Report No. 1160-1
CONTROL OF NITROGEN OXIDE
EMISSIONS FROM DIESEL ENGINES:
A THEORETICAL ANALYSIS
Northern Research and Engineering Corporation
Cambridge, Massachusetts
London, England
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Copy No.
Report No. 1I60-1
CONTROL OF NITROGEN OXIDE
EMISSIONS FROM DIESEL ENGINES:
A THEORETICAL ANALYSIS
E. K. Bastress
K. M. Chng
D. M. Dix
R. J. Murad
Prepared for
Office of Air Programs
Environmental Protection Agency
(Contract No. EHS 70-116)
NORTHERN RESEARCH AND ENGINEERING CORPORATION
219 Vassar Street
Cambridge, Massachusetts 02139
June 8, 1971
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This work was carried out under the direction of Dr. D. M. Dix
with Dr. E. K. Bastress assuming project responsibility. The other prin-
cipal participants in this program were K. M. Chng, Dr. R. S. Fletcher,
and R. J. Murad. Professor J. B. Heywood, Massachusetts Institute of
Technology, contributed in a consulting capacity.
The Project Officer for this program was Mr. Barry McNutt of
the Division of Emission Control Technology, Office of Air Programs,
Environmental Protection Agency.
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TABLE OF CONTENTS
INTRODUCTION 1
Problem Description ]
Program Objective 2
Program Approach 2
SUMMARY OF RESULTS 5
Model Development 5
Design-Performance-Emission Correlations 5
NOx Emission Control Methods 6
CONCLUSIONS AND RECOMMENDATIONS 8
GENERAL DESCRIPTION OF ENGINE MODELS 10
Nature of the Models 10
Modeling Concept 10
Model Assumptions 13
Model Descriptions 19
DESCRIPTION OF THE D1RECT-1NJECT1 ON ENGINE MODEL 20
Physical Description 20
Governing Relationships 22
Rate Processes 28
Engine Performance Parameters 31
Model Summary 32
Analysis Procedure 32
Thermodynamic Properties 33
DESCRIPTION OF THE INDIRECT-INJECTI ON ENGINE MODEL 36
Physical Description of the Model 36
Rate Processes 39
Governing Equations ^
Model Summary ^+9
Analysis Procedure 50
ENGINE DESIGN-PERFORMANCE-EMISSION CORRELATIONS 52
Methodology 52
Direct-Injection Engine 52
1ndirect-Injection Engine 58
Summary of Results 61
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ENGINE DESIGN CRITERIA FOR NOx EMISSION CONTROL 63
Direct-Injection Engines 63
Indirect-Injection Engines 6^
AUXILIARY METHODS OF NOx EMISSION CONTROL 65
Control Methods Considered 65
Evaluation Results 65
Effects of Control Methods on Other Emissions 70
Summary of Effects 71
REFERENCES . . : 72
TABLES 71*
FIGURES 81
NOMENCLATURE 96
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LIST OF TABLES
Table I: Reference Engine Input Data Used with Direct-
Injection Engine Models 75
Table II: Reference Engine Input Data Used with Indirect-
Injection Engine Model ..... 76
Table III: Predicted Effects of Turbocharging on Direct-
Injection Engine Performance and NO Emission 77
Table IV: Predicted Effects of Pilot Injection on Direct-
Injection Engine Performance and NO Emission 78
Table V: Predicted Effects of Fumigation on Direct-
Injection Engine Performance and NO Emission 79
Table VI: Summary of Control Method Effectiveness 80
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LIST OF FIGURES
Figure 1: Fluid Systems and Mass Transport Processes:
Direct-Injection Engine Model 82
Figure 2: Fluid Systems and Mass Transport Processes:
Indirect-Injection Engine Model 83
Figure 3: Direct-Injection Engine Cylinder Design Variables ... 84
Figure k: Direct-Injection Engine Combustion Cycle and Mass
Transport Processes 85
Figure 5: Indirect-Injection Engine Cylinder Design Variables . . 86
Figure 6: Mean Chamber Gas Properties, Direct-Injection Reference
Engines 87
Figure 7: Predicted Performance of the Reference Direct-
Injection Engine 88
Figure 8: Sensitivity of Predicted Direct-Inject ion Engine
Performance to Model Parameters 89
Figure 9: Sensitivity of Predicted NO Emission Rate to
Heat Transfer Parameters 90
Figure 10: Sensitivity of Predicted Direct-Injection Engine
Performance to Design Parameters 91
Figure 11: Predicted Performance of the Reference Indirect-
Injection Engine 92
Figure 12: Sensitivity of Predicted 1ndirect-Injection Engine
Performance to Model Parameters 93
Figure 13: Sensitivity of Predicted Indirect-Injection Engine
Performance to Design Parameters 9^
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INTRODUCTION
Problem Description
Diesel engines are a class of reciprocating, interna1-com-
bustion engines, or "piston" engines, which are characterized by a
unique ignition process. Relatively high compression ratios are used
in diesel engines, and the resulting high air-charge temperatures cause
ignition of fuel to occur spontaneously. Hence, the diesel is also
referred to as a "compression-ignition" engine. Various references are
readily available which describe the operating and design characteristics
of diesel engines (e.g., Ref 1).
Exhaust emissions from diesel engines consist of the same
classes of pollutants which are of concern for other combustion systems
operating on petroleum-based fuels:
1. Carbon monoxide (CO).
2. Organics (hydrocarbons, aldehydes, and other organic-based
materials in gaseous or liquid state).
3. Nitrogen oxides (NOx).
k. Dry particulates (DP) (materials emitted as solid particles).
5. Sulfur dioxide (SO^)•
SO2 emissions result from the presence of sulfur-containing impurities in
diesel fuels, and, hence, SO^ emissions and their control are inevitably
linked to fuel characteristics. The other emissions, however, are not
inevitable, but are formed during the combustion process, and are, in a
sense, results of the failure of the process to limit its products to the
"ideal" constituents-- carbon dioxide and water. The nature of diesel
engine emissions and their origins are discussed by Hurn in Reference 2.
Hurn and others have identified the emissions of principal concern from
diesel engines as nitrogen oxides and organics. Carbon monoxide emission
rates are very low throughout the normal operating range of the diesel
engine. Dry particulate emissions from diesel engines consist predomi-
nantly of carbon particles and their emission rates can be controlled
through proper engine design, selection (or rating), and maintenance
procedures, and proper fuel selection (Ref 2).
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Diesel engine emissions add to the atmospheric concentrations
of the pollutant classes listed above, and also result in undesirable
sensory effects— smoke and odor. Smoke is caused by excessive emissions
of organics (white smoke) or particulates (black smoke), and control of
smoke is achieved by control of these emission classes. The origin of
diesel engine odors is unclear, though it is generally associated with
emission of organics.
Program Objective
The program described in this report has been concerned with
the control of NOx emissions from diesel engines. The program has been
based upon an over-all approach to NOx control consisting of the following
sequence of steps
1. Development of design criteria for controlling NOx emissions
by theoretical analysis.
2. Verification of the theoretically-derived NOx control
criteria by experimental testing.
3. Demonstration of the utility of the engine design criteria
by development and operation of engines with controlled
NOx emissions.
This sequence represents a logical, orderly approach to emission control
which is being pursued to varying degrees for other types of sources.
The program described in this report was directed toward the
first step. The objective of the program was to correlate engine design,
performance, and emission characteristics by theoretical analysis, and
to develop NOx-control criteria.
Program Approach
To achieve the objective defined above, the following sequence
of tasks was undertaken:
1. Development of mathematical models of combustion and NO forma
t i on in diesel engines.
2. Correlation of engine design, performance, and emission
character i st i cs.
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3- Identification and evaluation of methods for controlling
NO emi ss ions.
These tasks were related through the models which were developed in the
first task and subsequently employed to accomplish tasks 2 and 3. Thus,
the program was oriented toward the theoretical modeling of diesel engine
combustion systems.
The program was concerned primarily with diesel engines used for
heavy duty vehicle propulsion. Therefore, in the modeling task, it was
necessary to develop analysis techniques applicable to the types of auto-
motive diesel engines in general use. Since the models were to represent
combustion and nitrogen oxide formation processes, it was only necessary
to include those features of engines and their combustion systems which
directly affect these processes. For this purpose, it was necessary to
distinguish between two classes of combustion chamber design. The first
class consists of open-chamber or "direct-injection" engines, and the
second class includes divided-chamber or "indirect-inject ion" engines.
A separate model was developed for each engine class.
The design-performance-emission correlations, which were the
objective of the second task, were produced by parametric analyses con-
ducted with the combustion models. Engine design variables were studied
to determine their effects on performance and emissions. Engine perfor-
mance was monitored by calculating indicated values of power output and
specific fuel consumption. The use of indicated performance parameters
permitted the analyses to be limited to processes occurring within the
engine combustion chamber. This limitation was justified on the grounds
that indicated performance can be related to actual engine output, or
"brake" performance, by means of more comprehensive engine models which
have been developed earlier (e.g., Ref 3)* This limitation allowed a
more detailed analysis of combustion processes to be conducted which is
necessary for an investigation of pollutant formation.
In the final task, the results of the previous tasks were
analyzed to identify concepts for controlling NOx emissions. Two cate-
gories of control methods were defined based on these concepts-- the first
category including engine design modifications, and the second category
including auxiliary control devices. Design criteria were defined for
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controlling NOx emissions by
a qualitative evaluation was
control devices.
it
means" of engine design modifications, and
made of the performance of auxiliary
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SUMMARY OF RESULTS
Model Development
Two mathematical models were developed— one for direct-injection
engines and the other for indirect-injection engines. To use either of
these models for evaluating engine performance, a specific engine design
and operating condition are represented by a set of input data. The model
predicts indicated values of horsepower, specific fuel consumption, and
specific NO emission rate for the engine and its operating condition. The
model also calculates the time history of combustion chamber properties,
including pressure, mean temperature, and fraction of fuel burned.
Thus, performance characteristics such as peak pressure and pressure rise
rate can be predicted.
The models have been used to predict performance of two auto-
motive diesel engines for which performance and emission data have been
published. The performance and NO emission predictions obtained are
consistent with performance generally observed for diesel engines and for
these two engines in particular. No attempt was made to "calibrate" the
models. That is, model parameters were not varied to attempt to obtain
precise agreement between predicted and observed engine performance. The
available engine performance data were not sufficiently complete to pro-
vide for calibration of the models.
Even without calibration, the models produce realistic values
of engine power and fuel consumption and values of NO emission rate
which agree reasonably well with measured values. Thus, the models were
considered to be satisfactory for use in the remaining tasks of the pro-
gram.
Pes i gn-Performance-Em i ss i on Cor re lat i ons
Parametric analyses were conducted, using both engine models,
to determine the sensitivity of predicted engine performance and NO
emission rate to various parameters. Model sensitivity analyses were con-
ducted to determine the relative influence of different processes occurring
The term "emission rate", as used in this report, indicates a normalized
rate, i.e., exhaust mass fraction (ppm) or specific emission rate (gr/hp-hr).
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in the combustion chamber. These analyses indicated that predicted NO
emission rates are very sensitive to the values assigned to parameters
which represent processes such as fuel vaporization, fuel burning, and
heat transfer. This sensitivity is less pronounced in the IDI engine
model than in the Dl engine model.
Design sensitivity analyses were conducted to produce correla-
tions between engine design, performance, and emission parameters. These
correlations indicate the effects on performance and NO emissions of
variations in design variables which are directly controlled by the engine
designer. The NO emission rate from Dl engines is found to be very sen-
sitive to fuel injection variables. IDI engine emissions, however, appear
to be less sensitive to fuel injection characteristics, but are very sen-
sitive to the amount of fuel which passes unburned into the main chamber.
NOx Emission Control Methods
The design-performance-emission correlations were used in an
attempt to formulate criteria for reducing NO emission rate through en-
gine design variations. It appears from the results of this effort that
NO emissions can be reduced from Dl engines through variation in fuel
injection characteristics. NO emissions from IDI engines might be re-
duced by modifying fuel spray characteristics to increase fuel residence
time in the precombustion chamber. Emission rate reductions achievable
by these approaches appear to be significant— of the order of 50 per
cent for Dl engines— but probably will be accompanied by reductions in
engine performance.
The models also were used to investigate the effects of other
engine design approaches on NO emissions- Design features examined were
turbocharging, pilot injection, and fumigation. The results indicated
that neither turbocharging nor pilot injection offers an effective ap-
proach to NO emission control. However, the predicted effects of fumi-
gation included substantial reductions of NO emission rate. These ef-
fects are not considered to be conclusive since fumigation was only
represented in the model in an approximate manner.
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Auxiliary methods of NO emission control, such as water injec-
tion and exhaust gas recirculation, were not evaluated. However, ap-
proaches to incorporating these control methods into the engine models
were indicated*
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CONCLUSIONS AND RECOMMENDATIONS
The diesel engine combustion models which have been developed can
be used to provide qualitative correlations between engine performance, NO
emission rate, and engine design characteristics. It is anticipated that
the predictive abilities of the models can be made quantitatively accurate
by calibration with experimental data obtained by engine testing. These
models can be used as convenient tools, either alone or in conjunction with
experiments, to evaluate effects of engine design variations on indicated
engine performance and NO emissions.
