497+02
.635+02-.609+02

2540-02.2391-02
3037-06.1238-07

5797-02.5590-02
7946.03.6733.03

2131-03.2661-03
2575-02.2738-02

1597-02.1643-02
6004-02.6131-02

3456-03.3656-03
2962-03.2429-03

2861-03.3435-03
6998-03.5438-03

1024-03.1251-03
9666-06.4494-07

6200-05.9371-05
1324-07.3431-09

1386-09.5622-09
5350-08.1360-08

3207-05.3136-05
1340-06.9411-07

1420-06.9069-06
1326-03.8513-04

1S53-08.3531-07
8699.04.6052-04
.05
.1000+01

-.472+02
-.599+02

.2213-02
.5227-09

.5345-02
.5866-03

.3322-03
.2656-02

.2126-02
.6239.02

.3868-03
.1650-03

.4122-03
.4271-03

.1528-03
.1611-06

.1072-04
.9178-11

.1731-08
.7982-09

.3064-05
.6491-07

,2184-Ob
.5035-04

.1334-06
.3966-04
                                                                             1600-06,.*)* 3 8-06,1274-05

-------
112.    .2534. 05. 5019.05.1019.04. 2033. 04. 6352. 04.1412. 03. 2476-03. 2558. 03.2338. 03.2019- 03
113.    .1762-03.1536-03.1374.03.1265-03
111.    2588-01.2587-01.2589.01.2591-01.2592-01.2593-01.2594-01.2595-01.2597-01.2598-01
115.    2600-01.2601-01.2601-01.2600-01.2600-01.2597-01.2597-01.2595-01.259<-Ol.259H-Ol
116.    2593-01.2593-01.2593-01.2593-01
117.    *6990-09.1839-OA.3679.08.4*07.06.4786-08.3820.08.2572-08.1332.08.7816.09.3660.09
116.    .1901-09. 4019.09.1455.08. 5250. 08. 3904. 07.1415.06. 9501-07. 9348- 08.5035-09.1664-10
119.    .6065-12.1746-13.4491-15.102>-l6
120.    .1135-07.2250-07.3519.07.4098.07.4092-07.3798.07.3369.07.31<7-07.3568-07.5183.07
121.    .6926.07.1676-06.3245.06.6137.06.1628.05.2150.OS.5194.06.3478-07.16*7.08.6072.10
122.    .2083.11.6469-13.1782.14.4282-16

-------
                       PREFIXED OME DIMENSIONAL FLAML CODE SOLUTION (PROD
                     PROGRAM DOCUMENTED IN THE "PROF CODE USER'S MANUAL",
                       ACROTHERN/ACUREX CORP FINAL REPORT 76-277
                               PHONE 415/961-3200
   CH4/AIR  SAROFIM  PslATM  T=296  PHI=,952


                              * INTEGRAL PARAMETERS 

COLUMN                                            COLUMN
   3  NO. SPECIES CONSERVATION EOS.  16              6  PROBLEM TYPE AND ENERGY EG.     3

   9  NO. OF SPECIES                 16             12  NO. AXIAL GRID PTS.            25

  IS  NO. GRID SOLUTION ITERATIONS    8             10  SOLUTION CYCLE CONTROL NO.      3

  21  READ IMTIAL MOLE FRACTION      1             24  READ NONINTEGRAL PARAMETERS     1

  27  THERMO DATA s HEAT LOSS MODEL  -3             30  CONSTRAINT SWITCH               i

  33  READ KINETIC DATA               1             36  CONSTRAINT APPLIED TO VARIABLE  1

  39  CONSTRAINT APPLIED TO GRID PT. 12             42  OUTPUT CONTROL NO.              2

  45  FLAMEHCLOER TEMP ASSIGN SWITCH  0             40  INPUT MASS FLOWRATE SWITCH      0



                                NONINTEGRAL PARAMETERS *


   APRsDEL/MCOTs .36671-01   BPcOBAR/
-------
                          * SPECIES INITIAL MOLE FRACTIONS .FIRST GUESSES, AND DIFFUSION FACTORS *


                         SPECIE                  ALPF                ALPE          DIFFUSION FACTOR
                                                 .910-01             .100-02              1.0523
                          02                     .191*00             .100-02              1.0H68
                          C02                    .100-08             .100*00               .8000
                          H20                    .100-08             ,600-Ul              1.2980
                          H2                     .100-08             .100-02              3.533S
                          CO                     .100-08             .100-02               .9830
                          CH3                    .100-08             .100-02              1.3257
                          CH20                   .100-08             .100-02              l.290
                          CHO                    .100-08             .100-02               .960<
                          H02                    .100-08             .100-02               .9016
                          H                       .100-08             .100-02              5. 1537
                          0                       .100-08             .100-02              l.*158
                          HO                     .100-08             .100-02              1.375
                          N2                     .716*00             .718+00               .9732
                          CH                     .100-08             .100-02              1.H300
                          CH2                    .100-08             .100-02              1.3700
cr>

-------
                       * THERMOCHEMISTRY DATA *
        CURVE FIT OF DATA IN FORM CP=RB+RC*T+RD/IT*T>  
-------
                * KINFTIC REACTION DATA *
MJHBER OF REACTIONS:: 37

      REACTION
PRE EXP FACTOR
 (MOLE-CM-S)
TEMP EXP
1
2
3
4
5
6
7
8
9
10
11
12
13
11
15
16
r1 "
00 16
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
CH4 4
CH4 4HO
CH4 4H
CH4 +0
CH3 40
CH3 402
CH204
CH204HO
CH2040
CH204H
CHO 402
CHO 4HO
CHO 40
CHO 4
CO 4HO
CO 40
H02 40
H02 4HO
H02 4H
H02 4H
H 402
H 402
0 4H2
HO 4H2
HO 4HO
H 4HO
0 4H
H +H
0 40
CHS 4HO
CH2 4HO
CH2 402
CH 402
CH2 40
CH 4HO
CH 40
CH2 4H
+H
4
4
4
4
4
4H
4
4
4
4
4
4
4H
4
4H
4
4
4
4
4M
4
4
4
4
4M
4N
4M
4N
4
4
4
4
4
4
4
4
-B
S
-8
-S
S
-S
S
-3
s
--S
S
--S
  s
--=
  B
--S
--=
--=
--S
-B
S
"S
--S
--=
-"S
--S
  B
--S
-S
--C
S
--S
S
S
"=
--=
 S
CH3 4H
CHS 4H20
CHS 4H2
CH3 4HO
CH204H
CH204HO
CO 4H2
CHO 4H20
CHO 4HO
CHO 4H2
CO 4H02
CO 4H20
CO 4HO
CO 4H
C02 4H
C02 4
02 4HO
02 4H20
HO 4HO
02 4H2
H02 4
HO 40
HO +H
H20 4H
H20 40
H20 4
HO 4
H2 4
02 4
CH2 4H2Q
CH 4H20
CH2040
CHO 40
CHO 4H
CHO 4H
CO 4H
CH 4H2
.15004194 0.
.10004144 0.
.20004154 0.
.20004144 0.
.35004144 0.
.10004134 0.
.20004174 0.
.25004144 0.
.30004144 0.
.17004144 0.
.30004144 0.
.10004154 0.
.54004124 0.
.20004134 0.
.55004124 0.
.36004194 0.
.25004144 0.
.25004144 0.
.25004154 0.
.25004144 0.
.20004164 0.
.22004154 0.
.17004144 0.
.22004144 0.
.60004134 0.
.70004204 0.
.40004194 0.
.20004204 0.
.40004194 0.
.60004104 0.
.50004124 0.
.50004124 0.
.50004124 0.
.50004124 0.
.50004124 0.
.50004124 0.
.30004124 0.
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.500
.500
.000
-1.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
1.000
-1.000
-1.000
-1.000
,700
.500
.bOO
.500
.500
.500
.500
.700
ACTIVATION
(KCAL/HOLE)

 100.0000
   6.0000
  11.9000
   6.9000
   3.3000
  15.0000
  35.0000
   1.0000
    .0000
   3.0000
    .0000
    .0000
    .0000
  26.8000
   1.0600
   2.5000
    .0000
    .0000
   2.0000
    .0000
    .6700
  16.8000
   9.4600
   5.2000
    .7800
    .0000
    .0000
    .0000
    .0000
   2.0000
   6.0000
   7.0000
   6.0000
   i*.0000
  10.0000
   4.0000
  26.0000
                               INDIVIDUAL THIRD BODY EFFIC.
                               NAMEl     ETB1  NANE2    ETB2
                                                                                H20
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                       20.000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                         .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000
                                                       .000

-------
                 MOLE FLUXES AT GRID POINTS
-------
                                *  6RIO  INFORMATION  SUMMARY TABLE  *
          ITERATIONS   6        NUMBER OF GRID POINTSs  25
            FLAME SPEED PAR=  .39096-01          FLAME SPECQs  .37049402 CM/SEC
            GRID COORDINATES(CM)

             .00000       .12355.01    .20430.01    .26333.01    .29550-01    .31255.01    .33042.01    .34920.01
                  .36900.01    .36995.01    .41215.01    .43572.01    .46077.01    .48743.01    .51581-01    .57771.01
                       .64595.01    .79386.01    .11869+00    .15949+00    .24308+00    .32605+00    .49987+00    .67291+00
                            .10204+01

           NONDIMENSIONAL GRID  INCREMENTS
             .50000+00    .30000400    .20000400    .10000400    .50000-01    .50000-01    .50000-01    .50000-01
                  .50000-01    .50000-01    .50000-01    .50000-01    .50000-01    .50000-01    .10000400    .10000+00
                       .20000+00    .50000+00    .50000+00    .10000+01    .10000+01    .20000+01    .20000+01    .40000+01
                            .40000401
-4
^         TIME(SEC)
O
             .00000       .30979.03    .48572-03    .59680-03    .64960-03    .67511-03    .69995-03    .72409-03
                  .74751.03    .77019-03    .79211-03    .81328.03    .83366-03    .85335-03    .87233-03    .90844.03
                       .94261.03    .10085.02    .11703.02    .13313-02    .16524-02    .19730-02    .26141-02    .32554-02
                            .45366-02

          ENTHALPY(CALXGM)

            -.58691402  -.39301402  -.58483402  -.56683402  -.54830+02  -.53498+02  -.51915+02  -.50068+02
                -.47959+02  -.45615+02  -.43083+02  -.40479+02  -.37982+02  -.35924+02  -.34837+02  -.37314+02
                     ..47699+02  -.63504+02  -.63877+02  -.61844+02  -.61400+02  -.61463+02  -.62565+02  -.64171+02
                          -.66432402

          TEMPERATURE(K)

            .29800403   .34300+03   .?9l4l+03   .45714+03    .51233+03    .54914+03    .59182+03    ,64110+03
                 .69775+03   .76252+03   .83616+03   .91932+03    .10125+04    .11159+04    .12289+04    .14577+04
                      .16638+04   .16507+04   .19693+04    .20406+04    .20928+04    .21269+04    .21497+04    .21631+04
                           .21689+04

          DENSITY(GM/CM3)

            .11323-02   .97820-03   .85484-03   .72994-03    .65015-03    .60595-03    .56167-03    .51792-03
                 .47530-03    .43429-03   .39544-03   .35900-03    .32533-03    .29467-03    .26719-03    .22463-03
                      .19668-03   .17762-03   .16812-03    .16290-03    .15941-03    .15722-03    .15584-03    .15507-03
                           .15479-03

          SYSTEM  MOLECULAR  UFIGHT

-------
?76e7+0?    27530*02    .?75* + 02    .27381+02   .27333+02   .27305+02    .27277 + 02    .2727+02
     2721H+02   .27m+0?    .27132+02    .27081+02   .27029+02   .26981+02    .2693+02   .26869+02
         .2685*+5?.    .2697H + 52    .27167+02   .27280+02   .27376+02    .?7-39+02    .27*90 + 02   .27525+02
              ,275*9+02

-------
                            * HOLE FRACTIONS OF   16   SPECIES  *



       CH4

          .91000-01    .66373-01    .65626-01   .82353-01    .79372-01    .77340-01    .74936-01    .72081-01
               .66694-01    .64657-01    .59655-01    .54163-01   .47489-01    .39629-01    .31378-01    .15224.01
                    *4?645-02    .25452-03    .96100-05    .39293-06    .16692-07    .70666-09    .28210-10    .96201-12
                         .29459-13
       02

          .191004-00    .18683*00    .163004-00   .17784+00    .17345400    .17047*00    .16695+00    .16281 + 00
               .15792+00    .15217+00    .14540+00    .13744+00   .12615+00    .11736+00    .10501+00    .78312-01
                    .52274.01    .29323-01    .21833.01    .18527-01    .16169.01    .14496.01    .13257.01    .12370-01
                         .11774-01
       C02

          .10000-06    .31109-03    .77665-03   .15494-02    .23188-02    .28940.02    .36109-02    .45040-02
               .56156.02    .69984.02    .67155-02    .10643.01   .13471.01    .16699-01    .20621-01    .29778-01
                    .40679-01    .98695-01    .69599-01    .74487-01    .76052-01    .80603-01    .82685-01    .84187-01
                         .65231-01
       H20

          .10000-06    .59751-02    .11466-01   .18537-01    .24212-01    .27914-01    .32177-01    .37064-01
               .42726-01    .49206-01    .56639-01    .65129-01   .74770-01    .85590-01    .97479-01    .12154+00
-J                  .14219+00    .15716+00    .16289+00    .16706+00    .17065+00    .17316+00    .17496+00    .17623+00
Jj                       .17707+00
CO     H2

          .10000-06    .41333-02    .55350-02   .67830-02    .75463-02    .79706-02    .84184-02    .86910-02
               .93903-02    .99179.02    .10476.01    .11063.01   .11677.01    .12300-01    ,12894.01    .13726.01
                    .13247.01    .10215-01    .62144.02    .67314-02    .51450-02    .40538-02    .31755-02    .25857-02
                         .21852-02
       CO

         .10000-08    .64784-03    .14370-02   .26006-02    .36521-02    .43895-02    .52746-02    .63366-02
               .76102-02    .91362-02    .10963-01    .13145-01   .15741-01    .16608-01    .22362-01    .29891-01
                    .35065.01    .28382-01    .19352-01    .15046-01    .11838-01    .95421-02    .76412-02    .62707-02
                         .53151-02
       CHS

         .10000-06    .47981-03   .91333-03   .14622-02    .19017-02    .21892-02    .25237-02    .29171-02
               .33859.02    .39503.02    .46309.02    .54369-02   .63567-02    .73013-02    .80756.02    .80184.02
                    .47099-02    .55042-03    .30214-04    .14242-05    .58115-07    .22238-08    .78075-10    .24293-11
                         .66386-13
       CH20

         .10000-Ofl   .29263-04   .56272-04   .90829-04    .11671-03    .13695-03    .15603-03    .16246-03
              .21090-03   .24424.03    .26348-03    .32917-03   .37957-03    .42683-03    .45322-03    .37229-03
                   .17686.03   .15607-04    .43212-06    .11345-07    .30015-09    .31079-10    .15651-10    .10375-10
                        .74411-11
       CHO

         .10000-08   .36663-12   .32464-11   .30P57-10    .15P02-09    .39252-09    ,1023-0fl    .27164-08
              .72564-08   .19255-07    .50811-07    .1345-5-06   .35638-06    .94264-06    .23387-05    .fl5<*2b-OS
                   .13432-04   ,3005-05    .1639-0f>    .38654-07    .22418-07    .15l?l-f)7    .10317-07

-------
                    .59146-08
   H02

     .10000-08   .47079-05   .10945-04    .20562-04    .29495-04    .35736-04    .42969-04   .50918-04
          .58967-04   .66356-04    .72710-04    .78477-04    .84752-04    .91973-04    .97826-04   .85178.04
               .42956-04    .79940-05    .37320-05    .26307-05    .18284-05    .13024-05   .93536-06   .71116-06
                    .57740-06
   H

     .10000-08   .70929-11   .20880-11    .89551-08    .16090-06    .69889-06    .22599-05   .62295-05
          .15001-04   .32257-04    .63416-04    .11681-03    .20640-03    .35666-03    .60785-03   .15635.02
               .32148.02    .51455-02    .37082-02    .23999-02    .14229-02    .91117-03   .59159-03   .41462-03
                    .31251-03
   0

     .10000.08   .85966-09   .31741-08    .13810-07    .39901-07    .74684-07    .14429.06   .29820-06
          .66815-06   .16057-05    .40288-05    .10240-04    .25757-04    .63167-04    .14933-03   .61045.03
               .17030-02    .31391-02    .24175-02    .16920-02    .11159-02    .78146-03   .55711-03   .42205-03
                    .33906-03
   HO

     .10000-08   .64702-08   .30994-07    .15735-06    .54226-06    .11274-05    .22958-05   .46463-05
          .92588-05   .18081.04    .34903-04    .67768.04    .13391-03    .26771-03    .52851-03   .16294.02
               .36338-02    .66267-02    .69743-02    .64134-02    .55531-02    .48407-02   .41990-02   .37153-02
I                    .33569-02
W N2

     .718004-00   .71313+00   .71093+00    .70888+00    .70759+00    .70688+00    .70613+00   .70535+00
          .70493+00   .70369+00    .70286+00    .70206+00    .70134+00    .70073+00    .70020+00   .69913+00
               .69853+00    .70047+00    .70496+00    .70764+00    .71005+00    .71161+00   .71293+00   .71381+00
                    .71442*00
   CH

      .10000-08    .36147-09   .R0144-09    .16755-08    .b!694-08    .10978-07    .11259.07   .53688-08
           .18615-08   .16563-08    .81259-11    .18286-08    .11585-07    .37156-07    .13354-06   .96964.06
               .35653.05    .27551-05    .28749.06    .15938-07    .60085-09    .19839-10   .58036-12   .15306-13
                    .36359-15
   CH2

      .10000-08    .10097-07   .22125-07    .47679-07    .86381-07    .12554.06    .18763-06   .29043.06
           .46650-06   .77763-06    .13482-05    .24357-05    .45714-05    .87266-05    .16276-04   .42575.04
               .58899.04    .15527-04    .10828-05    .52021-07    .19583.08    .68142.10   .21571.11   .61332-13
                    .15550-14

-------
            *  NET  FORWARD KINETIC  PRODUCTION  RATES(MOLE/-13
                  .75840-15
 REACTICN  NUMBER    7
   .00000       .36291.19    .30753-16    .23551-13    .15575-11    .15663.10    .15753-09   .15284-08
        .13669-07    .11506-06    .64974.06   .54917.05    .30466.04    .14137-03    .52886-03    .29298-02
             .48271-02    .99210.03   .43022.04    .14309-05    .38925-07    .99202-09  -.29271-11  -.12374-10
                -.96895-11
 REACTION  NUMBER    6
   .00000       .13647-08   .11597-07    .64009-07    .33982-06    .75853-06    .16405-05   .34887-05
        .72330-09   .14567-04    .28776-04   .56684-04    .11198-03    .21699-03    .39081-03    .74982-03
            .64356.03    .85326.04   .22325-05    .50600-07    .10809-08    .74476-10   .24395.10    .10716.10
                  .47931-11
 REACTION  NUMBER    9
   .00000       .93330-09   .50434-08    .25876.07    .76101-07    .14878-06    .28727-06   .58664-06
        .12869.05   .30044-05    .72795-05   .17776-04    .42501-04    .96475-04    .19961-03    .47616-03
            .46982-03    .63666-04    .11991-05    .20502-07    .33161-09    .18309-10   .49211-11    .18489-11
                  .73505-12
REACTION NUMBER  10
   .00000       .57860-13   .40827-11    .40161-09    .97376-08    .51267-07    .20055-06   .66168-06
        .18831-05   .47199-05    .10665-04   .22222-04    .43419-04    .79738-04    .13471-03    .24523-03
            .21139.03    .26150.04    .48406-06    .78615-06    .11639-09    .59289-11   .14597-11    .50913-12
                  .19013-12
REACTTCN NUMBER  11
   .00000       .25489-08   .16913-07    .11226-06    .43805-06    .97702-06    .21541-05   .47671-05
        .10U56.Q4   .22405-04    .46952-04   .97143-04   .19863-03    .39327-03    .71845-03    ,138b6-02

-------
                      *  RATIO  OF  FORWARD TD BACKWARD KINETIC PRODUCTION RATE'S FOR  37  REACTIONS *



           REACTION  NUMBER   1
             .00000       .00000       .00000      .13489-33   .17235-29   .36487-27   .10598-2"*   .33509-22
                  .10180-19    .26517-17   .53511-15   .76795-13   .73109-11   .43809.09   .16003-07   .31324-05
                       .74136*04    .64123-03   .35944-02   .12694-01   .43228-01   .11340+00   .26039*00    .48648+00
                            .75760+00
           REACTION  NUMBER   2
             .00000       .17341+07   .16137+06   .21512+05   .77554+04   .46439+04   .27009+04   .15646+04
                  .90318+03    .52068+03   .30399+03   .1*353+03   .11627+03   .77143+02   t52680+02   .25189+02
                       .12302+02    .65539+01   .35796+01   .24316+01   .195S1+01   .17521+01   .16462+01    .15822+01
                            .15471+01
           REACTION  NUMBER   3
             .00000       .24917-05   .30322-04   .83690-03   .10272-01   .38071-01   .10556+00   .24802+00
                  .50298+00    .89420+00   .14185+01   .20466+01   .27387+01   .34627+01   .41875+01   .52080+01
                       .54225+01    .57427+01   .35312+01   .24121+01   .19428+01   .17435+01   .16408+01    .15786+01
                            .15449+01
           REACTION  NUMBER   4
             .00000       .22188+02   .14219+02   .12351+02   .10956+02   .10340+02   .10182+02   .10683+02
                  .12139+02    .14728+02   .18285+02   .22032+02   .24753+02   .25630+02   .24793+02   .192574-0?
                       .12844+02    .70550+01   .36649+01   .24583+01   .19692+01   .17610+01   .16520+01    .15858+01
                            .15493+01
           REACTION  NUMBER    s
             .00000       .60909-07   .64333-06   .66405-05   .19007+30   .82461+27   .48062+25   .36917+23
7J                .39531+21    .60577+19   .132SO+1A   .40666+16   .17197+15   .99384+13   .79021+12   .17118*11
_                     .14472+10    .26707+09   .18172+09   .18961+09   .21279+09   .65815+08   .42358+07    .19433+06
w                          .75607+04
           REACTICN  NUMBER    6
             .00000       .13457-07   .31804-06   .63212+33   .32205+30   .45487+28   .64543+26   .95364+24
                  .15547*23    .29341+21   .65756+19   .17633+18   .56976+16   .22695+15   .11629+14   .10877+12
                       .40253+10    .32222+09   .18782+09   .19242+09   .21532+09   .66517+08   .42742+07    .19569+06
                            .75975+04
           REACTION  NUMBER    7
             .00000       .93219+06   .80741+06   .82757+06   .88708+06   .93498+06   .99461+06   .10662+07
                  .11495+07    .12441+07   .13478+07   .14548+07   .15491+07   .15962+07   .15446+07   .10769+07
                       .51239+06    .77132+05   .40366+04   .16940+03   .75424+01   .12386+01   .99894+00    .99356+00
                            .99593+00
           REACTION  NUMBER    8
             .00000       .37154+30   .92014+26   .19846+23   .89565+20   .43909+19   .20810+18   .99175+16
                  .49595+15    .27224+14   .17003+13   .12419+12   .10805+11   .11279+10   .14136+09   .49325+07
                       .45015+06    .76312+05   .19221+05   .12947+04   .38240+02   .42538+01   .24065+01    .17940+01
                            .14428+01
           REACTICN NUMBER    9
             .00000       .47540+25   .81078+22   .11395+20   .12653+18   .97766+16   .78450+15   .67707+14
                  .66655+13   .77004+12   ,102?7+12   .14908+11   .23004+10   .37475+09   .66528+08   .37710+07
                       .46999+06    .82147+05   .19678+05   .13090+04   .38515+02   .42753+01   .24150+01    .17982+01
                            .14449+01
           REACTION NUMBER   10
             .00000       .53386+18   .17290+17   .77209+15   .1186?+15   .35997+14   .81335+13   .15719+13
                  .27619+12   .46754+11   .79341+10   .13848+10   .25451+09   .50629+08   .11237+08   .10196+07
                       .19842+06   .66867+05   .18960+05   .12844+04   .37998+0?   .42328+01   .23987+01    .17900+01
                            .14408+01
           REACTICN NUMBER   11
             .00000       .82338 + 07   .47777 + 06   .41331 + 05   .11159 + 05   .57907 + 04   .30130+04   .lf,351 + 0<
                  ,93f48+03   .56915+03   .37100+03   .26098+03   .19638+03   .15483+01   .12533+03   .87907+0?

-------
                        * KINETIC CONTRIHUTIONS5 TO INDIVIDUAL SPtCIESIHOLE/CC*SEC))  REACTION/CONTRIBUTION  *
CT)
GRID
CH4
02

C02
H20

H2

CO

CHS

CH20

CHO

H02
H
POINT 2
( I/ .303-08), ( 2/-. 107-08), ( 3/ .175-08), ( 4/-. 718-10), (
( 6/-. 311-10), (ll/-. 255-06), (17/ .125-09), (18/ .952-09), (20/ .112-11),
(22/ .846-13), (29/ .371-15), (32/-. 760-09) , I33/-. 104-09) , I
(]5/ .991-09), (16/ .655-11), (
( 2/ .107-08), ( A/ .136-06). (12/ .292-15). (18/ .952-09), (24/ .357-09),
(26/ .442-15). (SO/ .737-10), (SI/ .113-15), (
( 3/-. 175-08), ( 7/ .363-19), (10/ .579-13), (20/ .112-11). (23/-. 696-13) ,
(26/ .146-18), (37/-. 373-26), 1
( 7/ .363-19). (ll/ .255-06), (12/ .292-15), (IS/ .383-17), ( 14/-. 424-14) ,
(16/-. 655-11), (36/ .660-17), (
( I/-. 303-06), ( 2/ .107-08), ( 3/-. 175-08), ( 4/ .718-10), ( 5/-. 141-09),
(SO/-. 737-10), (
( 5/ .141-09), ( 6/ .311-10), ( 7/-. 363-19). ( 8/-. 136-08), ( 9/-. 933-09),
(32/ .760-09), (
( 6/ .136-08), ( 9/ .933-09), (ID/ .579-13), (ll/-. 253-06) , (12/-. 292-15) .
(14/ .424-14), (3S/ .104-09), 1 34/ .280-15). (35/ .100-19), (
(ll/ .255-08). (17/-. 125-09), (18/-. 952-09) , ( 19/-. 593-12 ), (20/-. 112-11 ),
( I/-. 303-08), ( 3/ .175-06), ( 5/ .141-09), (10/-. 579-13) , (14/-. 424-14) ,


(21/-. 394-10),


(25/ .992-13).

(24/-. 357-09),

(15/-. 591-09).

( 6/-. 311-10),

(10/-. 579-13).

(IS/-. 383-17),

(21/ .394-10),
(15/ .591-09),
(19/-. 593-12), (20/-. 112-11), (21/-. 394-10) , (22/ .846-13), (23/ .698-13), (24/ .357-09)

37/ .373-26)
0
(26/-. 442-15) (27/-. 332-17) (28/-. 296-18) (34/ .260-15) (35/
(
( 4/-. 718-10), ( 5/-. 141-09), ( 9/-. 933-09), ( IS/-. 363-17) , ( 16/-. 655-11 ),



















,
.100-19) (36/ .880-17)

(17/-. 125-09),
(22/-. 648-13), (23/-. 698-13), (25/ .992-13), (27/-. 332-17) , (29/-. 742-15) , (32/ .760-09)

HO
(3S/ .104-09) (34/-. 260-15) (36/-.880-17) (
( 2/-. 107-08), ( 4/ .716-10), ( 6/ .311-10), ( 8/-. 136-08), ( 9/ .933-09),

(12/-. 292-15),
(13/ .383-17). (IS/-. 591-09), (17/ .125-09), (18/-.952-09) , (19/ .119-11), (22/-. 848-13 )

SI/-. 113-15)
CH
CH2
GRIP
CH4
02

C02
H20

H2

CO

CH3

CH20

CHD

HO?
H
(23/ .698-13) (24/.. 357-09) ( 25/-. 198-12) (26/-. 442-15) (27/
(35/-. 100-19) (
(31/ .113-15), (33/-. 104-09), (35/-. 100-19) , (36/-. 880-17) , ( 37/-. 373-26 ),
(SO/ .737-10), (SI/-. 113-15), (32/-. 760-09) , (34/-. 260-15) , (37/ .373-26),
POINT 3
( I/ .479-07), ( 2/-. 114-07), ( 3/ .256-07). ( 4/-. 667-09), (
( 6/-. 677-09), (ll/-. 169-07), (17/ .817-09), (16/ .816-08), (20/ .553-10),
(22/ .112-11). (29/ .293-14). (32/-. 477-08 ), (33/-. 263-09) , (
(IS/ .586-06), (16/ .493-10), (
( 2/ .114-07), ( P/ .116-07), (12/ .949-14), (18/ .816-08), (24/ .453-08).
(26/ .347-13), (SO/ .815-09), (31/ .290-14), (
( 3/-. 258-07), ( 7/ .308-16), (10/ .408-11), (20/ .553-10), ( 23/-. 146-11 >,
(28/ .672-16). (37/.. 733-24). (
( 7/ .308.16), (ll/ .169-07), (12/ .949-14), (13/ .102-15), ( 14/-. 214-12 ),
(16/-. 493-10), (36/ .580-16), (
( I/-. 479-07), ( 2/ .114-07), ( 3/-. 258-07), ( 4/ .667-09), ( 5/-. 137-08),
(SO/-. 615-09), (
( 5/ .137-08). ( 6/ .677-09), ( 7/-.30A-16), ( 8/-. 116-07), { 9/-. 504-08),
(32/ .477-08), (
( 6/ .116-07), ( 9/ .504-08), (10/ .408-11), ( ll/- .169-07 ), ( 12/-. 949-14 ),
(14/ .214-12), (33/ .263-09), (34/ .381-14), (35/ .25A-18), (
(ll/ .169-07), (17/-. 817-09), ( 18/- .816-08 ), ( 19/-.4?2-10 ) , ( 20/-. 553-10 ),
( I/-. 479-07), ( */ .25P-Q7), 1 5/ .137-08), ( 10/- .408-11 ), ( 1 4/-. 214-12 ),


,


,
.332-17) (TO/-. 737-10)

(
(


(21/-. 926-09),


(25/ .202-11),

(24/-. 453-08),

(IS/-. 588-08),

( 6/-. 677-09),

(10/-. 408-11),

(IS/-. 102-15),

(21/ .926-09),
(15/ .5H8-08),






















                          (19/-.422-10),   (?0/-.553-10),   (21/-.9?6-09),   (2?/  .112-11),   (23/ .146-11),   (?*/ .453-08),
                                   '-.347-13)    (27/-.198-15)    (28/-.134-15)    (34/  .3*1-14)    (35/ .25S-18)   (36/ .580-16)

-------
solution can be found.  Besides giving valuable information on flame speed,
free  flame predictions can be used as good enthalpy and species first guesses
for attached flame calculations.  Thus, it is advantageous to run a free
flame calculation prior to running an attached flame calculation at the same
reactant initial conditions.
       This free flame sample case consists of an unconfined, atmospheric
pressure, methane/air flame which has an initial methane concentration of
9.1 percent and an initial temperature of 298K.  The nonunity Lewis number
option and radiation heat loss, are specified for this case.  Curve fit
thermochemical data is used in this calculation.  Curve fit data, though
slightly less accurate than tabular data, gives precise property derivatives
which improves solution convergence characteristics.
       In order to align the solution grid in an efficient manner, the code
makes use of an arbitrary constraint condition.  Typically the finer grid
zone is aligned with the flame zone by this process.  The flame zone is
arbitrarily identified by the concentration of some species or a specified
temperature.  For this case the constraint is applied to the methane concentration
which monotonically decreases through the flame.  A value roughly two thirds
of the initial concentration is chosen as the contraint value.  Typically, a
value of the constraint variable midway between its preflame and postflame
values should be selected.  This provides the best numerical stability and
assures-adequate definition of the flame in the zone of steepest gradients.
The constraint condition is applied to the 12th grid point, which is roughly
one half the total number of grid points specified.   As indicated on the input
listing, the grid spacings surrounding the constraint location are small.
Further from the constraint grid point, where gradients diminish, the grid
spacings can be increased without adversely affecting gradient definition
                                   7-17

-------
and solution accuracy.  Therefore, as shown on the input, grid spacings .are
increased away from the constraint grid point.
       Two important flame problem parameters are APR and BP the "time scale"
and "diffusion" parameters respectively.  Utilizing the development given in
Sections 3.1.1 and 4.1.1 the nondimensional BP parameter divided by an can
be written as:
                    BP   D DAT1"659
                       ~
                            *dsn   "      Pd5nu
       One way to characterize BP is to note that BP/o"  represents the ratio
of the diffusion to the convection contribution to the conservation equations.
Values of the order of 1.0 should be appropriate when these phenomena contribute
equally to the physical events.  Of course, a  the nondimensional grid spacing,
varies through the flame and hence BP/a  also varies through the flame.  The
objective in selecting values for BP and an is to adequately cover with grid
points all property gradients in the flame.  Thus, the initial selection of
BP or a  might be revised once a solution is obtained and gradient definition
is seen to be inadequate.
       To estimate initial values for BP and a, the following approach can
be taken.  For example, atmospheric CH^/air experiments indicate a flame zone
thickness of the order of .1 cm.  Breaking this zone into 25 increments yields
a AsR (nee ds) of .004 cm in the flame zone.  In the flame zone a mean temp-
erature is in the range of 1200K and we expect a flame speed of 30 cm/sec.
These lead to a value of BP/crn from the above equation of greater than 4.  If
the arbitrary values of an in the flame zone have been selected as .05 (down
from 1.0 in the pre- and postflame zones) then a good value for BP will be on
                                    7-18