It has been possible to establish qualitative design criteria for
reducing NO emissions from direct-injection engines. NO emission rate is
found to vary monotonical1y with fuel injection time, injection rate, and
over-all fuel-air ratio. These design variables also affect engine perfor-
mance factors including specific fuel consumption, specific power, peak pres-
sure, pressure rise rate, and smoke emission. Qualitative guidelines have
been defined for reducing NO emissions by manipulation of these design vari-
ables while minimizing the associated penalties in engine performance.
The tendency for indirect-injection engines to produce lower NO
emissions than direct-injection engines has been confirmed by the IDI engine
model. However, this effect is strongly influenced by the fuel injection
pattern of the IDI engine. If a significant fraction of the injected fuel
passes directly into the main chamber, the advantage of the prechamber in
reducing NO emissions is reduced.
The direct-injection engine model has been used to evaluate turbo-
charging, pilot injection, and fumigation as methods for reducing NO emissions.
Of the approaches considered, only fumigation was found to decrease NO emis-
sions. Further evaluation of this control method will be required to deter-
mine the extent of NO emission control actually attainable. With minor modi-
fications, the models also can be used to evaluate water injection and exhaust
gas recirculation, and combinations of these and other emission control
methods.
It is recommended that the development of predictive techniques for
diesel engine performance and emissions be continued. These predictive tech-
niques are likely to be useful to engine manufacturers in their efforts to
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comply with future emission standards. Therefore, it is important that the
tehcniques be as accurate as possible and have broad applicability.
Two specific recommendations for additional effort are as follows:
1. The engine models developed in this program should be modified
and extended to increase their general utility in research on
emission control. Modifications recommended involve the intro-
duction of more general, or flexible, sub-models of combustion
processes which have been found to affect NO emissions strongly,
including ignition delay, fuel burning, and heat transfer. Ex-
tensions recommended include the incorporation of water injection
and exhaust gas recirculation into the models.
2. A carefully-controlled experimental program should be undertaken
to calibrate the engine models developed in this program, and
to verify the predicted correlations between engine design, per-
formance, and emission parameters. The experimental program
should include measurements of engine performance and emissions
with variations in design characteristics which appear to affect
NO emissions most strongly. Primary emphasis should be directed
toward the effects of fuel injection characteristics.
This recommended additional effort constitutes a logical continuation
of the work that has been accomplished and should lead to the development of
effective emission control methods for diesel engines.
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GENERAL DESCRIPTION OF ENGINE MODELS
Nature of the Models
The engine models are sets of mathematical relationships
which relate the performance and emission characterictics of diesel
engines to their design characteristics and operating conditions.
The models include those factors and processes normally considered in
calculating engine performance. These processes are:
Heat release rate
Heat losses
Internal losses
The models also include additional factors which are believed to affect
the rate of NO emission most strongly:
Nonuniform gas composition
Nonuniform gas temperature
Real gas composition and thermal properties
Finite-rate kinetics of NO formation
The models represent explicitly the processes of fuel injection,
vaporization, ignition, and combustion so that heat release rate is
calculated instead of being prescribed as input data. Thus, the models
provide a utilitarian procedure for relating engine performance and
emission rate to design variables and operating conditions.
Modeling Concept
Mathematical models of combustion chambers can be developed with
varying degrees of complexity. The complexity of a model is dependent upon
the degree to which fluid properties within the combustion chamber are
represented as functions of time and spatial dimensions. For discussion
purposes, such models can be classifed as follows:
1. Homogeneous.
2. Heterogeneous, nondimensiona1.
3- Heterogeneous, dimensional.
Within each class, a model can be either steady or unsteady (i.e., time-
dependent) .
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In a homogeneous model of a combustion chamber, fluid properties
within the chamber are uniform and particles of fluid do not retain their
identity as they pass through the chamber. A common example of this
type of model is the "perfectly-stirred reactor" concept which has been
used to model many combustion systems. Unsteady homogeneous models can
be used to represent systems where the over-all system properties, such
as volume, mass, or composition vary with time.
In a heterogeneous, nondimensional model, certain nonuniform
fluid properties can be represented. Distributions of properties such
as composition and temperature can be assigned to the fluid within the
chamber. However, the spatial distribution of these properties is not
represented. An example of this type of model is the "wel1-stirred"
or "partially-stirred reactor" concept which has been utilized as an
extension of the perfectly-stirred reactor. Heterogeneous, nondimensiona1
models may be unsteady in their over-all properties or in the distribution
of fluid properties within the chamber.
In a heterogeneous, dimensional model, the distribution of all
fluid properties can be represented and their spatial distributions are
indicated. Such models can be of one, two, or three dimensions and
may be either steady or unsteady.
Of the model types discussed above, the steady, homogeneous
model is the simplest, and the unsteady, heterogeneous, three-dimensional
model is the most complex. As model complexity increases, the number of
features of the combustion system represented by the model also increases.
However, the effort required to develop and use a model increases very
rapidly with model complexity. Therefore, when selecting a model for a
particular application, it is good practice to choose the least complex
model which will meet the requirements of the specific application. The
use of an unnecessarily complex model always results in a waste of
resources.
In the case of diesel engine combustion chambers, most models
used in the past (e.g., Ref 3) have been of the unsteady, homogeneous
type. This simple model form has been found to be entirely adequate for
predicting cylinder pressure and heat transfer rates from which over-all
engine performance can be derived. It has not been found necessary to
For example, see Reference 18.
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model the heterogeneous fluid properties in the cylinder to predict
engine performance.
In this program, the requirements of the models include the
prediction of exhaust gas NOx concentration as well as engine performance.
For this purpose it is necessary to calculate the rate at which NO is
formed and to integrate this rate over the duration of the engine cycle.
The formation rate of NO is dependent upon gas composition and temperature,
and the temperature dependence is highly nonlinear. Thus, average
properties of the cylinder gases cannot be used. The heterogeneous
character of the gases must be modeled, and NO formation rates must be
calculated individually for each portion of the gas mixture. Thus, it
is necessary to model the distribution of fluid properties in the cylinder
gases as a function of time during the cycle. It is not necessary,
however, to model the spat i a 1 distribution of gas properties. The forma-
tion of NO in an element of the gas mixture, is not dependent on the
location of the element in the cylinder. The properties of the element
may be dependent upon its location, but in the case of the diesel
combustion chamber this spatial dependence is only of secondary impor-
tance. Therefore, it is not necessary to model the spatial distribution
of elements of gas mixture to determine their properties.
On the basis of these considerations, the class of models
selected for this program is the unsteady, heterogeneous, nondimensiona1
type. In this model type, the gas mixture is represented as a finite
number of elements or "systems". The properties of each system are
uniform at any time, but vary with time during the cycle. It is not
assumed that a system exists as one continuous volume of fluid in the
cylinder. It may take any shape and may consist of many individual
fluid elements, all with the same properties. This type of model is
well suited to the diesel combustion chamber since the fluid systems
present in the early stages of the cycle, i.e., air and liquid fuel, are
well defined. The properties of these systems and other systems which are
formed can be determined during the remainder of the cycle by appropriate
modeling of transport processes.
A critical aspect of the combustion chamber models is the
representation of chemical rate processes occurring within fluid systems
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and mass and energy transport processes occurring among systems and between
systems and the chamber walls. These processes, which are referred to
in this report as "rate processes", result in changes in properties of
fluid systems and the formation of new systems. Models of rate processes
can become very complex and can incorporate dimensional features of the
combustion chamber and its contents. In modeling diesel engine combustion,
several rate processes must be modeled which are not well understood. In
these instances, the approach used here is the formulation of heuristic
models which embody the correct functional dependencies among the variables
involved, and the incorporation in these models of accessible empirical
constants which can be used to obtain quantitative agreement between theo-
retical predictions and experimental observations. Generally, the over-all
combustion model is constructed in a way which will allow these empirical
rate process models to be replaced by theoretically-based models as they
become avai1ab1e.
The intent of this discussion has been to present the rationale
for the selection of the model concept used in this program. The detailed
nature of each model is presented in subsequent sections of this report.
Model Assumptions
A number of significant assumptions are involved in the engine
models. Certain of these assumptions result directly from the selection of
the model concept, and others result from the formulation of the model and
its analysis procedure. These assumptions are identified and discussed here
so that the reader may have a clearer understanding of the capabilities
and limitations of the models.
Two separate models have been developed, one for direct-injection
(Dl) engines and the other for indirect-injection (I D I) engines. These
assumptions, in general, pertain separately to the two chambers of the IDI
engine combustion chamber. That is, the two chambers are treated indepen-
dently in the specification of fluid systems and rate processes.
Fluid Systems
It is assumed in each model that the contents of the engine com-
bustion chamber consist of a finite number of fluid systems, each of which
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\b
has uniform properties. These systems and the mass transport processes
occurring among them are indicated in Figures 1 and 2 for the Dl and ID!
models, and are discussed below.
1. Ai r - One system which may contain an initial NOx concen-
tration. Mass is lost from this system through fuel
burning and dilution of burned mixture systems.
2. L i qu i d fue1 - One system which gains mass through fuel
injection and loses mass through fuel vaporization.
3. Gaseous fuel - One system which gains mass through vapori-
zation of liquid fuel and loses mass through fuel burning.
k. Burned mixture - The burned mixture consists of the products
of combustion which exist in the combustion chamber at any
given time, and is highly nonuniform in composition. This
mixture is represented in the model by a large number of
uniform systems with individual properties which are deter-
mined by the time at which the combustion of each system
occurred and its subsequent air dilution history. Once
formed, there is no loss of mass from a burned mixture
system. However, the system gains mass by dilution with
air.
In this formulation of fluid systems, fuel and air mixing and burning are
assumed to occur simultaneously. The presence of a fuel vapor-air mixture
is not represented, even though such mixtures exist during early stages
of combustion. The omission of a fuel vapor-air mixture as a system was
justified on the basis that the additional complexity would not improve
the ability of the model to predict engine performance or NO emission rate.
The effects of fuel and air mixing processes on fuel burning rate must
be incorporated in the fuel burning rate model.
Mass Transport Processes
Fuel Vaporization
Fuel vaporization is represented by an empirical model based upon
the description of the "preparation-to-burn" process by Lyn (Ref b). The
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model includes one variable parameter which controls the vaporization
schedule of each increment of fuel injected into the combustion chamber.
This modeling method was selected because it combines all of the processes
affecting fuel vaporization into one simple model which has been shown to
be a realistic representation of vaporization rate. The model is limiting
in that it does not explicitly represent fuel injector design variables
which may affect vaporization.
Fuel Burning
Fuel burning is considered to occur in two distinct phases. In
the first, fuel vapor and air are assumed to be premixed and to burn over
a range of fuel-air ratios. Ignition is assumed to occur in a near-
stoichiometric fuel-air mixture, and combustion proceeds by flame spreading
through rich and lean fuel-air mixtures. The burning rate in the initial
burning phase exceeds the vaporization rate so that eventually all gaseous
fuel is consumed. The final burning phase commences when all gaseous fuel
has been burned. Burning in the final phase proceeds at the same rate as
fuel vaporization and occurs at a fixed fuel-air ratio, usually stoichio-
metric. This burning rate model also is patterned after Lyn's description
of diesel combustion processes (Ref k). The assumption that ignition and
final stages of burning occur at stoichiometric mixture ratios is based
upon laboratory observations of thermal ignition and diffusion flame com-
bustion. This modeling concept was selected because it is considered to
represent the processes which determine the time and mixture ratio at
which each increment of fuel burns-- factors which strongly influence the
formation of NO.
Ign i t i on De1 ay
The interval between the start of fuel injection and fuel burning
(ignition) is determined by an empirical ignition delay correlation, or
alternatively, it may be specified as an input data item. The empirical
correlation included in the model was developed by Tsao (Ref 5). This
correlation did not provide realistic ignition delay times at all operating
conditions, and thus was not used in the analyses conducted in this program.
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Burned Mixture Dilution
The dilution of the burned mixture with additional air is included
in the model because the dilution process significantly affects combustion
efficiency and NO formation. Burned mixture systems with rich fuel-air ratios
require additional air for completion of fuel burning. Once burned, the
NO concentration in each system would be predicted to reach unrea1istica11y
high levels if dilution were ignored. The rate of dilution of each burned
mixture system is assumed to be proportional to both the amount of excess
air present and the mass of the burned mixture system. This modeling concept
is based upon the assumption that mixing occurs at a uniform rate throughout
the combustion chamber and across the boundaries between systems.
Inter-Chamber Mass Flow (IDI Engine)
In the IDI model, ignition is assumed to occur first in the precom-
bustion chamber. Prior to ignition, fluid flows from the chamber with the
higher pressure to the other. The composition of the flow is the same as
the over-all composition of the fluid in the chamber of origin. After igni-
tion in the precombustion chamber, flow occurs only from this chamber to
the main chamber, and the composition of this flow is equal to the mass
average composition of burned mixture systems in the precombustion chamber.
This assumption-- that after ignition, only burned mixture flows from the
prechamber-- is based on the concept that the fluid issuing from the pre-
chamber is well-mixed and can be represented effectively as a burned mixture
system. The burned mixture entering the main chamber is not combined with
existing burned mixture systems, but is retained in separate systems. This
assumption is made to avoid the analysis procedures which would be required
to model mixing of burned mixture systems. The effect of this assumption
on predicted performance probably is negligible.
Other Mass Transport Processes
It is assumed that no other mass transfer between fluid systems
occurs other than that represented by the processes listed above. Speci-
fically neglected are mixing of different burned mixture systems and
mixing of fuel vapor with burned mixture systems. Omission of these
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processes simplifies the model analysis procedures without detracting
significantly from the ability of the model to predict engine performance
and NO emission rate.
Other Rate Processes
Heat Transfer
Heat transfer is assumed to occur between all gaseous fluid
systems and the chamber wall in accordance with a Newtonian rate expression.
The heat transfer rate is a fixed parameter and the driving temperature
difference is that between the wall temperature and a mean fluid temperature.
The wall temperature is assumed to be uniform and constant. The mean fluid
temperature is derived from an empirical temperature-energy correlation
using a fuel-air ratio based on total fuel burned and total air present.
The energy transferred is distributed among all gaseous systems in proportion
to their masses. It is assumed that no heat transfer occurs between fluid
systems except for the convective transfer associated with the mass transport
processes described above. This heat transfer model represents effectively
that portion of the cycle prior to ignition where heating of the air system
occurs over a relatively long time period. A uniform distribution of heat
transfer is a reasonable assumption because of the high turbulence level in
the chamber during this period.
The model is less effective after ignition where the heat loss from
burned mixture systems is more dependent upon the individual system tempera-
ture than on the mean fluid temperature. Also, heat loss from burned mixture
systems is dependent upon location within the chamber-- systems near the wall
losing energy at the highest rate. These effects could be represented by
using a model with heat transfer rate based upon individual system tempera-
ture and introducing a distribution of heat transfer coefficients to account
for spatial effects. This additional complexity was not considered to be
justified in this initial program. However, in view of the apparent influ-
ence of heat transfer on NO formation (discussed in later sections of the
report), modification of the heat transfer model should be considered in a
future program.
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Compression and Expansion Work
The transfer of energy due to compression and expansion work is
distributed among all gaseous systems present in the chamber. All systems
are assumed to expand or contract polytropica11y with the same polytropic
i ndex.
Nitrogen Oxide Formation
The formation of nitric oxide (NO) is modeled and the concen-
tration of all nitrogen oxides (NOx) in the exhaust gas is assumed to be
equal to the NO concentration predicted by the model. This assumption
implies that conversion of NO to other oxides (predominantly NO^) does
not affect the NO formation rate. NO formation is assumed to proceed in
each burned mixture system in accordance with a model developed by Fletcher
and Heywood (Ref 6). This model is based upon a six reaction NO formation
scheme, and the formation rate increases with the departure of the NO
concentration from its equilibrium value.
The NO formation rate in the air system is assumed to be zero.
This assumption has been substantiated by observing the temperature
history of the air system as calculated by each model. The air system
temperature remains well below the temperature regime wherein NO formation
occurs at a significant rate.
Chamber Pressure
Combustion chamber pressure is calculated by means of a homogeneous
fluid model integrated within the over-all model. The homogeneous system
is assumed to consist of combustion products from all fuel burned and the
total air charge. The gaseous and liquid fuel systems are neglected. Chamber
pressure is calculated by an energy conservation equation and an equation of
state using real gas property correlations by Borman (Ref 3)- Calculation
of chamber pressure by means of a homogeneous fluid model is a key assumption
in that the resulting analysis procedures are great;ly simplified. The
assumption that pressure can be predicted effectively by this approach is
justified by past experience in the successful prediction of chamber pressure
and engine performance by means of homogeneous fluid models (Refs 3 and 4).
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19
Model Descriptions
The direct-injection (Dl) and the indirect-injection (iDl)
engine models are described in the following sections of this report.
The discussion of each model is divided into four topics:
1. Physical description.
2. Governing relationships.
3. Rate processes.
U. Analysis procedure.
The physical description indicates the concept of the diesel combustion
process which forms the basis for the model, and the governing relation-
ships are the conservation and state equations which are relevant to the
combustion concept. The discussion of rate processes indicates the
approaches used to prescribe transport and chemical processes occurring
during the combustion cycle. The discussion of analysis procedures
outlines the technique used to solve the mathematical relationships to
obtain the predicted engine performance and NO emission rate.
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20
DESCRIPTION OF THE DIRECT-INJECTI ON ENGINE MODEL
Physical Description
The model is concerned with the properties of the fluid system
contained in a direct-injection engine cylinder, as represented in Figure 3.
The variables which define the cylinder design for modeling purposes are;
0 = cy1i nder bore
Vc = clearance volume
L = connecting rod length
R = crank length
& = crank position {& = 0 at TDC)
N = engine speed = d<9/dt.
The model includes only those processes occurring during the portions of
the compression and expansion strokes when all valves are closed. Thus,
the model treats a fixed mass of air and residual gas trapped in the
cylinder when the intake valves close. The model, therefore, is appli-
cable to either two-stroke or four-stroke cycle engines, and valve design
characteristics need not be considered in formulating the model. However,
inlet valve design features may be included in prescribing certain trans-
port processes as discussed in the next section.
The fluid within the cylinder is considered to be uniform in
pressure and to consist of a set of open or variable mass systems as fol-
1 ows:
1. Air-residua1-gas mixture (referred to as "air" in this
discussion) - one system designated by subscripted.
2. Liquid fuel - one system designated by subscript
3- Vaporized fuel - one system designated by subscript -Pg .
k. Burned mixture (combustion products and excess air) - L
systems designated by subscript bw*,i .
These systems are assumed to exist within the cylinder, but their loca-
tions or distributions are not prescribed by the model.
The conditions within each of the systems are controlled by
the following rate processes:
1. Liquid fuel injection, Vv\£p.
2. Fuel vaporization, •
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21
3« Ignition delay, tig.
k. Fuel burning,
5* Bu rned .m i xture dilution, (dv*/d&)Q .
6. Heat transfer, Q .
7. Nitrogen oxide formation,
The interaction of these rate processes in determining system
properties is described in terms of a five-phase cycle in which the phases
are defined by certain crank positions, as indicated in Figure h:
1. Valve closure,
2. Start of fuel injection, &¦ -LVSi .
3- Ignition, .
k. Start of final burning,
5- End of combustion, •
6. Valve opening, •
The phases in the cycle are described as follows.
1. initial Compression . Only the air system is
present in the chamber.
2. Ignition Delay ( . Phys i cal 1 y , 1 iqu i d fuel i s
injected into the chamber and begins to vaporize and mix
with the air to form a mixture of varying fuel-air ratio
in both chambers. In the model, consideration of this mixing
process is deferred until the next phase, so that in general
three systems ( j Vv\^j) are present in the chamber.
3- Initial Burning ( <. Q £ ). Phys i cal 1 y, i gn i t ion
occurs during this phase and burning occurs via flame
propagation through all elements of combustible mixture,
resulting in combustion over a wide range of fuel-air ratios,
until all of the vaporized fuel accumulated during the
ignition delay phase has been burned. In the model, an
elemental quantity of fuel vapor is assumed to mix with an
appropriate amount of air to burn instantaneously at a
specified fuel-air ratio during each crank-angle increment.
The specification of the fuel-air ratio at which burning
occurs, as a function of crank angle, simulates the quality
of fuel-air mixing achieved during the ignition delay phase.
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22
Subsequent to the formation of each element of burned mixture,
it is diluted by mixing with part of the excess air. In general,
then, there are three 4-1 systems (vv, >^iov*,i) present
in the chamber during this phase, where L is the number of
crank-angle increments taken.
4. Final Burning ( 0$^ - ® — Set )• During this phase, it is
assumed that burning is diffusion controlled, and hence,
that combustion occurs at a constant fuel-air ratio near
stoichiometric. Thus, in the model, there are two +1 sys-
tems ( Vajl, , W\bvv, t) present in the chamber.
5. Final Expansion (^gfefr 0 £ &„.0). All fuel burning is
complete in this phase, and the only significant process
occurring is the further dilution of the burned mixture
systems with excess air. One -hL systems (vw^, VH|,M"L ) are
present in the chamber.
The above cycle is based upon phenomenological descriptions of diesel
combustion by various workers, such as Obert (Ref 1) and Lyn (Ref 4).
The temperature and composition of each burned mass system are
assumed to be equal to thermodynamic equilibrium values, except for con-
centrations of N,-N20,,and NO. Formation reactions for' N and N^O are '
assumed to be'rn steady state. These assumptions lead to a single reac-
tion rate equation governing the increase in NO concentration from its initial
valuer This "pseudo-equilibrium" assumption is reasonable in modeling
NO formation, since these reactions are not energetically significant to
the over-all hydrocarbon combustion process. Thus, in general, the prop-
erties of any system are completely determined from the pressure (p), the
fuel mass fraction ( F ), the NO mass fraction ( ), and the tempera-
ture ( T") or the internal energy ( £ ) or the enthalpy(K ).
Governing Relationships
The governing equations for the properties of the fluid systems
are the conservation of mass (air and fuel), conservation of species (NO),
conservation of energy, and thermal and caloric equations of state. Appro-
priate forms of the conservation relations for the over-all mixture are
-------
23
used to determine the chamber pressure, while the conservation relations
for each system are used to determine the system properties in terms of
the mass of the air system, the mass of fuel in the other systems, the
fuel mass fraction in the burned mixture systems ( )> the internal
energy of all systems, and the NO mass fraction of all systems. Mathemati-
cal relationships describing the various rate processes complete the
model formulation.
assumed that the mixture within the chamber is homogeneous and in thermo-
dynamic equilibrium. These assumptions exclude the presence of unburned
fuel, and the relevant relationships are as follows:
Over-All Relationships
To determine chamber pressure and mean temperature, it is
Conservation of mass:
Wt
h
+- ^
L
(1)
Conservation of energy:
(2)
Equation of state:
PV = wih Th
(3a)
(3b)
Caloric equations of state.
(^a)
h
h
-------
2k
where h = subscript referring to properties of homogeneous mixture
Ft, = mass fraction of burned fuel = VY\^ ^ 'L ^ ^
VW = mass
^ polytropic index
V = rate of change of chamber volume per unit crank angle
Q = rate of energy transfer to chamber walls per unit crank angle
R = gas constant.
System Equations of State
Each system is assumed to oehave as a semiperfect gas, and hence,
the caloric equations of state are of the following form:
t'P.'O (5a,b)
V C ^ j i (6a,b)
•» (7a,b)
(8a,b)
The exact relationships used are described at the end of this section of
the report.
Conservation of System Energy
The energy conservation relations for the air system can be
written as:
^ = - £«. (££)«. + "z. (ir'f' ~ (9)
<£> , & o
/ pv»A (¦ f i\n\ J „ _ ( i - i-^ .
where lseJa = - J <• rsv de ) -pr- ">uie
^ . k»i*l
For the liquid fuel system:
*s ~ (vKtc -
(10)
-------
25
For the vapor fuel system:
d
rfo^f3£ft)=l'lMvw(j) "£f5wU + ^ ~ Q)
(ii)
For already formed burned mixture systems:
_d_ /mfbwy p /<*Wi\ (Vt,p P
For burned mixtures forming as a result of combustion:
_ *
V*
A, ( ^ A __ c J " • c i *" 1
c* / ^-£0 ^ Vk> «- tr
- (k?v
v ^ p /
(12b)
where the "rtT's" determine the distribution of energy transfer to each
system by compression or expansion work and heat transfer:
— V*ta_ I o- / Vo~ft (13)
AT-— VV\ / VcLp (1^)
Wb»t,L - '**,L ^ lo iH, tTt,*,: /Fb^i V,
(15)
where
Vc^ +¦ (16)
- / \
"fa "=• ' K Cif-l) = polytropic exponent (17)
The energy transfer distribution assumed here is, in physical terms,
equivalent to assuming that all nonreacting systems expand or contract
po1ytropica1ly, with the volume available for the reacting system being
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26
equal to the remaining chamber volume plus the initial volume of the
reactants. While this is not a completely accurate distribution of
energy transfer, it incorporates the essential processes.
Conservation of System Mass
The conservation of air in the air system can be written
as:
t=>
- W -h f ( (18)
C-
The fuel contents of the various systems are determined by
the following equations: ^
= j C9>
~ Je (2°)
A&;
= J (2I)
where i s the crank-angle interval during which the Lih system is
formed.