-------
the order of 0.25.  This is the value applied in the calculation.  It should
be noted that if the initial pressure or temperature is altered, the form of
BP is such that it is not very sensitive to these changes.  Therefore, flame
calculations at conditions in the vicinity of this sample problem can use the
value of BP applied in this case without serious problems.  The criteria for
whether a good value of BP and an distribution has been selected for the problem
is that, in the final answer, the physical grid should cover the flame sufficiently
well such that gradients are well defined.  If definition is not adequate,
either BP should be increased and/or a  decreased until gradient definition
is adequate.
       Once BP has been fixed, APR is estimated by applying expressions 35 and 36
in Section 4.1.1.  Since unburnt gas velocity and density can typically be
estimated, expressions 35 and 36 are used at the first grid station.  The
value of APR is then given by:

                         APR =     D     =  0.172. IP"4
where the best estimates of p, and Uj are substituted into the above.  APR
is continuously updated during the calculation and the input value only
represents a first guess.  Further, if punched card first guesses are used
from a previous calculation, as in this sample problem, then the APR value
initia-lly input is superseded by the punched card input from the prior run.
       The cross sectional area change for this free flame is expected to
be on the order of 10 percent and the distribution is unknown.   Therefore,
the flame relative area parameter, AP(N), is set equal to one over the
entire grid.  The grid spacing, an or DS(N) distribution, is a very important
parameter and determines how well the gradients through the flame are

                                   7-19

-------
defined.  The 25 grid spacings are distributed such that initially, where
the temperature is low and reactions slow, moderate sized increments are
                                                  i
applied.  Through the "flame zone", where the grid constraint is applied
and the relatively fast reactions are kinetically controlled, small incre-
ments are used to define the gradients.   Finally, downstream of the flame
the increments are made large since concentrations are slowly changing in
this region.  If the equilibrium state of the products are of interest a
single very large step can be added to the end of the calculation.   Of course,
in this case radiation heat loss is active and the final equilibrium state
will reflect this energy loss.
       The species names and initial  concentrations input are straightforward.
However, the diffusion factor input requires some description.   The quantities
input are the inverses of the diffusion  factors described in Section 3.1.1.
These quantities are all referenced to molecular oxygen, and a tabulation
of values for the carbon, hydrogen, nitrogen and oxygen system is  given in
Reference 3.  In the absence of such data a good estimate for 1/F^  can be
obtained using the expression (Appendix A):
                             /H
                          Fi~
MA -0.461
As indicated previously, the reference diffusion coefficient value for 02
has been incorporated into the code.  It might be noted that all  D..  can be
increased by a factor by multiplying all l/Fi by the square root of that
factor.  Thus, diffusion can be either increased or decreased for all species
by increasing or decreasing all 1/F.. uniformly.  This will  result in  a corre-
sponding increase or decrease in thermal conductivity and viscosity.
       The kinetic reaction data given on the listing is straightforward and
needs no explanation.  The punched card first guess data, which appears last
                                    7-20

-------
on the input listing, was obtained from a prior run.  This data supersedes
species concentration guesses obtained from a linear interpolation between
the previously input initial and final species concentrations.
       Selected sections of output for this flame problem are presented to
illustrate the type of output to be expected.  The first two pages list the
input data along with descriptive headings.  The third page of output lists
the thermochemical data to be used in the calculation.  This curve fit data
was obtained from the storage device denoted Unit 11.  Following the listing
of reaction data is the first guess species concentration data.  This data
is scaled to the present problem by the ratio of the current nondimensional
grid spacings, an or DS (N) to those input on the prior run punched card deck.
For this problem the grid spacing distribution from the prior run and the
current calculation are the same and the scaling is one to one.
       The chemistry solution output gives the properties at each grid point.
These properties are functions of the initially guessed downstream conditions
and have a physical meaning only when the solution is converged.  The number
of iterations associated with the solution at each grid point indicates the
difficulty in converging to a solution.  Initially, the number of iterations
are high because the properties are changing from the unreacted initial
condition to a partially reacted state over a large step size.  Away from
the initial grid point the roughly constant number of iterations for each
point indicate that the grid spacing distribution is reasonable.  A single
point with a large number of iterations indicates that too large a step
has been taken.  One test of the adequacy of the grid is to plot the
species concentration as a function of distance and determine if concentra-
tion gradients have been adequately defined.
       The predictor/corrector output indicates if the solution is converged.
If the species concentrations in the first three lines of output are close
                                   7-21

-------
to those in the following three lines, then the solution is converged.  This
also holds true for the last three items Output, which are the enthalpy, tem-
perature and enthalpy tilda (mixture enthalpy weighted by the diffusion
factors).  The last line of output gives the flame speed parameter, it's
current correction, the maximum error in concentration, enthalpy, temperature
or enthalpy tilda and the scale factor applied to the corrections to the
solution estimates.  A converged solution will exhibit a small flame speed
parameter correction relative to the magnitude of the flame speed parameter.
Also, the damping will be one, indicating full linear corrections are being
made to the variables.  At convergence the maximum variable error will be
below 0.001, which is the code built in relative error criteria.
       Prior to the condensed output for the final iteration appears the
individual species reaction creation, diffusion and convective flux output
for each grid point.  This output is useful in assessing whether reaction
or diffusion is controlling the species concentrations at a grid point.
       The species equation at each grid point can be constructed from this
output by taking the convective and diffusion flux output at the grid
point upstream from the point of interest and adding to it the reaction crea-
tion and subtracting from it the convective and diffusion flux output at the
point of interest.  If the solution is converged, this equation will have a
very small error.  For nonconverged solutions this is not the case and the
flux output is not physically meaningful._
       The grid information summary table gives all of the important pro-
perties along the grid.  In addition, forward kinetic reaction rate and the
ratio of forward to backward kinetic reaction rate information is output at
each grid point.  This information is useful in assessing where each kinetic
                                    7-22

-------
reaction becomes active and also whether that reaction approaches equilibrium
along the grid.  Following this, the kinetic reaction rate contribution to
each species at all grid points is output.  This information is useful in
assessing the impact of reactions on the species concentrations.along the
grid.  If the contribution of the reaction is not important relative to other
reactions, that reaction can be removed from the data set without causing
serious error.  Proceeding in this manner, the dominant reactions and reac-
tion paths can be determined using this output.  This feature is very useful
in testing proposed reaction mechanisms.
7.2    Sample Case 2 - Methane/Air Flame Attached to a Flameholder
       This sample case demonstrates the PROF flameholder and assigned mass
flowrate option.  The conditions for this sample case are the same as in
case 1 except that the mass rate, and hence the unreacted gas velocity, is
assigned along with flameholder heat and species losses.  For this case it
is assumed that sufficient cooling is provided to the flameholder to maintain
the gas temperature adjacent to the flameholder at 298K.  Specifying the
mass flowrate then defines the heat and reactive species losses to the
flameholder.
       As mentioned in Section 7.1, an assigned mass rate with flameholder
calculation should use a converged free flame calculation as the first guess.
The results of the free flame calculation provide reasonable enthalpy and
species concentration guesses for the flameholder calculation and gives the
flame speed for the chemical mechanism input.  Flame speed is an important
parameter to know since the assigned flame speed or mass flowrate must always
be smaller than the free flame speed.  Values larger than the flame speed
will cause flame blow-off.  For this sample case, the assigned flame speed
represents a velocity roughly 73 percent of the free flame speed.
                                    7-23

-------
                                                    SAMPLE PROBLEM  7.2
I
ro
1.
2 
I.
4.
5.
6.
7.
e.
9.
to.
11.
12.
13.
14.
15.
16.
17.
18.
IS.
20.
21.
22.
22.
24.
25.
26.
27.
28.
2S.
30.
31.
32.
33.
?4.
35.
36.
37.
36.
39.
40.
HI.
42.
42.
44.
45.
46.
47.
46.
4S.
so.
51.
K* .
52.
*4.
CH4/AIR
16 3 16
.03
1.
1.
1.
1.
.05
.05
.2
4.0
CH4
02
C02
H20
H2
CO
CH3
CH20
CHO
H02
H
0
HO
N2
CH
CH2
END
37
CH4
CH4 HO
CH4 H
CH4 0
CHS 0
CH3 02
CH20
CH20 HO
CH20 0
CH20 H
CHO 02
CHO HO
CHO 0
CHO
CO HO
CO 0
H02 0
H02 HO
H02 H
H02 H
H 02
H 02
0 H2
HO H2
HO MO
SAROFTN P=1ATM
25 8 3 1 1
.25 1.0
1. 1.
1. 1.
1. 1.
1. 1.
.05 .05
.05 .05
.5 .5

.091
.191
1.-9.1
1.-9.06
1.-9
1.-9
1.-9
1.-9
1.-9
1.-9
1.-9
1.-9
1.-9
.716 .718
1.-9
1.-9


M CH3 H
CH3 H20
CH3 H2
CH3 HO
CH20 H
CH20 HO
M CO H2
CHO H20
CHO HO
CHO H2
CO H02
CO Hi-0
CO HO
M CO H
C02 H
M C02
02 HO
02 HJjO
HO HO
02 Wf
M H02
HO 0
MO H
H20 H
M20 0
T=29B PHI=.952
-31 1 1 12 2

1
296. .00?
1. 1.
1. 1.
1. 1.
1. 1.
.05
.05
1.0 1

1. -31. 0523
1. -31. 0*68
.ft
1.2980
1. -33. 5333
1.-3 .9830
1. -31. 3257
1. -31. 2980
1.-3 .9604
1.-3 .9016
1. -35. 1557
1. -31. 4158
l.-31.375
.9732
1. -31.43
1.-31.37


1.504-18
1.00+13
2.00414
2.00>13
3. 50+13
1.00+12
2.00+16
2.50+13
3.00+13
1.70+13
3.00+13
1.00+14
5.40+11
2.00+1?
5.50+11
3.60+18
2.50+13
2.50+13
2.50+14
2.50+13
2.00+15
2.20+14
1.70+13
2.20+13
6.nu+12




05
05
.0




















0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.5
0.5
0.0
-1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
u.o

1
298.
1.
1.
1.
1.
.Ob
.05
2.0



















0. 100,0
6.000
11.900
6.900
3.300
15.000
35.000
1.000
0.
3.000
0.
0.
0.
28.800
1.080
2.500
0.
0.
2.000
.000
.870
16.800
9.460
5.200
.780
                                                                                  i.         1.
                                                                                  1.         1.
                                                                                  1.         1.
                                                                                  1.         1.
                                                                                   .05        .05
                                                                                   .1         .1
                                                                                   2.0        4.0
                                                                                 H20  20.

-------
ro
CJ1
55.
56.
57.
56.
59.
60.
61.
62.
63.
64.
65.
66.
67.
H
0
H
0
CHS
CH2
CH2
CH
CH2
CH
CH
CH2
HO
H
H
0
HO
HO
02
02
0
HO
0
H
CH4/AIR
pi
n
M
M








H?0
HO
H2
r,2
CH2
CH
CH20
CHO
CHO
CHO
CO
CM
SAROFT"




H20
H20
0
0
H
H
H
H2
P=1A
 69.
 70.
 71.
 72.
 73.
 74.
 75.
 76.
 77.
 78.
 79.
 60.
 61.
 82.
 62.
 44.
 85.
 86.
 67.
 46.
 69.
 90.
 91.
 92.
 93.
 94.
 95.
 96.
 97.
 98.
 95.
100.
101.
102.
                     104 .
                     10E.
                     107.
                     inp.
                     in=.
                     no.
                     ill.
                           T=298
 25 16 .40331-01 .25000+00
 .05     .05     .05     .05
.5000-01.5000-01.5000-01 .5000-01.
.1000+01.2000+01.2000+01.4000+01.
-.604+02-,604 + 0?-.594+02-.560+02-
-.446+02-.419+02-.396+02-.381+02-
-.591+02-.569+02-.586+0?-.547+02
.3211-02.3130-02.3018-02.2920-02.
.2000-02.1749-02.1459.02.1139.02,
.2185-10.6520-12.2843-13.7919-15
.6779-02.6655-0?.6467-02.6341-02.
. 50^3-02.4709-02.4305.02.3440-02,
.5256-03.4612-03.4503.03.4309.03
.1153-04.2490-04.5796.04.8712-04,
.4140-03.5151-03.6389.03.7894-03.
.2941-02.3009-02.3056.02.3087-02
.21B9.03.4226.03.6849.03.8977-03,
.2449.02.2815.02.3225.02.3675-02,
.6314.Q2.6365-02.6401-02.6422-02
.1495-03.2009.03.2473.03.2760-03,
.4091.03.4324-03.4558.0?.4780-03,
.1457-03.1147-03.9449.04.8167.04
.2435-04.5410-04.9401-04.1376.03.
.4944-03.5922-01.7075.03.8410-03.
.3444-03.2772-01.2303-03.1999-03
.1134-04.2196-04.3609-04.4849.04.
.1857.03.2229-03.2609.03.2919.03,
.6829-10.2345-11.7027.13.1799-14
.1033-05.2046-05.3443-05.4609-05.
.1230-04.1406-04.1572-04.1659-04,
.1066-11.5619-1?.3825.12.2874-12
.146(9-11.9261-11.3293-10.6421-10,
.4441*. 08. 1327-07. 3565. 07. 8995-07.
.5414.09.3769-09.26S6.09.2354-09
.2175-06.7213-06.1661-05.2430-05,
.3065.05..1187-0*.1411_0*.360B-05,
.4599-07.3301-07.25?9-07.2093-07
.4742-11. 3796-in. 3956-09. 2107.(IP,
.4276-05.7723-05.1349.04.2119.04.
.3229-04.2114-04.1509-04.n78-04
,lP60-P9.6446-09.17l7.0<.30no-08,
. 3734-06.9750-0*.3414-n*.?fl19-05,
.2797-04.20ll-OU.l549-04.l?H3-04
7.00+19
4.oo+itt
2.00+19
4.00+18
6.00+09
5.00+11
5.00+11
5.00+11
5.00+11
5.00+11
5.00+11
3.00+11
PHI=.*52
-1.0
-1.0
-1.0
-1.0




.5
.b
.5
.7





.7
.5
.5
.5





n.
n.
0.
n.
2.0
6.0
7.
6.0
4.0
10.0
4.0
26.0

                                                              .05      .05
                                                              1000+00.1000+00
                                                              4000+01
                                                              .569+02-.555+02
                                                              .400+0?-.497+02
                 .05      .05      .05      .05
                .2000+00.5000+00.5000+00.1000+01

                -.539+02-.519+02-.497+Q2-.472+02
                -.639+02-.635+02-.609+02-.599+02

2850-02.?765-0?.2663-02.?540-02.2391-02.2213-02
53.1J-03. 1403-03. 8115-05. 3037-06. 1236-07. 5227-09

6239-02.6116-02.5970-02.5797-02.55*0-02.5345-02
24.17-02.1471-02.1065.02. 7948-03.6733-03. 5866-03

1090.03.1363-03.1705-03.2131.03.2661-03.3322-03
1141.02.1560-02.2204-02.2575.02.2738.02.2856-02

1037-02.11^7-02.1383-02.1597-02.1643-02.2126-02
4545-02.5341.02.5840.02.6004-02.6131.02.6239.02

2920-03.3066-03.3267-03.3456-03.3656-03.3868-03
5083-03.4855-03.3734.03.29*2-03.2429-03.1850-03

1653-03.1944-03.2383-03.2861.03.3435.03.4122-03
1123-02.1304.02.1030-02.6998-03.5438.03.4271.03

576?-04.6921-04.8393-04.1024.03.1251-03.1528-03
2890.03.1606.03.1801-04.9666-06.4494-07.1811.08

5367-05.6217-05.7159-05.6200-05.9371-05.1072-04
13?9.04.6032-05.492P-06.1324.07.34^1-09. 9178-11

>5894.10.2805-10.2149-10.1386-09.5622-09.1731-08
331 2-06. 41'?9.06.9734-07. 5350-08. 1360-06. 7982-09

2801-05.3070-05.3202-05.3207-05.3136-05.3064-05
, 3 064 - 05. 14 f,?_ 05.278.1-06.1340-06.9411-07. 6491-07

,4409-0A.77?7_04.1206-07.1420-06.9069-06.2184-05
,6039-04.1236.03.1685-0.1.1326-03.8513-04.5035-04

,332"-08.3034-Oft.2407-08.1653-06.3511-07.1334-06

-------
112.
113.
114.
115.
116.
117.
lie.
115 .
120.
121.
122.
.2534-05
.1762-03
.2508-01
.2600-01
.2593-01
.6990-09
.1901-09
.6065-12
.1135-07
.8926-07
.2083-11
.5049-U*.
,1536-OT,
.2567-01,
.2601-01,
.2593-01,
.1839. 0,
.4019-09,
.1746-13,
.2250-07,
.1676-06,
.6469-13,
.1019-04
,1374-03
,2589-01
,2601-01
,2593.01
,3679.08
,1455-08
,4491-15
,3519.07
,324b.06
,1782-14
.2033-04
.1265-03
. 2591-01
.2600-01
.2593-01
.4807.08
.5250-08
.1024.16
.4098-07
.6137.06
.4282.16
.6352-04

.?b
-------
                       PREMIXED
                                 OIMFNSIONAL FLApiF COOF SOLUTION (PROF)
                  PHORRAM DOCUMENTED IN THE "PROF CODE USER'S MANUAL" .
                    AFROTHERM/ACURFX CPRP FINAL REPORT 76-277
                            PHnMF
   CHI/AIR  SAROFIM
ro
">J
COLUMN
   3  NO. SPECIES CONSERVATION EOS.  16
   9  NO. OP SPECIES                 16
  IS  NO. GRID SOLUTION ITERATIONS    8
  21  READ IMTIAL MOLE FRACTION      i
  27  THERMO DATA * I-EAT LOSS MODEL  -s
  33  READ KINETIC DATA               1
  39  CONSTRAINT APPLIED TO GRID PT. 12
  
-------
                                                        * FIRST GUE?S  ALPHAS  *
ro
CO
                          CH4/AIR  SAROFIM  PslATM  T=298  PHI=.952



                                    NORMALIZED  SLPY(CAL/6M) ,M=1.25
-.6040+02
.4970+02
.6390+02

.3211-02
.2391-02
.6115-05
.6779-02
.5590-02
.1065-02
.1153-01
.266i-03
.2204-02
,2169-03
.1643.02
.58HO-02
.1495-03
.3656-03
.3734-03
.2435-04
.3135-03
.1030-02
.1134.04
.1251.03
.1601-01
.1033-05
.9371-05
.4926.06
.1468.11
.5622.09
.9734-07
.2175-06
.3136.05
.2763-06
.4782-11
.9069-06
.1885-03
.1880-09
-.60(10 + 0? -
-.47204-02 -
-.63SO+02 -
(ALPhA(I,NI
.3130-0?
.2213-02
.3037-06
.6655.02
.5345-02
.7948-03
.2890-04
.3322-03
.2575-02
.4526-03
.2126-02
.6004-02
.2009-03
.3*68-03
.2962-03
.5410-04
.4122-03
.6998-03
.2156-04
.1528-03
.9666-06
.20M6-05
.1072-04
.1324.07
.9261.11
.17J1-08
.5*50-08
.7213-06
.3064.05
.1340-06
.3798-10
.2ie4-o^
.IJJf-Ol
.6'M6-09
.5940+0?
.4460+02
.6090+02
-.5800+0?
-.4190+02
-.5990+02
-.5690+02
-.3960+02
-.5910+02
-.5550+02
-.3810+02
-.5890+02
-.5390+02
-.4000+02
-.5880+02
-.5190+02
-.4970+02
-.^870+02
tI=1.16N=l25)
.3018-02
.2000-02
.1238-07
.6487-02
.5053-02
.6733-03
.5796-04
.4140-03
.2738.02
.6849-03
.2449-02
.6131.02
.2473-03
.4091-03
.2439-03
.9801-04
.4944-03
.5436.03
.3609.04
.1857-03
.4494.07
.3443-05
.1230-04
.3431.09
.3293-10
.4844-QA
.1360-08
.1661-05
.3065.05
. 9411.07
,39'i6-0s
.4276-05
.PM3-04
.1717-00
.2920-02
.1749-02
.5227-09
.6341-02
.4709-02
.5866-03
.8712-04
,5i5i-03
.2856-02
.8977-03
.2815-02
.6239-02
.2760-03
.4324-03
.1850-03
.1376-03
.5922-03
.4271-03
.4849-04
.2229-03
.1811-08
.4609-05
.1406-04
.917rt.ll
.6421-10
.1327-07
.798?-09
.2430-05
.3187-05
.6491-07
.2107.08
,7721-n*
.5i)3ri-04
.SOOn-fiA
.2850-02
.1459-02
.2185-10
.6239-02
.4305-02
.5256-03
.1090-03
.6389-03
.2941-02
.1037.02
.3225-02
.6314.02
.2920-03
.4558-03
.1457.03
.1653-03
.7075-03
.3444-03
.5762-01*
.2609-03
.6829.10
.5367-05
.1572-04
.1066.11
.5*94.10
.3565.07
.5414-09
.2801-05
.3411.05
.4599-07
.4409.08
.114V-04
.3?2'<-0<4
.M2H-I1H
.2765-02
.1139-02
.8520-12
.6116-02
.3840-02
.4812-03
.1363-03
.7894-03
.3009-02
.1197-02
.3675-02
.6365-02
.3068-03
.4780-03
.1147-03
.1964-03
.8410-03
.2772-03
.6921-04
.2919-03
.2345-11
.6217-05
.1659-04
.5619-12
.2805-10
.8995-07
.3769-09
.3070-05
.3608-05
.3301-07
.7727-08
.2319-04
.211M-QU
.303<*-0
.2663-02
.5332-03
.2843-13
.5970-02
.2837-02
.4503-03
.1705-03
.1141-02
.3056-02
.1383-02
.4585-02
.6401-02
.3267-03
.5083-03
.9449-04
.2383-03
.1123-02
.2303-03
.8393-04
.2890-03
.7027-13
,7i59-05
.1329-04
.3825-12
.2149-10
.3^12-06
.2856-09
.3202-05
.3064-05
.2529-07
.1206-07
.f,039-04
.Ifi09-04
,?<4U7-ON
.2540-02
.1403-03
.7919-15
.5797-02
.1871-02
.4309-03
.2131-03
.1560-02
.3087-02
.1597-02
.5341-02
.6422-02
.3456-03
.4855-03
.8167-04
.2861-03
.1304-02
.1999-03
.1024-03
.1606-03
.1799-14
.8200-05
.6032-05
.2874-12
.1386-09
.4929-06
.2354-09
.3207-05
.1462-05
.2093-07
.1420.06
.1236-03
.1178-04
. IflbJ-OH

-------
.3531-07
.115*-03
.3575-09
.5830.06
.2176-03
.2566.01
.2597-01
.2597-01
.6990-09
.7816.09
.9501-07
.1135.07
.3568.07
.5191.06
.1*21-06
.8699-01
,1073-0
. 1271-05
.2558-03
.2*67-01
.2598-01
.2595-01
.1P39-08
.3660.09
,9318-oa
.2250-07
.5183-07
.3178-07
..3738-06
.6052-01
,2409-OA
.2531-05
.2338-03
.2589-01
.2600-01
.2591-01
.3679.08
.1901.09
.5035-09
.3519.07
.8926.07
.1637.08
.9750-06
.3986-01
.5295-OP
.5049-05
.2019-03
.2591-01
.2601-01
.259H-01
.1807-08
.1019.09
.1861-10
.1096-07
.1676-06
.6072-10
.2131-05
.2797-01
.6660. 08
.1019.01
.1762-03
.2592-01
.2601-01
.2593-01
.1786-OA
.1155.08
.6065.12
.1092.07
.3215.06
.2083.11
.5819-05
.2011-01
.7611-06
.2033.01
.1536.03
.2593-01
.2600-01
.2593-01
.3820-08
.5250-08
.1716-13
.3798-07
.6137-06
.6169-13
.2102-01
.1519-01
.8106-08
.6352-01
.1371-03
.2591-01
.2600-01
.2693-01
,2572-OB
.3901-07
.1191-15
.3369-07
.1628-05
.1782-11
.6672-01
.1263-01
.1600-06
.1112-03
.1265-03
.2595-01
.2597-01
.2593-01
.1332-08
.1115.06
.102L16
.3117.07
.2150-05
.1282.16
                        APRRs  .10331-01
                            BPR= .250004-00
           SCALED  H AltO ALPHA  FIRST  GUESS  VALUES
               H(N>,N=1. 25
l\3
vo
 -.58691+02  -.60100+02  -.60100+02  ..59100+02  ..58000+02  -.56900+02   -.55500+02   ..53900+02
      -.51900+02  -.19700+02  ..17200+02  -.11600+02  -.11900+02  -.39600+02   -.38100+02   -.10000+02
           -.19700+02  -.63900+02  ..63500+02  ..60900+02  ..59900+02  ..59100+02  -.58900+02  -.58800+02
                -.56700402

ALPHA(ItN),!=!,16tN=lt25

  .32667.02   .32110.02   .31300-02   .30180-02   .29200-02    .28500-02    .27650-02    .26630-02
       .25100.02   .23910.0?   .22130.02   .20000.02   .17190-02    .11590-02    .11390-02    .53320.03
            .11030.03   .8115Q.o5   .30370-06   .12360-07    .52270-09    .21650-10    .85200.12    .26130.13
                 .79190-15
  .66961.02   .67790-02   .66550-02   .61870-02   .63110-02    .62390-02    .61160-02    .59700-02
       .57970-02   .55900-0?   .53150-02   .50530-02   .17090-02    .13050-02    .38100-02    .26370-02
            .16710-02   .10650.02   .791&0-03   .67330-03    .58660-03    .52560-03    .18120-03    .15030-03
                 .13090-03
  .36118.10   .11530.01   .28900-01   .57960-01   .87120-01    .10900-03    .13630-03    .17050-03
       .21310-03   .26610-03   .33220-03   .11100-03   .51510-03    .63890-03    .78910-03    .11110.02
            .15600-0?   .22010-02   .25750-02   .27380-02    .28560-02    .29110-02    .30090-0*    .30560-02
                 .30870-02
  .36116.10   .21890-03   .12260-03   .68190-03   .9770-03    ,10370-02    .11970-02    .13630-02
       .15970-02   .18130-02   .21260-02   .21190-02   ,28i50-02    .32250-02    .36750-02    .15850-0?
            .53110-02   .58100.02   .60040-02   .61310-02    .62390-02    .63110-02    .63650-02    .61010-02
                 .61220-02
  .36116.10   .11950-03   .20090-03   .21730-03   .27600-03    .29200-03    .30880-03    .32670-03
       .31560-03   .36560-03   ..386o-o3   .*091o-o3   .13210-03    .15580-03    .47800-03    .5o83o-o3
            .18550-03   .37340-03   .29820-03   .21290-03    .185()0-u3    .11570-03    .11170-03    .91190-01
                 .81670-01
  .36118-10   .21350-01   .54100-04   .96010-04   .13760-03    .165311-03    .19840-03    .23830-03
       .28610-03   .31350-03   .11220-03   .19110-03   ,b92?0-03    .70750-03    .84100-03    .11230-02
            .13010-0?   .10300-02   .69980-03   .51380-1)3    .12710-03    .31110-03    .27720-0^    .230-30-03
                 .19990-03
  .36118-10    .11310-01   .?19bO-n4   .36090-01   .48490-04    ,57623-04    .69210-04    .B3930-04
       ,10?40-03   .12510-0*   .1?20-03   .18570-03   .22290-03    ,2feO-0-03    .^9190-03    .2690L--03

-------
                             o3    .lenio-o1*    .*6ij6n-nf>    .1*4940-07    .imio-on    .t>e?9o-io    .PSUSO-II    .70?70-i3
                           .17990-m
            .'6118-10   .10330-05   ,?04f,n-05    .34430-0">    ."f>090-05    .53670-05    .2170-01    .71590-05
                 .82000-0*   .93710-05   ,lP7?0-04   .12300-04    .140*0-04    .15720-0"*    .16590-04    .1329U-04
                      .603,20-05    .49?fn-06    .13240-07    .34310-09    .91780-11    .10660-11    .56190-12    .38250-12
                           .28740-12
            .36118-10   .14680-11   ,9?6in-11    .32930-10    .6H210-10    .5B9UO-10    .28050-in    ,2l90-10
                 .13860-09   .^6220-09   .17310-08   ,t&un-06    .13270-07    .35650-07    .B9950-07    ,33l2U-Of>
                      .H9290-06    .973UO-07    .53500-0    .13600-08    .79020-09    .5<*mO-n9    .37690-09    .28560-09
                           .2351*0-09
            .36116-10   .21750-06   .72130-06    .16610-05    ,2*300-05    .28010-05    .30700-05    .32020-05
                 .32070-05   .31360-05   ,306<0-n5   .SOeSO-O^    .31670-05    .34110-05    .360AO-05    .3064U-05
                      .14620-05    .27P30-06    .13400-06    .94110-07    .64910-07    .45990-07    .33010-07    .25290-07
                           .20930-07
            .36118-10   .47820-11   .37980-10    .39560-09    .21070-08    .44090-08    ,7727o-0    .12060-07
                 .14200-06   .90690-06   .21840-05   .42760-05    .77230-05    .13490-04    .23190-04    .6039U-04
                      .12360-03    ,!8P5n-03    .13360-03    .85130-04    .50350-04    .32290-04    .21140-04    .15090-04
                           .11780-04
            .36118.10   .18800-09   .64460-09    .17170-08    .30000-08    .33280-08    .30340-0"    .24070-08
                 .18530-08   .35310-07   .13340-06   .37380-06    .97500-06    .24340-05    .58190-05    .24020-04
                      .66720-04    .11540-03    .86990-04    .60520-04    .39860-04    .27970-04    .20110-04    .15490-04
                           .12830-04
            .36116-10   .35750-09   .]0730-08    .28090-08    .52950-08    .66600-08    .76410-08    .84060-08
^               .16000-06   .58360-06   .12740-05   .25340-05    .50490-05    .10190-04    .20330-04    .63520-04
CO                    .14120-03    .24760-03    .25580-03    .23*80-03    .20190-03    .17620-03    .15360-04    .13740-03
0                         .12650-03"
            .25932-01   .25880-01   .25870-01    .25890-01    .25910-01    .25920-01    .25930-01    .25940-01
                 .25950-01   .25970-0}   .25980-01   .26000-01    .26010-01    .26010-01    .26000-01    .26000-01
                      .2597Q.01    .25970-01    .25950-01    .25940-01    .25940-01    .25930-01    .25930-01    .25930-01
                           .25930-01
            .36118-10   .69900-09   .18390-08    .36790-08    .48070-08    .47860-08    .38200-08    .25720-08
                 .13320-08   .78160-09   .36600-09   .19010-09    .40190-09    .14550-08    .52500-08    .39040-07
                      .14150-06    .95010-07    .93480-08    .50350-09    .18640-10    .60650-12    .17460-1$    .44910-15
                           .10240-16
            .76116-10   .11350-07   .22500-07    .35190-07    .40980-07    .40920-07    .37980-07    .33690-07
                 .31470-07   .35660-07   .5i830-07   .89260-07    .16760-06    .32450-06    .61370-06    .16280-05
                      .21500-05    .51940-06    .34780-07    .16370-08    .60720-10    .20830-11    .64690-13    .17820-14
                           .42820-16

-------
                                  GRID INFORMATION SUMMARY TABLE *
           ITERATIONS   6        NUMBER OF GRID POINTS:  25
              FLAME  SPEED PARs .67391-01           FLAME SPEEO= .26495*02 CIA/SEC.
             6RIO COOROINATES(CM)

              .00000       .14494-02   .29336.02   .45069.02   .61776.02   .79570.02   .96560*02   .11686.01
                   .14061.01    .16391.01    .18692.01   .21574.01   .24450.01   ,27533'.01   .30836-01   .381QH.01
                        .46227.01    .64053.01   .11172*00   .16117*00   .26216*00   .36456*00   .57103*00    .77842*00
                             .11939*01

            NONOIMENSIONAL  GRID INCREMENTS
              .50000.01    .50000-01   .50000-01   .50000-01   .50000-01   .50000-01   .50000-01   .50000-01
                   .50000-01    .50000.Oi    .50000-01   .50000-01   .50000-01   .50000-01   .10000*00   .10000*00
                        .20000*00    .50000*00   .50000*00   .10000*01   .10000*01   .20000*01   .20000*01    .40000*01
71                           .40000*01
CO
~"          TIME(SEC

              .00000       .54430.04   .10751-03   .15693-03   .20863-03   .25663.03   .30293-03   .34756.03
                   .39054.03    .43168.03    .47163-03   .50983-03   .54653-03   .58160-03   .61574-03   ,680li>-03
                        .74082.03    .85711.03   .11420.02   .14251.02   .19697.02   .25536.02   .36618.02    .48105.02
                             .70707-02

            ENTHALPY(CAL/GMI

             -.58691*02   -.10161*03  ..10084*03  -.10001*03  ..99023*02  -.97632*02  ..96448*02  ..94869*02
                  ..93094*02   ..91158*0?   ..89085*02  -.8698?*02  -.64958*02  -.83213*02  -.62107*02  -.83322*02
                       -.92093*02   >.10802*03  ..10773*03  ..10602*03  ..10613*03  ..10692*03  ..10665*03  -.11156*03
                            -.11520*03

            TEMPERATURE!K>

              ,P900*OA    .29600*03   .32506*03   .35610*03   .39162*03   .43218*03   .47640*03   .53095*03
                   .59051*03    .65772*0^    ,7331*+01   .81746+03   .91096*03.   .10139+04   .11261*04   .13582*04
                        .15811+04    .17S05+04   .19082*04   .19724+04   .20151*04   .20406*04   .20552*04    .20613*04
                             .20604*04

            DENSITYIGM/CM3)

              .11323-02    .11209-02   .10272-02   .93673-03   .5060-03   .77028-U3   .69525-0.5   .62587-03
                   .56220-03    .50414-01    .45170-03   .40452-04   .36244-03   ,325ifl-OJ   .29249-03   .24206-03
                        .20794-03    .18453-03   .17432-03   .16925-03   .16615-03   .16438-03   .16344-03    .16311-03
                             .16329-03

            SYSTEf MOLECULAR  WEIGHT

-------
                           .27H09+02   .?7<*01+02    .27372+02    ,?73
-------
                            * HOLE FRACTIONS OF   16   SPECIES  *



       CHi*

         .91000-01   .82463-01    .H1152-01   .79625-01    .77858-01    .75613-01   .73440-01   .70683-01
              .671*77-01   .63740-01    .59375-01    .54267-01    .48308-01    .41421-01   .33644-01   .17590-01
                   .51239-02    .25893-03    .87180-05    .31378-06    .14530-07   .63009-09.   .26271-10   .98855-12
                        .33241-13
       02

         .19100+00   .17746+00    .17543+00   .17306+00    .17032+00    .16716+00   .16350+00   .15925+00
              .15432+00   .14860+00    .14198+00    .13431+00    .12546+00    .11528+00   .10366+00   .78017-01
                   .51333-01    .26612-01    .19282-01    .16179-01    .14065-01   .12655-01   .11657-01   .10965-01
                        .10500-01
       C02

         .10000-08   .18216-02    .22214-02   .27083-02    .33013-02    .40236-02   .49031-02   .59735.02
              .72758-02   .88596-02    .107B4-01    .13120-01    .15951-01    .19369-01   .23472-01   .33070-01
                   .44895-01    .64117-01    .74463-01    .78840-01    .81986-01   .64123-01   .85794-01   .86962-01
                        .87776-01
       H20

         ,10000-Ofl   .19377-01    .21998-01   .24970-01    .28340-01    .32163-01   .36496-01   .41408.01
>J            .46974-01   .53277-01    .60411-01    .68472-01    .77551-01    .87713-01   .98943-01   .12247+00
CO                 .14422+00    .16072+00    .16680+00    .17081+00    .17393+00   .17597+00   .17739+00   .17637+00
00                      .17904+00
       H2

         .10000-06   .57793-02    .60665-02   .63676-02    .66834-02    ,7oH7-02   .73619-0?   .77261-02
              .61081.02   .85091.02    .89307.02    .93749.02    .98430-02    .10331.01   .10823-01   .11655.01
                   .11515-01    .86487.02    .65575.02    .50811-02    .36701-02   .27635-02   .20609-02   .15979.02
                        .12796-02
       CO

         .10000.06   .22947-02    .27046-02   .31871-02    .37551-02    .44238-02   .52107-02   .61367-02
              .72256-02   .65063-0?    .10011-01    .11779-01    .13851-01    .16272-01   .19076-01   .25259-01
                   .30274.01    .23442.01    .14924.01    .11072-01    .82324.02   .63055.02   .47760-02   .37096-02
                        .29641-02
       CHS

         .10000-08   .11592-02    .13126-02   .14864-02    .16629-02    .19052-02   .21569-02   .24428-02
              .27710-02   .31550-02    .3*142-02    .41704-02    .48373-02    .55972-02   .63554-02   .70728.02
                   .47351-02    .50082-03    .24648-04    ,10928-Ob    .43262-07   .16653-09   .60197-10   .19992-11
                        .60349-13
       CH20

         .10000-08   .70546-04    .80092-04   .90921-04    .10321-03    .11716.03   .13300-04   .15101-03
              .17154.03   .19504-03    .22213-03    .253fib-0*    .28945-03    .32717-03   .35699-03   ,3297b_03
                   .17752-03    .139S8-04    .31584-U6    .74197-08    .10109-09   .15294-10   .65161-11   .38766-11
                        .24855-11
       CHO

          .10000-08    ,?0944-ll    .^6425-11    .77396-11    .I79bl-10    .44332-10   .11922-09   .33995-09
               ,1U695-U    .34052-0*    .10^7-07    ,31H?H-07    .9Jfa2-07    .27327-0*   .7762B-06   .39514-05
                    .9l7()b-0'D    .i-3711-db    ,10769-Ub    .2393*-n7    ,12b72-07   .76171-00   ,45690-OB   .29532-08

-------
                 .20191-08
H02

  .10000-Ofl   ,lt600-0i*   .17112-01   ,?0833-01   .21876-01   . 29693- 01   .35416-01   .12151-01
       .19428-01   .57893-01   .65232-01   .70Bai.ni   .71752-01   .78262-01   .81829-01   .77821-01
            .11181-01   ,7606J-Ob   ,3366?-Ob   .22752-05   .15050-05   .10300-05   .70921-06    .51*56-06
                 .10393-06
H

  .10000-09   .18298-11   .10911-12   .57375-12   .19190-11   .50617-08   .53092-07   .37269-06
       .18023-05   .63196-0*   .17510-01   .10619.01   .83559.01   .16021-03   .29637.03   .87230-03
            .21161.02   .39370-02   .25182-02   .15105-02   .82755.03   .19961-03   .30118-03    .20023.03
                 .11035*03
0

  .10000.08   .10183-08   .16626-08   .32050-08   .61523-08   .13068-07   .26803-07   .55980-07
       .12699.06   .31108-0*   .812*9-06   .21369.05   .71121-05   .20397.01   .55796.01   .28553.03
            .10270-02   .23191.02   .16506.02   .10801-02   .67212-03   .15275-03   .31010-03    .22571-03
                 .17296-03
HO

  .10000-08   .26090-07   .35803-07   .57238-07   .10116-06   .19190-06   .10118-06   .90296.06
       .21103-05   .19161-05   .11006-01   .23613-01   .50050-01   .10721-03   .23219-03   .87551-03
            .21530-02   .53980-02   .51168-02   .18220-02   .10257-02   .31115-02   .28817-0?    .21819-02
                 .21755-02
N2

  .71*00+00   .70983+00   .709324-00   .70873+00   .70815+00   .70758+00   .70700+00   .70610+00
       .70578+00   .70515+00   .70151+00   .70397+00   .70318+00   .70311+00   .70282+00   .70230+00
            .7Q203+00   .70109+00   .70830+00   .71060+00   .71259+00   .71382+00   .71183+00    .71519+00
                 .71595+00
CH

  .10000-08   .29195.10   .32385-10   .36762-10   .11313-10   .59006-10   .59798-10   .20765.08
       .11663.10   .55716-11   .29577.n   .27367.09   .11286-08   .78182-08   .33192-0?   .32961-06
            .20075.05   .21198.05   .19153-06   .91703-08   .32217.Q9   .10118.10   .28818.12    .76972-11
                 .19016-15
CH2

  .10000-08   .51823-07   .58107-07   .66098-07   .7*560-07   .88290-07   .10755-06   .11013-06
       .19915-06   .31082-06   .52237.Q6   .93310-06   .17630-05   .35150-05   .71908-05   .21122.01
            .15932.01   ,13116-nl   .8091P-06   .35318-07   .12171.08   .12*56-10   .13517.11    ,39997-13
                 .10900-11

-------
       Another important difference between this sample case and the free
flame case is the distribution of grid spacings.  For the flameholder problem
it is expected that the flame zone or "action zone" will approach the flame-
holder.  To define gradients in this region the grid spacings must be made
small.  Unlike the free flame case where grid spacings go from relatively
large values at the upstream boundary to small values at the constraint, the
flameholder calculation uses small grid spacings from the upstream boundary
to the constraint.  This can be seen in the input listing.  Downstream of
the constraint, where gradients are less steep, larger grid spacings are applied.
       As in the free flame calculation, a constraint condition is applied
in this problem.  This fixes the value of a variable at the constraint value
at a given grid location.  The value assigned can be arbitrarily selected
within the bounds of the minimum and maximum values found for the variable
within the flame.  Typically a value midway between the pre- and post-flame
value is selected.  The grid location where the constraint is applied, should
be in the middle of the grid where the zone of maximum action is expected.  The
constraint is not fixed at a given physical location in space.  The constraint
applied in this case is used to adjust the physical spacing of the grid rather
than to determine flame speed.  This adjustment is important since the spatial
extent of the flame is unknown prior to the solution.  The automatic adjustment
of the grid places the points where they are needed to define steep gradients.
       The grid spacings on the first guess input are altered to be consistent
with the current problem grid spacings.  This important change is made in
anticipation of the flame moving close to the flameholder.  This grid spacing
has been found to give better first guesses than the typical  free flame grid
spacing.
       The output from this calculation is similar to sample case 1  output.
The summary output information given on the following pages  illustrates the

                                  7-35

-------
main differences between sample case 1 and 2 results.  The flame speed dif-
ference and temperature difference at the second grid point are obvious.
The enthalpy decrease at the second grid point for this case is an indica-
tion of the amount of energy loss at the flameholder.  A comparison of final
temperatures between the two cases also indicates that energy has been lost
to the flameholder.
       In the flameholder case, the flame lies very close to the flameholder.
However, the actual spatial extent of the flame or "action" zone is probably
not significantly different from the free flame results presented in sample
case 1.  For lower mass flowrates and greater flameholder losses, the
spatial extent of the flame will be significantly different from the free
flame case.
7.3    Sample Case 3 - Methane/Air Chemical Evolution in an Internal
                       Combustion Engine
       This sample case demonstrates the PROF time evolution chemical kinetic
option.  The problem consists of an unburnt mixture of methane and air which
is subjected to an assigned pressure and temperature history.  This problem
represents the chemical reaction history of the last element of fuel and air
to be burned during the expansion stroke of an internal combustion engine.
Initial concentration of methane is 5.9 percent and the initial temperature
and pressure are 2393K and 54.2 atmosphere respectively.  The calculation
is carried out over four decades in time.
       Most of the input for this problem is straightforward.  The APR and
AP(N) parameters are input in the form suggested in the input guide.  For
this sample case, APR is set equal to 1 and AP(2) is set equal to the time
step between the initial and second station, etc.  Since APR and AP(N) are
multiplicative, the time step can be distributed between these in any manner
as long as the product equals the required value.  Input unique to this type

                                    7-36

-------
                                                   SAMPLE PROBLEM 7.3
I
CO
1.
2.
3.
.
5.
6.
7.
e.
s.
10.
11.
12.
12.
14.
15.
16*
17.
18.
19.
20.
21.
22.
23.
2
-------
                               55.    CO   HO
                               96.    H    02
                               57.    HO   H2
                               fl.    CHO  HO
COP  H
HO?
H    M20
CO   H20
1.00+09    .5
          0.0
          0.0
3.00+1U    1.
  .0
1.00
5.20
0.00
00

-------
                           PREMIXED ONE DIMENSIONAL FLAME  CODE  SOLUTION (PROFI
                         PROGRAM DOCUMENTED  IN  THE  "PROF  CODE  USER'S MANUAL",

                           AEROTHERM/ACUREX  CORP FINAL  REPORT  76-277

                                   PHONE 415/964-3200
        TIME EVOLUTION PROBLEM
i
ca
vo
COLUMN
   3  NO. SPECIES CONSERVATION EOS.  14


   9  NO. OF SPECIES                 14


  15  NO. GRID SOLUTION ITERATIONS    1


  21  READ IMTIAL MOLE FRACTION      i


  27  THERMO DATA * HEAT LOSS MODEL  -1


  33  READ KINETIC DATA               1


  39  CONSTRAINT APPLIED TO GRID PT.  0


  45  PLACEHOLDER TEMP ASSIGN SWITCH  0
                                  *  INTEGRAL PARAMETERS  *


                                                       COLUMN
 6  PROBLEM TYPE AND ENERGY 0.     1


12  NU. AXIAL GRID PTS.            30


18  SOLUTION CYCLE CONTROL NO.      0


24  READ NONINTEGRAL PARAMETERS     1


30  CONSTRAINT SWITCH               0


36  CONSTRAINT APPLIED TO VARIABLE  0


42  OUTPUT CONTROL NO.              2


46  INPUT MASS FLOWRATE SWITCH      0
                                      NONINTEGRAL  PARAMETERS  *
        APR'DEL/MCOTs .10000+01    BPOBAR/(OEL*MDOT>  .00000


              TKAPS    .00000    TFLAMEr  2393.CMK)
                                                              Ps  54.200UTM)   TI=  2393.0(K>
                                     *  GRID  PARAMETERS *
             A(N)*2 tNslf  30
              .1000-OA  .2000.OA   .7000-06   .2000-0?   .3000-07  .4000-07  .2000-06   .3000-06   .1000-06   .2000-05

                   .2000-0%  .2000-05   .1000-0*   .1000-05  .1000-05  .1000-05  .1000-05   .1000-05   .1000-05  .1000-05

                        .1000-05   .1000-05   .1000-05   .1000-05  .1000-05  .5000-05   .5000-05   .1000-04   .1000-04   .2000-04
              SIGfA(N),N=l.  30



              .1000+01  .1000+01  .1000+01   .1000+01   .1000+01  .1000+01   .1000+01   .1000+01   .1000+01   .1000+01

                   .1000*01   .1000+01   .1000*01   .1000+01   .1000+01   .1000+01   .1000*01   .1000+01   .1000+01   .1000+01

                        .1000+01  .1000+01   .1000+01   .1000+01  .1000+01   .1000+01   .1000+01   .1000+01   .1000+01   .1000*01

-------
                                      * ASSIGNED T AND P  DISTRIBUTION *


           TEMPERATURE DISTRIBUTION (K)
              .239*0+04    .23930+0200+02    .5*200+02   .5*>190+02
                   .5*190+02    .51*180+02   .5**l30+02   .54080+02   .5*030+02    .54010+02   .33980+02    .53960+02
                         .53940+02   .53910+0?   .53890+02    .53860+02   ,538**0+02    .53820+02   .53790+02    .53770+02
                              .53740+02   .53720+02   .53600+02   .53480+02    .53250+02   .53010+02
k

-------
 * SPECIES INITIAL HOLE FRACTIONS.FIRST GUESSES,AND DIFFUSION FACTORS
SPECIE

 CHH
 02
 C02
 H20
 H2
 CO
 CHS
 CH20
 CHO
 H02
 H
 0
 HO
 N2
ALPF

.5*6-01
.196+00
.100-06
.100-06
.100-06
.100-06
.100-06
.100-06
.100-06
.100-06
.100-06
.100-06
.100-06
.7*3+00
ALPE          DIFFUSION FACTOR

.100-02              1.0523
.100-02              1.0466
.100-02               .6000
.100-02              1.2960
.100-03              3.5333
.100-03               .9630
.100-03              1.3257
.100-03              1.2960
.100-^3               .9601*
.100-03               .9016
.100-03              5.1557
.loo-os              i.mse
.100-03              1.3U75
.71*3+00               .9732

-------
                                        * THERMOCHEHISTRY DATA *
-F
ro
CURVE FIT OF DATA IN FOR* CPsRB*RCT*RO/ITT  (CAL/CHOLE*K)



     H(CAL/HOLI     RB           C            RO       S(CAL/MOL/K)
TUCK)
                                                                                                           NAME
CO
- .26417*09
..261(17*05
C02
-.91051*05
..91051*05
Chi*
-.17699*05
..17899*09
H20
..97796*09
..97798*09
02
.00000
.00000
N2
.79000*00
.79000*00
H2
.20000*00
.20000*00
H
.92100*05
.92100*09
0
.59559*05
.99999*09
HO
.9i*320*0*
.9*320*01
HO?
.50000*01
.50000*01
CHS
.31620*05
.31620*05
CH20
..27700*05
..27700*09
CHO
..29000*01
.. 29000*01
26.011
.29539*05
.22179*09
11.011
.11136*05
.36973*05
16.013
.66727*05
.53270*05
18.016
.31716*05
.30303*05
32.000
.29911*05
.23190*09
26.016
.23993*09
.22166*05
2.016
.20180*05
.21258*05
1.006
.13123*05
.13123*05
16.000
.13119*05
.13517*05
17.006
.21099*05
.21152*05
33.008
.36387*05
.32593*05
15.035
.18677*05
.12779*05
30.027
.51351*05
.13898*05
29.019
.37003*05
.32121*05

.56610*01
.57636*01

.95776*01
.13972*02

.56930*01
.20336*02

.68290*01
.99696*01

.67011*01
.807254-01

.61391*01
.63019*01

.67559*01
.65812*01

.19660*01
.19680*01

.50132*01
.19175*01

.61676*01
.72179*01

.62185*01
.12102*02

.60157*01
.15712*02

.66621*01
.17110*02

.71602*01
.12301*02

.21199*02
.11821-02

.36020-02
.36119-03

.11565-01
.16707-02

.29575-02
.12771-02

.16795.02
.50513-03

.16115-02
.23357.03

.13063-03
.82395-03

-.79563-06
-.21157-08

-.35760-01
.10901-01

.77321.03
.56712-03

.32199.02
.51010-03

.60835.02
.12359-02

.80906-02
.85501-03

.36023.02
.19109-03

.12295*05
.11103*07

..16369*06
..13112*07

-.66950*05
-.18155*07

.27813*05
-.11328*07

..19119*05
-.21319*06

.29727*05
-.72606*06

,21903*01
-.216*5*06

-.65166*00
-.38277*01

.21105*05
.10116*05

.11128*05
-.50251*06

-.62931*05
-.12571*07

-.58069*05
-.29061*07

-82595*05
-.30913*07

-.33115*05
-.15653*07

.66789*02
.65216*02

.61997*02
.79867*02

.68196*02
.82681*02

.69022*02
.66163*02

.66906*02
.67976*02

.61516*02
.63771*02

.17986*02
.16181*02

.38862*02
.36862*02

.50061*02
.50091*02

.61183*02
.61372*02

.61651*02
.60006*02

.61066*02
.78562*02

.69190*02
.61938*02

.60992*02
.79009*02

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

300.
1000.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

1000.
2500.

CO
CO

C02
C02

CHI
CHI

H20
H2Q

02
02

N2
N2

H2
H2

H
H

0
0

HO
HO

HQ2
H02

CHS
CHS

CH20
CH20

CHO
CHo

-------
                * KINETIC REACTION DATA 
           i
MJMBER OF REACTIONS* 23
">l

CO
      REACTION
1
2
3
4
5
6
7
6
9
10
11
12
IS
14
IS
16
17
16
19
20
21
22
23
CO 402
H20 *
H? 
02 4
CH4 4HO
HO *HO
HO 40
H *HO
H 4H02
CH4 40
CH4 4H
CH4 *
CHS 40
CHS 402
CH20*HO
CH20*H
CH2Q40
CHO *0
C02 *
CO *HO
H 402
HQ 4H2
CHO 4 HO
* 
+n
*H
*H
* 
* 
* -
* -
* 
* -
* -
*H
* -
+ 
+ m
* -
* -
* -
*M
* 
4H
*
* -
X
>x
>8
X
>x
g

X
X
X
X
X
X
X
X
s
X
X
X
X
X
X
X
C02 *0
HO 4H
H *H
0 *0
CHS *H20
H20 *0
H 402
H2 *0
HO *HO
CHS *HO
CHS *H2
CHS *H
CH20*H
CH2Q4HO
CHO *H20
CHO *H2
CHO 4 HO
CO +HO
CO *0
C02 *H
H02 *
H *H2Q
CO 4H20
PRE EXP FACTOR
 (MOLE-CH-S)

 .1000414* o.
 .30004-164 0.
 .2000*154- 0.
 .2500+204- 0*
 .3000*14+ 0.
 .60004-134- 0,
 .2500*14* 0.
 .AOOO^IO* Ot
 .25004-15* 0.
 .1000*11* 0.
 .5000*11* 0.
 .2000*16* 0.
 .2000*13* 0.
 .3000*14* 0.
 .3000*10* 0.
 .1250*11* 0.
 .2000*12* 0.
 .3000*12* 0*
 .1000*16* 0.
 .i000*10* 0.
 .1500*16* 0*
 .2500*14* 0.
 .3000*11* 0.
TEMP EXP
                                                     .000
                                                     .000
                                                     .000
                                                   1.000
                                                     .000
                                                     .000
                                                     .000
                                                    1.000
                                                     .000
                                                    1.000
                                                    1.000
                                                     .000
                                                     .500
                                                     .000
                                                    1.000
                                                    1.000
                                                    1.000
                                                    1.000
                                                     .000
                                                     .500
                                                     .000
                                                     .000
                                                    1.000
ACTIVATION
(KCAL/HOLE)

  60.0000
 105.0000
  96.0000
 116.7000
   5.0000
   1.0000
    .0000
   7.0000
   1.9000
   6.0000
  10.0000
  66.0000
   -.3000
  30.0000
   1.0000
   3.2000
   4.4000
    .5000
 100.0000
    .0000
   1.0000
   5.2000
    .0000
INDIVIDUAL THIRD BODY EFFIC.
NAflEl     ETBl  NAHE2    ETB2
                                         .000
                                          000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                                         .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000.
                        .000'
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000
                        .000

-------
                       GRID INFORMATION SUMMARY TABLE *
ITERATIONS   1        NUMBER Of GRID POINTS:  30
  GRID COORDINATES ICH)

   .00000      .00000      .00000      .00000      .00000      .00000      .00000      .00000
        .00000      .00000      .00000      .00000      .00000      .00000      .00000      .00000
             .00000       .00000      .00000      .00000      .00000      .00000      .00000      .00000
                  .00000      .00000      .00000      .00000      .00000      .00000

 NONQIMENSIONAL GRID INCREMENTS
   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01
        .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .100004.01
             .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01
                  .10000+01   .10000+01   .10000+01   .10000+01   .10000+01   .10000+01

 TIME(SEC)

   .00000      .20000.08   .90000.08   .29000.07   .59000*07   .99000.07   .29900-06   .59900.06
        .99900.06   .29990.05   .19990.05   .69990.05   .79990.05   .89990.05   .99990.05   .10999.01*
             .11999.01   .12999.01   .13999.01   .11999.01   .15999.01   .16999.01   .17999.01   .18999.01
                  .19999.01   .21999.01   .29999.01   .39999.01   .19999.01   .69999.01

 ENTHALPY 
-------
*          H2
01
                                 * HOLE FRACTIONS OF  1<  SPECIES *



            CH4

              .*9850.01   .B9764-01   .59307-01   .571*76-01   .54464-01   .50546.01   .36221.01   .24179. 01
                   .16609-01   .77028-02   .39123-02   .18724-02   .10424-02   .59794-04   .26103-05   .11396-06
                        .53166.08   .26948-09   .14A54.10   .88715-12   .57100-13   .39397-14   .29092-15    .23778.16
                             .29513-17   .90703-18   .73212-18   .61667-18   .55102-16   .50506-18
            02

              .19731*00   .19747*00   .19727*00   .19650*00   .19506*00   .19294*00   .16120*00   .16629*00
                   .15231*00   .12705*00   .11514*00   .10607*00   .10483*00   .93509-01   .67039-01   .63356-01
                        .81185.01   .79855.01   .79009.01   .76453-01   .76078.01   .77619.01   .77636-01    .77505-01
                             .77411-01   .77237-01   .77173-01   .77147-01   .77147-01   .77153-01
            C02

              .10000-06   .99995.09   .10105-08   .11225-07   .11547.06   .51870-06   .19786-04   .10442-03
                   .26634.03   .16697.02   .31927.02   .51393.02   .66295.02   .20933-01   .33529-01   .41790.01
                        .47018.01   .50395.01   .52646.01   .54197.01   .55296-01   .56098.01   .56695-01    .57149-01
                             .57501.01   .58263-01   .58674.01   .56975.01   .59107-01   .59192.01
            H20

              .10000-06   .77698.05   .13394-03   .93634-03   .25926-02   .51100-02   .16795.01   .36172.01
                   .52682.01   .64101.01   .99291-01   .10800*00   .11156*00   .11323*00   .11282*00   .11326*00
                        .11393+00   .11452*00   .11501*00   .11541*00   .11574*00   .11600*00   .11623*00    .11641*00
                             .11657*00   .11700*00   .11727*00   .11752*00   .11765*00   .11775*00
              .10000-06   .10749.04   .69037-04   .27363-03   .59031-03   .94459.03   .14556-02   .14315-02
                   .12944.02   .10638.02   .65947.03   .59379.03   .43795.03   .69459-03   .10274-02   .10502.02
                        .96117.03   .65395.03   .75620-03   .67347-03   .60466-03   .54612-03   .50103-03   .46165-03
                             .42651.03   .34005.03   .28633.03   .24127-03   .21775.03   .20067.03
            CO

              .10000.06   .10232.06   .10608. 06   .19937-04   .12172-03   .34773.03   .29762-02   .64996-02
                   .15711.01   .33901-01   .42925-01   .47309.01   .46495.01   .37490-01   .25345-01   .17330-01
                        .12270.01   .90092.02   .68390-02   .53469-02   .42899-02   .35212-02   .29491-02   .25144.02
                             .21762-02   .14342-02   .10638-02   r7804l-03   .65659-03   .57762-03
            CH3

              .10000-06   .61513.04   .50602-03   .20010-02   .41608.02   .66604.02   .12344.01   .13061.01
                   .10235-01   .36810.02   .15512.02   .76004.03   .52560.03   .43961-04   .16713-05   .61797.07
                        .39640-06   .21510-09   .12692-10   .60956-12   .55342-13   .40332-14   .31675-15   .30620-16
                             .71790-17   .37734-17   .29650-17   .23422-17   .20116-17   .17662-17
            CH20

              .10000-OA   .59134.06   .20796-04   .27395-03   .88808-03   .18609.02   .70666-02   .12097-01
                   .14676.01   .10532.01   .61611-02   .29340-02   .14710.02   .42519-04   .13087-05   .52173.07
                        .24921-08   .14592-09   .19050-10   .10410-10   .89421-11   .81059-11   .74448-11   .69002-11
                             .64446-11   .53693-11   .46637-11   .40546-11   .37068-11   .34664-11
            CHO

              .10000-Ofl   .25546-08   .73145-06   .29854-04   .11687-03   .26012-03   .88138-03   .13632-02
                   .16368-02   .12368-0?   .75759-03   .37873-03   .20232-03   .99952-03   .36467-06   .41626.07
                        .22356-07   .17165-07   .13920-07   .113P1-07   .96328-OP   .B4932-08   .74468-08   .66173-08

-------
                 .5949A-08   .44058.06   .35291-OA   .26132-06   .24572-06   .22205-08
H02

  .10000-Oft   .77542.06   .44014-05   .13408-04   .22402.01   .27743.0"*   .29124-04   .16164.0<
       .12442.04   .60058.05   .96033.05   .26079.05   .26257.05   .49070.04   .71223.04   .68952.U4
            .61367.04   .53454.0*   .46441.04   .40523-04   .35622.04   .31577.04   .26231-04   .25456.04
                 .23136.04   .17063.04   .13706.04   .10762.04   .93794.05   .64076-05
H

  .10000.06   .22323.04   .34964-04   .45272-04   .51461-04   .51126.04   .40561-04   .30501.04
       .22587.04   .13156*04   .66997-05   .67066.05   .75599.05   .19670-03   .37617.03   .37729.03
            .32349-03   .26739-03   .22095-03   .18468-03   .15660-03   .13473.03   .11753-03   .10382.03
                 .92756-04   .65463-04   .51116.04   .39156-04   .33615-04   .29776-04
0

  .10000.06   .23006.04   .10342-03   .15976.03   .12234.03   .76636-04   .24462-04   .12266-04
       .77670.05   .57213.05   .58359-05   .62909.05   .15909-04   .11176.02   .16163.02   .17937.02
            .15973.02   .13936.02   .12193.02   .10771.02   .96195.03   .66625.03   .79139-03   .72766-03
                 .67440-03   .53352-03   .45165-03   .37790-03   .34099-03   .31420-03
HO

  .10000-06   .22526-04   .10492-03   .23923.03   .34115.03   .40742-03   .53837-03   .57212-03
       .50206.03   .35077.03   .30452-03   .35545.03   .53554.03   .57613-02   .73572-02   .73656.02
            .69649.02   .65470-02   .61397-02   .57616-02   .54723-02   .52051-02   .49740-02   .47732-02
                 .45979-02   .40966-02   .377l6-02   .34504-02   .32746-02   .3l399-02
N2

  .74264*00   .74260+00   .74244*00   .74203*00   .74145*00   .74075*00   .73641*00   .73615*00
       .73401*00   .72666*00   .72569*00   .72457*00   .72423*00   .72667*00   .73061*00   .73356+00
            .73567*00   .73711*00   .73611*00   .73664*00   .73937*00   .73977*00   .74006*00   .74033*00
                 .74052*00   .74099*00   .74124*00   .74146*00   .74156*00   .74164*00

-------
of problem are the temperature and pressure distributions.  These values are
given for each grid point and are associated with the sum of time steps
(i.e. APR*AP(N)) or total time, to that grid point.
       The output for this problem is standard except for the printing of
temperature and pressure time histories.  These appear on the first page of
output.
7.4    Sample Case 4 - Methane/Air Well-Stirred Reactor
       This sample case demonstrates the PROF code well-stirred reactor
option.  This problem models a well-stirred combustor operating at 3.4 atmos-
pheres.  Initial conditions are 3 percent concentration methane in air at a
temperature of 700K.  Five sequential calculations are made for increasing
mass rates through the fixed volume reactor.  Initial conditons remain the
same for these calculations.  The increasing mass rates take the calculations
in the direction from equilibrium to more kinetically controlled conditions.
Typically, the code has the greatest difficulty with solutions near blow-out
(i.e., kinetically dominated).  Therefore, proceeding from easily obtained
near equilibrium solutions to more kinetically controlled solutions increases
the probability for solution convergence.  To further increase the probability
for solution convergence, good estimates for final species concentrations and
temperature should be input into the Initial species concentration guesses
and TFLAME input respectively.
       Most of the output is standard for this case.  The first station
output represents the initial conditions and the following station outputs
represent the outlet conditions for the sequence of calculations.   In  the
time output the reactor residence times are printed.  These are defined as
the reactor volume density product divided by the mass rates through the
reactor.
                                      7-47

-------
                                                     SAMPLE PROBLEM 7.4
i
oo
t.
.
a.
*.
9.
i.
7.
6.
9.
to.
11.
II.
13.
ft*.
ft!.
16.
17.
16.
19.
20.
21.
22.
23.
2*.
29.
26.
27.
26.
29.
30.
31.
32.
33.
3*.
35.
36.
37.
36.
39.
*0.
*1.
*2.
*3.
**.
*S.
*6.
*7.
*6.
*9.
30.
WELL STIRRED REACTOR
.937 6.
ft.
ft.
CH*
02
C02
H20
H2
CO
CHS
CH20
CHO
H02
H
0
HO
N2
END
29
CH*
CH*
CH*
CH*
CHS
CHS
CH20
CH20
CH20
CH20
CHO
CHO
CHO
CHO
CO
CO
H02
H02
HQ2
H02
H
H
0
HO
HO
H
0
H
0



















HO
H
0
0
02

HO
0
H
02
HO
0

HO
0
0
HO
H
H
02
02
H2
H2
HO
HO
H
H
0
100.
ft.
.0369
.2087
ft.








i!
&.
.7698


N CH3
CH3
CHS
CHS
CH20
CH20
N CO
CHO
CHO
CHO
CO
CO
CO
H CO
C02
H C02
02
02
HO
02
H H02
HO
HO
H2Q
H20
H H20
H HO
H H2
M 02
3.*
90.
i.
.
.13*
.0266
.036
.92-*
 2*S
.17-*
.2* -6
.2*-9
.29*9
.10-9
.23-*
.19-3
.7696


H
H20
H2
HO
H
HO
H2
H20
HO
H2
HO 2
H20
HO
H
H

HO
H20
HO
H2

0
H
H
0




In n
U V
700.
21.
ft.
ft. 9923
ft. 6*679
.6
ft. 296
3.3339
.9930
ft. 3297
1.298
.960*
.9016
3.1557
ft.*l96
1.3*79
.9732


1.90*16
' ft. 00*13
2.00*1*
2.00*1*
3.30*13
1.00*12
2.00*16
2.90*13
3.00*13
1.70*13
3.00*13
1.00*1*
9.*0*11
2.00*12
9.90*11
3.60*16
2.90*13
2.90*13
2.90*1*
2.90*13
2.00*13
2.20*1*
1.70*13
2.20*13
6.00*12
7.00*19
*. 00*16
2.00*19
*. 00*16
>n n
V U
o.
ft*.
1.
















o.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.5
0.9
0.0
-1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-1.0
-1.0
-1.0
-1.0

1*00.
6.
ft.
















100.
6.000
11.900
6.900
3.300
19.000
39.000
1.000
0.
3.000
0.
0.
0.
26.800
1.060
2.900
0.
0.
2.000
.000
.670
16.600
9.H60
9.200
.760
0.
0.
0.
0.
                                                                                         H20  20.
           END  ELT.  TirEt 0.3760 SECONDS.