Finally, it is necessary to specify the initial fuel mass
fraction ( ) in each burned mass system. During the initial
burni ng per iod, 4: & — , thi s speci f icat i on is:
P*b*H — ~ X ^ ) £¦ (22a)
+ 7 Afr ) i- e«r«n (22b)
where = specified mean mixture ratio at which burning occurs
fof = specified increment in mixture ratio for each crank-angle
i nterva1
i = number of crank-angle increments after ignition (which is
also equal to the number of burned mixture systems present).
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27
As I increases, the values of F^,*, diverge from i n accordance with
Equations 22a and 22b. However, divergence limits, and FM(W, are imposed
so that the fuel fraction at burning is constrained within realistic limits
(e.g., flammability limits). After the initial burning period, it is assumed
that burning occurs at a constant mixture ratio :
O
~ I- w (22c)
Thus, the initial fuel fractions of the burned mixture systems varies as
shown below:
F,
'm#*
Q.
'3
lb
9
efc
Conservation, of ai r in the'burned mixture systems is represented
by the instantaneous values of the fuel mass fractions*
d Mgbvk,i
dS>
where is the rate iof dilution of system i.
(23)
Conservation of Nitr.ic Oxide
It is assumed that the NO reactions do not proceed in the air
system, so that is constant, and hence, the only relevant NO
conservation relations are those for the burned mixture systems.
it L^o] to I r • [KJOla-/ d Fb^.a "1
d 9 6>A/L bv*>'L Fbw.c ^ ) J
where /v) is the engine speed in rpm.
The fuel fraction at burning is automatically increased if for any reason
there is insufficient air to burn all fuel present at Fj,£ = F*, •
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28
Rate Processes
Fuel Injection Rate
Fuel injection rate is assumed to be a function of crank angle
only and is prescribed arbitrarily as input data.
Fuel Vaporization Rate
To represent the rate of fuel vaporization, a rate equation was
adopted which is patterned after Lyn's description of the "preparation to
burn" process (Ref 4). Each increment of liquid fuel, injected during a
crank-angle interval -j, is assumed to vaporize at a rate described as follows:
de c • J
(25)
where = mass °f liquid fuel injected during fuel injection
interval
C and C, are vaporization rate factors, C, being considered inde-
pendent, and C determined by the requirement:
+ l?o
/" 7F* de * <26>
where ^ = initial value of ^
The total fuel vaporization rate in the cylinder at any crank position &
is the sum of the rates for all fuel elements:
There remains, then, one rate factor to be specified C^>) which has units of
crank angle and determines the rate or "schedule" of fuel vaporization.
Iqni tion Delay
To specify the ignition delay, an empirical correlation devel-
oped by Tsao (Ref 5) can be used as shown below, or the ignition delay
can be specified arbitrarily as an item of input data.
-------
29
. (ig , o^(-+ o.ozt) w
+ flZ±L^$. 2Li#. -
I 4 U>, WW) T — - I ,f3 If —-
\ Tfl.,^ J \ IOi A <*°
(28)
where CLn = cylinder pressure at & = (psia)
= air temperature at Q = @Lh. (deg R)
tJ = engine speed (rpm)
Tic| = ignition delay (msec).
Fuel Burning Rate
After ignition, fuel burning is assumed to occur at a rate ex-
ceeding the fuel vaporization rate until the fuel vaporized during the
ignition delay has been consumed, as described by Lyn (Ref k). During
this initial burning period, the fuel burning rate is specified as follows;
W\_fb - VVv^ ijl£l (29)
whe re
+ -a) for(e-e^^£i
and = mass of fuel vapor present at S -
The parameter i s the crank-angle interval e<-$ cor-
responding to the initial burning period. This formulation of the ini-
tial burning rate provides a "spike" burning rate profile of the form
obtained from cylinder pressure analyses (Ref k). The parameter Cj must
be specified as input data. During the final burning period where
& > ©ft , the fuel burning and vaporization rates are equal.
Burned Mixture Dilution Rate
Mixing of air with each burned mixture system is assumed to
proceed at a rate proportional to the mass of the system as follows;
6G
o
-------
30
(d«rL = c3 [
where C3 is a mixing-rate parameter which should be specified as a function
of engine design variables and operating conditions. It is assumed that
this dilution is proportioned according to the mass of individual burned
mixture systems.
Fbn,L ( iiH\
U,4Ki " (3°
Specification of the dilution rate parameter, Cj , therefore, determines
the distribution of air in burned mixture systems throughout the cycle.
-I
(30)
Heat Transfer Rate
The energy transfer to the walls is expressed as:
Q = C-4- A (_Th -tJ) (32)
where is the surface area of the chamber
and = mean temperature of the fluid in chamber (spatial mean)
Xr = mean wall temperature of chamber (constant)
= average heat transfer coefficient in chamber (constant).
Nitric Oxide Reaction Rate
The NO reaction rate is expressed in the form developed by
Fletcher and Heywood (Ref 6):
_ ^ Mw0 / _
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31
K\ K = reacti°n rate parameters
*' R, - Kv ClOleLjJOle
R<,= Kb [0]e
= equilibrium mole fraction.
Equilibrium concentrations of the various species are determined by means
of a program developed by the NASA Lewis Research Laboratory (Ref 7)-
Engine Performance Parameters
The following relationships are used to calculate indicated
performance parameters for the engine (Ref I):
°
Xme? °PL = [ / ? dG " f? Te J +" , a^o (3*0
Jcx,
ISFC = ~FT (35)
where C = appropriate conversion constant for horsepower units
X = number of revolutions per power stroke
^ = mean fuel consumption rate per cylinder.
The fraction of I ME P generated during the portions of the cycle when inlet
or outlet valves are open is indicated by P^-v-o and, in principle, is
calculated as follows:
-H?o ©are.
" TTBaR L ] r de*° J r 46P
©atO — |£o
This quantity generally is positive, but is a small fraction of the total
IMEP. It may be neglected in comparing performance of engines of the same
type, but must be included when comparing engines with widely differing valve
timing or manifold pressures.
-------
32
Model Summary
The model described here treats the fluid within cylinder as
composed of distinct systems, and results, in general, in the determination
of the pressure, the thermodynamic variables £• , T , h , and Vv\ for each
system present, and the mixture ratio F and NO concentration for each
burned mixture system present. In addition, the total fluid within the
cylinder is described in terms of average quantities ).
Thus, in general, the system of equations described above results in
1- 13 unknowns, where i is the number of burned mixture systems.
Specification of appropriate initial conditions and the use of the pre-
viously defined rate processes complete the model formulation.
Analysis Procedure
The technique for solving the model equations to predict engine
performance consists of the following sequence of steps;
1. Pressure Calculation - Cylinder pressures at all values of
Q are calculated using Equations 1 through k assuming that
the contents of the cylinder are homogeneous. I ME P and ISFC
also are calculated during this step using Equations and 35-
2. Fuel Distribution Calculation - The mass of fuel in each sys-
tem is calculated at the end of each crank angle interval
A &i using Equations 19) 20, and 21.
3- Fuel Mass Fraction Calculation - The fuel mass fraction of
each burned mass system is calculated using Equation 22
for the system formed during the interval and Equation 23
for systems formed in previous intervals.
k. Air System Mass Calculation - Mass of the air system remaining
at the end of each & interval is calculated using Equation 18.
5* Thermodynamic Property Calculations - The temperature and
enthalpy of each system at the end of each © interval are
calculated using Equations 5 through 17- Equations for the
internal energy and enthalpy of the various systems (Equations
5 through 8) are described below.
6. NO Concentration Calculation - The NO concentration in each
-------
burned mass system is calculated for the end of each
interval using Equation 26.
7« NO Emission Rate Calculation - Engine NO emission rate
is calculated at the end of the cycle by summing the
masses of NO in all burned mass systems and in the air
system.
Thermodynamic Properties
The thermodynamic properties of the various systems are as
follows:
Ai r Propert i es
These properties are obtained from Borman (Ref 3):
- 0,e>k^S"S" x 77S XZZ.Z. ( - ib? /slu-g
- 772 X 32..;* *[o.71. +* S'.I'm xio^TL*
-b 3/IOiCj A io"nTa.3 - x
-t-G.sis-fe x.0*,7r/] (*t -lb? Al^
Liquid Fuel Properties
These properties are:
where is the specific heat of the liquid fuel.
Vapor Fuel Properties
Vapor fuel is assumed to behave as a perfect gas with:
-------
3*+
- LI SS"7 X 778- X 3*.* /m^
£• H ^ ~ R*S TW
h^<3 "* Cp/fg T** ~" AIi?3
where is the molecular weight of the fuel vapor.Cjof^ 's the
specific heat of the vapor (assumed constant), and is the heat of
vaporization of the fuel.
Burned Mixture Properties
For lean mixtures, Ft where Fs is the stoichiometric mixture
ratio, the curve-fits of Borman (Ref 3) are used.
Bbvw - 77S- X 32.Z *Ct ~ F") * (o.o +
- ^byy\ +•
where
= equivalence ratio = F" (. 1 - /^Fs ( t - ^
2, -> /•» >_ 3
A = O.lUS^S Ifa^ + SI I'm * to Tb^ I- 3A0Uo Mo Tbtn
-(3 4. -17 b"
X I O Tt,rw -+¦ (a , S t i) iff X / o ~fb m
3 = Ahc - I.SW3 Uu>i +
t>k - <0, 4-i06>C* + 7,%5-iZSr 4> - 3.H2Z7 <$>3
t>z = C""^7,Co
-------
35
(-jr-)Ahc. = lower heating value of fuel in Btu/lbm
2
p = pressure in lbf/ft .
For rich mixtures, the properties are obtained by the crude approximation
that the mixture can be represented by a mixture of stoichiometric com-
bustion products and excess fuel vapor provided that a suitable value
for the vapor specific heat is selected. Thus, for F 7 Fs :
^ = rb£t,+v>Rs
£ bw - T7J 1v T4»»Y]
where
^5 — ^bwi ^"S = Vor- l~" ~ ^"5
h H ~ Tfcrn —
^P fSd = ^'ct't'ous value of vapor specific heat.
It is anticipated that this approximation will be adequate since only
the peak temperature range is of interest in determining NO formation
rates.
Homogeneous Mixture Properties
For those calculations where the mixture in the chamber is
assumed to be homogeneous, the above equations for burned mixtures are
used. The fuel fraction F is based on the total amount of fuel which
has been burned and the initial air mass.
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36
DESCRIPTION OF THE INDIRECT-INJECTI ON ENGINE MODEL
Physical Description of the Model
The model is concerned with the properties of the fluid system
contained in an indirect-injection engine cylinder, as represented in
Figure 5* The variables which define the cylinder for modeling purposes
are:
0 = cy1i nder bore
V( = volume of precombustion chamber
A = interchamber port area
i = surface area of precombustion chamber
Vc = clearance volume
L = connecting rod length
R = crank length
© = crank pos i t i on
fvJ = engine speed.
The model includes only those processes occurring during the portions of
the compression and expansion strokes when all valves are closed. Thus,
the model treats a fixed mass of air and residual gas trapped in the cyl-
inder when the intake valves close.
The pressure in each chamber is assumed to be uniform with values
pj and ^ , where the subscripts! and^refer to quantities in the precom-
bustion chamber and the main chamber, respectively. Within each chamber,
the fluid is considered to consist of a set of open or variable mass sys-
tems as fol1ow.
1. Air-residual-gas mixture (referred to as "air" in this dis-
cussion) - one system in each chamber designated by the
subscripts Af\ and .
2. Liquid Fuel - one system in each chamber designated by the
subscr i pts £4' and .
3• Vaporized fuel - one system in each chamber designated by the
subscr ipts fg/1 and
k. Burned mixture - L systems in each chamber designated by the
subscripts and .
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37
These systems are assumed to exist within each chamber, but their loca-
tions or distributions are not prescribed by the model.
The conditions within each of the systems are controlled by
the following rate processes:
1. Liquid fuel injection, •
2. Fuel vaporization, WVfg.i and
3- Fuel burning, VV\^^| and •
k. Burned mixture dilution, Wia|jW(i 1 and •
5- Heat transfer, ^and^.
• •
6. Nitrogen oxide format ion, anc'•
7. Interchamber mass flow, and .
As in the case of the direct-injection engine, the interaction
of these rate processes in determining system properties is described in
terms of a five-phase cycle which is similar in each chamber, and in which
the phases are defined by certain crank positions, as indicated in Figure 4;
1. Valve closure, .
2. Start of fuel i nj ect i on, &iv\.
3- Igni t ion, .
k. Start of final burning, ©fb-
5. End of combustion, ©eb .
6. Valve open i ng, ©v-o •
The phases in the cycle are described as follows.
1. Initial Compression (9^ £ 0 6 ). Only air is pres-
ent in each chamber, and in general mass flows from the main
chamber to the precombustion chamber.
2. Igni tion Delay )• Physically, liquid fuel is
injected into the precombustion chamber or, in some cases, into
both chambers, and begins to vaporize and mix with the air to
form a mixture of varying fuel-air ratio in both chambers. In
the model, consideration of this mixing process is deferred
until the next phase, so that in general three systems (WV,
) are present in each chamber, and mass flows from
the main chamber to the precombustion chamber.