-------
                       PKEMIXED ONE DIMENSIONAL FLAMF CODE SOLUTION  (PROF)
                     PROGRAM DOCUMENTED IN THE "PROF CODE USER'S  MANUAL'S
                       AEROTHERM/ACUREX CORP FINAL REPORT 76-277
                               PHONE <*15/96t-3200
    WELL STIRRED REACTOR
                              * INTEGRAL PARAMETERS *
COLUMN                                            COLUMN
   3  NO. SPECIES CONSERVATION EOS.  1*              6  PROBLEM  TYPE  AND  ENERGY  EO.     -l

   9  NO. OF SPECIES                 1H              12  NO.  AXIAL  GRID  PTS.              6

  15  NO. GRID SOLUTION ITERATIONS    1              18  SOLUTION CYCLE  CONTROL NO.       0

  21  READ IMTIAL HOLE FRACTION      1              2<  READ NONINTEGRAL  PARAMETERS      1

  27  THERMO DATA S HEAT LOSS MODEL  -1              30  CONSTRAINT SWITCH               0

  33  READ KINETIC DATA               1              36  CONSTRAINT APPLIED TO VARIABLE   0

  39  CONSTRAINT APPLIED TO GRID PT.  0              2  OUTPUT CONTROL  NO.               2

  *5  FLAMEHOLDER TEMP ASSIGN SWITCH  0              US  INPUT MASS FLOWRATE  SWITCH       0



                               * NONINTEGRAL PARAMETERS *


   APRsOEL/MCOTs .55700400   BP=OBAR/(DEL*MDOT)=  .00000       Ps   3.
-------
                * SPECIES  INITIAL HOLE FRACTIONS.FIRST SUCSSPS.AND DIFFUSION FACTORS  *


               SPECIE                  ALPF                ALPE          DIFFUSION FACTOR

                CH4                    .305-01             .100-04               1.0923
                02                     .2011+00             .136+00               1.0468
                C02                    .100-08             .268-01                .8000
                H20                    .100-08             .580-01               1.2980
                H2                     .100-08             .320-04               3.5333
                CO                     .100-08             .240-03                .9830
                CH3                    .100-08             .170-04               1.3257
                CH20                   .100-08             .240-06               1.2980
                CHO                    .100-08             .240-09                .9604
                H02                    .100-08             .290-05                .9016
                H                      .100-08             .100-05               5.1557
                0                      .100-08             .230-04               1.4158
                HO                     .100-08             .150-03               1.3475
                N2                     .766+00             .766+00                .9732
01
o

-------
                       * THERMOCHEMISTRY DATA *
                 1
        CURVE FIT OF DATA IN FORM CPsRB+RC*T+RO/TT (CAL/(hOLE*K I
HFICAL/POL)  H(CAL/MOL)     RB           RC           RO       S
-------
                               * KINETIC REACTION DATA *
               MJNBER OF REACTIONS: 29
                     REACTION
ro
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
CH4 + +M
CH4 +HO +
CH4 +H +
CW4 +0 +
CHS +0 +
CHS +02 +
CH20+ +M
CH20+HO +
CH20+0 +
CH20+H +
CHO +02 +
CHO +HO +
CHO +0 +
CHO + +N
CO +HO +
co +o +n
H02 +0 +
H02 +HO +
H02 +H +
H02 +H +
H +02 +M
H +02 +
0 +H2 +
HO +H2 +
HO +HO +
H +HO +
0 +H +H
H +H +H
0 +0 +1
--a
a
--a
a
--a
--a
--a
-a
--a
--a
a
--a
 -a
--a
--a
--a
-a
a
--a
--a
--a
--a
-a
--a
--a
 -a
a
--a
--a
CHS +H
CHS +H20
CHS +H2
CHS +HO
CH20+H
CH20+HO
CO +H2
CHO +H20
CHO +HO
CHO +H2
CO +H02
CO +H20
CO +HO
CO +H
C02 +H
C02 +
02 +HO
02 +H20
HO +HO
02 +H2
H02 +
HO +0
HO +H
H20 +H
H20 +0
H20 +
HO +
H2 +
02 +
PRE EXP FACTOR
 CMOLE-CK-S)

 .1900+19* 0.
 .1000+14+ 0.
 .2000415+ 0.
 .2000+14+ 0*
 .3500+14+ 0.
 .1000+13+ 0*
 .2000+17+ 0.
 .2500+14+ 0.
 .3000+14+ 0.
 .1700+14+ 0.
 .3000+11*+ 0.
 .1000+15+ 0.
 .5400+12+ 0.
 .2000+13+ 0.
 .5500+12+ 0.
 .3600+19+ 0.
 .2500+10+ 0.
 .2500+14+ 0.
 .2500+15+ 0.
 .2500+14+ 0.
 .2000+16+ 0.
 .2200+15+ 0.
 .1700+14+ 0.
 .2200+14+ 0.
 .6000+13+ 0.
 .7000+20+ 0.
 .4000+19+ 0.
 .2000+20+ 0.
 .4000+19+ 0.
TEMP EXP
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .500
   .500
   .000
 1.000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
   .000
 -1.000
 -1.000
 -1.000
 -1.000
ACTIVATION
(KCAL/ttOLE)

 100.0000
   6.0000
  11.9000
   6.9000
   3.3000
  15.0000
  35.0000
   1.0000
    .0000
   3.0000
    .0000
    .0000
    .0000
  28.6000
   1.0800
   2.5000
    .0000
    .0000
   2.0000
    .0000
    .8700
  16.8000
   9.4600
   5.2000
    .7800
    .0000
    .0000
    .0000
    .0000
                                                                                               INDIVIDUAL THIRD BODY EFFTC.
                                                                                               NAME1     ETB1  NAME2    ETB2
                                                                                               H20
  .000
   000
  .000
  .000
   000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
  .000
20.000
  .000
  .000
  .000
  .000
   000
  .000
  .000
  .000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000

-------
                                       *  GRID  INFORMATION SUMMARY TABLE *






                 ITERATIONS    1         NUMBER  OF  GRID POINTS=   6








                   6RIO  COORDINATES


                    .00000       .00000       .00000      .00000      .00000      .00000



                  NONOmNSlONAL GRID INCREMENTS

                    .10000*01    .1000001   .10000401   .10000401   .10000401   .10000401



                  TIMEISEC)


                    .00000       .46796-01   .23452-01   .11766-01   .56849-02   .28726-02


                  ENTHALPY
-------
                                            HOLE  FRACTIONS  OF   14   SPFCIES  *
en
                     CH

                       .30900-01
                     02

                       .20370+00
                     C02

                       .10000-09
                     H20
                    H2
CO

  .10000-06
CHS

  .10000-OA
CH20

  .10000-08
CHO

  .10000-06
H02
                    HO
                    N2
              .80940-04   .12701-03   .20056-03
              .11296+00   .14315+00   .11346+00
              .50094-01   .29641-01   .29426-01
                       .10000-08    .60649-01    .60479-01    .60216-01
                       .10000-06    .38795-04    .626Q2-Q4    .10172-03
                                   .29565-03    .46286-03    .79347-03
                                   .21772-04    .37218-04    .61793-04
                                   .29325-06    .58945-06    .11943-05
                                   .32345-09    .62067-09    .20790-08
                       .10000-08    .34452-05    .53221-05    .81628-05
                      .10000-08    .14966-05    .26405-05    .53078-05
                      .10000-06    .32907-04    .49037-04    .71534-04
                       ,10000-06   .20126-03    .24216-03    .26703-03
                      .76580+00    .76562+00    .76552+00    .76536+00
.33130-03
.14404+00
.26678-01
.59771-01
.17241-03
.13562-02
.10393-03
.25667-05
.3530*>-08
.12768-04
.10009-04
.10256-03
.33432-03
.76509+00
.55747-03
.14503+00
.27424-01
.59034-01
.29251-03
.22946-02
.17265-03
.54639-05
.13720-07
.19603-04
.17405-04
.13398-03
.36795-03
.76465+00

-------
7.5    Sample Problem 5 - Catalytic Combustor
       Fuel Conversion Efficiency
       This sample problem demonstrates the PROF code plug-flow reactor and
wall heat and species loss options.  The problem consists of 530K, 200 per-
cent theoretical air methane/air mixture flowing into a monolithic catalytic
combustor with 0.16cm radius channels.   The interior surfaces  of  these  channels
are coated with a catalyst material which helps convert fuel and air to com-
bustion products.  The special input needed for this option is the transfer
coefficient, wall temperature and gas composition at the wall.  These quanti-
ties are given  in the input card and output listings.  A constant Nusselt
number case is  specified by inputting a value of one for both the Reynolds
and Schmidt number exponents.  The transfer coefficient parameter then
becomes the mean Nusselt number divided by the hydraulic diameter squared.
This is the number 40 which appears on the output listing.  Following this
output, the wall species concentrations are printed  in the same order as
the initial concentrations.  Wall species  concentrations and  temperature
are assigned at values characteristic of fully combusted inlet gases at
equilibrium and with no heat loss.
       The final summary output shows that most of  the fuel has been converted
to  products within the combustor.  This conversion  of fuel  is due  solely to
wall reactions  since the homogeneous reactions have  remained  inactive over
the length of the combustor.  The  activity of the reactions can be assessed
by examining the major and  minor species concentrations and reaction rate
output for all  of the grid  points.
                                     7-55

-------
                                                   SAMPLE PROBLEM 7.5
*J
en
1.
2.
3.
4.
5.
6.
7.
a.
9.
10.
11*
12.
13.
1.
19.
16.
17.
16.
19.
20.
21.
22.
23.
21.
25.
26.
27.
26.
29.
30.
31.
32.
33.
3
-------
55.
56.
57.
se.
55.
60.
61.
62.
63.
6*1.
0
HO
HO
H
0
H
0
HO
N
0
H2
H2
HO
HO
H
H
0
N
02
N2



n
M
M
H



HO
H20
H20
H20
HO
H2
02
H
NO
N
H
H
0




NO
0
NO
1.70+13
2.20+13
6.00+12
7.00+19
. 00 + 18
2.00+19
. 00 + 18
if. 00+13
6.50+09
l.fl+1*
0.0
0.0
0.0
-1.0
-1.0
-1.0
-1.0
.5
1.
.0
9.H60
5.200
.780
0.
0.
0.
0.
.00
6.30
75.2
I
01

-------
  CHI/AIR CAT COMB
                       PREMIXED ONE DIMENSIONAL FLAME CODE SOLUTION (PROF)
                     PROGRAM DOCUMENTED IN THE "PROF CODE USER'S MANUAL'S
                       AEROTHERM/ACUREX CORP FINAL REPORT 78-277
                               PHONE 2  OUTPUT CONTROL NO.              2

                                            its  INPUT MASS FLOWRATE SWITCH      o
                               * NONINTEGRAL PARAMETERS *
   APRsOEL/MCOTs .1<000+02   BP=DBAR/(DEL*MDOT >= .00000

         TKAP=    .00000   TFLAMEs     .0(K>
                                                      Ps   l.OOO(ATM)   TI=   530.0(K)
                                * GRID PARAMETERS 
A(N)*2
                      25
         .1000+01  .1000+01  .1000+01  .1000+01  .1000+01  .1000+01  .1000+01  .1000+01  .1000+01  .1000+01
              .1000+01  .1000+01  .1000+01  .1000+01  .1000+01  .inoo+oi  .1000+01  .1000+01  .1000+01  .1000+01
                   .1000+01  .1000+01  .1000+01  .1000+01  .1000+01

         ?IGfA(N)tN=l. 25

                   .1500+00  .1500+00  .1500+00  .1500+00  .1500+00  .1500+00  .1500+00  .1500+00  .15UO+OU
              .2000+00  .2000+00  .2000+00  .2000+00  .2000+00  .3000+00  .3000 + 00  .MOOO+00  .4000 + 00  .4000 + 00
                   .5000+00  .5000+00  .5000+00  .1000+01  .1000+01

-------
                                           * HEAT LOSS DATA *




                NO. OP STATIONS:   1        OLS= .HOOOO+02




                     REACTIVITY PAR= 2    WALL TEHP= .ItlOO+OU




                     REYNOLDS EXPONENT = .10000+01     SCHMIDT EXPONENT = .10000*01




                WALL SPECIES CONCENTRATIONS




                 .10000-06 .75170-01 .37593-01 .75197-01 .10000-00 .10000-08  .10000-08 .10000-08

                                .10000-08 .10000-08 .10000-08 .10000-08 .10000-08 .81204+00 .10000-08 .10000-08
en
vo

-------
                                  *  GRID  INFORMATION  SUMMARY  TABLE  *
            ITERATIONS    1        NUMBER  OF  GRID  POINTS=   25
             GRID COORDINATES(CM)

               .00000       ,15000*00    .30000*00    .45000+00    .60000*00    .75000*00    .90000*00    .10500*01
                    .12000401    .13500*01    .15000*01    .17000*01    .19000*01    .21000*01    .23000*01    .25000*01
                         .26000*01    .31000*01    .350004-01    .39000*01    .43000*01    .10000+01    .53000+01    .56000*01
                              .60000+01

            NONOIMENSIONAL GRID  INCREMENTS
               .15000+00    .15000+00    .15000+00    .15000+00    .15000+00    .15000+00    .15000+00    .15000*00
                    .15000+00    .15000+00    .20000+00    .20000+00    .20000+00    .20000+00    .20000+00    .30000*00
                         .30000+00    .40000+00    .40000+00    .40000+00    .50000+00    .50000+00    .50000+00    .10000+01
                              .10000+01

            TIME*SEC)

               .OOOQO       .12044.02    .21663.02    .29950-02    .37352-02    .44169.02    .50576-02    .56603.02
                    .62566-02    .60204-02    .73064-02    .01149-02    .00313-02    .95309-02    .10240-01    .10936-01
                         .11973.01    .13005.01    .14376.01    .15744.01    .17110-01    .10016-01    .20521-01    .22226-01
I                             .25635-01
at
          ENTHALPYICAL/6M)

               .35202+0?    .35035+02    .35160+02    .35447+02    .35793+02    .36126+02    .36407*02    .36609*02
                    .36720+02    .36767+02    .36720+02    .36574+02    .36364+02    .36116+02    .35040+02    .35512+02
                         .35135+02    ,34754+02    .34400+02    .34124+02    .33095+02    .33710+02    .33596*02    .33491*02
                              .33422+02

            TEMPERATURE

               .53000+03    .60649+03    .01071+03    .92070+03    .10193+04    .10936+04    .11542+04    .12036+04
                    .12436+04    .12761+04    .13050+04    .13314+04    .13500+04    .13655+04    .13765+04    .13863+04
                         .13942+04    .14000+04    .14040+04    .14064+04    .14079+04    .14069+04    .14094*04    .14U97+04
                              .14099+04

            DENSITY<6H/CN3I

               .64761*03    .49945.03    .41052>03    .36005.03    .33604.03    .31327-03    .29607-03    .26477-03
                    .27567.03    .26672-03    .26269.03    .25769.03    .25404.03    .?5l35-03    .24936-03    .24762.03
                         .24623-03    .24521-03    .24451-03    .24409-03    .24381-03    .24364-03    .24355-03    .24346-03
                              .24345-03

            SYSTEM MOLECULAR WEIGHT

               .98165+02    .28135+02    .P8117+02    .28109+0?    .26108+02    .21111*02    .24117+02    .2pl2
-------
                                * MOLE FRACTIONS OF  16  SPECIES *



           CH4

             .37558-01   .31466-01   .26094-01   .211*92-01   .17610-01    .14370-01    .11669-01    .91*830-02
                  .76776-02   .62059-02   .46526-02   .36737-02   .27777-02    .20962-02    .15637-02   .11254-02
                       .79926-03   .1*6012-03   .26967-03   .17489-03    .10048-03    .55097-04   .30205-04   .13505-04
                            .90962-05
           02

             .150364-00   .13607*00   .12732+00   .11812+00   .11036+00    .10390+00    .98548-01    .94151-01
                  .90552-01   .67616-01   .84920-01   .62567-01   .60778-01    .79419-01    .78386-01   .77467-01
                       .76721-01   .76164-01   .75776-01   .755<*0-0l    .75385-01    .75290-01   .75237-01   .75201-01
                            .75182-01
           C02

             .10000-08   .48179.02   .92277-02   .13180-01   .16673-01    .19727.01    .22377-01    .21662.01
                  .26624.01   .26302.01   .29931-01   .31438.01   .32654.01    .33633-01    .34420-01   .35173.01
                       .35832.01   .36366.01   .36776.01   .37049.01    .37245.01    .37379.01   .37461.01   .37525-01
                            .37563-01
           H20

             ,10000-Ofl   .14480.01   .26706.01   .36767.01   .41*964.01    ,51518.01    .56726.01    .60835.01
                  .64060.01   .66580.01   .68766.01   .70611.01   .71922.01    .72663-01    .73537.01   .74099.01
                       .74519.01   .74806-01   .71*986-01   .75084-01    ,751<*1-01    .75171-01   .75185-01   .75193-01
i                           .75196-01
2         H2

             .10000-08   .12628.08   .15542.06   .30260-08   .58225-08    .66103-06    .11426-07    .14623.07
                  .16729.07   .24712.07   .36256.07   .58184.07   .90019.07    .13018.06    .17459.06   .22765.06
                       .27480.06   .29747.06   .28369.06   .24230.06    .18406.06    .125<*9-06   .81068.07   .13317.07
                            .21206.07
           CO

             .10000.06   .19971.06   .21823.08   .41340-08   .85799-06    .14039.07    .20400-07    .26016-07
                  .37653-07   .50666-07   .75073-07   .12075-06   .18947-06    .26176-06    .39276-06   .54396-06
                       .71042.06   .84460.06   .89665.06   .65549.06    .73577.06    .57240-06   .41847-06   .25172.06
                            .12666-06
           CHS

             .10000.04   .63925.08   .70793-08   .76500-08   .66916-08    .95753.08    .10607.07    .12U60-07
                  .14531.07   .18761-07   .27383-07   .43194-07   .64591-07    .89356.07    .11420-06   .14036.06
                       .15699-06   .16126.06   .14392-06   .11519-06    .81829-07    .51980-07   .31183.07   .14690-07
                            .58900-06
           CH20

              .10000-0*   .12179.08   .19209.08   .20356-08   .11057-08    .54233-09    .33387-09    .24987-09
                  .21901-09   .22148-09   .26075-09   .34369-09   .45047-09    .56533-09    .67201-09   .77525-09
                       .83474-09   .61580-09   ,7o99o-o9   .55976-09    .39406-09    .24917-09   .14936-0*   .716<5-10
                            .28664-10
           CHO

              .10000-08   .15251-13   .37425-14   .5H097-14   .71920-14    .89991-14    .10759-13    .12417-13
                  .13936-13   .15296-13   .16656-13   .17952-13   .19031-13    .19947-13    .207H7-13   .21616-13
                       .22511-13   .23332-13   .23904-13   .24082-13    .23932-13    .23569.i4   .23246-13   .2290.5-13

-------
                             .22674-13
            H02

              .10000-08   .32184-06   .34175-08   .3<312-08   .33610-08   .32611-08   .32162-08   .34113-08
                   .41033-06   .54773-08   .79158-08   .11259-07   .14573-07   .17468-07   .19806-07   .21926.07
                        .23606-07   .24796-07   .25552-07   .25954-07   .26167-07   .26265-07   .26301-07   .2631S-07
                             .26318-07
            H

              .10000-08   .22733-10   .98715-11   .78217-11   .66144-11   .60700-11   .60641-11   .66286-11
                   .81122-11   .11304-10   .16397-10   .31494-10   .48841-10   .68172-10   .87299-10   .10822-09
                        .12826-09   .14530-09   .15805-09   .16557-09   .16950-09   .17078-09   .17070-09   .17002-09
                             .16937-09
            0

              .10000-08   .33909-10   .71705-11   .76474-11   .91341-11   .11173-10   .13906-10   .17750-10
                   .23830-10   .34765-10   .58968-10   .10803-09   .18144-09   .27321-09   .37359-09   .49420-09
                        .62094-09   .73993-09   .84127-09   .91368-09   .96569-09   .99823-09   .10150-08   t!0245-08
                             .10279-08

r
0}            .10000-08   .56076-10   .26841-10   .48864-10   .86569-10   .14370-09   .23041-09   .37105-09
                 .62092-09   .10942-08   .22107-08   .48423-08   .98158-08   .18161-07   .30805-07   .53117-07
                        .88900-07   .14009-06   .20381-06   .26547-06   .32246-06   .36726-06   .39600-06   .41694-06
                             .42770-06
            N2

              .81204400   .81117400   .81066400   .81042400   .81039400   .81049400   .81066400   .81087400
                   .81109400   .81129400   .81151400   .81171400   .81187400   .81199400   .81207400   .81213400
                        .81217400   .81218400   .81217400   .61215400   .81213400   .81210400   .81209400   .81207400
                             .81205400
            N

              .10000-08   .11044.10   .15605-11   .12173-11   .10877-11   .10270-11   .99888-12   .98767-12
                   .98540-12   .98780-12   .99322-12   .10004-11   .10073-11   .10134-11   .10164-11   .10231-11
                        .10267-11   .10291.11   .10303-11   .10306-11   .10304-11   .10301-11   .10299-11   .10297-11
                             .10296-11
            NO

              .10000-08   .19955-08   .20111-08   .20169-08   .20217-06   .20258-08   .20293-08   .20321-06
                   .20345-06   ,20364-08   .20381-08   .20396-08   .20407-08   .20415-08   .20420-06   .20424-08
                        .20427.08   .20429-08   .20430-08   .20429-06   .20429-06   .20429-08   .20428-08   .20428-08
                             .20426-08

-------
                                 SECTION 8
                  DEBUG OUTPUT AND PROBLEMS AND PITFALLS
       This section discusses the output which is printed when the chemistry
routine fails to converge in the allotted number of iterations.   This debug
output does not signal the end of a solution attempt.   Rescue procedures are
built into the code which allows the chemistry routine to converge on one or
more intermediate solutions before proceeding to the solution of interest.
Through this procedure, first guesses are sequentially improved until it
becomes an easy matter to converge to the solution of interest.
       Nonconvergences and the resulting debug output are typically the
result of bad input data and poor first guesses.  Some pointers on how to
avoid nonconvergences are discussed in the problems and pitfalls subsection.
8.1    Debug Output Description
       The chemistry solver routine has 50 iterations in which to converge.
If 47 iterations are exceeded, the routine begins to print out detailed
information on the conservation equations and kinetic reaction rates.  This
output can also be activated by inputting a KR7 value greater than three
(See Section 5.1, Card 2).
       The first output to appear, listed on the following pages, gives
thermochemical information for the individual species.  Quantities output
include molar specific heat, enthalpy, and partial and log partial pressure.
The next group of output gives information on the errors in the equations
and the derivatives of the change in equation error with respect to the
change in the variables.   This output is headed by the iteration number.
Following this output, the equation error and derivatives of equation
                                   8-1

-------
errors with respect to the log of the variables are printed out.  This
information, labeled A(I,J), R(I), is arranged in the following matrix
form:
                         JlnT    JlnPM
                                                    Error
                                                                E1
Enthalpy
Sum of
partial
pressures
Species 1
Species 2
Species IS
where E- represents the equation error and V^ is the log of the variable.
        '                                    J
The effects of kinetics have not yet been included in these equations and
derivatives.  Recalling the discussion in Section 4.1.2, after the addition
of kinetics to the above matrix, the chemistry routine determines the needed
corrections to the present solution estimates by inverting the matrix and
multiplying by the equation errors.  Examining these derivatives and errors
prior to inversion can give useful insights into solution problems.  Also
comparison of the matrix and errors before and after kinetics indicates the
importance of kinetics on the solution.
        The BIG(N) output gives the biggest positive or negative term found
in each species equation.  The kinetic contribution to the equation is
compared to this term to establish if kinetics is dominating the equations.
If kinetics is dominating, the group of equations will be rearranged so as
to introduce the kinetics into only one equation.
                                    8-2

-------
       The PRMU, M, etc. output appears for each kinetic reaction.   The
first lines of numbers are the PRMU values which are the product of the
time or space step parameter and the reaction stoichiometric coefficients.
The order of PRMU is the same as the species concentration  input.   The line
of output beginning with an integer, which is the reaction  number,  gives de-
tailed information on reaction rates.  FKF and PPX are the  log of the reaction
rate constant coefficient and the third body rate coefficient multiplier
respectively.  SUMK and SUMR, when combined with VLK, give  the backward and
forward rates of the reaction.  These are printed out as PKP and PKR
respectively.  The difference between these rates is the net reaction rate,
PMR.  EXK and EAK are the same quantities as defined in the input.
       The second BIG(N) output gives the largest positive  term followed
by the largest negative term found in the species equations after the
addition of kinetics.  Comparison of this output with the first BIG(N) output
indicates the significance of kinetics on the equations.
       The LL(I) output indicates if specific dominating reactions have
been assigned to the mass balances.  Zero indicates that no specific reaction
has been assigned and a negative sign indicates that the mass balance has
been reconfigured to behave like an equilibrium equation.
       The MA(L) output gives the order of the reactions from fast to slow.
The fast reactions will dominate the solution behavior.
      .The second A(I,J), RHS(I) output gives the derivatives matrix and
equation errors after kinetics have been added to the solution.  Comparison
of this matrix and errors with those printed out before the addition of
kinetics indicates the impact of kinetics on the solution.   This matrix
                                     8-3

-------
of derivatives is inverted and multiplied by the equation errors to obtain
the corrections to the variables.
       The final A(I,J) and RHS(I)  outputs are the partial  matrix inverse
of the above-mentioned A(I,J) and the log of the corrections to the variables,
respectively.  The relative magnitude of the corrections with respect to
the variables indicates how close the solution is to convergence.   When
the relative corrections become less than 0.00001 the solution procedure
is converged.
       The DAMP, T and PM output are the correction multiplier, temperature
inKand pressure molecular weight product in atmosphere-gm-mole units
respectively.  The DAMP multiplying factor is used when the corrections
exceed built-in limits on the percent of variable increase or decrease per
iteration.  The multiplying factor is applied uniformly to all variable
corrections.  DAMP typically starts out less than one and approaches one
as the solution converges.  Values of DAMP much less than one indicate that
the solution is far from convergence.
       Output following DAMP, T and PM is the log partial pressure of the
species concentrations listed in the same order as the input species
concentrations.
       The "allowed iterations exceeded" output  indicates that the solution
has failed to converge in 50 iterations and the time or space step has been
cut by a factor of 2, as indicated by IB = 2.  Cutting the time or space
step by a factor of 2 (or more for subsequent nonconvergences) allows
the solution procedure to converge on a more easily obtained intermediate
solution before proceeding to the solution of interest.  However, if the
time or space step is cut by a factor of 256 and the solution still has not
                                     8-4

-------
converged, it is then assumed that a serious problem exists and the solution
procedure is terminated.
8.2    Flame Solution. Problems and Pitfalls
       The PROF code flame option treats problems which are steady in time.
Transient problems, such as flames being extinguished at the flameholder or
"blown off" the burner, are not handled by the code.  If the code is given
poor flame speed parameter or species concentrations first guesses, these
unsteady solutions might be sought by the code.  In these cases the final
result will be a prediction of unburnt gas or the trivial unignited flame
case.  To avoid these solutions, some care must be taken in developing
first guess input data.
       To maximize the probability of convergence to a hot solution, always
use downstream stable species guesses which are characteristic of the burnt
gas mixture.  These can be guessed at or they can be scaled from a prior
solution.  If punched card output from a prior solution is input, make
sure that there are no discontinuities in concentrations from the initial
point to the first grid station.  If punched cards are not used for first
guesses, input downstream unstable species concentrations characteristic of
the maximum values which are found in the flame.  These first guess concen-
trations will help "light off" the flame.
       First guess values for the flame speed parameter must also be care-
fully chosen.  Large and small values of the parameter relative to the cor-
rect value, will lead to extinction and blowoff respectively.  An estimate
of flame speed should be used to calculate the flame speed parameter.  Large
values of DAPR relative to APR indicate that either poor guesses for APR or
                                    8-5

-------
species concentrations have been input into the code.  If this type of
output persists for several iterations, along with small  damp valves, then
the first guesses should be carefully reviewed and revised as needed.  The
constraint condition should also be examined at this time.
       To maximize the probability of convergence, the constraint condition
should be applied to a monotonically increasing or decreasing species con-
centration in a region where the concentration is changing rapidly.   A
value between one-third and two-thirds of the maximum value found within the
flame is suggested.  A stable species which represents a sizeable fraction
of the total gas is a good candidate for the constraint variable.
       The solution procedure, being fully implicit in nature, does  not have
any limitations on step size or grid spacing.  However, for accurate results,
grid spacings must be made sufficiently small to define species gradients.
Problems arise when step sizes are too large and the "flame zone" is
captured within one grid spacing.  These cases will have very large errors.
For free flame cases, grid spacings near the constraint condition should
be on the order of one-tenth of the values at the upstream and downstream
boundaries.  This distribution of grid spacings should give adequate gradient
resolution over the entire flame length.  For flames attached to flameholders,
gradients at the upstream boundary near the f landholder, are substantial
and small grid spacings should be applied from the upstream boundary through
to the constraint location.  Downstream of the constraint, larger grid spacings
can be applied without adversely affecting accuracy.
       Once the solution is converged, the adequacy of the selected grid
spacings can be assessed and needed revisions can be made to the grid spacings.
                                     8-6

-------
       It should be noted that many free flame calculations have been made
with the PROF code using crude first guesses.  Nearly all of these cases
converged to hot flames.  When the solution did not converge, it was typi-
cally because extremely poor first guesses were input.  Therefore, some
care in input preparation should be exercised to maximize the probability
of convergence.
8.3    Well-Stirred,  Plug-Flow and Time-Evolution Chemical Kinetic
       Solution  Problems and Pitfalls
       The PROF  nonflame code options employ the flame chemistry routine
with simple  driver logic to either march in space or time.  Problems
encountered  with these  options are typically associated with the chemistry
routine not  receiving adequate first guesses for temperature (where appli-
cable) and species concentrations.  Since the upstream conditions are used
as first  guesses in  these marching procedures, the solution problems are
associated with  taking  too large a time or space step.  Simply reducing the
step size will alleviate the problem in most cases.
       For the well-stirred reactor option the time  step  is  large and fixed.
This can  lead  to solution problems.  However, first  guesses  to the  solution
can be sequentially  improved by converging on a number of easily  obtained
well-stirred reactor solutions.  The solution at the last reactor time  step
is used as the first guess for the current reactor solution.  By  this pro-
cedure the code  can  "creep" to the solution  of interest.
       Well-stirred  reactor initial conditions are usually cold and unreacted.
To ensure "ignition" of the reactor, a temperature characteristic of the
burnt gas should be  inserted in the TFLAME input  (See Section 5.1,  input
card set  3).  This  input  is used as the  temperature  first guess  for the
solution  of  interest.
                                    8-7

-------
       The well-stirred reactor solution procedure has the greatest diffi-
culty when the reactor time constant is near the blowout limit.   Starting
with poor first guesses, solution excursions during intermediate iterations
can result in nonconvergences.  To improve first guesses in these cases, a
sequence of solutions should be carried out, starting from the easily
obtained near equilibrium case (i.e. very large time step).  As the blowout
limit is approached the difference in reactor time constants between solu-
tions should be reduced.  Solutions for intermediate and final time constants
of interest should be achievable by this approach.
                                    8-8

-------
                              8.1 SAMPLE DEBUG OUTPUT
CPF,HI,SB,TCtEtPP
    CH4
    02
    CQ2
    H20
    H2
    CO
    CHS
    CH20
    CHO
    H02
    H
    0
    HO
    N2
.2030402
.669101
.1307402
.1110402
.7655401
.7990401
.1609402
.1662402
.1224402
.1226402
.1*968401
.4903401
.7613401
.6284401
-.9763403
.9106404
-.6025405
-.4705405
.6149404
-.1779405
.4967405
-.1246405
.9087+04
.1719405
.5773+05
.6526405
.1770405
,6614404
.5048402
.3157402
.3702402
.3144402
.3604402
.3933402
.5614402
.5376+02
.5344402
.5509402
.4098402
.4333402
.4184402
.2794402
.2027400
-,320<401
.2823402
.1655402
-.2866401
.6259401
-.1747402
.4391401
-.3196401
-.6046401
-.2031402
-.229b402
-.6227401
..3030401
,5068+02
.2836402
.6524402
.4799402
.3316402
.4559402
.3867402
.581540?
.5025402
.4904402
.2068402
.2037402
.3561402
.2491402
.3094-07
.4805400
.1116400
.2097400
.4051-06
.6236-04
.8737-10
.1943-07
.9291-08
.2990-08
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   .0000      .0000      .0000      .0000      .0000     .0000     .OUOO     .0000     .0000
    .0000     .0000     .0000     .1000*01  ..6868.03
 DAMP*  .26709*00- TO  .14252*04 PH=  .96637*02
     -.18631*02-.73027*00-.22123*01-.15653*01-.14891+02-.11254+02-.23190*02-.19360*02-.23099*02-.18450+02
     -.22170*02-.18167*02-.12765*02 .95761*00

 ALLOWED  ITERATIONS EXCEEDED
 FLAME PARAMETERS ITERsSO   IBs 1
                                                                                             .0000

                                                                                             .0000

                                                                                             .0000

                                                                                             .0000

                                                                                             .0000

                                                                                             .ocoo
.1000+01


.OUOO

.OUOO

.0000

.0000

.0000
 .4485*01

 .1171-03

-.1495-08

 .4685-03

 .ooog



 .1212-08

 .OUOO

-.4231.01

..7350-09

-.1262-07

..1630.08

 .9554.07

..7617-09

..2600.07

 .3261.08

..3199-05

 .1000*01

 .OUOO

 .0000

 .0000

 .0000
 CPFtHI,8BiTC.EfPP
     CH4       .2027*02 -.1020*04  .4399*02  .3644*00  .4435*02
     02        .6677*01  .6919*04  .3149*02 -.3186+01
     CQ2       .1384+02 -.8055*05  .3698*02  .2877+02
     H20       ,1105*02 ..4729*05  .3136*02  .1689+02  .4b26+02
                                                                 .1749-04 -.1096*02
                                                       .2830*02  .4852*00 -.7232*00
                                                       .6575*02  .1057+00 -.2266+01
                                                                 .2074*00 -.Ib73+01
     H2
               ,7633*01  .7982*04  .4106*02 -.2651*01  ,4B21+Ok  ,2t>25-0d -.1980*02

-------
                                 SECTION 9
               PROGRAM FORTRAN VARIABLES LIST AND DEFINITIONS

       In Table 1 and 2 the common and local variables of the major
routines used in the PROF code are defined.  In many cases the program
variable names can be related to specific variables defined in the text of
this document.  In other cases the terms are defined and used locally in
the code for algebraic convenience.  Some variable names relate to input
options and are used as option flags throughout the code.  All variables
are included in the tables so that the user can quickly identify the
nature of every variable name used.  The dimensions indicated for each
variable are defined at the beginning of the program list of the major
routines.
                                    9-1

-------
                        TABLE 1.  COMMON  VARIABLES
  Variable
Common
                  Description
A (JEX.JEZ)
AFF (JX)

ALA (JQ,JS)




ALB (JQ, JS)


ALDEN (JP)
ALFW (JE)

ALPE (JQ)



ALPF (JQ)



ALPHI (JQ)




ALPHZ (JQ)

AP (JS)
Fl
AA (JEZ,JEZ)     F3
F2

EPRP
F3


LIN
Fl

F3



F3



Fl
F3

F3
Basic matrix of coefficients set up  in FLAME,
fully inverted on last iteration in  FLAME,  and
used to set up linearized corrections in ACEF.
Equivalenced to DAA for storage economy only.

Inverse of A loaded into AA and corrected for
rearrangements in kinetics package of FLAME.

Affinity of given kinetic reaction,  (= TAS)

The "corrector" values of the species a-j's  for
each species at each station.  They  also serve
as "error" variables during matrix solution of
"corrector" equations.

The "predictor" value of the species a.'s for
each species at each station.

The denominator by which each term of the conser-
vation equations (Eq. 37 and 38) is  divided to
produce a unity coefficient on a.  (or h  for
1=ISfl).                         nn      n
Wall
values of a.,  for each species.
Guessed exit or equilibrium values of  the  ot-j's
which are input to the code.  Used only  to  set
up initial first guesses under certain options.

Assigned initial or frozen values of the a.'s
which are input to the code.  These values  are
assigned to station one and are never  varied.

The current set of a-j's at a given station  as
generated by the FLAME subroutine.  Entering
FLAME these variables contain the terms  cc.
introduced in Eq. 44.
The terms a.
         introduced in Eq. 44
The area ratio parameter read with  card  set  4.
For the FLAME transformations (Eq.  36) the
parameter is squared  immediately  after input.
                                    9-2

-------
                           TABLE 1.  Continued
  Variable
Gomroon
                Description
ARHM (JQ,JQ)
 F3
AX (JS)


BMU (JS)

BP



BPA (JQ)
 F4


 EPRP

 Fl



 F3
CHI (JS)

CHIW


CKIN (JQ)
 EPRP

 Fl


 Fl
CKINI (JQ)
 F3
The matrix to the right of the diagonal during
the "corrector" block tridiagonal solution pro-
cedure.  This matrix is set up after each FLAME
computation, the diagonal matrix is solved in
terms of its variable, the subsequent left-hand
matrix is folded into it, and then it is stored
on peripheral hardware.  After completion of
the last station FLAME computation, the ARHM
are extracted and solved for the "corrector"
a-j's starting from the last station.  During
the manipulation,the zero and (-1) columns of
this matrix are temporarily equivalenced to
the constant of the linear equations and the
coefficient on an, respectively.  (Note DUD
(JQ) and DUMB (JQ) prior to ARHM (JQ,JQ) in
Common list.)

Defined for local output of species mass
fractions in ACEF.

BMU (1) - nM - U2l

Defined by Eq. 36.  Input for FLAME options.
Updated during iterations for assigned m
option.

Defined by Eq. 36.  Input for all diffusion
options (axial or wall loss).  Updated during
iterations for assigned m option.  Initially
input as 1/F  but immediately multipled by BP.

Defined immediately following equation 38.
               _    ^
Value of (Kui/pD) - C
calculation (see Eq.
                      used in wall heat flux
                     26).
Constant coefficient on kinetic production term
as developed at each station for each mass bal-
ance.  Identical to CKINI (JQ) except as damped
for reduced time steps prior to call of FLAME
in ACEF.

Constant coefficient on kinetic production
term.  (See CKIN (JQ).)  This coefficient is
normalized to yield unit coefficient on cu
in mass balance equation.
                                   9-3

-------
TABLE 1.  Continued
Variable
CPF (JP)
CPG
CPT (JP.50)
CPTIL
DM (JE2,JE2)
DKPT (JX)
DQRDP (3)
DQRDT
DH (JSO
DUD (JQ)
DUMB (JQ)
E (JP)
EAK (JX)
EGYDS
EXK (JX)
Common
Fl
Fl
LIN
EPRP
Fl
F2
Fl
Fl
F4
F3
F3
Fl
F2
HTL
F2
Description
Molal heat capacity of each species.
Heat capacity of gas mixture in cal/gmK.
Within FLAME, CPG is heat capacity times PM.
Tabular values of molal heat capacity for each
species at 100K increments to 5000 K.
Modified heat capacity Cn. Within FLAME,
CPTIL is Cp times PM. p
DAA (i, k) becomes the aa-j/aa0. and is used
for setting up corrector matrix.
The partial of log K with respect to log T
for each kinetic reaction.
Partial of the emitted radiation flux per unit
volume with respect to the log partial pressure
C02, H20 and CO, respectively.
Partial of the emitted radiation flux per unit
volume with respect to log of temperature.
Elapsed times as computed from flow data.
Equals CKIN (I)* BUMP in FLAME.
Not used.
Prior to inversion in FLAME, equal to error of
mass balance and equilibrium equations; after
inversion equal to corrections in log partial
pressures of species.
Activation energy of kinetic reaction,
cal/mole.
Not used.
Temperature exponenet of kinetic reaction.
Modified depending on nature of mass balance
to include additional temperature factors
multiplying kinetic production term.
        9-4

-------
                           TABLE 1.  Continued
  Variable
Common
                Description
EXM

EXN

FKF (JX)
FLUX (JQ)

FT

FW (JP)



GT (JP,50)



H
 Fl

 Fl

 F2
 F3

 Fl

 Fl



 LIN



 Fl
HBC
HH (JS)
HI (JP)
HOS (JP)
HRF '(JP)
HT (JP, 50)
Fl
F4
Fl
Fl
LIN
LIN
HTCOE
 EPRP
Exponent m introduced after Equation 13.

Exponent n introduced in Equation 13.

Log of pre-exponential factor of kinetic
reaction.  Modified, depending on nature of
mass balance, for additional multiples of the
perfect gas constant.  Saved in XX (JX) and
then modified in each interation to  include PM
factors and third body terms.

Not used.

Not used.

Difussion factor F for each species  as used in
wall flux relations.  (Equals laminar F raised
to n power.)

Tabular values of standard state free energy
function, (G-H29s)/T for each species at
100K increments to 5000K

Enthalpy of gas mixture as input to  FLAME.  In
flame solutions the parameter includes other
input terms (h).

Not used.

Enthalpy of gas mixture at each station
(Predictor value).

Molal enthalpy of each species.

Product of molal enthalpy and partial pressure
of each species; modified to include heat
transfer terms for computational efficiency.

Molal heat of formation of species at 298K.

Tabular molal enthalpy of each species relative
to its value at 298K, given at 100K
increments to 5000K.

Coefficient on hn in flame energy equation.
                                   9-5

-------
                           TABLE 1.  Continued
  Variable
Common
                Description
HTW
IB
ICC
 Fl
 Fl
 Fl
ICON
IH
IQV (16,4)
IS
Fl
Fl
LIN
Fl
ISP               Fl
ITER              Fl
IWANT (3,JP)      WANTS

KNY               LIN

KR                Fl
KR6               Fl
KR7
L
MA (JX)
Fl
Fl
F2
Value of h at wall as in Eq. 26.
Counter on step size halving procedure.
Value of ITC as carried by program with regard
to heat loss options (see Section 5.1).
Flag indicating convergence (=0) or
nonconvergence (=1) of FLAME routine.
Index flag defining wall flux option.  See
page 5-8.
Equivalent species name table (see page 5-10).
Number of mass balances to be considered.
Same as number of species if no equilibrium
reactions.  (Equilibrium option inoperative.)
IS+1.
Iteration count in FLAME (starts at 1).
Flag (IWANT (1,J) and species name (IWANT
(2&3,J)) of desired species.
Number of equivalent species name pairs to be
considered (read as number of cards and
multiplied by 4).
Kinetics flag in FLAME.
Flag on solution type to be obtained (see page
5-1).  Note that -1 goes to 0 and 3 goes to 2,
after setting up special flags.
Debug flag (see page 5-3).
Axial station number.
Ordering array for kinetic equations.  MA (1)
is index of fastest reaction.
                                   9-6

-------
                           TABLE 1.  Continued
Variable
MP (JX)
MT
N
NAMA (OP)
NAMB (JP)
NEQ
NFHS
NRS (3)
NWANT
P
PI (JS)
PKP (JX)
PKR (JX)
PLN
PLP (JP)
PML (JX,JS)
Common
F2
Fl
Fl
Fl
Fl
Fl
Fl
Fl
WANTS
Fl
EPRP
F2
F2
Fl
Fl
F4
Description
Flag indicating those equations rearranged in
FLAME to assist kinetic convergence. If MP
(2) = -3 then 2nd fastest reaction was isolated
into mass balance 3.
Number of kinetic reactions.
Number of species.
First four characters of species name.
Second four characters of species name.
Total number of equations^used in corrector
step. May include T and h equations.
F landholder flag (NFH) as transmitted to FLAME
where L = 2. When L 1 2, NFHS = 0.
Indexes of C02, H20, and CO, respectively.
Number of species in input list. Must equal
IS.
Pressure in atmospheres.
Not used.
Reverse rate of kinetic reaction.
Forward rate of kinetic reaction.
Log of pressure.
Log of partial pressure of each species.
Net forward rate of each reaction at each
PMR (JX)

PMU (JE,JX)
F2
F2
station as output.
Net forward rate of each reaction as used in
FLAME.
Stoichiometric coefficient of each product
species in each reaction.
                                   9-7

-------
                           TABLE 1.  Continued
Variable
PMW
PP (JP)
PPI (JP)
PPP
PPS (JP)
PPTC (JP)
PPV
PPX (JX)
PRMU (JE,JX)

PW (JP)
Q (OS)
QLS
QRAD
RAT (JX)
RB (JP,2)
RC JP.2)
RD JP,2)
RE JP,2)
Common
Fl
Fl
F3
Fl
F3
Fl
Fl
F2
F2

Fl
HTL
HTL
Fl
F2
Fl
Description
Pressure, molecular weight product at wall.
Partial pressure of each species.
Log partial pressure of species at first
station.
Exponent on PM for wall flux term in mass and
energy balances.
Saved value of converged log partial pressure
of each species used during time step halving
rescue logic.
PP (I)*IC (I)
Exponent on PM for volumetric heat loss term
in energy balance.
Third body factor for each reaction.
Net stoichiometric product coefficient for
each species in each reaction subsequently
multiplied by CKIN (JE) for computational
convenience.
Partial pressure of each species at the wall.
Normalized wall heat loss or wall convective
transfer factor as tabulated against axial
location, SSS (JS). Multiplied by QL
(normalizing parameter) after reading.
Value looked up in Q (JS) table or radiation
flux calculated in subroutine RDFLX.
Radiation heat loss per unit value.
Maximum of PKP (JX) and PKR (JX). Basis of
ordering reactions.
Curve fit constants for enthalpy, entropy and
Cp of each species. See page 5-14. RB = F-j +
F2, RC = F3, RD = F4, RE = F5 and RF = Fg.
RF (JP,2
                                   9-8

-------
                           TABLE 1.  Continued
Variable
RH (JS)
RHS (JE2)
RML (JX, JS)
RMU (JE, JX)
RUU (JS)
SB (JP)
SS (JS)
SSS (JS)
T
TC (JP)
TCOE
Common
F4
Fl
F4
F2
EPRP
Fl
F4
HTL
Fl
Fl
EPRP
Description
Density at each station as output, predictor
value.
Right hand side of equations to be solved in
FLAME. After inversion these become solution.
Ratio of forwar to reverse rate of each
reaction at each station as output.
Stoichiometric coefficient of each reactant
species in each reaction.
Generated in EPROP as l/M-j, then modified in
ACEF to include other axial convection factors.
Entropy/R of each species at pressure (not
standard state). Later modified to be log K
of formation. p
Axial distance as calculated and output. Also
used to interpolate input data from prior
solution, in which case SS (JS) correspond to
normalized axial distance parameter.
Table of axial distances against which Q (JS)
are tabulated.
Temperature.
-HI (JP)/RT = -d log K /d log T.
Temperature coefficient on axial energy flux
TERM2


TERV2
Fl


Fl
THMU (JE1.JX)     F2
in flame energy equation.

Composite term used in wall flux calculation
developed in ACEF, and invariant in FLAME.

Composite term used in volumetric heat loss
calculation developed in ACEF, and invariant in
FLAME.  'ri

Third body efficiency of each species in each
kinetic reaction.  First subscript at IS + 1
yield efficiencies for general third body.
                                   9-9

-------
                           TABLE 1.  Concluded
  Variable
Common
                Description
TITLE

TL (JS)


TTT


TTV


TU (JP,2)



TW

TWL (JS)

UNIT (JQ,JQ)
VNU (JP,JE)
 F4

 F3


 Fl


 Fl


 Fl



 Fl

 F3

 Fl
 Fl
WM (JP)
WML (JS)
XALPE (JP)
XALPF (JP)
XX (JX)
LIN
F4
WANTS
WANTS
F2
80 character title of problem set.

Temperature array as output for each station
(predictor values).

Exponent on T for wall flux term in mass and
energy balances.

Exponent on T for volumetric heat loss term in
energy balance.

Temperature at which switch is made from low
temperature to high temperature thermodynamic
data curve fits (see page 5-14).

Wall temperature.

Not used.

Set of vectors used to rearrange FLAME coeffi-
cient matrix during introduction of kinetic
equations.  After inversion of matrix, appli-
cation of vectors in reverse order restores
inverse of non-rearranged matrix.  Also used
as on-diagonal matrix in corrector solution.

Stoichiometric coefficients for equilibrium
reactions.

Molecular weight of each species as input.

Molecular weight array as output for each
station (predictor values).

ALPE (JP) as read.

ALPF (JP) as read.

Saved values of FKF (JX) prior to pressure and
third body modifications.
                                   9-10

-------
                        TABLE 2.  LOCAL VARIABLES
   Variable
               Definition
ACEF
 ALD
 ALZISP
 API

 APR

 APRR
 BLANK
 BPR
 CPTW

 CTKN (JX)

 DA

 DAR (JQ,JS)

 DCL (JQ)
 DCR (JQ)
 DEN
 DIS'

 DIST

 DLS (JS)
 DMAX
Main Routine
Locally defined and used.
ALPHZ (IS + 1).
Input value for APR.  If nonzero, APR
set equal to API.
Parameter defined by Eq. 36, or as
described in card set 3.
Value of APR read from restart cards.
Holerith field of blanks.
BP value read from restart cards.
Value of Cp at wall conditions as
used in wall heat flux calculations.
Contribution of each reaction to
specific mass balance as output.
Predicted correction in APR based on
predictor logic.
In predictor logic, the set of vectors
representing the coefficients on APR
for each equation at each station.
Coefficients on ai. -j terms.
Coefficients on ain+-j terms.
Locally defined variable.
Axial distance used in look up of QLS
in Q (JS) vs. SSS (JS) table.
Used to generate SS (JS) for plug flow
reactor problems.
Nodal width of each station.
Damping parameter for corrector step.
                                   9-11

-------
                          TABLE 2.  Continued
  Variable                             Definition
DOTM                    Assigned m for flame problems.
DS (JS)                 Input axial step size.  In flame problems DS = a.
DTIL                    "D with definition implied by EQ. 8.
DUM, DUML,              Locally defined variables.
DUMMX, DUMR, DUMZ
EM12                    Equals Mn * nin Eq. 35.
                                nx 9 n
EM21                    Equals Mn n-1 in Eq. 35.
EM23                    Equals Mp n+1 in Eq. 35.
EM32                    Equals Mp+] n  in Eq. 35.
FACT                    Locally defined variable.
FCN (JE)                Convective flux into nodal volumes.
FFF                     Locally defined variable.
FIB                     Locally defined variable.
HDN                     Locally defined variable.
I                       Locally defined index.
IALF                    Input data flag, see page 5-2.
IAP                     Input data flag, see page 5-2.
IARG                    Subroutine argument indicating remaining seconds
                        in run.
ICT                     Input data flag, see page 5-2.
IEN                     Locally defined index.
IFV                     Input data flag, see page 5-3.
IH                      Input data flag, see page 5-8.
IJ                      Locally defined index.
                                  9-12

-------
                          TABLE 2.  Continued
  Variable
            Definition
IKAP
IKN
INA
INPCH

INS
IQ
ISS
IS2
I S3
IT
I TAB
ITC
IWSR
12, J, JJ
JQI
JQS
JQS2
K
KAP
KR77
K2
LL
LM1
Input data flag, see page 5-3.
Input data flag, see page 5-3.
Input data flag, see page 5-2.
Output data flag, nominally 1, set to 2 when
IARG < 20 or converged or last iteration.
Number of entries in Q (JS) vs. SSS (JS) table.
Locally defined flag to RERAY.
= IS + 2.
= IS + 2.
= IS + 3.
Iteration count in ACEF-
Absolute value of ICC.
Input data flag, see page 5-2.
Well stirred reactor flag.
Locally defined indexes.
Running index in local table look up.
Number of sectors in overlay set.
2*JQS
Locally defined index.
Input data flag, see page 5-3.
Locally saved value of KR7.
Locally defined index.
Locally defined index.
Locally defined index.
                                  9-13

-------
                          TABLE 2.  Continued
  Variable                             Definition
LSI                     Flag indicating status of NTRAN
M                       Locally defined index.
MCTT (JX)               Locally defined indexes.
MOOT                    Flag Indicating a flame problem with assigned
                        mass flowrate.
MM                      Locally defined index.
MZ                      Locally defined index.
NCTT                    Locally defined index.
NFH                     Input data flag, see page 5-4.
NIS                     Number of species in initial guess dataset, see
                        page 5-12.
NIT                     Number of corrector step iterations,see page 5-2.
NITM                    Locally defined Index.
NL                      Number of axial stations or well stirred reactor
                        solutions plus one.
NN                      Locally defined Index.
NOORV                   Diagnostic flag, inactive.
NRA (6)                 Names of radiating species.
NS                      Number of stations in initial guess data set,
                        see page 5-12.
NVL                      0
HZ                      Locally defined index.
PINT                    Saved Initial value of PM.
PMS                     Saved converged value of PM.
PPB (JS)                Table of pressures for assigned T and P
                        problems.
                                  9-14

-------
                          TABLE 2.  Continued
  Variable
               Definition
QL

R
RATIO
RTDD
RTDS

SADB, SAOB2

SCALE
SCMN

SM
SMP
SMRT (JE)

SMTT (JE)

SN
SNM
SPB
SPD

STEP

SUM
Input nomalizing flux (QL) or transfer coef-
ficient (Cj).  See page 5-7 or 5-8 respectively.
= 82.057, perfect gas constant
Locally defined interpolation variable.
Locally defined variable related to time.
Composite parameter for distance cal-
culation from transformed variables
(=ds/da).
Composite "parameter" for time, distance and
flame speed.
Damping parameter for corrector step.
Schmidt Number raised to m-n power as
used in wall flux calculations.
Locally defined summation of DS(L).
Locally defined summation variable.
Kinetic production term in nodal volume
as output.
Diffusive flux into a nodal volume
as output.
Locally defined summation of SS(L)
Locally defined interpolation variable.
P/BP
Flame speed as locally calculated and
output.
Factor used to reduce axial or time step
size if FLAME does not converge.
Locally defined summation variable.
                                  9-15

-------
                          TABLE 2.  Continued
  Variable
               Definition
ICON

TERM1, TERV1

TFLAME

TIME

TINT
TKAP

TSQ
TTDS

TTS

TVECA

VB, VC, VD

VMU1, VMU2
VMU12, VMU21,
VMU23, VMU32
VI
UMU1, WMU3
Right hand side of constraint equation
for evaluation APR in corrector step.
The station independent parameters used
in calculating the wall fluxes and volu-
metric heat loss, respectively.
Input assigned flame holder temperature
(see page 5-6).
Summation of APR*AP(L) ~ a time param-
eter equated to DTT(L) for KR6 = 1.
Initial temperature.
Concentration or temperature constraint
value input.  See page 5-6.
TW*TW
Composite parameter for time calculation  in
transformed coordinates (=dt/da)
Saved value of temperature from most
recent converged FLAME solution.
Coefficient on temperature when tempera-
ture used as grid constraint variable.
Locally defined variables used in thermo-
dynamic property calculations.
Variables y-., and u2 as defined by Eq. 5 for bulk
gas mixture.
Variables v-* as defined by EQ. 35 where
indices n-l,Jn and n+1 are indicated  by 1, 2  and
3, respectively.
Locally defined variable.
The variables u-i, and y~ as defined by
equations 5 and 25, respectively, as  evaluated
at the wall for the wall flux terms.
                                   9-16

-------
                          TABLE 2.  Continued
  Variable
               Definition
FLAME
Subroutine
ALPM
ALT
BE

BIG (JE)

BIGIE
BIGN (JE)

BIGPN, BIGPP
BUMP

BUST
CPTB

CPTW

DAMP

DNE
DNT

DOM
DUM, DUMB, DUM1,
DUM2, DUM3
EMAX
Equals log of PM.
Equals log of T.
Exponent on PM for kinetic terms for various
mass balance options.
Largest positive contribution to each mass
balance.  After kinetics package becomes largest
absolute 'contribution.
Locally defined variable.
Largest negative contribution to each mass
balance.
Locally defined variable
Factor to temporarily kick solution toward
equilibrium for convergence purposes.
Value assigned to BUMP
               .*
Local value of C  as used in wall convective
fluxes.         P
              >w
Wall value of C  as used in wall convective
fluxes.        p
Vactor used to scale down all corrections
developed for each iteration.
Number of reactants in a kinetic reaction.
Check sum to establish presence of third body
reactant.
Log of mole fraction of a species.
Locally defined variable.
Maximum correction in species partial pressure
on a given iteration
                                  9-17

-------
                          TABLE 2.  Continued
  Variable                             Definition
EMXP                    EMAX from prior iteration.
ESUM                    Locally defined variable.
FACT                    Locally defined factor used in restructuring
                        mass balance equation toward equilibrium form.
G                       Free energy of a species.
6N, GP                  Locally defined to avoid divide by zero.
                                       j,
HTB                     Local value of h as used in wall convective
                        fluxes.
I                       Locally defined index.
ICB                     Count of iterations with BUMP activated.
ICT                     Number of extra iterations after convergence test
                        satisfied.
II, IK, IP              Locally defined indices.
ISS                     Equals IS+2.
ITMX                    Maximum number of iterations allowed.
II, 12                  Lower and upper limit of equation indices to
                        which a given kinetic reaction will be  added.
J, JJ, Jl, K, Kl        Locally defined indices.
LL (JE)                 For the Kth mass balance, LL(K) = IK if the
                        kinetic reaction of rank IK (IK - 1 for fastest
                        reaction) is isolated into that mass balance.
                        Otherwise LL(K) = 0.
MM                      Locally defined index.
MX                      Limit on DO loop for bubble ordering scheme.
NUL                     = 0.
PLIM                    Maximum allowed change  in log partial pressures.
R                       Perfect gas constant, 1.9865.
                                  9-18

-------
                          TABLE 2.  Continued
  Variable
               Definition
RATIO
RRT
RT
SCMN
SUMD, SUMH, SUMHT,
SUMK, SUMR
TCPMT
TERM
TERM 3
TEST
TSQ
TST
TST1, TST2
VA, VB, VC, VD,
VE, VF
VLK
VMU1
VMU2
VQ
VI, V2
WATE
WJ
UMU1
WMU3
WQ
Local interpolation parameter.
Equals 1/RT.
Equals R*temperature.
Schmidt Number raised to m-n power (see Eq. 13)
Locally defined summation variables.
Locally defined product variable.
Locally defined wall flux variable.
Locally dfined wall flux variable.
Locally defined test variable.
T*T
Locally defined small number test variable.
Locally defined test variables.
Locally defined variables.
Log of kf (see Eq. 12).
Value of w.
Value of y2
Volumetric heat loss rate.
Locally defined variables
Locally defined weighing parameter.
Wall species flux term.
Value of u,, used in wall fluxes
Value of y3 used in wall fluxes
Wall heat flux term.
                                  9-19

-------
                          TABLE 2.  Continued
  Variable
               Definition
READIN
I
IEND
ISPECI
J
JMAX
XBP
XE, XF

OBTAIN
I
IDUM

IEND
I EOF
IHDG
ITEST1, ITEST2

J
Jl, J2
LNGTH
MATCH

NLNGTH
OK
Subroutine
Local index.
Flag indicating end of input species set.
Species name.
Local index.
Maximum number of species limit.  Equal to JP.
Diffusion factor.  Equal to BPA(J).
Species concentrations, first guess and initial
respectively.  Equal to ALPE(J) and ALPF(J)
respectively.
Subroutine
Local index.
Used in skipping over nonrelevant thermochemical
(T.C.) data files.
Flag which defines end of the data file.
flag indicating end of data file.
Used to skip over T.C. file title.
Used in matching species name to T.C. data file
names.
Local index.
Index for equivalenced species names.
Length of T.C. data files
Flag indicating match of species names and T.C.
file names.
Length of T.C. data files
Flag indicating T.C. data for unknown species
has been requested.
                                  9-20

-------
                          TABLE 2.  Continued
  Variable
               Definition
GETDAT
K
RA
ZZ

KINKIN
FX

I
I FLAG

II
ISW

JJ, Jl, J2, K
KIN
KNY
KOUT
L, M
MLET
NA, NB
NT, NTB
PSUM, RSUM
TB
Subroutine
Local index.
Heat of formation in curve fit data.
Used to print temperature bounds of curve fit
T.C. data.
Subroutine
Exponent on power of 10 part of coefficient a  in
equation 12.
Local index.
Stops program if there is a problem with kinetic
data.
Local index used in equivalencing.
Flag on whether a species name in a reaction can
be matched with the species input names.
Local index used in equivalencing.
Input unit designation.
Flag indicating equivalenced species name.
Output unit designation.
Local index.
Third body flag name.
Species name in reactions.
Name of individual third  body.
Used in reaction balance  check.
Third body efficiency.
                                  9-21

-------
                          TABLE 2.  Continued
  Variable
               Definition
EPROP
Subroutine
CPGS, CPG1


CPTILS, CPTIL1


EMI 2, EM21

I, J

KRS

KR6S

L

NL

RLB


RL1, RL2, RL1S
Ull, U12, U21, U22
U11S, U21S

VMU1, VMU12, VMU21,
MVU3, VMU6

RDFLX
DKPDT


FAC

II, 12, 13, J

PKCO, PKC02, PKH20
Gas specific heat at first station and at
previous station respectively.

Weighted gas specific heat at first station and
at previous station respectively.

Defined the same as in ACEF-

LOCAL index.

Save KR in KRS.

Save KR6 in KR6S.

Local index.

Last station.

Average of upstream and downstream Lewis number
parameter.

Reciprocal of Lewis number parameter at upstream
and downstream stations and first station
respectively.

Variable y-j as defined in Equation 5 for
various stations.

Variable M2 as defined in Equation 5 for
various stations.

Subroutine
Derivative of absorption coefficient with
respect to temperature.

Local variable as defined.

Local index.

Planck mean absorption coefficient for CO,
and \\  respectively.
                                  9-22

-------
                          TABLE 2.  Concluded
  Variable
               Definition
PPI1, PPI2, PPI3

RATIO
SIGMA
SUMKP
TEMP
Tl, T2, T3

XKPCO, XKPC09,
XKPH20
Partial pressure of C0?, H?0 and CO
respectively.
Interpolation  ratio.
Stefan-BoItzmann constant.
Composite absorption coefficient.
Temperature.
Derivative of absorption coefficient with
temperature.
Planck mean absorption coefficients in table
form
                                   9-23

-------
                                  SECTION 10
                            PROGRAM AND SUBROUTINES
       Brief descriptions of the PROF main program and subroutines are given
in this section.  The code consists of the main program, ACEF, and eight sub-
routines.
10.1   ACEF Main Program
       The main program, ACEF, has a number of functions and serves as the
driver for the chemistry solver routine.
       ACEF initializes some constants and reads a variety of input parameters,
Integral and nonintegral parameters, grid spacings and heat loss data are
read by ACEF.  Subroutines READIN, OBTAIN and KINKIN are called by ACEF to
read in initial species concentration, thermochemical and kinetic reaction
data respectively.  If needed, punched card first guess data is read by
ACEF.  Following this operation, the main program loop on grid solution
iterations is entered.  The EPROP subroutine is then called to calculate
energy and species equation parameters at each grid point.  These parameters
are held fixed during each iteration cycle.  In this loop, space or time
step quantities and diffusion terms are constructed.  The FLAME subroutine
is then called to calculate the change in concentrations due to chemical
kinetic reactions.  Following this, output quantities are set up and the
corrector step partial derivative matrix is constructed.  The RERAY subrou-
tine is then called to invert the corrector step matrix.  Predictor/corrector
step information is printed out and, for the last iteration or a converged
solution, summary information is printed.
                                    10-1

-------
10.2   READIN Subroutine
       This subroutine reads the species names, initial  and final  species
concentrations and diffusion factors.  If called for, this subroutine also
equivalences species names so that names other than those on the thermo-
chemical  data file can be used on the initial concentration or kinetic
reaction inputs.
10.3   OBTAIN Subroutine
       This subroutine scans either the tabular or curve fit thermochemical
data file for the species of interest.  Once the proper species thermochemical
data file is found, subroutine GETDAT is called to extract and store the data.
10.4   GETDAT Subroutine
       This subroutine extracts tabular or curve fit thermochemical data
from input/output unit 12 or 11 respectively and stores the data for use
during a calculation.
10.5   KINKIN Subroutine
       This subroutine reads in the kinetic reactions and their associated
rates.  It then developes the stoichiometric coefficients for the reactions
and checks to see if the reactions balance.  The stoichiometric coefficients
are applied in the FLAME subroutine.
10.6   EPROP Subroutine
       This subroutine develops the parameters which remain effectively con-
stant in the energy and species equations during a predictor/corrector step
iteration.  The FLAME subroutine is called by EPROP to determine thermo-
dynamic properties for a fixed composition and enthalpy.  These properties
                                     10-2

-------
are then used to generate composite parameters which are held fixed during
the predictor/corrector step iteration.
10.7   FLAME Subroutine
       This is the program's key subroutine which solves the species and
energy equations including the effects of chemical kinetics.  The routine
begins by setting up the individual species thermochemical  properties.   If
needed, the radiation heat loss subroutine, RDFLX, is then  called to determine
the gas mixture absorption coefficient.  This coefficient is used in establish-
ing radiative heat loss from the flame gases.  Utilizing current solution
estimates, errors and their derivatives with respect to the variables are
formed for the enthalpy, total pressure and species mass balance equations.
At this point, these equations include the effects of wall  heat loss but do
not include the effects of chemical kinetics.  Chemical kinetic reaction
contributions to the equations are constructed and ordered  from fast to slow.
These contributions are then factored into the equations making necessary
equation rearrangements to introduce the dominant reactions into only a
single mass balance equation.  The resulting equation errors are then checked
for convergence.  If convergence is not achieved the matrix of error deriva-
tives is inverted and multiplied by the errors to obtain the corrections to
the variables needed to drive the equation errors to zero.   If the correc-
tions exceed a certain multiple of the variables, all of the corrections are
uniformly damped so as not to overcorrect the variables.   Corrections  are
then made and the solution procedure cycles to the top of the subroutine to
repeat the above process until either a converged solution  is found or  the
allowed number of iterations is exceeded.
                                    10-3

-------
10.8   RDFLX Subroutine
       This subroutine uses correlations of Planck mean absorption coefficient
data for hLO, COp and CO to develop the gas mixture absorption coefficient.
This coefficient is used in the radiative heat loss model  applied in the
FLAME subroutine.
10.9   RERAY Subroutine
       This subroutine is a generalized matrix inversion routine which either
gives a set of solution vectors or the solution vectors plus the full  matrix
inversion.
                                    10-4

-------
                                SECTION 11

            PROGRAM SOURCE DECK LISTING AND SYSTEM REQUIREMENTS


       Listings of the PROF code main and subroutine Fortran V source decks

are presented in this section.  Also, sample problem run times and system

requirements are presented below.

Sample Problem Run Time

       Computation time depends, of course, on the problem being computed.

The times associated with each sample problem are given below.

       Sample Problem               Time (sec)

            7.1                    45   per iteration (roughly six iterations
                                        are need for convergence)
            7.2                    45
            7.3                    60
            7.4                     21  per individual  solution
            7.5                    50

       Tape Requirements

       Internal program assignments are as follows:

            Tape Unit 5:   Read
            Tape Unit 6:   Write
            Tape Unit 7:   Punch
            Tape Unit 10:  Unit number of NTRAN
            Tape Unit 11:  Curve fit thermocheraical data
            Tape Unit 12:  Tabular thermochemical data

       System Specifics
       The specific UNIVAC 1108 exec 8 items used by the program are:

       1.   TLEFT (IARG)
            TLEFT returns the number of system seconds (as IARG) left before
            a maximum time abort will occur.