3. Initial Burning ( QLg ^ O ^ )• Physical ly, ignition
occurs during this phase and burning occurs via flame
-------
38
propagation through all elements of combustible mixture,
resulting in combustion over a wide range of fuel-air ratios,
until all of the vaporized fuel accumulated during the ig-
nition delay phase has been burned. In the model, an ele-
mental quantity of fuel vapor is assumed to mix with an
appropriate amount of air to burn instantaneously at a speci-
fied fuel-air ratio during each crank angle increment. The
specification of the fuel-air ratio at which burning occurs,
as a function of crank angle, simulates the quality of fuel-
air mixing achieved during the ignition delay phase. Subse-
quent to the formation of each element of burned mixture, it
is diluted by mixing with remaining excess air. In general,
then, there are three 4-1 systems ( VVt^, )
present in each chamber during this phase, where C is the
number of crank-angle increments taken. It is assumed that
ignition in the main chamber occurs later than in the precom-
bustion chamber, and hence, in general, some mass of the burned
mixture in the precombustion chamber flows into the main chamber.
k. Final Burning ). During this phase, it is
assumed that burning is diffusion controlled, and hence, that
combustion occurs at a constant fuel-air ratio near stoichio-
metric. Thus, in the model, there are two + l systems ( ,
, VWijtoji. ) present in each chamber, and mass flows from
the precombustion chamber to the main chamber.
5- Final Expansion ( ®et> ^ &a.ro )• Burning of fuel
is complete in this phase, and the only significant process
occurring is the further dilution of the burned mixture sys-
tems with excess air. One + L systems (VfltoVM(L ) are
present in each chamber, and flow continues from the precom-
bustion chamber to the main chamber.
As in the case of the direct-injection engine, the temperature
and composition of each burned-mixture system are assumed to be the thermo-
dynamic equilibrium values corresponding to the known pressure and elemental
composition, except for concentrations of NO-related species. Thus, in
general, the properties of any system are completely determined from the
-------
39
pressure (P), the fuel mass fraction ( F )» the NO mass fraction ( LwQ] ),
and the temperature (T ) or the internal energy ( £. ) or the enthalpy ( ).
Rate Processes
Various rate processes, involving transport and convective phe-
nomena identified previously, must be formulated in terms of the model
var iables.
Fuel Injection Rate
It is assumed that the total fuel injection rate into the cylinder,
¦ is prescribed as a function or crank ang.le, in units of mass per unit
crank angle. It is further assumed that a specified fraction of this fuel,
(^)» is injected into the main chamber while the remainder is injected
into the precombustion chamber. Hence,
~ 0)
(2)
where the subscripts / and ^ refer to the precombustion chamber and main
chamber, respectively.
Fuel Vaporization Rate
The fuel vaporization rate in each chamber, which physically
includes all processes necessary to form the combustible mixture elements,
is assumed to be analogous to that in the direct-injection engine. Hence,
the vaporization rate is given by
&
where
r / ' \ _ e'~e
V ' C* ^ I - [j +(Ofir0 ~
Vr\^„ = liquid fuel flow from chamber l< to chamber J? due to droplet
entrainment (always non-negative)
-------
ko
^ = rate parameter specified as input
and the latter subscripts K and JL refer to either chamber with the under-
standing thatl<7*>f.
Iqn i t i on Del ay
In the precombustion chamber, the same empirical correlation for
ignition delay used with the D1 engine model can be used, or the ignition
delay can be specified as input data. It is assumed that ignition in the
main chamber is further delayed by a specified time
= Li3>' *
Fuel Burning Rate
As in the direct-injection engine, fuel burning after ignition is
assumed to occur at a rate exceeding the fuel vaporization rate until the
fuel vaporized during the ignition delay period has been consumed. Hence,
for chamber K .
4 N
= + (&'0£3,x) (5)
for <9< (& < > and
^ 4 (r +c>. _ A
= N-lk TnV3,lK ^ ~ c* (6)
/
for < («?-£g<)< CX)< , and
~ + (7)
for , where
= crank-angle interval ~~ ®l
-------
41
burning period, ^ < 0 < t^l'S sPec'^'cat'on 's:
Ffe^K = F*iK - VAF< ; £ odd (8a)
Fb°v< — FWjl< + T ^ > L e,/ew (8b)
where specified mean mixture ratio at which burning occurs in chamber K
AF^ = specified increment in mixture ratio for each crank-angle interval
i = number of crank-angle increments after ignition (which is also
equal to the number of burned mixture systems present) in chamber
l< .
As in the Dl model, divergence limits, FMltn and > are imposed on the
_ O
range of values which can be assigned to F^wi^ • After the initial
burning period, it is assumed that burning occurs at constant mixture ratio:
P" ~' Fyy^K (8c)
The mixture ratio at burning ( Ffoni°,i< ) 's automatically increased by the
model if, in either chamber, there is insufficient air to burn all fuel
present at Ffcm, k= ^vv\, K-
Burned Mixture Dilution Rate
In a manner which is again completely analogous to the treatment
of the direct-injection engine, it is assumed that mixing of air with the
burned mixture systems is proportional to the amount of air present:
ca,K v^-|f +• xK)~\ (9)
where Cj ^ is a mixing-rate parameter which should be specified as a
function of engine design variables and operating conditions. It is
assumed that this dilution is proportioned according to the mass of indi-
vidual burned mixture systems:
{dl*) __ wfbw,L,K / Fk,wi,L,K / djM \ (]o)
W 6 ^a.bW,L K ZYyvU /c • \ \ dG/n ^
'' <7C.YVVfbv^)L,< / rynlL/i<) v K
Heat Transfer Rate
The energy transfer to the walls is expressed as.
-------
k2
^4-,K C"TS< -T^k) (II)
Where A« is the surface area of the chamber:
^ i = (spec i f i ed)
Ak = TL&Z +
2 ~U~
and
= mean temperature of the fluid in chamber l< (spatial mean)
T-r.K = mean wall temperature of chamber K (constant)
^ = average heat transfer coefficient in chamber K (constant).
Nitrogen Oxide Reaction Rate
The NO reaction rate in either chamber is expressed in a manner
identical to that for the direct-injection engine:
1 2M«0 / J . \/ _Rfc>w< \
- 6AJPWiiil< 11 '•w'lI +< (l2>
where ^*,1 n= NO formation rate (per unit crank angle) in burned mixture
system "l , chamber |<
Ita.i.K = f,uid density
= rat'° NO mass fraction to equilibrium NO mass fraction
K, K* K'o, = reaction rate parameters
' Rv = K» LM]tUwole.
ft. = K(,Lole.L^i03e.
C ] = equilibrium mole fraction.
Interchamber Mass Flow
The total interchamber flow is assumed to obey the usual orifice-
type relationship, before ignition.
4 -KPk/Px) j Pk>P«. (13a)
V ' h,l<
= 0 , (13b)
-------
43
where = total mass flow from chamber K to chamber A (always non-
negat i ve)
and
/?£.) ~ 0-exp[-2 ~\) ) \ (14a)
£ = °'sl s ^ > 1.3 (14b.)
Equation 14 is an approximate relationship which gives accurate results up
to pressure ratios of approximately 1.2, but less accurate results for
pressure ratios between 1.2 and 1.3. 11¦ i s also assumed that after ignition
in the precombustion chamber, the flow is always from this chamber to the
main chamber ( —O ).
The composition of the interchamber flow is in general, assumed
to be identical to that in the chamber of origin, with the exception that
after ignition in the precombustion chamber, it is assumed that only burned
mixture flows from this chamber to the main chamber. Thus, the constituent
flows are given by:
^<*-,•<¦4. — ( /< } ^ Kjg_ (15)
ICA = /vv\K^ V* (,6)
.,«jL = /^K Ft.m,L,K)
(17)
(18)
(19)
where
W \ bvvx.l ,K£. ~ « ^loW(L,kje.
f°r K=l , ®/vr^ ^ ® -^9,1 aPd f°r
VV\a;K k ^ -K- ^(VyVSbw,1L,K/fW,K>)
After ignition in the precombustion chamber, constituent flows from this
chamber are:
Interchamber port is considered to act as an ignition source, or "flame-
holder" so that any fuel in the flow burns during passage.
-------
kk
= Nv* " ° <20)
Vv* — F" W (22^
^fcVH.LjU
Governing Equations
The governing equations for the properties of the fluid systems
are the conservation of mass (air and fuel), conservation of species (NO),
conservation of energy, and thermal and caloric equations of state. Con-
sistent with the approach employed for the direct-injection engine, appro-
priate forms of the conservation relations for the over-all mixture in each
chamber will be used to determine the pressures, while the conservation
relations for each system will be used to determine the system properties in
terms of the mass of the air systems, the mass of fuel in the other systems,
the fuel mass fraction in the burned mixture systems ( "J, ), the inter-
nal energy of all systems, and the NO mass fraction of all systems. Mathe-
matical relationships describing the various rate processes complete the
model formulation.
Over-All Relationships
For the purposes of determining chamber pressures, it is assumed
that the mixture within each chamber is homogeneous and in thermodynamic
equilibrium. These assumptions exclude the presence of unburned fuel,
and the relevant relationships are as follows (in all of the following,
as before, the subscripts I and ^ refer to the precombustion chamber and
the main chamber, respectively, for convenience, the subscripts K and SL
are often used to represent these numerical subscripts with the under-
standing that K and J£ may both take the value of either I or ^ , except
that when they appear in the same equation, |< £ X ):
-------
45
Conservation of mass.
W, = W K + = (23)
K'K l F\o\h,1,K
Conservation. of energy (before ignition):
6& Kl(£ ^(*4 ^,K~
Conservation of energy (after ignition).
"Sk \t " V ^ V,< _
-------
46
Conservation of System Mass
Conservation of liquid fuel can be written:
G
(30)
The conservation of vapor fuel is:
e>
v»m<0> - f (\K - vifiiK - *f )lKJl <3I)
where = rate of fuel burning in chamber l<
rate of vapor fuel transfer from chamber K. to chamber .
The conservation of fuel in the burned mixture systems is, for
all systems except those which form in the main chamber as a result of
flow of burned mixture from the precombustion chamber.
A
wte)=/ S" (32a)
where AS- is the crank-angle interval during which the iih system is
formed and &• is the crank angle at the beginning of this interval. It
I
should be noted that = 'r°r t'ie turned mixture systems
formed in the main chamber as a result of flow of burned mixture from the
precombustion chamber, the conservation of fuel can be written as.
" T f de <32b)
The conservation of air in the air system can be written as:
& 9
VV.KC<9> +¦ VK, s„ dQ (33)
r\ /
^Art_ q
where
3$
^ 'a.K J '•< /A. bvv,<
f D>^\ / / a *v\\ I
//a. w", K
0 G*r<-
where r\ . is the mixture ratio at which burninq occurs in chamber K
b^iK
-------
bl
The conservation of air in the burned mixture systems can be
expressed in terms of fuel mass fraction as:
e e a.
0 k (I bn.l, K / d*\\ , , _ x
W*5 = +j W)
where is the crank-angle position defining the formation of the
p ©
burned system. f",»< 's given by Equations 8a through 8c for all burned
systems except those which form in the main chamber due to flow of burned
mixture from the prechamber. For these systems the composition of the
burned mixture is assumed to be a mass-weighted average of the burned
mixture systems existing in the prechamber-
ASl
r. w, f "—
bvn,t(v ^ 9 *• v
t J O^fcw^t.a/Fbvn^,! )
Conservation of System Energy
The energy conservation relations for the air system can be
wr i tten as.
~ ~ (36)
4- at: /^-PyX Pk _ Q \
For the liquid fuel system.
For the vapor fue.1 system.
dt(Wf9,K £^,k) = ~ £-fg,K (38)
+ * ^.K
-------
48
For already formed burned mixture systems
d ( ™$bvW|L,«. £bWi,L.fcr\ _ _ / ^ w\
Fuwv.t.ic /
*W.*Sfcj5A*\_ ^ /A»\ - ebM, . ***¦»•««.
< ' ' bVvi ( l , K
/ P* __ A \
+¦ bwi,i.,< C ^ p
(39a)
K
For burned mixtures forming as a result of combustion.
'VW - - 1 - °
bm,< ' (39b)
& / ¦fbtw.u.K ^ t»vn,L,<\ • I- R .
i«>( Fbw.C.K / = tb'K F^; ^
- (kkPk< + ^SiK\
For burned mixtures forming in the main chamber as a result of flow from
the precombustion chamber.