       2.   NTRAN (10, sequence of operation)
            NTRAN is used for writing and reading binary information, con-
            tained in the ARHM array, onto a drum.  This operation of writing
            and reading onto a drum reduces the processor storage requirement
            which would be needed for the block tri-diagonal matrix solution
            procedure.
                                    11-1

-------
            NTRAN roughly, corresponds to BUFFERIN and BUFFEROUT which are
            present on Control Data Corporation systems.
       Storage Requirements
       At least 15355 words decimal storage are needed for instruction
and 31978 words decimal storage are needed for data.
                                    11-2

-------
                                            ACEF  - MAIN PROGRAM

 1.          PARAMETER JP=29,JF=2fl,JO=JE+2,JX=70iJS=30.JE1=JE+1,JE2=JE+?,JOlsJO
 2.         *+2,JSM=JS-l,JOQ=JO*JO
 3.    C     JXsNO. OF REACTIONS
 4.    C     JPsNO. OF SPECIES
 5.    C     JS=NO. OF STATIONS
 6.    C     JEsNO. OF CLEMENTS
 7 .          DIMENSION NRA(6)PPB(JS),OCLIJQ).OCR(JO)t SMTT(JE).HAA(JF2,1),PLS(J
 6.         *S)
 9.          DIMENSION TVEC
11.          COMMON/EPRP/RUU(JS),RMU(JS > t CHI(JS),At A(JO,JS)
12.         *.CPTIUHTCOEtTCOE
13.          COHHON/F/TITLE(20 >.RML(JX.JS),PML(JX t JS)t AX(JS)t WML(JS),RH(J
14.         *SHH
25.         t   ,TERM2,TERV2,ORAO,TTV,PPV,TTT.PPPFW(JP),CPWI(JPI.ALFWIJE),CHIW
26.         St  HTW,EXM.EXNIH
27.          COMMON/F2/ THMU( Jl i JX I ,PPX (JX ) ,RMU( JE JX ) ,PMU( JE  JX ) ,PRMU( JE JX I .
26.         *   PKPIJX)PKR(JX)PMR(JX)VFwIXET)  0"F  nifTMS fOfiAL PLAME  CPOF  sr.L'.'TIO.  ( r>(-

-------
 ?5.         *OF),///2tX,52HPRCGRAM DOCUMENTS  IN  THE  "PROF  CODE  USER'S  MANUAL'S
 56.         */ 26X.       U3HAEROTHERM/ACURCX  CORP  FINAL  REPORT  78-277        ,/
 "7.         *  3X.           20HPHONE <*15/9
-------
      112.
      113.
      Hi*.
      115.
      116.
      117.
      116.
      119.
      120.
      121.
      122.
      123.
      124.
      12E.
      126.
      127.
      126.
      129.
      130.
      131.
      1*2.
      133.
I
en
13.
136.
137.
136.
139.
140.
141.
142.
143.
144.
145.
14.
147.
146
149.
150.
l*il.
       153.
       15M.
       15.
       157.
       1S.
       160.
       If- 1.
       162.
     TERV1=1.0
     PPV=1.0
     TTV=0.
     IFCKR6.NE.2) 60 TO 409
     DO 406 1=1. NL
 408 API)=AP(I)*AP(II
     TERV1=1./P
     PPV=2.
     TTV=0.659
 409 WRITE(6.136> ML
 136 FORMAT(1HO10X14H SIGMA ( N I .N=l i , 1 3/ )
     WRITE(6,4l)(DS(I),I=l.NL)                                          RMK10057
  36 FORMATdHO  .34X.19H* GRID PARAMETERS  *// lOX.mH A(N)**2 .Nrl.,13/
    *)
  41 FORMAT ( 10x  10E10 .4/15X . 10E10./20x . 10F10 .4/25X. 10E10 .   1=1 tNL )
     READI5.412)  ( PPP ( I I . T = l .NL )                                        RMK10107
     URITEI6.415)
 <*15 FORMATdHO, 30X.33H*  ASSIGNED T  AND  P  DISTRIBUTION * //)
     WRITE (6,i13)  (TTR(I).  1=1. NL)                                     RMK10057
     WRITE (6. < SSS ( J )  J=l  INS 
      READ  (5.4121  (Q( J) . J=l . INS I
      WRITEI6.5005)  INS
      WRITE(6t5008>   INS
      00 5006 Jsl.INS
 5006 OIJ)=Q(J)*OL
      WRITE (6,501)  (0( J) , J=l . INS)
      WRITE(6,501)   t SSS ( J ) . J=l . INS >
 5008 FORMAT(15X13HSS(N),N=1.INS)
 5010 IF (ITAB.LT.4)  GO TO 5000
C             READ WALL TEMPERATURE AND RELATIVE MOLK  CONCENTRATIONS    RMK10057
      REAO(5.5002)  IH, TW.EXM.EXN
 5007 FORMAT (12X.19HWALL  HEAT LOSS DATA   I
      WRITE (6.5003)  IH,  TW                                              PMK10057
      WRITE (6,5012)  fXM.LXM
      TTT=0.329f*EXM
      PPP=1.*EXM
      TFRM1=U.*(TW**0.3?95DTIL/R)*EXM
      IF(KR6.NE.2) GO TO 5011

-------
165.     5011 IFMH.LE.l) GO TO 5000
170.          REAO(5,11)  (PW(J)J=1.IS)
171.          WRITE(6,5S10>                                                     RMK10107
172.     5510 FORHAT(10X,28HWALL SPECIES CONCENTRATIONS //)
173.          WRITE (6,5001) (PW(J),0=1IS)                                     RMK10107
171.     5004 FORMAT(10X,6E10.5/25X,8E10.5/10X,6E10.5)
175.     5002 FORMAT(I1,6X,5E10.5)
17.     5003 FORMAT(15X,15HREACTIVITY PAR=,121X,10HWALL TEMPstE10,5//)
177.     5012 FORMAT(15X,19HREYNOLOS EXPONENT =E10.5, 5X18HSCHMIOT EXPONENT =
176.         $El0.5//
17S.     5001 FORMAT(10X16HNO. OF  STATIONS:,IX 1HOLS=,E10.5 //)
IRQ.     5005 FORMAT(15X13HO(N)/QLSN=1   .131
Ifll.      20 FORMATU6I3)
182.      209 FORMAT(33X23H* INTEGRAL PARAMETERS *,//T1, 6HCOLUMN.T5U.6HCOl.UMN.
18*.         */T6t33H 3  NO. SPECIES CONSERVATION EOS. , T0 . IS. T56.31H 6  PROBLEM
184.         * TYPE AND ENERGY EG.,T90.13.//
lfl.         *,T618H 9  NO. OF SPECIES. TlO.T3T5&
1A6.         *T56,23H12  NO. AXTAL  GRID PTS.T90,I3//T6,32H15  MO. GRID SOLUTI
187.         *ON ITERATTONST10,I3,T5630H18  SOLUTION CYCLE CONTROL NO..T90.I3
Iflfl.         *//T6,30H2l  READ INITIAL MOLE FRACTION.T10,13.T56.31H21  READ NONI
189.         *NTEGRAL PARAMETERS,T90,I3.//.T6.33H27  THERMO DATA * HEAT LOSS MOO
190.         *EL .TOiI3T56.2lH30  CONSTRAINT SWITCH,T90.13.//.T6i21H33  READ K
191.         *INETIC DATA,TtO,I3,T56,3'*H36  CONSTRAINT APPLIED TO VARIABLE. T90,
192.         *I3.//tT6i3?0.          DO 3 J = 1, IS
2?1.          VNIKT, J) = 0.0
22?.        3 IFII .EU. J)  VNUII, J)  = 1.0
            ? COMTINUE
              IFCIS.F.O.MI GO TO M
              t)0 3 I

-------
2P6.       38 PPI(I)=1.F-10
2?7.       39 CONTINUE
226.    C
225.       13 IFIIH.EQ.O) GO TO 15
230.          IFIITC.GT.O) 60 TO 372
231.          VB=TW-3000.
232.          VC=CTW+3000.)/2.
233.          VD=TW*3000.
234.          TSO=TW*TW
23!.          00 371 I=ltN
236.          J=2
237.          IF(TU.LT.TU(Itl))J=l
236 .          CPWI(I)=RC(IJ)+T*RD(I.J)+RE(I.J)/TSP
239.      371 HI/FWII(
 271.          HTW=HTH+V1*HI(I)
 272.          CPTW=CPTW+V1*CPWI(I)
 272.          WfU3=WMU3+Vl
 274.       376  ALFW(I)=PU(I)/P^W
 275.          HTWsHTU/PMW
 276.           CPTW=CPTW/P1W
 277.           WWU1=WMU1/P
 276.           W1=VMU1/P*RP
 279.           VWU2=VHU2/tPBP)
                                njVPMw
                                           M **(F.XM-F:XNI

-------
00
23.          PPPsPPP-EXM/2.
264.    C             RFAD KINETIC DATA                                         RHK10057
           15 IFIIKN.GT.O) CALL KIMN
              IF(IKN.GT.O) KKsS
        C             IDENTIFY INOFCIFS ON RADIATION SPECIES                    RMK10057
        C             C02, H20, CO                                              RHK10057
              00 3402 1=1.3
         3402 NRS(I) = 0
              00 3401 J=1,N
              DO 3401 1=1.3
         3401 IF(NRA(I).FO.NAPA(J NRS(II=J
         3404 FORMATI5X, 315)
        C             NORMALIZE ALPF AND ALPF                                   RMK10057
              WML<1>=0.
              DUM s 0.                                                          RMK10057
              SMP a 0.                                                          RMK10057
              DO 3400 1=1.IS                                                    RMK10057
                 SMP = SMP + ALPF(I)                                            RMK10057
              WML(1)=WML(1> *ALPF11)WM(I)
                 DUM = DUM + ALPE(I)*WP(I)                                      RMK10057
         3400 CONTINUE                                                          RMK10057
              00 3500 1=1.IS                                                    RMK10057
              ALPF(I)=ALPF(I)/HfL(U
                 ALPE(I) = ALPE(I) / DUM                                        RKK1Q057
         3500 CONTINUE                                                          RMK10057
              UMLI1) = UML(1> / SMP                                             RMK10057
              DO 55 1=1.IS                                                      RMK10057
              CKINHI) = 0.
              ALPHI(I)=ALPF(I)
              ALA(I.1)=ALPHI(I)
           55 ALB(I.D=ALPHI(I )
              INPCH=1
              PM=P*WML(1)
              IFIKR6.NE.1) GO TO 59                                             RMK10107
              T=TTB<1>                                                          RMK10107
              P=PPB(1)                                                          RMK10107
           59 CONTINUE                                                          RMK10107
              PLNsALOG(P)
              HTCOE=0.
              TCOE=0.
              ALA(IS+2.1)=T
              TINT  = T                                                          RMK10057
              PINTsPM
              TL1) = T                                                         RMK10057
              OLS=0.
        C    ****CALL EPROP <11)  *****  WHICH CALCULATES PROPS AT FIRST STATION
              CALL  EPROP (1.  1)                                                 RPK10057
              DO 62  J=ISP.IS3
              ALPHZ(J)=0.
              ALA(J.])=ALPHI(J>
           62 ALB(Jil)=AlPHI(J)
              HH(l)=ALA(ISP.l)
              IF (IALF .FO. 0,
              l)EN=ML-l
              00 10  Isl.IS
              0010  L=2,NL
IBS.          FACT=L-1
206.
2A7.
268*
249.
290.
291.
292.
293.
294.
295.
296.
297,
296.
29S.
300.
301*
302.
303.
304.
30*.
306.
307.
306.
309.
310.
311.
312.
313.
314.
315.
316.
317.
316.
319.
320.
321.
322.
323.
324.
325.
3?6.
3?7.
326.
      330.
      331.
      332.
      332.
      334.
      315.
      336.
      3.17.
                                .IALF.FQ.21 r,n TO 60

-------
I
to
310.
341.
342.
342.
344.
3<45.
346.
3117.
SHE.
345.
3SO.
351.
352.
353.
34.
355.
356.
357.
356.
35S.
360.
361.
362.
363.
36M.
36S.
366.
367.
366.
 369.
 370.
 371.
 372.
 373.
 37M.
 375.
 376.
 377.
 376.
 379.
 3flO.
 Sfll.
 382.
 362.
 384.
 3P.
 3A6.
 3*7.
 3P6.
 369.
 390.
 391.
 392.
 392.
 394.
 395.
                10
                60
             C
             C
                                                  APR=APRR
2130



2150

2060

2160
210


10*3

2140
FACT=FACT/PEN
IF(IWSR.EO.l) FACT=1.
ALA(I,L)sALPE
IF(MOD GO TO 42
        READ DETAILED RESTART INFORMATION  AND INTERPOLATE
        IF NECESSARY
WR1TE<6,2140)
REAO<5,210) TINPT
WRITE6210 TINPT
REAO<520f0) NS tNlS t APRR tBPR
IF(APRR.6T.O. .AND. MOOT. EQ.O)
IF L=1 tNS )
WRITE(62130) NS
FORMAT
REAP (5, <*8)  ( ALB< ISP .L ) L=2.NS)
URITE(62150) NS
FORMflT(lH0.10X?lHENTHALPY , 1 = 1 , , 12 ,fH,N=l , , 12/1
                    Of 43 1=1,IS
                          b,2j?)    (ALA(I,L),L=1,NL)

-------
       397.      213 FORMAT(1HC8X,23HALPHA VALUES INPUT L=l,I3/
       39C.      212 FORMATUOXB(E10.5,2X)/15X.8(E10.5,2X)/20X,8
       407.          IFIKR6.NE.2)  NlT=l
       406.    C   BEGIN MAJOR  LOOP ON ITERATIONS
       409.     1328 DO 45   IT=l,NlT
       410.          IFCKR6.NE.2)  GO TO 33
       411.    C   ******************************
       412.    C     CALL TO EPROP CALCULATES  PROPERTIES FOR STATIONS 2 TO NL
                     CALL EPROP (2,ND
                   ******************************
       415.          IF(NFH.EQ.l)  TL(2)=TFLAMF
       416.          00 31  L=2,NL
       417.       31 RUU     425.          PMS=PM
0     426.          SAOB=SORT(APRAP<1)/BP*DTIL)
                     RTOS=RH(1)*TL(1)**1.659*SADB
                     TTOSsRH(1)*APR*AP(1)*RTDS/SADB
                     DIS=0.
       430.          SN=0.
       431.          SM=0.
       432.          001=0
       433.          H=HH41I
       434.          SS<1)=0.
       435.          OTT(1)=0.
       436.          IF(KR7.GE.2.AND.INPCH.E0.1)  WRITE(6,52> IS
       4J7.       S2 FORHAT(lHl,/30X,3flH*  CHEMISTRY SOLUTIONS AT GRID POINTS *//
       436.         *          3X.4HITER,2X,1HL4X.2HPM,11X,1HT,11X,10HPP(I),I=1,I2I
       439.          IF(INPCH.EO.l)  GO TO  3218
       440.          OUMsSORT(.172E-4/(APR*AP(l)*P*BP))
       441.          DO 5200  1=1,IS
       442.          SMRT(I)=0.
       443.     5200 FCN(I)=       ALA(I1)*OUM
       4it4.          WRITE(6,3217)     IT
       445.     3217 FORMAT(1H1,20X54H* MOLE  FLUXES  AT  KRID POINTS(MOLE/(CM2*S))  ITEPA
       446.         *TION   ,I2  2H  *//
       4^7.         20X,58HREACTION CREATlON/DIFFUSlOr  FLUX OUT/CONVECTIVE FLUX OUT
       4e.         *    ////)
       449.          \_sl
       450.          DLS(1)=0.
                     WRITE(6<3?14) L.DLS(l)
                     WRITE(6.3?IS)    (NAMA(J).MAMRIJI,J=lIS)
                                  (SrP7 t I ) , 1 = 1, is)

-------
      454.          WRlTE(6t501) (SMRT1 = 1IS I
      455.          WRITE(6i5nl) +DS(L-l)
      464.          IFIKR6.NE.1) GO TO 216                                             RMK10107
      465.          T=TTB(L)                                                           RMK10107
      466.          P=PPB(L)                                                           RMK10107
      467.          DTTtL>=DTT
      466.      218 CONTINUE
      469.          OLS=0.
      470.          SADB=SORT(APRAP(L)  /BP*DTILI
      471.          IF(ITAB.EQ.l.OR.ITAR.EO.S) GO TO 6001
      472.     6016 QLS=OL
      473.          IF(INS.EQ.l) GO TO 6001
      474.          IFIKR6.EQ.2) GO TO 6006
      475.          DIS=SS(L)
      476.          GO TO 6003
      477.     C      CALCULATE DISTANCE  FROM TRANSFORMED COORDINATE
      476.     6006 CONTINUE
      479.          DIS=DIS*IRTOS+RHL)*TLU)**1.659*SAOB)*OS*.5
_    4flO.     C     LOOK UP HEAT LOSS PARAMETER  AS  FUNCTION OF DISTANCE
7*    461.     6003 JOI=JOI+1
    462.          IF(JQI.GE.INS) GO TO 6004
-1    *83.          IFISSS(JQII.LT.DIS)  GO TO 6003
      484.          SNM=SSS
-------
511.          VNU12=-.5BfU/WML(L)
51*.          00  57  1=1,IS
516.          FFFsBP/BPAII)
517.          ALDENm=l.*RUUIL-l>*l.+EM2l)/FFF+VMUl2)+RUU(LI*l.+EM23)/
516.         *FFF+VMU32)
51S.          DUML=RUUCL-1)'* /FFF+VMU231
521.          ALO*-RUU{L>*1.+EM23)/FFF+VPU32)
5921          SNTT 
52.          OCR(I)SOUHR/ALPFN(I)
525.          DCLmsll.+DUMU/ALOENCI)
526.          ALPHI(I)sALBsALPHJ(ISP)+DCL(I)*ALB(I,L-l)+DCR(I)*ALA(I,L+l)
SHU.       28 ALPHZIISP)sALPHI(ISP)
5H.          ALZISPsALPHKlSP)
5146.          ALDEN(ISP)=HON
5
-------
                   006H5 J=LIS
     569.          ALA=OTT(L-lI*nS(L-l)*(AP(L-l)*RH(L-l
      621.         *)+AP(LRHH.M*APR*t.S
      6?2.          IF(IWSR.EO.l) OTT(LI=APMAP(Ll*RH(l
      623.          HH(L)=ALPHI(ISP)

-------
6?.          TFIKR7.GE.2.AND.INPCH.EO.il
626.         *WRITE(6,206)ITER.L.PN,T(PP
697.          IFIKR6.EQ.2.ANO.NODRV.EQ.O) GO TO 523
626.          DO 322 1=1,NEC
6*9.          ALB(l,L>=ALPHI(I>
630.          ALPHHI)=ALA(I.L)
631.      322 ALA(I,L)=ALB(IL>
632.          IF*APR*AP(L)*RTDD
640.          OTTIL)aDTT=0.
646.          00 3210 J=1,HT
647.     3210 SHRT(I)=SMRT*OUM
6SO.          WRITE(6i3214)  L.OLS(L)
651.     3214 FORMAT(lHn4Xl2HSTATION N0.=  .I2.6X,12HNODAL UIDTHs .E10.5.1X,4H
692.         */15Xi8(2X,2A4.2X)
63!.         */20X8(2Xt2A42X)/25X8(2X.2A42X>)
656.          WRITE (6,501 MSMRT( I ).!=!, IS)
657.          DO 3215  1=1,IS
656.     3215 SMTT(I)ssTTCI)*DUM
659.          WRITEI6.50D  (SMTT(I),1=1,IS)
660.          WRITEC6t50l)  (FCNII),1=1IS)
661.     3212 CONTINUE
6*2.          IF(NODRV.NE.O) 60 TO  27
663.    C
664.    C      *** GENERATE  D(ALPII/D(ALPZ(K)) **
665.    C
666.    C    FIX INVERSE OF A FOR REARRANGEMENTS^ KINETICS PACKAGE
667.    C
666.          ISS=IS+2
669.          DO 106  1=1,ISS
670.          DO 106  Jsl,ISS
671.      106 AA(I,J)=A(I,J)
672.          MZ=MT
67*.          DO 110  NH=1,HT
674.          HsMAIHZ)
675.          IFIMP|N).GT.fl) f-0 TO  110
676.          K=-fPM)
677.          DO 109  J=1,IS
676.          IF(UNITIJ,K).EQ.O.) GO TO 109
679.          DO 108  1=1,ISS
680.      10*) AA(IK+?)=AA(IK+2)-liNlT( J,K)*AA( I.J+2)
          109 CONTINUE

-------
62.      HO fZ=MZ-l
663.    C
66*DljM
695.          00 112 J=liIS
696.          OUM=ALPHI(J)-ALPHZ(J)
697.          IF(nOOT.E0.1IDUH=DUM-ALPHZj)+(ALB(J.L-1I-ALPHI(Jl*d.-ALOENCj)I)/
696.         *ALOEN(JJ
699.          OUMsOUM/APR
700.          00 112  1=1.ISS
701.      112 AAd.2l=AAd.2>+AAdtJ-2)DUM
702.      lit CONTINUE
705.     C
70l.     C    --  SUM PARTIAL  PRESSURE  DERIVlTlVES TO GET  ALP OERIVITIVES  	
70S.     C
706.          NZ=1-IFV
707.          00 125 K=MZiISP                                                    RMK10057
708.          K2=K+2
709.          IF(K.EQ.ISP) K2=l
710.          DAA1IS3.K)  =-pM(  ALPHI(IS3)*A A(2,K2) - T*CPTILAA(1,K?I  )
711.          DAA(ISPK)=-PM*(ALPHI(ISP>*AA2.K2I-T*CP6*AA(1.K2) )
712.          SUMsO.
713.          00 115  1=1.IS
7m.          OUH=PP(I)*AA
-------
70.
7H.
7<2.
7,
7H.
7H5.
76.
7U7.
7i6.
7*5.
750.
751.
752.
752.
75.
755.
756.
757.
75C.
75S.
760.
761.
762.
762.
76M.
765.
766.
767.
766.
769.
770.
771.
772.
775.
7714.
775.
776.
777.
776.
779.
7flO.
7ftl.
7A2.
7AJ .
7AM.
7A.
766.
7A7.
7flfi.
7A9.
70.
791.
79?.
79?.
7q".
DO 126 1=1, NEO
12 = I + 2
IF (I .GE. ISP) 12 = 1
TVECII) = AAI1.I2) * DCL(I)
TVECRII) s AAI1,I2) * DCRII)
IF 1 1 .LE. ISP ) TCONsTCON+AA (1,12) * ALPHZ 1 1 1
126 CONTINUE
C
C ***SET UP RHS OF LINEAR EQUATION****
C
127 00 130 1=1, NEO
OAA(I,IS2) = DAA(I.ISP)
DAAII.IS3I = DAA(I.ISP)
ALBII.L) = ALPHIII)
ALPHI(I)=ALAIfL)
ALA(I,L)=ALR(I,L)
130 OARII,L)=nAA(INUL)
00 136 0=1, NEO
DUMRsDCRIJ)
OUMLsDCLlJ)
132 00 139 1=1, NEO
IF IJ .LE. ISP) ALA(I.L) s ALA(I.L)  ALPHZIJ) *
C
C
C
C SET UP DIAGONAL AND LEFT HAND MATRIX ****
C
AA(IJ)=-nUML*DAA(I,J)
UNIT(I,J)=0.
IFIL.NE.ND DAA(I,J)s-OUMR*OAA(I,J)
IFIL.EQ.2) ARHM|I,J)=nAA(I,J)
C
C ***** FOLD IN LEFT HAND MATRIX ****
C
IFIIFV.EQ.1)OAR(I,L)=DAR(I,L)-AA(I,J)*DAR(J,L-1)
139 ALA(I,L)=ALA(IL)-AA(I,J)*ALA(J,L-1)
I3fl UNIT(J,J)=1.0
IFIL.EQ.2) GO TO 35
CALL NTRAN(10,22)
IFILST.LT.O) STOP NTRANM
DO 1<2 J=1,NEO
ARHMIJ,NUL)=ALA|J,L)
ARHM(J,NUL-1)=DAR(JL)
00 1H2 IJsl.NEQ
IFIMDOT.EO.l)
*DAR(IJ,L-1)=DAR(IJL-1)-KALPHI(J)-AL8(J,L) )*ARHM(
DO 140 1=1, NEO
140 UMTII,J)=UMIT(I,J)-AA(I,IJ)*ARHM(IJ,J)
1*2 IFIL.NE.NL) APHMI IJ, J)=DAA( IJ, J)
C
C ***** INVERT AND MULTIPY DIAGONAL PY RIGHT HAND
C
10=0
UKl*MC*Ox1  t C \l
njnjwnir u* *  i r v
IFtL.EH.ML) NM=J+IFV





















DAA(I,J)























IJ,J)/APR




MATRIX AND



      RMK10057
      RMK10057
      RMK10057
      RMK10057

      RMK10057
      RMK10057
      RMK10057
      RHK100S7
RHS

-------
     797.          CALL PERAr(NEO.(lNIT.n.ARHf"(l.N7) .NN.O.IQ)
     746.          00 34 J=1,NEQ
     79?.          ALA(J.L>=ARHM(J,NUL)
     800.       34 QAP(J,L)sARHM(J,MUL-l)
     80J.       35 IF(L.LT.NL-l) CALL NTRANC10.1JOO.ARHM.LST>
     802.       27 CONTINUE
     803.    C  -FND OF MAJOR LOOP ON STATIONS
     804.          IF(KR6.NE.2) GO TO 153
     805.          JF(NODRV.ME.O) GO TO 153
     806.          CALL NTRAN(10.6,-JQS)
     807.    C
     80*.    C    )  FOLD RIGHT HAND MATRIX  INTO ALA
     805.    C
     810.          L s NL
     Ml.          00  150   LL  = 3, NL
     812.          L=L-1
     813.          IF(L.GE.NL-I) GO TO  148
     814.          CALL NTRAN(10,2,JOO,ARHM,LST)
     8l.          CALL NTRANU0.22)
     816.       '   CALL NTRAN(10,6,-JQS2)
     817.          IF(LST.LT.O)  STOP NTRANR
     816.       148 00  150  1=1,NEO
     M5.          DO  150  J =  l.NEO
     820.           IFjIFV.EO.lt  DAR5.           OAsO.
     826.           IFIIFV.EQ.O)  GO TO  153
     827.           IF(IKAP.NE.O) Go  TO  154
     826.           L=KAP
     825.           OENsTVECA
     8*0.           00  151 1=1.NEO
      831.           TCONsTCON-TVECR(I)*AL A(I,L+l-TVEC(11*ALA(I.L-l>
     832.       131  OEN=OEN+TVECR(I)OAR(1,L+1)+TVEC(I)*OAR(I,L-1)
      833.           DA.STCON/OEN
      ?4.           GO  TO  155
      815.       154  nA=(TKAP-ALA(!KAP,KAP))/OAR (TL URITE(6<404)  NAMA(I).NAMH(I
      fl0.
                    W^ITF(6.nl )  (AlP( I , Jl . Js

-------
      A
      874.      160 CONTINUE
      875.          IF (OMAX.LE.l.)  60 TO 175
      876.          SCALEsl./OMAX
      877.          no 170  L= 2.NL
      878.          DO 170 I = ItNEC
      79.      170 ALA(TtL) = ALB(ItL) * SCALE*(ALA(I.L)-ALB(I,L))
-    8AO.      175 CONTINUE
7*    881.          WRITEJ6.1UOO) APR,DA,OUMMX.SCALE
-^    882.     IfOO FORMATdHO.lSX.HHAPRziElO.S.tXiSHDAPHr.ElO.SttX.lfeHMAX  ALPHA  ERROR
00    ana.         *= IEIO.S.UX.SHOAMPS.EIO.S   )
      88M.          DUM=1.+SCALE*DA/APR
      an*.          APR=APR*SCALE*DA
      886.          IF(HDOT.EO.O) 60 TO 177
      87.          BPaBP/OUM
      8A6.          DO 176 1=1IS
      889.      176 BPAII)sBPA(II/Dun
      890.      177 CONTINUE
      891.          SPDsSORT(.172E-U/(P*APH*AP C1)*BP)I/RH(1)
      892.      110 FORHAT(lHOtlOXtl6HFLAME SPEED PAR= tElO.St10Xt12HFLAME  SPEED=E10.
      893.         *5t2X.6HCM/SEC///>
      894.     1401 FORMATlH0.9X,20HRRln COORDINATES'CM>   ,/)
      B9E.          IF(IARG.LT.IO)  60 TO 301
      896.          IFIINPCH.EQ.1.AND.KR6.GE.2) 60 TO 1220
      897.      522 WRITEI6.500) IT.NL
      896.      500 FORMAT(lH1//30Xt3

-------
911.      603 FORMAT(lHOt8Xi9HTIME(SEC)/
912.          WRITE(6,502)
913.      502 FORMAT(1HO,8X.16HFNTHALPY(CAL/GM)/)
914.          WRITE(6t50l)  (HH(J)tJ=l,NL)
915.          WRITE6t503)
916.      503 FORMAT(lHOflX.l4HTEMPERATURE
916.          WRITE<6.50)
919.      SOU FORMAT(1H0.8X15HDENSITY(GM/CM3)/)
920.          WRTTEC6.501)    (AX(J).J=l,NL)
932.          IFIKR7.EQ.O)  60  TO 1220
933.          WRITE(6t5o9  MT
934.      509 FORMATUH1/20X.56H* NET FORWARD KINETIC PRODUCTION RATFS(MOLE/(CC*
935.          1SECM  FOR   14 t2X. 11HREACTIONS * ///I
93.          00510   1=1.MT
937.          WRITE<6.5ll)  I
936.      511 FORMAT(9X,15HREACTION  NUMBER,IU )
 939.       510 WRITE<6.501)(PML(I.J).J=1.NL)
 9UO.          WRITEI6.512I  MT
 9U1.       512 FOPMAT(1H1/20XS9H* RATIO OF FORWARD TO BACKWARD KINETIC PRODUCTin
 92.          *N RATES FOR . I .2X. IIHREACUONS *  ///>
 9.          00513  isl.MT
 91M.           URITE(6,5ll|  I
 94.       513 WRITE16.501I  (RML( I . J) . J=l .NL >
 9i6.           WRITE(690R)
 97.       908 FORMAT(1H1/20X85H* KINETIC CONTRIBUTIONS TO INDIVIDUAL SPECIESCMO
 9H6.          LE/(CC*SEC)(  REACTION/CONTRIBUTION  *      )
               00907  JLS2.NL
               WRITE(6910>  JL
 951.       910 FORMAT(1HO,10X10H6RID POINT  , I")
 952*           00904  jsl.NEQ
 952.           NCTTsO
 954.           D090S   JJsl.MT
 95".           IF(RMU(J.JJ).EO.O..AMO.PMUIJ.JJ).EO.O. ) GO TO 905
 956.           NCTTaNCTT+1
 957.           CTKN(NCTT) = (PMU( J. JJ)-RMU< J. JJ) )*Pf"L (JJ.JL)
 956.           MCTTCNCTT)=JJ
 955.       90S CONTINUE
 96C.           TF(NCTT.EO.O) GO TO 904
 9AJ.           WRITE(6,906) NAMA(J>,NAMR(J,(MCTT(JJ),CTKN(JJ,JJ=1,NCTT)
 962.       906 FORMAT(10X.2A4.f
-------
       9*8.           IF IINPCH.rQ.2)  60  TO  47
       96$.           NITMsIT+l
       970.           IF(NODRV.ME.O)  DMAX=1.
       971.           IF
i      976.           PUNCH 1800,   < A|_A< ISP.L) ,L=2,NU
O     979.     1800  FORMATUOE8.3)
       980.           DO 16 1=1,IS
       981.        16  PUNCH 16,   (ALA(I,L),L=2NL  )
       902,        51  IFIINA.6T.3I  GO TO 53
       983.       301  STOP
       984.           END

-------
                                                              EPROP-ROUTINE
ro
 1.           SUBROUTINE  EPROP (L1.L2)
 2.           PARAMETER JP=29,JE=28,JQ=JE-2,JX=70,JS=30iJEl=JE+1,JE2xJE+2JOlsJO
 3.          *+2.JSMsJS-lJOO=JQ*jg
 4.     C     JX=NO. OF REACTIONS
 5.     C     JPsNfl. OF SPECIES
 6.     C     JS=NO. OF STATIONS
 7.     C     JEsNO. OF ELEMENTS
 6            COMHON/EPRP/RUU(JS).BMU(JS)CHI(JS)t ALA(JOiJSI
 5.          *tCPTIL.HTCOE.TCOE
10.           COMHON/F*/TlTLE(20).RML(jX.jS).PML(jX.JS).AX(JS)tWML(jS).RH(J
11.          *S).HH(JS),SS(JS).OTT tALPHZtJO)tFLUX(JO)tPPI(JP)tPPS(JP)i
13.              ALB < jo t js) TL < js).TWL < js,AP js >.AA cJEZ < JE21.QUO < JQ)DUMB(joi,
m.              ARHM(JOtJQ)BPA PP < JP >PLP(JP)HI(JPIt SB IJP >PPTC(JP)HOS(JPIt
18.              TC(JP).CPF(JP)iNAMA(JP)iNAMB(JP>.CPG,TW.HBC.PM.T,P.KR.KR6.KR7.
IS.              N,IStISPNEO,MT.CKIN(JO),H,PLN,ITER,ICON,IB,L,ICCtNFHS
20 .          *NRS(3)DOROT t OQROP(3),HRF(JP),WM(JP),
22.         S   KNYtIQV(16f3.          U12=U12*ALA(J,L)/BPA(J)
 ^^.          U22=U22*AUA(JL)*WM(J*BPA(J>
 IS.         2 WML(L)=WML(D*ALA(J.L)
 46.          UHL(L)sl./UML(L)
 47.          PM=P*UMLL
 46.          U12=U12BP*WML
 49.          U22=U22/BP*WML(L)
 50.           IFU12,U22,WML(L)
 SI.           IF(L.NE.l)   RO TO  11
 i2.          KH6=1
 52.           GO  TO 12
 5M.        11  IF(KR6S.Nr.3)  GO TO 4

-------
 55.          H=ALA(ISP.L)
 96.          T=AMAXKT,ALA(IS+2.L
 57.       12 00 3  J=1,IS
 56.          ALPHKJ)=AMAXKALA(J.L),1.E-30)
 5S.        3 PLP(J)=AL06ALPHHJ*PM
 60.    C   ****************************i*********
 61.    C   ******************************
 62.          CALL FLAME
 62.    C   ft***************************************
 6M*    C   ****************************************
 65.          IF(ICON.EO.O) 60 TO 7
 66.          WRITE(69>
 67.          STOP
 68.        9 FORMAT(23H BAD CHEMISTRY IN EPROP   I
 6S.        7 CONTINUE
 70.          RH
 71.          TL(LsT
 72.          DO 13   J=ISP,IS3
 73.       13 ALA(JtL)sALPHKJ)
 7q.          IF(KR6S.NE.3) GO TO 8
 79.          VMU3=0.
 76.          00 7001 1=1.IS                                                    RHK10107
 77.          VMU3 s VHU3 +ALA(IiL)*BPA(I)
 76.     7001 CONTINUE
 75.          VMU3=VMU3/BP
 60.          RL2=1,9865*.29*VMU3
 81.        8 IF(L.NE.l)   60 TO -WML(L))/WMLfL)*.5
 96.          EM21=-EM12*WML(L)/WML(L-1)
 97.          RLB=(RL2+RLl)/2.
 98.          CHI(L-l)::RLB-0.5*(CPTIL*EM21+CPG*VMU12tCPTILl*EMl2+CPGl*VMU2l)
 99.          RL1SRL2
100.          CPGlsCPG
101.          CPTILlsCPTIL
102.       10 Ull=Ul2
103.          U2l=U22
10M.        1 CONTINUE
105.          NL=L2
106.          RUU(1)=0.
107.          RUU(NL)=0.
108.          CHI(NL)=0.
10S.          BMU(NL)=0.
110.          WMLNL+1)=1.
^^1.        & KRfe=HIMO(KRfeS.2)

-------
112.          KRsKRS
113.          RETURN
IIM.          END

-------
                                            FLAME-ROUTINE

 1.          SUBROUTINE FLAME
 2.          PARAMETER JP=29,JE=2fl,JQ=JE+2,JX=70,JS=30.JEl=JE+l.JE2=JE+?.JQ1=JQ
 3.         *+2
 4.          DIMENSION RIG(JE).LL(JE)
 5.          DIMENSION PKPEIJXJtPKRF(JX)
 6.          DIMENSION BIGN(JE)
 7.          COMMON/EPRP/RUU< JS)t PMU < JS)t CHI< JS).AL A < JO,JS)
 8.         *,CPTIL.HTCOE.TCOE
 9 t          COMNON/F3/ALPF(JO)t ALPE(JO).ALPH2(JO IFLUX(JO).PPI(JP),PPS(JP)t
10*         *   ALB(JOJSTLIJS),TWL< JS)* AP < JS),AA < JE2 JE2),DUO < J9).DUMP < JO),
11.         *  ARHM(JQtJQ) tBPA(JQ) tCKIM(JQ)
12 .          COMMON/F1/RHS < JE2 )  A (JE2  JE2 ) t E I JP I  ALPHI t JO). UN IT (.JO, JO) ,
13.         *   VNUtRniJP,2>,RC.RD(JP,2)fRE(JP.2).RFfJPt2).
111.         *   TU(JPi2iPPJP) iPLP(JP) iHUJP) tSH(JP)PPTC(JP)HOS(JP).
!.         *   TC(JP).CPF(JP),NAMA.NAMB(JP),CPG.TWtHBC.PH.T,PtKR,KR6.KR7,
16.         *   N.ISISPNEO,MTiCKIN(JQ)H.PLN,ITERICON.IB.LtICC.NFHS
17.         *,NRS|3),OORDT,OQRDP<3).BP.PMW,FT,PW(JP)
1C.            tTERM2,TERV2.0RAD,.TTVtPPVtTTTiHpp,FW( JP) iCPWK JP) ,ALFW( JE) .CHIW
IS.         S  HTW.EXM.EXNtlH
?0.          COHMON/F2/ THU JF.l  JX ) PPX (JX) tRMU< JE  JX ) P*U( JE . JX ) tPRFIUI JE . JX ) *
21.         *   PKP(JX)tPKR(JX)tPMR(jX)tXX(JX)DKPT(JX)tFKFIJX)tAFF(JX)t
22.         *   EXK(JX)iEAK(JX)tRAT(JX)
23.         *  HPJX),HA(JX)
2l.          COMMON /LIN/ CPTIJP50I. HT , 10X*HVKT=5E12 .4 )
32.      202 FORMAT(<*H1 P=E12 .* , lOX . 2HH=E1? .1,10X"*HVKT=5E12 .t)
33.          DO 3 J=1.N
3<.          PLPJ)=AHAX1(PLP(J),-UO. I
3.        3 PP(J)=EXP(PLPJ))
36.          ICB=0
37.          RUST=100.
*fl.          DAHPrl.O
39.       11 ITERsl
40.    C     ICT IS NUMBER OF ITERATIONS AFTER CONVERGENCE  BEFORE RETURM,
n.    c     ITMX is MAXIMUM NUMBER OF ITERATIONS
u?.          ICT=O
3.          ITMX=50
U4.          IMXPsl
45.          EMXP=1.E*10
U6.          PLIM=2.3025851
47.    C
46.    C
49.    C
50.       30 CONTINUE
SI,          IF(ICC.GT.O) GO TO 806
52.    C     JANAF THEBMQCHEPICAL OATA SET
52.    C     EVALUATE SPECIE STANDARD STATF FREE ENtRGY AT  PARTIAL  PRESSURF
i.    C     AND SYSTEM

-------
                    55.          CPG=0.
                    56.          VA=ALOG(T/3000.)/1.9fl65
                    57.          VP=T-3000.
                    56.          VC=(T+3000.)/2.
                    55.          VD=T*3000.
                    60.          VE=VC/
-------
                                      FLAME

       112.           WRTTr<6.800)ALPHHI I
       112.       80.1  URITt<6.800)  *PP(I)*(J.+DUM*BPAUM
       130.           SUMH=SUMH4-HOS
       131.        7  CONTINUE
       132.           CPTIL=CPTIL/8P
       133.    C	  CP6 AND  CPTIL  ARE  DIVIDED  BY  PM JUST BEFORE RETURN TO ACEF
       13M.           TCPMT=TCOE*PM*T
       1.^5.           Altl) = (CP6-fHTCOE*CPTIL)*T + TCPMT
   ;    136.           A1.2)=-PM*H*TCPHT
_,     137.           RHSd )=PM*H-SUMH-TCPHT
"-    136.        6  RHS(2)=P-SUMP
rlj     139.    C
CT>     io.    c      COMPUTE ERRORS
       1<41.           DO 111  1 = 1. IS
                      DUMrpn*ALPHI  ft (11 + 2. i+? >=n .

-------
     161.           Ad + 2.I+2>=PPd)
     170.        It RHSd+2)=Ed>
     171.           IF(ISP.GT.N) GO TO 175
     172.           00 8 I=ISPN
     172.           A
     175.           A(2,ll=A(2,l)-PPTCd
     176.         6 CONTINUE 
     177.           A<2.2)=0.
     176.           DO 120 1=1, IS
     179.           DO 120 J=TSP,N
     ISO.   '    120 Ad + 2U=Ad+2l)-VNU=A( II+2. 1 + 2)*PP( JJI*VNU( JJi 1 1 )*VMU( JJ, I
     IPS.          DO 9 J=ISP,N
     190.          RHS(l)=RHs(U-HoSD*E(I)
     191.          PPTC(I)=PPCU*E
      209.       176 A(1,I+2)=A(1.I*?)+OUM*DORDP( J)
      210.           A(ltl>=A(l,l)+Dul*DQRDT
      211.           VOrQRAD
      212.     C     INPUT BULK HEAT LOSS
      213.       171 IFdABSIICCI .E0.2) VO=VO + ULS
      21M.           VQ=VO*DUM
      215.           RHS(l)=RHSd)-VO
      216.           Ad.l )=A< 1 ,1 )+VC*TTV
      217.           A(l,2)=A(l,2)*VO*PPtf
      216.     C     CONVECTIVE HEAT LOSS MODEL
      21S.       10 IFdH-1) 188,182,184
      2?0.     C     NOW-REACTIVE WALL
      221.       182 VMU2=0.
      222.           VMU1=0.
      2?3.           WMIJ1 = 0.
      2?5.          rPTW=0.

-------
      226.           00  183  1=1, N
      227.           VMU1=VMU1+PP/FW(I)
      231.           CPTWsCPTW+VKCPWKH
      232.       1*3  WHU3=WHU3+V1
      23S.           CPTW=CPTW/PM
      234.           WMU1=WMU1/P
      235.           VHUlaVNUl/P*RP
      236.           VMU2=VMU2/(P*BP)
      237.           CHIW=1.9865*.29WHU3/PM
      2*6.           SCMN=(VMU2*P/(PM*1.344*VNU1) )**-WC
      23.           A(l,l)sAlU+TTT*WO*TERM*T
      244.           A(l,2)=A(l2)-fPPP*WO
      24.           GO  TO 188
      246.       184  TERM=TERM2*T**TTT*PM**PPP
      247.           00  185  1 = 1, IS
      24C.           DUMSTERH/ALDEN(I)/FW(I>
      249.           DUMl=OUMPPm/PM
      250.           WJ=DUM1-DUMALFW(D
      251.           RHS(I+2)=RHS(I*2)-WJ
_,    252.           RIG(I)=AMAX1(BIG(I).-WJ)
-    253.           BIGN(I)=AMIN1(BI6N(I),-WJ)
'     254.           ACI+2.1)=AI*21)+WJ*TTT
00    255.           A(I+2.2)=A(I*2,2)+WJ*PPP-DUH1
      256.       185  A(I*2,I+2)=A(I*2.I*2)+OUM1
      257.           IFIIH.EQ.3)  GO TO  188
      256.           DUH = TERH/ALDEN(ISP)
      259.           HTB=0.
      260.           CPTBsO.
      261.           00  186  1=1. N
      262.           V1=PP(I)/(FW(I)*PH)
      263.           V2=V1*HI(I)
      264.           A(1.I*2)=A(1.I*2)+V2*OUM
      265.           HTB=HT8+V2
      266.       186  CPTB=CPTR+Vl*CPF(r)
      2fi7.           WO=DUM*(HTB-HTW+CHIW(T-TW) )
      266.           RHSU )=RHS<1-WQ
      26S.           A<1,1)=A(1,1+HO*TTT+DUH*(CHIW+CPTB)*T
      270 .           A ( 1 , 2 )=A ( 1 ,2 ) +WQ*PPP-OUK*HTB
      271 t       188  CONTINUE
      272.           IF  (KR7 .LE. 3) GO  TO 508
      273.           URITE(6>502)
      274.           D0501 1=1, ISS
      27?.       501  WRITE(6,500)  ( ( A ( T , J ) . J=l , ISS I .  RHS(I))
      276.       500  FORMAT! lX,12ri0.4/(2x , 12F10.4 ) )
      277.       502  FORMAT(1X,20HA(I,JIRMS( I) .HF.FORE)
      276.           WRITE(6.492)  (RIG ( I ) . 1=1 . IS )
      279.         . (PIGNI I ) i 1 = 1 ,1? )
                    FORHAT(14H  HIT, ( J ) , 1 = 1 . IS  miin.1)
      ?.2.     C      ^FGINMING OF  KINETICS  PACKiU,F

-------
23.      506 IF(KR-2) 390.310,255
24.      255 IF(KR-5I 334.333,334
285.      333 DO 332 Msl.MT
286.          HA(M)sH
287.          DNTsTHMUdSP.M)
266.          ONE=0.
269.          IFIKR6.EQ.1) ONE=1.
290.          D0336 1=1,IS
291.          ONE=nNE-RMU(I,H)
292.      336 ONT=DNT+THMU(IM
293.          IFtDNT.GT.O.) DNE=ONE-1.
294.          FKF(M>rFKF(M)+DNE*4.4n771fl7
29.          EXK(M)=EXK(M)+ONE
296.          IF(KR6.ME.2) GO TO 332
297.          FKF+0.659
299.      332 XX(M)=FKF(M)
300.          KR=4
301.      334 ALPM=ALOG(PM)
302.          BE=0.
303.          IF  (KR6.E8.0) BE=1.0
304.          IF  (KR6.E0.2) BE=2.0
30E.          DO  335  M=1,MT
306.          FKF(M)=XX(M)+BE*ALPM
307.          PPX(M)=THI*U( ISP,M)*P
306.          00  337  1=1.IS
309.       337 PPX(H)=PPX(M)+PP(D*THMUI.M>
310.          IF  (PPX(M)  .LE.  0.) GO  TO 335
 311.          FKF(M)=FKF(M)+ALOG(PPX(M) )
 312.          IF(NFHS.E0.2) FKF(M)=1000.
 313.       335 CONTINUE
 314.       310 RTsl.9865*T
 315.          RRT=1./RT
 316.           IFIICB.LE.O)  BUKP=1.
 317.           IF(PLIH.GT..1.0R.DAHP.GT..1>  RO TO 314
 316.          BUHPrBUST
 315.          BUST=BUST*BUST
 320.           ICB=10
 321.          PLIM=2.3025851
 322.          EKXP=1.E+10
 323.       314  ICB=ICB-1
 324.          DO  331  I=1,IS
 325.          LL(I)=0
 326.       331  OUn
-------
310.          SUMK=SUMK+PRMU
3m.          SUMD=SUHO+PRMUUM)*Him
38.          PRMUsEXP(PKRE(M) )
356.          PMR(M)=PKRIH)-PKP(M)
357.          RATMH)=AHAX1IPKP
36!.      3l FORMAT(I3,2X,11E11.5)
366.      3*0 CONTINUE
367.          ISSsIS+2
366.          MXsMT
369.    C     ORDER REACTIONS - FASTEST FIRST
370.          00 <*53 J=ll
371.      SO KsO
372.          00 S2 H=2,MX
373.          IF(RAT(M)-RAT(M-i( ) M52,52,i51
37i.      <51 K=MA(M)
37*.          HA(M)=MAM-1)
376.          MAM-1)=K
377.          KsH-1
376.          OUMsRATiMI
379.          RAT(MlsRAT(M-l)
3ftC.          RATIM-llsQUM
SAI.      US?. CONTINUE
362.          MX=K
38*.          IF(K.6E.2I  60 TO 450
SflM.      U53 CONTINUE
3P5.    C     INTRODUCE REACTIONS INTO CONSERVATION EQUATIONS
366.          DO 708 IKrl.MT
3A7.          M=MA  60 TO 700
393.          PIRPP=RIG(K)
39M.          BIGPN=-BIGN(K)
395.          IF(PRMUK,M))703i700t70?
396.      70? PTKPP=HIG^'(K)

-------
397.          BIGPN=-BIG(K)
396.      702 GP=BIGPP*l.E-3
39$.          GN=BIGPN*l.E-3
1*00 .          DUMsAMINl (BIGPP/(PRMU (KM ) *PKP(M) +GP) ,BIGPN/ (PRHU ( K . M) *PKR ( M) *GN) )
401.          IFCOUM.GT.TEST* GO  TO  700
<02.          TESTsDUM
403.          KlsK
404.      700 CONTINUE
f05.    C     INTR06UCE REACTION  INTO ALL MASS BALANCES
40(5.          IF(Kl.GT.O)  GO  TO 701.
407.          11=1
4oe.          I2=is
409.          GO TO  510
mo.    C     INTRODUCE REACTION  ONLY INTO MOST IMPORTANT MASS BALANCE  AFTER
mi.    C     REARRANGING
112.      701 K=K1
412.          OUM1=PRHU(K,M)
41.          IF  (KR7  .GE. 3)
15.         *      WRITE  16.493)  IK. M.RAT (IK ) ,K ,LL ( K ) ,PRMU (K, M) , BIG ( K )
H16.         *,BIGN(K)
HI7.      U93 FORMAT ( 2T3.E10 .<+/(2131 3E10 .1) )
              LL(K)=IK
              MP(H)s-K
H20.          0070U 1=1,IS
<*21.          UNIT(I.K)=0.
82.          IP(PRMUd.M) J 705,70i,705
*2J.      705 IF(I.EO.K)  GO To 70
              OUM2=PRMU(I.M)/OUM1
              UNIT(I,K)=DUM2
              PRMU(IMlsO.
 27.          TST=ABS(CKIN(D)*BUMP*l.E-5
 H?6.          DO 715 MM=1,MT
 *2S.           IF(PRMU(K,MM).EO.O.) GO TO 715
 30.           IF(MP(MM).tT.O) GO TO 715
 131.           PRMU(I.MM)=PRMU(I,MM)-OUM2*PRMU(K.MM)
 U-32.           IF(ABS(PRMU
-------
454.          IFCSUMD.EQ.O.) GO TO 37f,
45".          00375 I = IltI2
456.      375 AU+2(J+2)=A(I+2.J+2)-SUMn*PRMUII,M)
1*57.          SUMO=0.
456.      376 CONTINUE
45S .          SUD=-PKP ( M I *OKPT < M  - ( E AK < M ) /RT+
460.         *EXK(H) )*PMR(M)
461.          DO 381 1=11.12
462.          IFJPRMUU.MKEO.O.) GO TO 361
463.          DUMlsPMR(MI*PRlMltM)
46<4.          A URlTE(6t492) ( RIG ( I )  1=1  I S 
473.         *,(8IGN(I),I=1,IS)
474.    C     MODIFY MASS BALANCES AS REQUIRED TOWARD EQUILIBRIUM FORM.
47.          DO 750 1=1. IS
477.          IF(IK.EQ.O) GO TO 750
478.          H=MAeiGIE=-RIGN(I
483.          OUM1=DUH/(BIGIE+DUM*1.E-15>-1.0
484.          IF(DUMI.LT.O) GO TO 750
4B5.          RI6(I)=AMAX1(DUM,ABS(RHS(I42)
4P6.          IF (PMR(H)*PRMUI.M)/RHS(I+2).LE.O. ) GO TO 750
487.          DUH1=DUM1*OUH1
488.          WATE=OUMl/(10.+nUfl)
48S.          FACT=RHS(I*2)*WATE
490.          DUH3=FACT/PRHUUH)
491.          DUM=FACT/PPX(K>
492.          IF (DUM3 .LE. 0.) GO TO 736
493 .          DUM2=ALOG  DUH3+1 ,E- 15 ) -PKPE ( M )
49*4.          IF(DUM2.LT.20. I           DUM2=ALOG (1 . +DUM3/PKP ( M ) )
495.          GO TO 735
49C.      736 DUM1=ALOGCOUM3+1.E-15)-PKRE(M)
497.          IFIDUM1.LT.20.)           OUM1=ALOG( 1 .-DUM3/PKR (M I )
496.      732 DO 730 J=1.IS
499.      730 A(I+2,J+2)= RHU|J.M)*FACT*A(I+2.J+2)
500.         *+DUMTHMUJ.M)*PP(J)
5P1.          DUM=-PKR(M>*PRHU( I.")
502.          GO TO 745
503.      735 DO 740 0=1, IS
504.      740 A(I+2J+2)= PHU( J.M ) *FACT+A i 1+ 2 , J+2 )
505.         *+DUM*THMU( J.)PP( J)
506.          A(I+2l)=A(I*2.1)-FACT*nKPT(H)
507.
506.
5ns.      TH^t fl (1 + ?, 1)=A(I+21 ) + (EXK(M)+rAK ( M I /HT > *F ACT
51C.          A(T+2.2)=A(

-------
      511.           IF(KR7.GT.3>  WRITE(6.737)I.M,IK.OUM.OUM1,OUM2.PACT,RHS(1+?)WATE
      512.       737  FORNAT(6X.3I4,6E12.7)
      513.           RHS(1+2)=(FACT+DUH*WATE)*DUM1+RHS(1+2)-FACT
      514.           BIG(I)=AHAX1(BI6(I),RAT(IK)*A9S(PKMU(IM) ) )
      515.           LL(I)=-M
      516.       750  CONTINUE
      517.           IF  IKR7  .LE.  31  GO TP  390
      516.           WRITEC6,497)  (LL (I 1 = 1IS)
      515.           WRITE'<6,498)  ,
      553.          *    PKR(M),PKP(M).PMR(M)
      554.      30? CONTINUE
      555.      101 CONTINUE
      556.    C
      557.    C     NOW  INVERT TO GET CORRECTIONS ON  UNIT I.PM,AND BASE SPECIE
      596.    C     PRESSURES
      555.    C
      560.          Jl=l
      561.          IFKR6.NE.l.AND.NFHS.ECl.O) GO 10
      562.          00394  I=NilL,ISS
      563.          4(I.D=0.
      56<4.      394 A(1,I)=0.
      565.          A(l.l)=l.n
      566.      S^S CONTINUE
      567.          DO 31  I=MUL,ISS

-------
566.          DUM=AC2.I)
56S.          A<2.I)=A(ISStI>
570.      391 A(ISSI)=nUM
571.          D0392 1=1,ISS
572.          DUMsAU.2)
573.          A(I,2)=A(I,ISS>
57M.      392 A(I.ISS)=OUM
57.          00 32 1=1,ISS
576.          OUMsAd.II
577.          IFCDUM) SUS.
576.      3<3 A(I,I)=1.0
579.          IPsI+1
560.          J1=J1+ICON
561.          IF(Jl.GT.ISS) GO TO 311
SflS.          00 31 jsJl.ISS
583.       31 I,J)=A(I,J)/OuM
56<.      311 RHSmsRHSm/OUM
585.          IF(IP.GT.ISS GO TO 33
5A.          DO 32 KsIPfISS
567.          DUM=A(K,I)
56.          A=A(KJ)-OL'M*A(I,J)
591.       32 RHS(K)=RHS(K)-OllM*RHS(IJ
592.       33 IF(ICON.EQ.O) GO TO 36
593.          IP=ISS+1
59M.          00 35 1=1,ISP
595.          IPslP-1
596.          00 35 J=IP.ISS
597.       35 RHS(IP-1)=RHS(IP-1)-A(IP-1.J)*RHS(J)
598.          GO TO 36
599.       36 DO 37 1=1,ISP
600.          DO 37 J=1,I
601.          DUM=A(J,I+1)
602.          A(JtI+l)=0.
603.          DO 37 K=NUL.ISS
60M.       37 A(J,K)=A(JiK)-DuM*A(T--l.K
605.          00 371 1=1,ISS
606.          OUM=A(2,I)
607.          A<2,I)=A(ISS.I)
606.      371 A(ISS.I)=DUM
60S.          00 372 1=1tISS
610.          DUM=MI.2)
611.          AtI,2l=A(I,ISS)
612.      372 A(I,ISS)=nUM
612.       38 CONTINUE
614.          DUM=RHS(2)
615.          RHS(2)=RHS(ISS)
616.          PMS(ISS)=[)UM
617.          DO 169 1=1.IS
616.      1*9 E(I)=RHS(I*2)
619.          IF(ISP.GT.N) GO TO 191
62C.          00 190 I=ISP.N
6?1.          F(T)=E(I)-TCI>*RHSJ1)
6?5.          00 19U 11 = 1,IS
6?!.      liri F ( I 1=E< I )*VNUI I . IT )*HHS( II+2)
6?M.      1^1 rONTINUF

-------
      6?5.          IF(NFHS.NE.O)
      626.    C     NOW GET NON-BASE SPECIE CORRECTIONS
      627.    C
      626.    C
      625.    C     HFRE IS WHERE TO RAMP CORRECTIONS IF NECESSARY
      630.          IF)60  TO 42
      615.          EMAX=E(I)
      640.          IMAXsI
      641.       42 OOH=PLP(I)-PLN
      642.          IF(E(II) 20,15,18
      643.       18 OUN=(4.+4.*OOM)/(3.-DOM)
      644.          GO TO 13
      64!.       20 DUM=C3.*DOM-4.)/<4.+r)OM)
      646.          IF(DUM) 13.15,15
      647.       13 CONTINUE
      648.       19 DAHPsAMINl(DAMP,),ABS(RHS(21),.01 I
      657.          IF(OAMP.GT..99)  GO  TO 21
      656.          DO  27  1=1,N
      65S.       27 E(I>=DAMP*E(I)
      660.     C     MAKE CORRECTIONS
      661.       21 00  28  1=1,N
      662.          PLP(I=PLP  HAfP.T.PM
      669.       505 FORMATI1H ,6HOAMP=  .T10.5.4H  T= .F10.P.  5H  PM=  Ein.5  )
      670.          WRITE(6,306)  (PLP1=1.N)
      671.       506 FORMAT5X,10E10.5)
      672.       "*8  IF(ICON.GT.O)  GO TO 5
      673.           IF(IB.GT.l)  RETURN
      674.       52 SUMH=0.
      675.          SUMHT=0.
      676.          00 53 1=1,N
       677.           SUHHsSUMH+PPU |HI(I )
       676.        3  SUMHT = SUMHT+PP(I)*HI(I I*RPA(I)
       675.           0055 1=1,IS
       60.           ALPHT(I)=PP(U
       6PJ.           IF(ISP.GT.N) GO TO  ^^

-------
6P2.          0050 JsISP.N
662.       50 ALPHI(I)=ALPHI(I)-fVNu9 ICONsl
697.       51 FORMAT(1H0.2HSINGULAR MATRIX IN FLAME)
696.          URITE(6t5l)
699.          KR7a
700.          IFIITER.6E.ITMX) RETURN
701.          KR7=HAXO(KR7,1)
702.          ITERsITHX
702.          60 TO 30
704.          END

-------
                                                          GETDAT-ROUTINE

      1.          SUBROUTINE1 GETOAT(J)
      2.          PARAMETER JP=29t JFT=28 JG=JE+2 . JX=70 t JS=30 , JE1=JE+1 , JE2=JE+? . J01=JO
      *         *+2,JSM=JS-l,JOQ=JQ*JO
      1.          COMMON   /CARD1/    ISPECK2),      XMW,       XHRF
      5.          COMMON   /INUNIT/  INMAS
      6.          COMMON1 /LIN/ CPT(JP50)  HT
      iq.          COMMON/F3/ALPFIJOI t ALPE ( JO ) . ALPHZ ( JO ) ,FLUX { JO ) ,PPI(JP| ,PPS(JP) t
      ).         *   ALB(jQtJS)TL(JS) , TWL( JS) ,AP( JS)  A A ( JE2 . JE2 ) .DUO ( JO) .OUMB(JQ) ,
      16.         $   ARHM(JO.JO). BPA(JQ) tCKINI(JQ)
      17.          COMMON    /WANTS/    IWANT(3tJP),    NWANT,          XALPF(JP),
      1C.         $                    XALPE(JP)
      19.             DIMENSION  ZZIJP.2I
      20.          NAMA(J)  =  ISPECI(l)
      21.          NAMB(J)  =  ISPECK2)
      22.          ALPF(J)  =  XALPF(J)
      23.          ALPE(J)  =  XALPE(J)
_,    2<4.          WM(J)=XMW
 '    25.           IF(ICC.LT.O)  60 TO 200
'     26.          HRF(J)  * XHRF * 1000.
-J    27.     C             READ  CP DATA
      26.           READ (INMAS, 20120)  ( CPT ( J , K )  K=l , 50 )
      29.     20120 FORMAT  (5(1X, F9.4I)
      30.     C             READ  H DATA
      31.           READ (INMflS. 20120)  I HT ( J,K I ,K=1 , 50 )
      32.           DO 120  K=l,50
      33.              HT(JK) =  HT(J.K) *  1000.
      31.       120 CONTINUE
      3*.     C             READ F DATA
      *6.           READ (INMAS, 20120) (GTt J.K ) ,K=1 , 50 )
      37.     C             WRITE OUT DATA
      36.          WRITE (6,20mO) NAMA(J), NAMB ( J) , WM ( J ) ,HRF ( J)
      39.    20140 FORMAT (10X,  2AU , 2(2X, F10.3))
      <0.          WRITE (6.20320) (CPT ( J.K ) ,Ksl , SO )
      01.          WRITE (6,20320)  ( HT ( J,K ) ,K=1 , 50 )
      42.          WRITE (6*20320)  ( GT ( J ,K I K=1 ,50 )
      <4I.    20320 FORMAT(5(1X,E12.5) )
      uq.          60 TO 300
      .    C
      "6.    C             READ CURVE FIT  OATA
      07.    C
      U.      200 CONTINUE
      S.          DO 220 K=l,2
      iO.             RFAO (TNMAS, 20220) "A, PRIJ.K). RC(J.K),  RO(J.K),  Rf(J.K),
     ' il.         *   RF(J,K), ZZ(J.K), TU(JK)
      ?2.    20??0    FORMAT (6E9.6,  2FA.OI
                   WHITF  (ft,?01i*0) NAI*A(J), MAft< ( Jl ,i..M( J)

-------
                                 55.           00  20  K=li2
                                 56.              WRITE  (6,20240)  RA.  RB(J,H),  RC(J,K),  RD(J,K),  REIJ,K)
                                 57.          *  ,HF(JK), ZZ(J.K),  TU(J,K),  NAMA(J),  NAMfcHJ)
^                               58.     20240    FORMAT(5Xf  6(E12.5lX)t  2(Ffe.0,1X1,  2X,  2AU)
I                                 5S.              RB(J,K)  = RB(J,K)  +  RA
W                               gQ.              RF(JtK)  = RF(J.K)  /  1.9865
                                 61.       20 CONTINUE
                                 62.       300 RETURN
                                 62.           ENO

-------
                                              KINKIN-ROUTINE

 1.           SUBROUTINE KINlN
 2.           PARAMETER JP=29, JF=2fl , JQ=JE+2  JX=70 , JS=SO t JE1=JE+1 , JE2=JE+2 . JU1=JQ
 4.           INTEGER RLANK
 5 .           COMMON/F1/RHS ( JF2 ) t A ( JE2 . JF.2 ) , E ( JP )  ALPHI ( JO  t UNIT ( JO . JQ ) .
 6.          *   VNU(JP,JE)RR(JP2) ,RC(JP.?>RO(JP,2).RE(JP.2) .RF(JP.?),
 7.          *   TU(JP?J .PP(JP) tPLP( JP)HI(JP) SP(JP) ,PPTC(JP) tHOS(JP).
 e.          *   TC(JP),CPF(JP),NAMA(JP).NAM6(JP) t CPG .TW .HBC t PMt T .P.KR .KR6 ,KR7,
 9.          *   N.IS.ISPNEGMTCKIN< JO) ,H,PLNITERICON IBL, ICC,NFHS
10.          *.NRS(3) nOROT,OQROP<3) ,BPPMW ,FT ,^W( JP )
11.           COMMON/F2/ THMU(JE1JX).PPX(JX) ,RMU(JEJX) ,PMU( JE , JX ) ,PRMU( JET . JX ) ,
12.          *   PKPIJX) PKR( JX) ,PMR( JX) XX( JX > OKPT( JX) ,FKF( JX) , AFF( JX) .
U.          *   EXK(JX) tEAK(jX)RAT(JX)
14.          * MP< JX) .MA(JX)
15.           COMMON /LIN/ CPT(JP50) HT(JP50).  GTJP,50)  HRF(JP), WM(JP)
16.          *.KNYIQVC16,4) tALDENJJP)
17.           DIMENSION  NA ( 5 ) .NT ( 2 ) .NH ( 5 ) tNjfl ( 2 ) . TB ( 2 )
ie.           DATA MLET/IHM    /
19.           DATA BLANK/H    /
20.       51 FORMAT (213)
21.       152 FORMAT ( 5 < At , IX ) ,F5 . 0 . 3E1 0 . 4 , 2 < A4 , P6. 1 ) )
22.    C
22.          KIN=5
?<4.          KOUT=6
PS.          AL10=ALOG(10)
26.      <(00 REAOCKIN.itSl) MT
27.          URITE(6tfeO) MT
26.      80 FORMAT(lHl30Xt25H*  KINETIC REACTION DATA  *   //15X .20HNUMBFR OF R
29.          *EACTIONS=.I3/)
30.          URITEI6
-------
 5.          RHJ(I.M=0.
 56.          PNUeitHlsn.
 57.          If CNM3) ,NE. NAMA(I) .OR.NBO) .NE.NAHBdl ) GO TO 10
 58.          THMU(ItM)=l.
 59.          NA(3)=BLANK
 60.       10 DO 402 J=l,2
 61.          IF(NT(J).NE. NAWACl).OR.MTB(J).NE.NAMBm)GO TO 11
 62.          THNU(ItP)sTR
 63.          NT)GO TO 402
 72.          PHUCIiH)=PMU(If)*VMj )  GO TO 301
 86.      300 CONTINUE
 89.          GO TO 7
 90.      301 J1=4-JJ
 91.          J2=5-JJ
 92.          NA(K)=IQV(II,Jl)
 93.          NR(K)=IOV(II.J2)
 94.          ISW=1
 95.          GO TO 410
 96.        7 WRITE<6.409) NA(K)M
 97.      40^ FORMAT(5X,A4,13H  OF FQUATION I3.28H IS NOT IN THE  SPECIES TABLE)
 9fl.          IFLAG=1
 9.      410 CONTINUE
100.          IF(ISW.EO.l) GO TO 305
101.          IF(ABS(RSUM-PSUM.LE. .0001*RSUM)  GO TO 401
102.          WRITE(6406) M
103.      406 FORHAT<6feH SUM OF MOLECULAR WEIGHTS INDICATES IMBALANCE IN KINETIC
104.         * EQUATION 13)
105.          IFLAG = 1
106.      401 CONTINUE
107.          IF (IFLAG .CO. 1) STOP
109.          RETURN
ing.          FNO

-------
                                                      OBTAIN-ROUTINE
 6.
 7.
 e.
 s.
10.
11.
12.
13.
14.
IS.
16.
17.
ie.
19.
20.
21.
 SUBROUTINE OBTAIN
 PARAMETER JP=29,JE=2fl.JQ=JE+2.JX=70.JS=30.JE1=JE+1,JE?=JE+?.J01=JQ
*+2,JSM=JS-l,JOQ=JQ*JQ
 COMMON/F3/ALPFIJOIALPE(JO),ALPHZ .RF( JP.2) .
       TU < JP . 2 ) , PP { JP ) . PLH ( JP ) . H I ( JP > , SB ( JP  . PPTC ( JP ) , HOS < JP ) .
      TC(JP) ,CPF( JP) ,NAMA ( JP) tNAM8( JP) .CP6  TW .HBC .PM T.PKR . KR6 . KR7 .
      N.IS.ISP.NEO.MT,CKIN  WRITE  (^<11>
           11 FORMAT(1H0.1?X,12HTARULAR  UATA/12X, 4HNAME*  8X, 2HMW . 6X . 11HHF ( CAL/
             *MOL)/15X.    7Hcf(CAL/(MOL*K) ) ,H ( CAL/f OL ) F (CAL/ ( MOL*K ) RIVEN EVfR
             *Y 100K FRO"  inn  TO snoOK    i
             ORIGINALLY GETSpf! (

             REAO( INMA.S4)
              HrAMIINPAS.l)  ISI'FCI .
                  AT( 10V .2A4 ?X.?F1 0.0 I

-------
 5.          IF (ISPECK1)  .EG. TEND)  IEOF = 1
 56.
 57.          IF (IEOF .NE.  0) 60 TO POO
 5P.          IF(KNY.EQ.O) CO TO 150
 5$.          00 2 Isl.KNY
 60.          DO 2 0=1,U,2
 61.          IF(ISPECII1).NE.IQV(I,J)GO TO 2
 62.          IF (ISPECI(2).NF.IUV(I,J*1))GO TO  ?
 63.          J1=-J
 61.          iTESTlsIOV(I.Jl)
 6*.          J2s5-J
 66.          ITFST2sIQV(ItJ2)
 67.          GO TO 150
 66.        2 CONTINUE
 69.      ISO 00 160 IsitNWANT
 70.             IF (IWANTtltl) .NE. 0)  GO TO 160
 71.                DO 120 J=l2
 72.          IF(IUANT
 97.       6  FORMATdHO,  39H** Nn DATA IN SPECIES MASTEK FILE FOR ,  2At,
 96.         S          MM  ***
 99.         S)
100.             OK s OK * 1
101.        5 CONTINUE
102.
103.          IF(OK.EQ.O)  GO TO 7
ipw.             WRITE (6,20120)
105.    20l?0    FORMAT  (IHtl, 7H*** PROGRAM STOPPEf IN OBTAIN - UNKNOWN SPECIF?
106.         *,           1H REQUESTED  ***
107.         S)
1PP.             STOP
in?.        r
no.