6 I ^^Hbw\,L,Z. ^ £b^,t,
de ^ Fiow,1£1a. ' L FbVM'^
i £|-m•L', (39c)
where the "AT's" determine the distribution of energy transfer to each sys-
tem by compression or expansion work and heat transfer:
~ ^cl, k < Xk,< / ^f>/< (^0)
R$9ik"^v< /^/'< (z+,)
b*\,CtK — k ^af,k
where
«
"V\K = I + Kk (T~0 = polytropic exponent (43)
The energy transfer distribution assumed here is, in physical terms,
equivalent to assuming that all nonreacting systems expand or contract
polytropically, with the volume available for the reacting system being
equal to the remaining chamber volume plus the initial volume of the
reactants. While this is not a completely accurate distribution of energy
transfer, it incorporates the essential processes.
-------
*+9
Equations of State
Each system is assumed to behave as a semiperfect gas, and hence,
the caloric equations of state are:
£*,.<, ^ * CPk.tO
d-U,K, H**,* = ^ (?k > TVe,i<)
h^g.K "=¦ ^ ) "^3. 0
(45a,b)
(46a,b)
J - "f C ) T"L*,l,K, Ffewt.c,*) (47a,b)
The form of these equations is given at the end of the description of the Dl
engine model.
NO Conservation
It is assumed that the NO reactions do not proceed in the air
system, so that (< is constant, and hence, the only relevant N0-
conservation relations are those for the burned mixture systems.
¦icnoIW.k _ j__ r. / ifbiwA] {48)
i& ~ LU L <»«.'.< Ftw,L,K^ d® / J
where M is the engine speed in rpm. For the burned mixture systems which
are formed in the main chamber as a result of flow from the precombustion
chamber, the initial NO mass fraction is given by:
[Zol - si ( [wo] . m
I J Fb„ Li,
Model Summary
In its most general form, the model proposed here treats the fluid
within cylinder as composed of distinct systems within each chamber, and
results in general in the determination of the pressure, the thermodynamic
variables E. , T , h > and M for each system present, and the mixture ratio
P" and NO concentration for each burned mixture system present. In addition,
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50
the total fluid within each chamber is described in terms of average
quanti ties , hK , TS>h)- Thus, in general, the system of equations
described above results in 5 + ^ + 2^^ unknowns for each chamber, where
I is the total number of systems present and L|ow\ is the total number of
burned mixture systems present. The basic system of equations containing
these unknown quantities are, for each chamber.
1. The five over-all relations (Equations 23, 24 or 25, 26,
28, 29).
2. The four conservation and state relations for the air sys-
tem (Equations 33, 36, 46a, 46b).
3. The four conservation and state relations for the liquid
fuel (Equations 30, 37, 45a, 45b).
4. The four conservation and state relations for the vapor
fuel (Equations 3', 38, 46a, 46b).
5. The six conservation and state relations for each burned
mixture system (Equations 32a or 32b, or 35) 39a or 39b
or 39c, 47a, 47b, 48).
Specification of appropriate initial conditions and the use of the pre-
viously defined rate processes complete the model formulation. Of the rate
processes, those governing the interchamber mass flow (Equations 13 through
22) deserve special mention, since they represent the only coupling between
the two chambers.
Ana-lysis Procedure
The technique for solving the model equations is essentially a
stepwise procedure for successive increments && in crank-angle position
f rom to • For any i n terval, in which the initial cond i t i ons are
always known, the procedure is as follows.
1. Interchamber Mass Flow Calculation. The interchamber mass
flows are calculated for the interval from Equations 13
through 22.
2. Pressure Calculation. Chamber pressures are determined
from Equations 23 through 29-
3. Fuel Distribution Calculation. The mass of fuel in each
system is determined from Equations 30 through 32.
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51
4. Fuel Mass Fraction Calculation. The fuel mass fraction in
each burned mixture system is determined from Equation 34.
5- Air System Mass Calculation. The mass of the air system
is determined from Equation 33*
6. Internal Energy Calculation. The internal energy of each
system is determined from Equations 36 through 39-
7. Thermodynamic Property Calculation. The thermodynamic
properties T and V\ for each system are determined from
Equations 44 through kl.
8. NO Concentration Calculation. The NO concentration in each
burned mixture system is determined from Equation 48.
9- NO Emission Rate Calculation. The total NO emission rate
is determined by summing the masses of NO in all of the
burned mixture systems and the air system.
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52
ENGINE DESIGN-PERFORMANCE-EMISSION CORRELATIONS
Methodo)oqy
Parametric analyses of NO emissions rates from diesel engines
were conducted using the direct-injection (Dl) and indirect-inject ion
(IDI) engine models. The objectives of the parametric analyses were
twofold:
1. The relative importance of different combustion processes
in the production of NO were evaluated. This evaluation
was accomplished by "model sensitivity" analyses wherein
model parameters, representing processes such as fuel
vaporization and mixing, were varied parametrical1y. Cor-
relations between these model parameters and NO emission
rate developed in this manner indicate the combustion pro-
cesses which must be modeled most accurately.
2. Relationships between engine design variables and NO emis-
sion rate also were evaluated. This evaluation was accom-
plished by "design sensitivity" analyses wherein engine
design parameters were varied parametrica11y. Design-
emission correlations resulting from these analyses will
be used in the formulation of design criteria for mini-
mizing NO emissions. These analyses were conducted by
using sets of input data describing "reference engines".
Individual parameters were varied to determine the sen-
sitivity of the predicted engine performance and NO con-
centration to each input variable.
Direct-Iniection Engine
Reference Engine Description
Two reference engines were used with the Dl engine model. The
reference engines are identical except for their chamber wall heat trans-
fer characteristics. The reference engine data sets are listed in Table
I. The values of the model parameters used are, as far as possible,
-------
53
based upon experimental evidence relevant to the combustion processes
occurring in the cylinder. The heat transfer coefficient (C^) is based
on engine heat transfer data (Ref 8), and the mean fuel fraction (F ) is
' m
assigned a stoichiometric value in accordance with observations that com-
bustion rates in diffusion flames are greatest in regions where stoichio-
metric mixtures exist. The minimum and maximum fuel fractions (F . and
m i n
F ) correspond approximately to flammability limits for diesel engine
ms x
fuels. The values of other model parameters, however, are estimates
based upon phenomenological descriptions of diesel combustion (Refs 1 and b).
The values of the design parameters used correspond to an en-
gine for which emission data are available (Engine E, Ref 9)- This en-
gine is an eight-cylinder automotive direct-injection engine with a de-
sign power output of 200 bhp and 3200 rpm. An inlet manifold pressure of
0.9 atm was selected to represent a volumetric efficiency of SO per cent.
Valve timing and inlet manifold flow losses were represented in this man-
ner since their principal effects are to reduce the mass of the air
charge.
Reference Engine Performance
The predicted performance parameters for the reference direct-
injection engines operating at their design point (3200 rpm) are as
fol1ows:
P red i cted Va1ue
Performance Parameter Engine A Engine B
1MEP (psi) 139 107
I HP 323 2U7
ISFC 0.2^+9 0.325
Exhaust NO Concentration (ppm) 1750 2210
Specific NO Emission Rate (gr/IHP-hr) 5-89 9-73
The predicted exhaust NO concentrations of 1750 and 2210 ppm are reason-
ably consistent with reported values of 1300 ppm and 5*20 gr/BHP-hr for
approximately the same operating condition (186 bhp at 3000 rpm, Ref 9)*
The mean chamber pressure, temperature, and NO concentration,
as predicted by the model, are shown in Figure 6 for the two engines.
-------
54
In the analysis leading to these performance predictions, 51 burned mix-
ture systems were formed during the combustion cycle. The properties of
the over-all air charge and five of the burned mixture systems for Engine
A are shown in Figure 7» The initial characteristics of the five burned
mixture systems described in the figure are as follows:
Burned Mixture Q at Formation Initial Fue 1 F ract i on
System Number (DCA) (F/Fs )
1 2.05 1.0
3 3-32 0.843
4 3-87 1.31
18 11.lit 1.0
40 30.4 1.0
The first three systems were formed during the initial burning period.
The first was formed with a stoichiometric fuel fraction, and the second
and third were lean and rich, respectively. The last two systems were
formed during the final burning period when combustion is assumed to
occur in diffusion flames at stoichiometric fuel concentrations.
These results for the Dl reference engines reveal a number of
significant features of the Dl engine model and the NO formation process.
It appears that the model predicts engine performance parameters and NO
emission rates quite well. The pressure-time curves shown in Figure 6
match closely the characteristics which are observed in actual engines.
The power, fuel consumption, and emission parameters listed above are
consistent with the values of these quantities reported for the engine.
No attempt has been made to adjust the model to achieve better agreement
between measured and predicted values of performance parameters. Better
agreement could be obtained by varying several different parameters, and
there is no basis at this time for choosing one over another. The agree-
ment achieved by the model in its "unca1ibrated" form was considered suf-
ficient for the purposes of this program.
With regard to NO formation, the most striking observation from
the results with the Dl reference engines is that nearly all NO is formed
during a small fraction of the total combustion cycle. NO formation
occurs primarily during the early stages of the final burning phase. Very
. ..tie NO is formed during its initial burning period. The NO concentrations
-------
55
in a few burned mixture systems do reach high levels as seen in system k
in Figure 7* However, this behavior is limited to those systems which
burn at fuel fractions slightly richer than stoichiometrip. The over-all
NO formation rate increases abruptly when fuel begins to burn in diffusion
flames at stoichiometric mixture ratios during the final burning phase.
The high NO formation rate continues for about 30 degrees of crank angle
after which the rate slows due to reduced chamber temperatures.
The concentrations of NO formed in the burned mixture systems
vary widely. NO is formed rapidly in each system while its temperature
is high. As observed in Figure 7, when the temperature of a system falls
below about ^500 deg R, the NO formation rate effectively becomes zero.
The factors which appear to affect the final NO concentration in each sys-
tem most strongly are:
1. Initial fuel fraction at burning.
2. Time (crank angle) at burning.
3« Heat transfer rate.
k. Rate of dilution with excess air.
These factors determine the temperature history of the system and, in
particular, the length of time the system temperature is in the regime
where NO formation proceeds at significant rates.
Model Parameter Sensitivity
To determine the sensitivity of predicted engine performance
to the evaluation of model parameters; a series of analyses were con-
ducted using the data for reference Dl Engine A in Table I. Each of the
first six model parameters was varied individually about its reference
value, and the performance predictions obtained are shown in Figure 8.
The power output (IHP) and efficiency (ISFC) of the engine are found to
be insensitive to these parameters except for weak effects of the fuel
vaporization rate parameter (Cj) and the heat transfer coefficient (C^).
Reducing the fuel vaporization rate (increasing Cj) reduces power and
efficiency by delaying heat release, and increasing the heat transfer rate
increases the energy lost to the cooling system.
The exhaust NO concentration, on the other hand, is observed
to be very sensitive to all model parameters except the dilution rate
-------
56
parameter (C^)• All of these sensitivities can be explained in terms of the
characteristics of the model.
Increasing the fuel vaporization rate parameter (Cj), the fuel
burning rate parameter (C2) » or the fraction increment (&F) causes the
NO concentration to decrease. The effect of Cj is to prolong burning into
later portions of the expansion stroke so that flame temperatures are lower.
The effects of C2 and A F are similar in that they both increase the portion
of fuel burned late in the premixed burning period in lean or rich systems.
Increasing the heat transfer rate is seen to increase the NO con-
centration. This effect results from heating of the air charge during the
compression stroke which increases the initial temperatures of the burned
mixture systems. The magnitude of this effect also is dependent upon the
assumed cylinder wall temperature. A more detailed analysis of the effects
of heat transfer parameters was conducted and the results are shown in Fig-
ure 9* Changes in heat transfer rate and wall temperature produce large
changes in NO concentration, even though the corresponding changes in peak
temperature are smal1.
Finally, it is observed that varying the mean fuel fraction (F )
in either direction from stoichiometric reduces the NO concentration strongly.
This effect is due primarily to reduced flame temperatures.
Design Parameter Sensitivity
Sensitivities of engine performance to design parameters were deter-
mined in a manner similar to the model parameter sensitivity analysis. Six
design parameters were varied independently about their reference values and
the resulting variations in engine performance are shown in Figure 10. In
this figure, NO emissions are indicated both as exhaust concentration and
specific emission rate expressed in gr/IHP-hr.
An increase in clearance volume reduces power, efficiency, and NO
concentration. The reduced NO is a result of lower flame temperatures, due to
lower compression ratios and peak temperatures. The rate of NO emission in-
creases, but the effect is small.
An increase in engine speed increases power output because of the
increased frequency of power strokes, and reduces NO concentration because
of reduced time available for NO formation. The rate of NO emission also
decreases when expressed in gr/IHP-hr as in Figure 10.
-------
57
Increasing inlet pressure increases power output and efficiency,
and strongly reduces NO concentration. The decrease in NO concentration
results from more rapid dilution and cooling of burned mixture systems.
The rate of NO emission also is reduced as the inlet pressure is increased
to 2 atm, but is increased with farther increases in pressure. The in-
crease in emission rate at higher inlet pressures results from higher
peak temperatures due to the suppression of dissociation. This effect
appears to outweigh the dilution rate effect at inlet pressures above
2 atm. It should be noted here that in this analysis inlet pressure alone
was varied so that the effect is not fully representative of turbocharging
where inlet temperature and heat transfer rate would vary also.
Changing the fuel injection time has the effect of changing the
time of heat release in the cycle. When injection and heat release are
delayed, the power output and efficiency are reduced, and the NO concen-
tration and emission rate are reduced because of lower flame temperatures.
Changing the injection rate changes the time period over which
fuel is injected. A low injection rate prolongs the heat release period
leading to reduced power, efficiency, NO concentration, and emission rate.
A high injection rate increases power and efficiency but reduces NO con-
centration and emission rate. The latter effect is a result of burning
all or most of the fuel during the premixed burning period wherein many
systems are burned at lean or rich fuel fractions and, hence, low flame
temperatures. Increasing fuel injection rate increases pressure rise rate
and peak pressure which also are important engine performance parameters.
High pressure rise rates lead to engine "knock" and high peak pressures
increase mechanical stresses. These performance characteristics are pre-
dicted by the engine model as shown in Figure 6.
The effect of reduced fuel rate (over-all fuel-air ratio) was
analyzed by keeping the injection time and rate constant, but reducing
the injection period (constant beginning-variable ending injection).
Reducing the fuel rate in this manner has the effect of reducing power
output, improving efficiency because of earlier burning, and reducing NO
concentration and emission rate. The NO reduction results from elimina-
tion of the final burning portion of the combustion cycle wherein the
u'ahest NO concentrations are formed.
-------
58
Some of these design parameter effects can be compared with
experimental data, and the comparisons indicate generally that the ef-
fects predicted by the model are qualitatively realistic. The effect
of clearance volume has been shown to have a mild effect on NO exhaust
concentration (Ref 10) as predicted here. The predicted effects of in-
jection time and over-all fuel-air ratio also are consistent with ob-
served performance of similar engines (Ref 11).
1ndirect-Iniection Engine
Reference Engine Description
The reference engine data set used with the IDI model is listed
in Table II. The values of the model parameters are, in most cases, the
same as those used with the 01 model reference engines. The values of
the design parameters used correspond to an engine for which performance
and emission data are available (Engine I, Ref 9). This engine is a six-
cylinder automotive indirect-injection engine with a design power output
of 270 bhp at 2200 rpm. Intake air is turbocharged to approximately 2
atms and aftercooled.
Reference Engine Performance
The predicted performance parameters for the reference indirect-
injection engine, operating at its design point, are as follows:
Indicated Mean Effective Pressure (IMEP) 214 psi
Indicated Specific Fuel Consumption (ISFC) 0.295 lbm/IHP-hr
Indicated Horsepower (I HP) 378 hp
Exhaust NO Concentration 1275 ppm
Specific NO Emission Rate 5*46 gr/IHP-hr
The predicted exhaust NO concentration is higher than the reported value
of 700 ppm and 3-48 gr/BHP-hr for this engine operating at its design
point (279 ghp at 2200 rpm, Ref 9)*
The properties of the air charge in the engine cylinder, as
predicted by the model, are shown in Figure 11 for the compression and
expansion strokes. Peak pressure, temperature, and NO concentration are
-------
59
predicted to be higher in the prechamber than in the main chamber. The
reversal in the prechamber NO concentration is due partly to disso-
ciation of NO with decreasing temperature and partly to the efflux of
burned mixture from the prechamber.
Model Parameter Sensitivity
The model parameter sensitivity analysis was conducted in the
same manner as with the direct-injection engine model. Each model parame-
ter for each chamber was varied about its reference value with all other
parameters held constant, and the variations in predicted engine perform-
ance are shown in Figure 12. The engine performance parameters, ISFC and
IHP, were found to be insensitive to all model parameters. This lack of
sensitivity is more pronounced than with the direct-injection engine.
Slight effects on performance are observed with variations in the fuel
vaporization rate parameter and the heat transfer coefficient. The trends
are similar to those with the Dl engine.
The predicted exhaust NO concentration was found to be more
sensitive to model variables than engine performance, but again less than
with the Dl engine. The NO concentration is seen to be rather insensitive
to fuel vaporization rate parameter, the burning rate parameter, the heat
transfer coefficient, and the fuel fraction increment. Increases in the
dilution rate parameter in the main chamber, however, cause pronounced in-
creases in the NO concentration. This effect is the result of incomplete
fuel burning in the prechamber due to rich fuel mass fractions. When the
burned mixture systems pass into t-he main chamber, they are diluted with
air and their temperatures rise as the burning process is completed. With
increased dilution rates, burning is completed earlier in the cycle lead-
ing to increased NO concentrations.
The dependence of engine performance and NO concentration on
the mean fuel fraction at burning is shown in Figure 12 in tabular form.
The mean fuel fraction is expressed as a fraction of the stoichiometric
fuel fraction. The maximum NO concentration is predicted for the condition
where combustion occurs initially at stoichiometric conditions (F /F = 1.0).
m st '
Changes in the initial fuel fraction in either chamber cause a reduction in
-------
60
X0 concentration. This result is consistent with the results for the 01
ngine. In the IDI engine analysis, changes in were evaluated in the
rich direction in the prechamber and in the lean direction in the main
chamber since these are the directions in which variations are most
1ikely to occur.
Design Parameter Sensitivity
Sensitivities of engine performance, exhaust NO concentration,
and specific NO emission rate were determined for eight engine design and
operating parameters, and the results are shown in Figure 13« The first
six parameters are the same ones which were investigated with the Dl en-
gine. The last two parameters-- prechamber volume and the fraction of
fuel injected into the main chamber— are specific to the indirect-in-
jection engine.
The clearance volume was varied with the fraction occupied by
the prechamber held constant at 30 per cent. As with the Dl engine, an
increase in clearance volume is accompanied by a degradation of engine
performance and a slight reduction in NO concentration. As with the
Dl engine, the specific NO emission rate increases slightly with clear-
ance volume.
Changes in engine speed are accompanied by changes in power
output, as with the Dl engine, but also by changes in 1SFC. The exhaust
NO concentration and the specific emission rate vary inversely with en-
gine speed. All of these effects are observed to be mild.
Increases in inlet pressure are seen to improve performance,
but the exhaust NO concentration passes through a minimum at about 2 atms
pressure. The specific NO emission rate, which is dependent upon both
pressure and exhaust concentration, is a minimum at a somewhat lower in-
let pressure. The existence of a minimum emission rate is observed with
both the Dl and IDI engines, and occurs at inlet pressures above ambient.
The effects of fuel injection time and injection rate on en-
gine performance and NO concentration appear to be small. This lack of
sensitivity can be attributed to the influence of the divided chamber.
The heat release rate is controlled partly by the flow of fuel from the
prechamber so that the dependence upon injection parameters is reducpd.
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61
Somewhat greater sensitivity of NO emissions to fuel injection parameters
has been observed in experimental tests (Ref 12).
The over-all fuel-air ratio was investigated by keeping the
injection time and rate constant and reducing the injection duration (con
stant beginning-variable ending injection). The same procedure was used
with the Dl engine. As the fuel rate is reduced from the design point,
the power output and ISFC decrease. The exhaust NO concentration in-
creases to a maximum and then decreases. A maximum NO concentration
such as that predicted here is actually observed with some indirect-
injection engines (Ref 13)- However, a maximum was not reported for
the reference engine (Ref 9)• Such a maximum can be attributed to near-
stoichiometric fuel-air mixtures and high flame temperatures in the
prechamber which will occur at intermediate engine power levels.
Variations in prechamber volume were investigated by keeping
the total clearance volume constant and varying the fraction occupied by
the prechamber. This variation is observed to have only mild effects on
engine performance and NO concentration. Increasing the prechamber vol-
ume reduces performance and increases NO emission rate.
The fraction of fuel injected directly into the main chamber is
defined to represent that portion of the fuel which passes directly
through the interchamber port upon injection. This parameter was found
to have a strong effect on NO concentration and lesser effects upon en-
gine performance. Reducing this fraction appears to result in strong
reductions in NO concentration, but at the expense of milder reductions
in engine performance.
Summary of Results
The results of the parametric analyses which have been con-
ducted indicate that exhaust NO concentrations and specific NO emissions
rates in both direct- and indirect-injection engines are influenced by
a number of combustion processes (represented in these models by model
parameters) and a number of engine design parameters. Because of this
interdependence of parameters, it has not been possible to calibrate
either of the prediction techniques by means of existing performance and
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62
emission data. To calibrate the models it will be necessary to conduct
carefully controlled experiments wherein the engine design parameters
are known and can be controlled. Further evaluation of certain combus-
tion processes also will be necessary to evaluate those rriodel parameters
which influence NO emissions.
The performance and emission predictions appear to be in quali-
tative agreement with results reported for actual engines. D i rect-i nject i on
engine NOx emissions are sensitive to fuel injection parameters-- injection
time, injection rate, and ovei all fuel-air ratio. 1ndirect-injection en-
gines are less sensitive to fuel injection parameters. A general tendency
of indirect-injection engines to produce lower NO emissions than direct-
injection engines has been observed. However, the distribution of fuel
between the chambers appears to be an important factor in this effect.
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63
ENGINE DESIGN CRITERIA
FOR NOx EMISSION CONTROL
Direct-Injection Engines
In the previous section, it was observed that NOx emissions
from the Dl engine are affected by various engine design parameters,
particularly those related to fuel injection characteristics• Specifi-
cally, NOx exhaust concentrations and specific emission rates (gr/IHP-
hr) can be reduced by the following variations in design parameters:
1. Delay injection time.
2. Increase injection rate.
3- Reduce engine power level (over-all fuel-air ratio).
These variations are, of course, accompanied by changes in engine per-
formance parameters which include:
1. Specific fuel consumption (1b-fuel/HP-hr).
2. Specific power (HP/lb-engine).
3. Peak chamber pressure.
k. Pressure rise rate.
Design parameter variations may also affect the emission of pollutants
other than nitrogen oxides.
Different combinations of design parameter variations will
have different effects on engine performance. However, it is reasonable
to assume that engines currently are designed to attain a near optimum
combination of the performance parameters listed above. Any modification
of design parameters is likely to move engine performance away from this
Optimum condition. Thus, NOx emission control attained through engine
design modifications will result in a performance penalty.
The degree of NOx emission control attainable with Dl engines
appears to be dependent upon the amount of performance loss the engine de-
signer can tolerate. However, by carefully combining different emission
control approaches, it appears that significant reductions in specific
NOx emission rate— of the order of 50 per cent— should be attainable
with small losses in engine performance.
Of the three design parameter variations listed above, the most
attractive is the increased injection rate since this variation also
-------
improves specific fuel consumption. Delaying injection time increases
specific fuel consumption and smoke emission (Ref 11). Reducing fuel-air
ratio reduces specific engine power, but also reduces smoke and CO emis-
sions. Thus, a logical approach to NOx emission control with Dl engines
might involve the following sequence of steps:
1. Increase injection rate to maximum degree possible within
limits imposed by a peak pressure or pressure rise rate
cri terion.
2. Simultaneously retard injection timing and reduce over-all
fuel-air ratio (or engine power rating). Combined varia-
tions of these two quantities should allow control of smoke
emission to be maintained while NOx emission rate is re-
duced .
Indirect-Injection Engines
The use of indirect injection has been observed to reduce NOx
emissions from the levels characteristic of Dl engines. The results of
this study indicate that this natural advantage of ID1 engines can be
accentuated by restricting the injection of fuel to the precombustion
chamber. Changes in fuel injection rate and timing appear to have little
effect on NOx emissions in contrast to the Dl engine where these factors
have the greatest influence. As mentioned earlier, the precombustion
chamber appears to act as a fuel injection device. NOx emissions can be
minimized by retaining the fuel in the prechamber until burning occurs,
and then allowing the rich burned mixture to pass into the main chamber
where further burning and dilution occur quickly. It seems likely that
this approach could be exploited by modifications of fuel spray charac-
teristics which reduce the quantity of fuel injected directly through
the interchamber port and increase the fuel residence time in the pre-
combustion chamber. This approach appears from Figure 13 to involve an
increase in specific fuel consumption, and it is possible that other per-
formance penalties would be incurred which are not evident from the theo-
retical results. However, the NOx emission reduction effectiveness of
this approach appears to be high.
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65
AUXILIARY METHODS OF NOx EMISSION CONTROL
Control Methods Considered
Auxiliary methods of reducing the rate of NO emission from
diesel engines have been identified during this study and in investiga-
tions by other workers. One of the objectives of this study was to evalu-
ate these approaches, as far as possible, using the emission prediction
techniques which have been developed for direct and indirect-injection
engines. The control approaches which have been identified are the fol-
lowing:
1. Turbocharg i ng.
2. Staged fuel injection.
3- Water injection.
k. Exhaust gas recirculation.
Analyses of turbocharging and staged injection have been conducted. Water
injection and exhaust gas recirculation have not been evaluated since they
would require modifications to the models to account for the changes in
properties of the initial air charge. With these modifications, it will
be possible to investigate these control methods for both types of engines.