-------
                                             RDFLX-ROUTINE


 1.           SUBROUTINE RDFLX
 2.           PARAMETER JP=29, JE=2ft. JO=JE+2 . JX=70 . JS=30 t JE1=JE+1 , JE2=JE+2 . JQ1=JQ
 .          **2.JSM=JS-l,Joa=JQ*JO
 q .           COMMON/Fl/RHS C JE2 I  A ( JE2  JE2 )  E < J^ ) . ALPHI < JO J  UNI T < JQ , JO ) ,
 5.          *VNU(JPiJE) ,RB(JPt2> HC< JP2),RD(JP,2) ,RE  H I ( JP ) . SB ( JP ) , PPTC ( JP ) . HOS ( JP I ,
 7 .          *TC i JP )  CPF ( JP ) .NAMA ( JP  , NAMP ( JP ) t CPG  TW , HBC  PM . T  P . KR t KR6 , KR7 .
 6.          *   N,IS,ISPNEQ,MT.CKIN(JQ) ,H.PLN,ITER.ICON.IB,L,ICC.NFHS
 3.          *.NRS<3) ,DORDTiDOROP<3> . BP  PMW . F T t PW ( JP )
10.          S.  TERM2,TERV2HAn,TTV.PPV,TTT.PPPtFW(JP) ,CPWI(JP| ,ALFW( JE> ,CHIW
11.          St  HTW.EXMtEXN.IH
12.           COMHON/HTL/SSS1 JS) tO ( JS ) tOLStEGYDS
U.           DIMENSION  TEMP(12)t XKPC02H2I. XKPH20(12),  XKPCO(12)
1M.           DATA TEMP/ 00. ,600 . ,800 .< 1000 .. 1200 . t 1400 .< 1600 .. 1800 . t 2000 ., 2200
IS.          . ,2100., 2600. /
16.           DATA XKPC02/0. ll*31,n,127', 0.1 0779, 0.08005, 0.05761 5, 0.0+RATIO*(XKPC02(J+1I-XKPC02(J) )
?9 .          PKH20=XKPH20 ( J 1 *PATIO*  XKPH20 ( J*l ) -XKPH20 ( J ) )
30.          PKCO =XKPCO(J) 4RATIO*(XKPCO( J+1)-XKPCO( J) 
31.           II = NRSID
32.           12 = NRS(2>
32.           13 s NRSI3I
 34.           PPI1=0.
35.           PPI2=0.
36.           PPI3aO.
 37.           IF(NPSm.GT.O) PPI1=PP(I1>
 36.           IFNPS(2).GT.OI PPI2=PP(I2)
 3S.           IF(NRS(3).GT.O) PPI3=PP(I3)
 140.           SUMKP=PPI1*PKC02 + PPI2*PKH20+PPI3*PKCO
 42.           QRAD=FAC*SUHKP
 <*2.           T1=XKPCO? J+1)-XKPC02( J) /200.
 44.           T2=XKPH20
-------
55t       10 CONTINUE
?6.          ORftD=0.
57.          PQROT=0.0
96.          nORDPd 1=0.0
59.          nQRDP<2)=0.0
60.          OPRDP(3)=0.0
61.          RETURN
62.          END

-------
                                                              RE ADI N- ROUTINE

        1.           SUBROUTINE" REAOIN
        2.     c              READS IN THE CARDJSJ INDICATING  THE SPECIES AND
        3.     C              THE ALPF AND ALPE VALUES THE PROGRAM  WILL USE
        14.           PARAMETER JP=29. JF=2fl, JO=JE+2 , JX=70  JS=.SO , JE1=JE + 1 , JE2=JE+? , JQ1=JQ
        5.          *+2,JSN=JS-l,JOO=JO*JO
        6.           DIMENSION     ISPECK2)
        7.           COMMON/F5/ALPF< JO)  ALPE ( JO ) . ALPHZ ( JO ) tFLUX  JO ) .PPI < JP ) .PPS ( JP ) .
        6.          *   ALBCJQ.JS).TL(JS) ,TWL .CKINI (JQ)
       10.           COMMON   /WANTS/   IWANTO.JP),   NWANT,          XALPF(JP).
       11.                     '        XALPE(JP)
       12.           COMMON /LIN/ CPT(JP'SO). HT(JP50). GT(JPt50).  HRF(JP). WM(JP)
       13.          *,KNY,IOV<16,<+) .flLOEN(JP)
       m.           DATA     TEND /3HEND/
       IE.           JMAX = JP
       16.           J = 1
       17.              WRITE<6 10)
       16.        10 FORMATUH1.15X.70H* SPECIES INITIAL MOLE FRACTIONS, FIRST GUESSES, A
       19.          *NO DIFFUSION FACTORS *   ./)
       20.           WRITE (6.200901
       21.     20090 FORMAT!/. 15X, 6HSPECIE . 18X. itHALPF.  16X. HALPE, 10X
       28.          *.16HDIFFUSION FACTOR/)
       22.       100 READ  ( 5.2P100 ) ISPECI ,KNY XF . XE.XBP
_i     ?4.     20100 FORMAT(2Ai*,I2,2E10.3,F10.4)
 '     ?S.          IF  (ISPECKl)  .EO.  IEND) GO TO  180
Ja.     2.          WRITFI6. 20120)  TSPECI . XF , XE , XBP
d     27.    20120 FORMAT(16X,2At12X,E10.3,10X,E10.3.10XF10.
       2fi.          IF  (J ,GT. JMAXl  GO TO 200
       2S.              DO 1<*0  1 = 1.2
       30.                IWAMT(I*1,J)  =  ISPECKl)
       31.      1*0     CONTINUE
        32.              XALPF(J) =  XF
        33.              XALPE(J) =  XE
        3M.          PPA(J)=XBP
        35.              J  =  J +  1
        36.      160 GO  TO 100
        37.      180 NWANT = J  -  1
        36.           IF(KNY.EQ.O)GO  TO 220
        39.          KMYs<*KNY
        <0.          RE AD (5, 2) | UQV< I J) . J=1,U) I=1.KNY)
        <41.         2 FORMAT(fl(AH,A*,2X) )
        12.          WRITE(6,6)
        ;.         6 FORMAT(5X,5HHTHF  FOLLOWING  PAIRS OF NAMES ARE CONSIDERED EQUIVALFN
        KM.          *T./
        U6.          WRITE(6t7) ( ( IQV( I , J| , J=l ,14 ) , I = 1,KNY)
        17.        7 FORMATdOv 2A42X.2AH.2X.2At.2X.2A(.2X.2Ai4,2X,2A<.2X.2A(i
        e.         2X,2AM.2X)
        US.          GO TO 220
        50.    C
        si.    c             MORE  THAr1 J^AX SPECIES HEontSTLn
        5i.    C
        BJ.      ?on WHITE (fe.?02nni jtAx
        SM.    2020'! FC"MT (mHO*** PPO'.PAM STOFl>Fb IN PFftOlN -- MOHF THftM, I

-------
5S.         $        22H SPECIES REQUESTED ***
56.         S)
H.      210 READ (5.20100* IOUM
56.          IF (IDUH .NE. IENP) GO TO 210
59.      220 RETURN
60.          END

-------
                                                     RERAY-ROUTINE

      1.          SUBROUTINE RERAY(NC,NN,0,NNN,LS.TS)
      2.    C     DIRECT INVEPSIOM PROCEDURE      C  IS  REPLACED BY C**-l
      *.          PARAMETER  JE=2eJE2=JE+2
      1.          DIMENSION D(JE2,1).C=I
     15.        11 CONTINUE
     16.          IX=-1
     17.          IFdS+2)  111.109,111
     16.       106 FORMATU1H  L (I) 1 = 1,13 ,5X  (30I3M
     IS.       107 FORMATi15H   ((C(I,J),J=l,13,12H>.(0(J)J=l,13, 6H),1=1.13,15H)  RF
     20.          1FORE RERAY)
     21.       108 FORMAT<2X 11E10.3/U2X   10E10.3))
     22.       109 URITE(KOUT,107)  NP,NNN,N
-<   23.          WRlTE(KOUTil06)NP(L(I)I=l.NP)
T1   21.           IX=0
-p..   25.          DO  110  1=1.N
"^   26.       110 WRITE(KOUT,108)(CdJ)J=1NP),=C(I,K)*Olvr
      16.          IF(NNN) 17,17,163
      17.       163 00 161 M=],MNN
      up.       l*1* 0( I ,M)=D( r ,MI*OIV*D( j-i ,MI
      I4S.       17 CONTINUE
      50.     C    SEEK MAXIMUM PIVOT
      "1.       12 OIV=0.
      ^2.          K = L(I)
      "!.          J=I
      M .          PC 13 JJ=T,N

-------
        55.          M=L
        56.          IF(ABS   )
        se.          K=M
        59.          J=JJ
        60.       13 CONTINUE
        fl.          SnmsDIV/FIH)
        62*          L(J)=L(I)
        63.          L (I.L(I).SO(I).1=1.NP)
        47.    C     DIAGONALtZE MATRIX
        fle.      152 NH=N-1
        89.          DO 20 1=1,NM
        90.          K=L
        91.          DO 20 J=1,I
        92.          DIVs-C(J.K)
        92.          IF(OIV)19,?0.19
        94.       19 C(J.K)=0.
        IE.          IF(NNN) 1<1.191,192
        96.      192 DO 193 M=1,NNM
        97.      193 0(JiM)=0(J.M)+t.IV*IJ(I*l,H)
        98.      191 DO 201 Ms) ,fjp
        9=.      201 C(JiM)sC(JM)DTV*C(Il,M)
       100.       20 CONTINUE
       101.    C     INTERCHANGE COLUMNS
       in?.          no so 11=1 trip
       102.          I = H
       104.       21 J=L(I>
       in=.          L(T)=I
       lOf.          IF(J-H??,3n,??
       107.       ?? IF(ISl?5.?S,??i
       lot.       ?^ nr> ?M M=I,M
       irc.          sc--)=r C-.T 
       11 r .       y>\ r (''. i )=c ir ,.ji
       111.          i*=i

-------
112.          I=J
113.          GO TO 21
llq.       25 IF(IS-J>26.28,26
115.       26 DO 27 M=1,N
116.       ?7 C(MtI)=C(MJ)
117.          T=J  
116.          60 TO 21
115.       26 DO 29 M=1.N
120.       29 C(M,I)=S(M)
121.          TS=0
1?2.       30 CONTINUE
123.    C     INTERCHANGE  ROWS
12M.          DO <0 II=ltN
125.          I = H
126.       M J=LL(I)
127.          LL(I)=I
126.          IF(J-I)32,
 150.           IP(NNN)  393393,391
 1*1.       391  DO  392 M=1.NNN
 152.       392  nf flf''l
 161.       411  RETUPr
 if-;.           FNP

-------
                                  Section 12

                                  REFERENCES

 1.   Kendall, R.  M., Kelly, J.  T.  and Lanier, W. S., "Predictions of Premixed
     Laminar Flat Flame Kinetics - Including  the Effects of Diffusion,"  Pro-
     ceeding of the Stationary  Source Combustion Symposium. Volume I.  Funda-
     mental  Research, Environmental  Protection  Technology Series,
     EPA-600/2-76-152a, June 1976.

 2.   Kelly,  J. T. and Kendall,  R.  M., "Premixed One-Dimensional Flame (PROF)
     Code.   Development and Application", Proceedings  of the Second Stationary
     Source Combustion Symposium, Volume IV.  Fundamental Combustion Research,
     Interagency Energy - Environment Research  and Development Program Report,
     EPA-600/7-77-073d, July 1977.

 3.   Bartlett, E. P., Kendall,  R. M., and Rindal,  R. A., "A Unified Approxi-
     mation for Mixture Transport Properties  for  Multicomponent Boundary
     Layer Applications," Aerotherm Corporation Final  Report 66-7, Part IV
     (also NASA CR-1063), March 14, 1967.

 4.   Hirschfelder, J. 0., Curtiss, C. F., and Bird, R. B., Molecular Theory
     of Gases and Liquids, Second Printing, Corrected, with notes  added,
     John Wiley and Sons, Inc., New York, 1964.

 5.   Kendall, R. M., "An Analysis of the Coupled  Chemically  Reacting Boundary
     Layer and Charring Ablator,  Part V, A General Approach  to the Thermo-
     chemical Solution of Mixed Equilibrium - Nonequilibrium,  Homogeneous
     or Heterogeneous Systems," NASA CR-1064, June 1968.

 6.   Krieth, F., Principles of Heat Transfer, International  Textbook Company,
     July 1968.

 7.   Vincenti, W. G. and Kruger,  C. H., Physical  Gas Dynamics, John  Wiley  and
     Sons, New York, 1965.

 8.   Gaydon, A. G., The Spectroscopy of Flames, Chapman and Hall,  London,
     1974, pp. 221-230.

 9.   Edwards, D. K. and Balakrishnan, A., "Thermal Radiation by Combustion
     Gases," Int. J. Heat and Mass Transfer, Vol. 16,  1973,  pp.  221-230.

10.   Sparrow, E. M. and Cess, R.  D., Radiation Heat Transfer,  Brooks/Cole
     Publishing Company, Belmont, California, 1970, pp. 218-219.

11.   Hottel, H. C. and Sarofim, A. F., Radiative Transfer, McGraw-Hill Book
     Company, New York, 1967, pp. 229-236.

12.   Mason, E. A. and Saxena, S.  C., "An Approximate Formula  for the Thermal
     Conductivity of Multicomponent Gas Mixtures,"  Physics  of Fluid,  Vol.  1,
     No. 5, September-October 1958, pp. 361-369.
                                      12-1

-------
13.  Hirschfelder, J.  0., "Heat Conductivity in  Polyatomic,  Electronically
     Excited, or Chemically Reacting Mixtures,"  Sixth  Symposium (International)
     on Combustion, Reinhold Publishing  Corp., New York,  1957,  pp.  351-366.

14.  Svehla, R.  A., "Estimated Viscosities  and Thermal  Conductivities  of
     Gases at High Temperatures,"  NASA TR R-132,  1962.

15.  Svehla, R.  A., "Thermodynamic and Transport Properties  for the Hydrogen-
     Oxygen System," NASA SP-3011, 1964.

16.  Buddenberg, J. W.  and Wilke,  C.  R.,  "Calculation  of  Gas Mixture
     Viscosities," Ind. and Eng. Chem.,  Vol.  41,  No. 7, July 1949,  pp.  1345-1347.
                                   12-2

-------
                                APPENDIX A
                     BRIEF DEVELOPMENT AND DEMONSTRATION
           OF BIFURCATION  APPROXIMATIONS TO DIFFUSION COEFFICIENTS

       Because  the  development  of  the set of transport relations used in
this code  is not  in the readily available combustion literature, it is
appropriate to  include a  brief  summary of the development in this report.
       The formulation derives  much of its utility from the simplification
introduced when binary diffusion coefficients are approximated with the
bifurcation relations.  These are
where the F. are  diffusion  factors  for individual  species which are independent
of the system of  species  involved.   They  could  be  temperature  dependent but
this flexibility  is  rarely  justified.   The  accuracy  of  the  approximation
has been tested for  a  variety  of systems.   Two  examples taken  from Reference 3
are shown in Tables  A-l and A-2.  These results are  typical when  good (and
consistent) sets  of  diffusion  data  are correlated.   Note that  these particular
correlations have arbitrarily  taken Fn as  1.0  to  anchor an otherwise floating
                                     U2
correlation.
       'In order to develop  an  explicit flux relationship using this approximation,
it is appropriate to start  with  the Stefan- Maxwell relation
        8x 
         "T      ^   '~TT   ^ i     ii   n~^   t      i        t   ' -*  /     /*\\
        9s  ~    , pp..
Kj
                                     A-l

-------
TABLE A-l.   CORRELATION OF BINARY DIFFUSION COEFFICIENTS FOR A
            HYDROGEN-OXYGEN SYSTEM USING PRESENT METHOD
            TEMPERATURE = 12,000R, PRESSURE = 1  ATM
Species
1 J

H H2
H H20
H 0
H 02
H OH
H2 H20
H2 0
H2 02
H2 OH
H20 0
H20 02
H20 OH
0 02
0 OH
02 OH
OH
Average


H H2
H H20
H 0
H 02
H OH
H2 H20
H2 0
H2 02
H2 OH
H20 0
H20 02
H20 OH
0 02
0 OH
02 OH
OH
Average
t?ij From
Kinetic Theory
(ft2/sec) x 100
(a)
36.0260
25.9891
26.6238
22.8038
26.4341
17.3862
17.7166
15.0085
17.5759
7.0928
5.2795
6.9078
5.6458
7.2643
5.4946

Absolute Error
(b)

67.6000
28.3200
27.7200
24.5500
29.5900
19.5800
23.6000
17.1900
20.1600
8.2950
5.7150
7.1450
6.8500
8.6060
5.5520

Absolute Error
t?ij From Pres- Error Using
ent Correlation Present
F' (2/seOx,00 Conxion
Diffusion
potential
0.24713




0.3720

Error If All
t?ij Are As-
sumed Equal
(Percent)
coefficients calculated using Lennard-Jones
with force data fromSvehla (Ref. 14)
53.1613 47.6
23.7639
24.7360
19.7757
24.3147
15.7877
16.4335
8.6
7.1
13.3
8.0
9.2
7.2
13.1381 -12.5

0.8322


0.7995

1.0000
0.8133

Diffusion
collision
0.2208




0.3034



0.8360


0.7317

1.0000
0.8192

16.1537
7.3461
5.8730
7.2210
6.1132
7.5163
6.0091


coefficients calculated
cross-sections suggested
74.4024
27.0030
30.8482
22.5734
27.5549
19.6568
22.4560
16.4323
20.0586
8.1500
5.9638
7.2799
6.8131
8.3166
6.0857


8.1
3.6
11.2
4.5
8.3
3.5
9.4

10.8
- 63.1
- 48.9
- 50.1
- 41.7
- 49.7
- 23.5
- 24.9
- 11.4
- 24.4
87.4
151.6
92.4
135.4
82.9
141.9

68.6
using values for
by Svehla
10.1
4.7
11.3
8.1
6.9
0.4
4.8
4.4
0.5
1.7
4.4
1.9
0.5
3.4
9.6

4.8
(Ref. 15)
- 77.1
- 45.4
- M.3
- 37.1
- 47.8
- 21.1
- 34.5
- 10.1
- 23.3
86.3
170.4
116.3
125.6
79.6
178.3

73.1
                               A-2

-------
TABLE A-2.  CORRELATION OF BINARY DIFFUSION COEFFICIENTS FOR AN
            OXYGEN-NITROGEN-CARBON-HYGROGEN SYSTEM BASED ON DATA
            OF SVEHLA (Refs. 14 and 15)

            TEMPERATURE = 12,000R, PRESSURE = 1  ATM
Species
i j
0
0
0
0
0
0
0
0
0
0
0
0,
0
0
0
02
02
02
02
02
02
02
02
02
02
02
02
02
02
N
N
N
N
N
C
N
N
N
N
N
N
N
02
N
N2
CO
C02
C
C3
CN
H
H2
H20
OH
CH4
C2H
HCN
N
N2
CO
C02
C
C3
CN
H
H2
H20
OH
CH4
C2H
HCN
N2
CO
C02
C
C3
CN
H
H2
H20
OH
CH4
C2H
HCN
flij From t>ij From Pres-
Kinetic Theory ent Correlation
(ft2/sec) x 100 Fi (ft2/sec) x 100
6.8500 0.7393
7.3372
5.3995
5.4662
4.4638
8.0754
5.1820
5 . 3620
27.7200
23.6000
8.2950
8.6060
5.8190
4.8947
4.8625
5.6566 1.0000
3.9611
4.0028
3.1637
6.3129
3.7100
3.9623
24.5500
17.1900
5.7150
5.5520
4.4735
3.6310
3.5678
5.4277 0.7907
5.4763
- 4.5136
7.9727
5.2069
5.3784
25.5139
17.1218
6.9743
7.1732
5.7836
4.9083
4.8645
6.0528
7.6554
5.6277
5.6846
4.6277
8.3865
5.3597
5.5958
29.8130
20.4311
7.5057
7.7923
6.0848
5.0977
5.0401
5.6595
4.1604
4.2025
3.4212
6.2000
3.9624
4.1369
22.0402
15.1043
5.5489
5.7607
4.4984
3.7686
3.7260
5.2620
5.3153
4.3270
7.8416
5.0115
5.2323
27.8700
19.1036
7.0181
7.2861
5.6895
4.7665
4.7126
Error Using
Present
Correlation
f Percent)
-11.6
4.3
4.2
4.0
3.7
3.9
3.4
4.4
7.6
-13.4
- 9.5
- 9.5
4.6
4.1
3.7
0.1
5.0
5.0
8.1
- 1.8
6.8
4.4
-10.2
-12.1
- 2.9
3.8
0.6
3.8
4.4
- 3.1
- 2.9
- 4.1
- 1.6
- 3.8
- 2.7
9.3
11.6
0.6
1.6
- 1.6
- 2.9
- 3.1
Error If All
P-JJ Are As-
sumed Equal
(Percent)
4.5
10.8
21.1
19,7
46.5
- 19.0
26.2
22.0
- 76.3
- 72.2
- 21.1
- 24.0
12.4
33.6
34.5
15.6
65.1
63.4
106.7
3.6
76.3
65.1
- 73.5
- 62.0
14.5
17.8
46.2
80.1
83.3
20.5
19.4
44.9
11 f\
7.9
or* f
25.6
01 f*
21 .6
-7 * *
- 74.4
f 1 O
- 61 .8
6n
.2
80
.0
13.1
33.3
34.5
                              A-3

-------
TABLE A-2.  Continued
PJJ From
Species Kinetic Theory
1 J (ft2/sec) x 100 Fi
N2 CO
N2 C02
N2 C
N2 C3
N2 CN
N2 H
N2 H2
N2 H20
N2 OH
N2 CH4
N2 C2H
N2 HCN
CO C02
CO C
CO C3
CO CN
CO H
CO H2
CO H20
CO OH
CO CH4
CO C2H
CO HCN
C02 C
C02 C3
C02 CN
C02 H
C02 H2
C02 H20
C02 OH
C02 CH4
C02 C2H
C02 HCN
C C3
C CN
C H
C H2
C H20
C OH
C CH4
C C2H
C HCN
3.8943 1.0756
3.1114
6.0528
3.6214
3.8603
21.3750
14.1671
5.0300
5.2629
4.3182
3.5367
3.4655
3.1390 1.0647
6.1194
3.6584
3.8938
21.6122
14.2296
5.1001
5.3305
4. 3595
3.5680
3.5023
4.9902 1.3079
2.8753
3.1245
18.4881
12.2917
4.1217
4.3441
3.5835
2.8685
2.7965
5.7767 0.7218
6.0033
26.1719
18.0635
7.5630
7.9334
6.3330
5.3831
5.3406
t?ij From Pres- Error Using
ent Correlation Present
/ft2, x lnn Correlation
(ft /sec) x 100 (percent)
3.9074
3.1809
5.7645
3.6840
3.8463
20.4922
14.0435
5.1591
5.3561
4.1824
3.5039
3.4643
3.2131
5.8229
3.7213
3.8853
20.6996
14.1856
5.2113
,5.4103
4.2248
3.5394
3.4994
4.7402
3.0294
3.1629
16.8510
11.5481
4.2424
4.4044
3.4393
2.8813
2.8488
5.4901
5.7319
30.5380
20.9280
7.6883
7.9818
6.2328
5.2217
5.1626
0.3
2.2
- 4.8
1.7
- 0.4
- 4.1
- 0.9
2.6
1.8
- 3.1
- 0.9
- 0.0
2.4
- 4.8
1.7
- 0.2
- 4.2
- 0.3
2.2
1.5
- 3.1
- 0.8
- 0.1
- 5.0
5.4
1.2
- 8.9
- 6.0
2.9
1.4
- 4.0
0.4
1.9
- 5.0
- 4.5
16.7
15.9
1.7
0.6
- 1.6
- 3.0
- 3.3
Error If All
P-jj Are As-
sumed Equal
(Percent)
68.0
110.2
8.1
80.6
69.4
- 69.4
- 53.8
30.0
24.3
51.5
84.9
84.8
99.2 .
9.9
72.0
64.8
- 66.9
- 50.4
27.1
22.3
51.5
80.9
82.9
35.0
111.3
102.4
- 59.4
- 39.1
58.7
50.6
82.5
128.0
133.9
13.2
8.9
- 75.0
- 63.8
- 13.5
- 17.5
3.3
21.5
22.5
          A-4

-------
TABLE A-2.   Concluded
Species
i j
C3 CN
C3 H
C3 H2
C3 H20
C3 OH
C3 CH4
C3 C2H
C3 HCN
CN H
CN H2
CN H20
CN OH
CN CH4
CN C2H
CN HCN
H H2
H H20
H OH
H CH4
H C2H
H HCN
H2 H20
H2 OH
H2 CH4
H2 C2H
H2 HCN
H20 OH
H20 CH4
H20 C2H
H20 HCN
OH CH4
OH C2H
OH HCN
CH4 C2H
CH4 HCN
C2H HCN
HCN
Average
P-JJ From
Kinetic Theory
(ft2/sec) x 100 Fi
3.6276 1.1293
21.0069
13.9792
4.8271
5.0416
4.1210
3.3265
3.2583
20.9403 1.0817
13.8853
4.9948
5.2299
4.2953
3.5330
3.4626
67.6000 0.2030
28. 3200
29.5900
20.3467
18.6611
18.8560
19.5800 0.2963
20.1600
13.7590
12.5045
12.5953
7.1450 0.8064
5.4665
4.5559
4.5242
5.6987 0.7767
4.7817
4.7388
3.9244 0.9948
3.8677
3.1729 1.1874
1.2009
Absolute Error
P-JJ From Pres-
ent Correlation
(ft2/sec) x 100
3.6632
19.5166
13.3749
4.9135
5.1011
3.9833
3.3371
3.2994
20.3763
13.9641
5.1300
5.3259
4.1588
3.4841
3.4447
74.3967
27.3309
28.3745
22.1568
18.5624
18.3525
18.7301
19.4453
15.1843
12.7210
12.5771
7.1436
5.5782
4.6733
4.6205
5.7912
4.8517
4.7969
3.7886
3.7457
3.1381


Error Using
Present
Correlation
(Percent)
1.0
7.1
- 4.3
1.8
1.2
- 3.3
0.3
1.3
- 2.7
0.6
2.7
1.8
- 3.2
- 1.4
- 0.5
10.1
- 3.5
- 4.1
8.9
- 0.5
- 2.7
- 4.3
- 3.5
10.4
1.7
- 0.1
- 0.0
2.0
2.6
2.1
1.6
1.5
1.2
- 3.5
- 3.2
- 1.1

3.7
Error If All
P-JJ Are As-
sumed Equal
(Percent)
80.3
- 68.9
- 53.2
35.5
29.7
58 7
96.6
100.7
- 68.8
- 52.9
30.9
25.1
52.3
85.1
88.9
- 90.4
- 76.9
- 78.0
- 68.0
- 64.9
- 65.3
66.7
67.6
52.4
- 47.7
48.1
- 8.5
19.6
43.6
AH f
44.6
In f\
4.8
*\^ ft
36.8
OO f\
38.0
f / "7
66.7
f>f\ T
69. 1
1 f\C T
106. 1

50.9
            A-5

-------
where x^ is the mole fraction of species i, T is the temperature, P is the
binary diffusion coefficient for species i and j, and D.  is the multi-
component thermal diffusion coefficient for species i.  Substituting the
approximation for binary diffusion coefficients (Eq. A-l) into the Stefan-
Maxwell relation (Eq. A-2) and rewriting in terms of mass fractions, Y- yields
3X
"9T
                   i   M2/YiFi  ^  JiFi   Fiji  V   YiFi\
                   1 _ M  /  11  X   J J -  11  \    1 J \          i -v
                     - pol  M_.   Z   Mi    TIT  Z    M1  y          (A 3)
                          \       j    j      i    j     j  /
where, for convenience, a total diffusion mass flux has been defined as
the sum of the molecular and thermal diffusional fluxes.
Multiplying each side of Eq. (A-3) by M../F. , summing over all i, and
noting that the sum of the diffusive fluxes is zero and the sum of the mass
fractions is unity yields:
                                      __            ._
                            M2  i  T7 3s  - M2  j  F. 3s

Substituting Eq. (A-5) into Eq. (A-3) results in
                  3X1   Y.F1  y Mj 3X..   M2 F.J.
                    ~                 ~                               (A"6)
At this point is is convenient to define several new quantities
                                Mi =
                                      J
                                     A-6

-------
                                                                      (A-H)
                               V*  =          F     df/dT)              (A-9)

                                     J
Taking  the  derivitor of Eq.  A-8 yields
                      dy2      M.  dX,         M.X.J dF, HT

                      IT -I* d-" I  ^^f
                               J             h
                                          M


 Introducing  Equations  A-7 through  A-10  into  A-6 yields after some rearranging
           J
            1
dYi .  Yi   dM
      w
       The  variation  of F^ with  temperature  as  determined with a nine component


system over a  range from 4000 to  16000R  in Reference  3 were found to rarely


exceed 0.1%.   Consequently y^ has  been  taken as  zero and a universal set of


F.. determined  for  all  species.   Correlations of these values with molecular


weight have been reasonably  good as  indicated in Figure A-l.  The correlating


equation



                                   /  M,  -461
                              F. -(




is recommended when specific values  of  F-  are not available from other correlations.


It is apparent that D  must represent the temperature and pressure dependence of


the P...   Although "D need have no  specific relation to a real diffusion coefficient,
     ' J

the arbitrary choice of  Fn  as 1.0 prompts the interpretation of U as the self

                         U
                                    A-7

-------
10.0
 8.0
 6.0

 4.0
 2.0
 0.1
Symbol
0
A
V
Chemical
System
0,N,C,H
0,N,C
0,H
Source of
Kinetic Data
Table A-2
Table A-l
                                       10
100
                             Molecular Weight,  M..
   Figure A-l.   Correlation of diffusion factors with molecular weight.
                                    A-8

-------
diffusion coefficient of 02, VQ   Q .  This would force  a  precise  fit of
the correlation to VQ   Q  but would not in general  provide  the  best overall
                     ^   
correlation.  Ignoring this caveat we can evaluate Pn n  from the equation
                                                    U2,U2
of Reference 4 as given by Equation 7 of the text:

                                3  T
-------
     10.0
                                                                                                            I-
                                                                                                            I
to

CT>
QJ
O
i
I/)
O
u

10
0)
c
O
-3


i
(O
c
                      Exact (Ref. 4)
1.0
      0.1
                                         10
                                                                    100
1000
                                               Reduced temperature,  T^ .
                     Figure A-2.   Collision integral  for  Lennard-Jones potential

-------
By introducing the bifurcation relations, taking from Reference 4 the  relation
for pure component viscosity
                             M  =

assuming A..* ~ 1.12 (actually varies from 1.10 to 1.14 in the temperature
range of interest), and adjusting 1.385 to 1.344 for simplification, there
is obtained
                                = PD
The results presented  in  this Appendix show that the bifurcation approximation
can result in major  simplification  in transport property evaluations with only
minimal loss in accuracy.
                                    A-ll

-------
                                TECHNICAL REPORT DATA
                         (Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-78-172a
    2.
                                                      3. RECIPIENT'S ACCESSION NO.
4. T,TLE AND SUBTITLE premixed One-dimensional Flame
 (PROF) Code User's Manual
                               5. REPORT DATE
                               August 1978
                                                      6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)

 Robert M. Kendall and John T. Kelly
                                                      8. PERFORMING ORGANIZATION REPORT NO.
                               78-277 (Project 7317)
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Acurex Corporation/Energy and Environmental Division
485 Clyde Avenue
Mountain View, California 94042
                                                      10. PROGRAM ELEMENT NO.
                               EHE624A
                               11. CONTRACT/GRANT NO.
                               68-02-2611, Task 7
12. SPONSORING AGENCY NAME AND ADDRESS
 EPA, Office of Research and Development
 Industrial Environmental Research Laboratory
 Research Triangle Park, NC  27711
                                                      13. TYPE OF REPORT AND PJEFUOD
                                                      Task Final; 5/77-2/78
                                                                           COVERED
                               14. SPONSORING AGENCY CODE
                                 EPA/600/13
is. SUPPLEMENTARY NOTES ffiRL-RTP project officer is W. Steven Lanier, Mail Drop 65, 919/
 541-2432.
16. ABSTRACT
              report is a. user's manual that describes the problems that can be trea-
 ted by the Premixed One -dimensional Flame  (PROF) code. It also describes the math-
 ematical models and solution procedures applied to these problems .  Complete input
 instructions and a description of output are given.  Several sample problem input and
 output listings are presented to demonstrate code options. A program listing and
 code Fortran variable definitions are included. The PROF code numerically models
 complex chemistry and diffusion processes in premixed laminar flames . Since the
 code includes diffusion, it gives realistic solutions of coupled combustion and pollu-
 tant formation processes in the flame zone , as well as downstream in the postflame
 region.  The code can be a valuable aid when interpreting experimental flame data.
 In addition to flames , the PROF code can also treat problems involving well-stirred
 reactors, plug-flow reactors, and time -evolution chemical kinetics. A wide variety
 of conventional and experimental combustion systems can be treated by the code's
 flame and reactor options.
17.
                             KEY WORDS AND DOCUMENT ANALYSIS
                DESCRIPTORS
                   b.lDENTIFIERS/OPEN ENDED TERMS
                        c. COS ATI Held/Group
 Pollution
 Computer Programs
 Combustion
 Flames
 Kinetics
 Methane
Carbon Monoxide
Diffusion
FORTRAN
Mathematical
 Models
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Stationary Sources
PROF Code
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Plug-flow Reactors
13B
09B
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2i

P
I OK
7C
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-------