Evaluation Results
Turbocha rq ing
The effect of turbocharging was investigated using the direct-
injection engine model and a series of data sets representing different
engines. These engines were as follows:
Engine B - Nonturbocharged reference engine. (Engine B in
Table l).
Engine C - Same as Engine B with turbocharging to double the
inlet pressure. Compressor efficiency assumed to
be 82 per cent, and no aftercool ing.
Engine D - Same as Engine C with aftercool ing.
Engine E - A high MEP, low compression ratio engine. Displace-
ment equal to Engine B. Turbocharged to approximately
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66
6 atms with aftercooling, and compression ratio
reduced to 10:1.
This series of engines represents the introduction of turbocharging with-
out and with aftercool ing, and the extension of the turbocharging concept
to very high operating pressure engines. The engine parameters which
were varied and the predicted performance for the engines are listed in
Table III.
The predicted results indicate that a reduction in NO emission
will not result directly from the use of conventional turbocharging. The
exhaust NO concentration is reduced only slightly because the increase in
inlet temperature offsets the effect of the reduction in fuel-air ratio.
The rate of NO emission from the engine is predicted to increase substan-
tially either with or without aftercooling. It is possible, however, that
changes in fuel injection timing and ignition delay, associated with the
use of turbocharging, could result in reduced NO emission rates. Fuel
injection and ignition delay effects were not included in this analysis,
but investigation of these effects would appear to be warranted.
The results for Engine E indicate that the use of high HEP en-
gines with reduced compression ratios may lead to reduced NO emissions.
However, the reduction does not appear to be large, and it is obtained at
the expense of a severe increase in peak cylinder pressure. The favorable
power and specific fuel consumption predicted by the model are not real-
istic because the pumping losses are not included.
Staged Fuel Injection
Modeling Techniques
The term "staged injection" is used to describe diesel engine
fuel injection systems wherein fuel is introduced into the combustion
chamber in two steps. Typically, a portion of the fuel is injected as in
conventional engines, while another portion is introduced earlier in the
combustion cycle. Three methods of early introduction of fuel have been
developed (Ref 1):
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67
1. Pilot injection - injection early in the compression stroke.
2. Vigom injection - injection into the residual gas at the eno
of the exhaust stroke.
3- Fumigation - injection or carburetion into the inlet air.
These methods of early fuel introduction were developed as methods for
improving combustion performance or to allow operation with alternate
fuels. Descriptions of engine performance resulting from these fuel in-
troduction techniques are contained in References 1^+ through 17-
In this program, separate models were not required to represent
combustion in diesel engines with staged fuel injection. The pilot in-
jection approach was investigated with the existing direct-injection
model by appropriate variation of the fuel injection schedule. The Vigom
and fumigation approaches were represented by introducing minor changes
in the existing Dl model.
In both Vigom injection and fumigation, the fuel introduced
early can be assumed to be completely vaporized and uniformly mixed with
the air charge by the time the main fuel injection process begins. The
fuel premixed in the air charge was represented in the Dl model by intro-
ducing two new variables;
F. - The true fuel fraction of system i.
i ,t
F - The fuel fraction of the air charge due to early intro-
a
duction of fuel.
These variables are related to the fuel fraction F. in the model as follows:
i
F. = F. (1 - F ) + F
i , t i a a
With no early introduction of fuel (F =0), the fuel fraction F. and the
3 I
true fuel fraction F. are equal. If fuel is introduced early (F >0),
i , t 3
the fuel fraction F. must be interpreted as the mass fraction of i ni ected
fuel .
The true fuel fraction F. ^ must be utilized in determining the
' » L
internal energy or enthalpy of a burned mass system, and in calculating
the NO formation rate in a burned mass system. The injected fuel fraction
F. continues to serve in the conservation of injected fuel.
This approach to modeling staged injection is adequate as long
as the fraction of fuel introduced early is small. The physical properties
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68
of the air charge need not be modified to account for the effect of the
premixed fuel.
Pilot Injection Results
Pilot injection was investigated in a series of direct-injection
engines with variations in the quantity and timing of the early injected
fuel. The engine parameters varied and the predicted performance are
listed in Table IV. The reference engine is similar to the reference Dl
Engine B described in Table I, but with one model parameter changed as
fol1ows:
Fuel fraction increment = 0.005-
The other engines listed in Table IV are similar to the refer-
ence engine, but with pilot injection of a part of the fuel. Variations
in pilot injection time, pilot injection fraction, and main fuel injec-
tion time were investigated. No significant changes in engine perform-
ance were predicted, and in all cases exhaust NO concentration was pre-
dicted to increase or remain unchanged.
In modeling pilot injection with the direct-injection engine
model, it is being assumed implicitly that no fundamental differences
in combustion processes result from pilot injection. Early injection of
fuel results in an increase in the quantity of fuel vapor present at
ignition, and a larger fraction of the fuel burned during the initial
burning period. This fuel burns at rich and lean fuel fractions (in
the model) because of the fuel burning model employed. The effect of
pilot injection on ignition delay is not known precisely, but a reduced
delay time would be expected. Therefore, a shorter ignition delay was
assumed with all engines with pilot injection, and one variation in
delay time (engine F) was examined to determine its effect. The net
result of this investigation of pilot injection is that, within the
constraints imposed by the use of the Dl model, there is no indication
of a reduction in NO emissions from the use of pilot injection.
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69
Fumi gat i on Results
The effects of fumigation (or Vigom injection) on performance
and NO concentration were investigated in a series of engines with varia-
tions in the quantity of ear 1y-injected fuel and the injection time of
the main charge. The results of this investigation are listed in Table
V. The ignition time was varied since the effect of fumigation on igni-
tion time was not incorporated in the model.
The reference engine is a direct-injection engine similar to
that described in Table I and the same reference engine used to study
pilot injection. With fumigation, the mean fuel fraction at burning (F ),
which now only represents injected fuel, was adjusted so that the total
fuel fraction at burning was stoichiometric. Also, the total amount of
fuel burned per cycle, including injected and fumigated fuel, was held
constant.
With 20 per cent of the fuel introduced by fumigation, a large
reduction in NO concentration is predicted with a modest penalty in en-
gine performance. At higher fumigation rates, NO concentration is further
reduced, but the predicted e'ngine performance reductions are more severe.
These results appear to represent an attractive approach to NO emission
control. However, limited data available on the effects of fumigation
(Ref 11) do not confirm the degree of NO emission reduction which is pre-
dicted. It appears that there is a strong possibility that the model does
not represent the effects of fumigation accurately and that the effects
on NO emission are exaggerated. Nevertheless, because of the predicted
trend, which is qualitatively consistent with experimental results, it
seems that fumigation deserves further investigation as a means for NO
emi ss ion control.
Water Injection
The addition of water to the inlet air of diesel engines has
been found to reduce NOx emissions (Ref 11), and similar results are ob-
served with other combustion systems. With certain modifications, the
engine models developed in this program can be used to evaluate the
effectiveness of water injection as an emission control method. The
-------
modifications of the models required to conduct this evaluation are
as follows:
1. The thermodynamic properties of the air charge must be
modified to represent a mixture of air and water vapor.
2. Equilibrium composition of burned mixtures must be calcu-
lated for combustion of fue1-air-water mixtures.
3- Caloric equations of state must be introduced for burned
mixtures resulting from fuel-air-water combustion.
Other changes due to water injection, such as variations of inlet air con-
ditions, can be represented by variations of model input data.
Exhaust Gas Recircu1 ation
Exhaust gas recirculation also has been found to be effective
in reducing NOx emissions from diesel engines (Ref 11). This effective-
ness can be evaluated with the engine models developed in this program
with modifications. The modifications required are as.follows:
1. The thermodynamic properties of the air charge must be
modified to represent a mixture of air and exhaust gas.
2. The exhaust gas concentration must be incorporated in the
burned mixture composition calculation procedure.
Other modifications, such as changes in stoichiometric air-fuel ratios,
can be made by varying model input data.
Effects of Control Methods on Other Emissions
Exhaust concentrations or emission rates of other pollutants of
concern-- CO, hydrocarbons, and particulates— are not predicted by the
engine models. However, sufficient experimental data on these emissions
exist to allow qualitative predictions to be made of the effects of the
various control methods examined in this study. A comprehensive review of
published data on diesel engine design-emission correlations has been
prepared recently by Bascom, Broering, and Wulfhorst (Ref 11).
Observations of the effects of control methods on other emis-
sions are as follows:
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71
1. Turbocharqinq reduces exhaust particulates (smoke) and has
no appreciable effect on CO or hydrocarbons.
2. Fumigation is found to increase CO and hydrocarbon emis-
sions, particularly at intermediate power levels. Effects
on particulate emissions depend upon the nature of the fuel,
but fumigation with kerosene appears to increase smoke.
Effects of pilot injection on emissions have not been re-
ported.
3« Water injection does not appear to have significant effects
on other emissions. However, the relevant data are limited.
k. Exhaust gas recirculation tends to increase CO and particu-
late emission because of. the reduced availability of oxygen.
Summary of Effects
The effects of the various control methods on emissions are sum-
marized qualitatively in Table VI. Certain of these methods can be com-
bined to produce more effective emission control. A very attractive
combination which is included in the table is exhaust gas recirculation
with turbocharging and aftercooling (Ref 11).
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72
REFERENCES
1. Obert, Edward F., Internal Combustion Engines, Third Edition, Inter-
national Textbook Company, Scranton, Penna., 1970.
2. Hurn, R. W., "Air Pollution and the Compression-Ignition Engine",
Twelfth Symposium (international) on Combustion. The Combustion
Institute, Pittsburgh, Penna., 1969. PP- 677-687-
3- Borman, G. L., Mathematical Simulation of Internal Combustion Engine
Processes and Performance Including Comparisons with Experiment. PhD
Thesis, University of Wisconsin, Ann Arbor, Mich., 196^f.
k. Lyn, W. T., "Study of Burning Rate and Nature of Combustion in Diesel
Engines", Ninth Symposium (international) on Combustion, Academic Press,
New York, N- V., 1963, pp. 1069-1082.
5- Tsao, K. C-, Myers, P. S., and Uyehara, 0. A., "Gas Temperature During
Compression in Motored and Fired Diesel Engines", SAE Trans. . vol. 70,
1962, pp. 136-145.
6. Fletcher, R. S. and Heywood, J. B., A Model for Nitric Oxide Emissions
from Aircraft Gas Turbine Engines (AIAA Paper No. 71-123), American
Institute of Aeronautics and Astronautics, New York, N. Y., January,
1971.
7. Zeleznik, F. J. and Gordon, S., A General IBM 704 or 7090 Computer
Program for Computation of Chemical Equilibrium Compositions. Rocket
Performance, and Chapman-Jouquet Detonations (NASA TN D-1454 and TN D-
1737). National Aeronautics and Space Administration, Lewis Research
Center, Cleveland, Ohio, October, 1962 and October, 1963-
8. LeFeuvre, T., Myers, P. S., and Uyehara, 0. A., Experimental Instan-
taneous Heat Fluxes in a Diesel Engine and Their Correlations (SAE
Paper No. 690464), Society of Automotive Engineers, Mid-Year Meeting,
Chicago, 111., May 19_23» 1969-
3. Marshall, W. F. and Fleming, R. D., Diesel Emissions Reinventoried.
(Bureau of Mines Report of Investigations 7530), United States Depart-
ment of the Interior, Bureau of Mines, Bartlesvi1le, Okla., July, 1971•
10. Timoney, S. G., Variable Compression Ratio Diesel Engine (SAE Paper
No- 719052), Society of Automotive Engineers, August, 1971•
11. Bascom, R. C., Broering, L. C., and Wulfhorst, D. E., Design Factors
that Affect Diesel Emissions, Cummins Engine Company, Inc., Prepared
for the 1971 SAE Lecture Series "Engineering Know-How in Engine De-
s i gn", Ma rch 12, 197'•
12. Landen, E. W. , Nitrogen Oxides and Variables in Precombustion Chamber
Type Diesel Engines (SAE Paper No. 714B), Society of Automotive Engi-
neers, June, 1963•
13- Perez, J. M. and Landen, E. W. , Exhaust Emission Characteristics of
Precombustion Chamber Engines (SAE Paper No. 680421), Society of Auto-
motive Engineers, Mid-Year Meeting, Detroit, Mich., May 20-24, 1968.
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73
1U. Schweitzer, P. H., "Pilot Injection", Automotive Industries. October 29,
1938, p. 533-
15« Gupta, C., Shipinski, J., Uyehara, 0., and Myers, P., Effects of Mul-
tiple Introduction of Fuel on Performance of CI Engine (SAE Paper No.
929A), Society of Automotive Engineers, October, 1964.
16. Eyzat, P., Baudry, J., and Sale, B. , The Effect of the Vigom Process
on Combustion in Diesel Engines (SAE Paper No. 929B), Society of Auto-
motive Engineers, October, 1964.
17- Alperstein, M., Swim, W., and Schweitzer, P., "Fumigation Kills Smoke",
SAE Trans. . Society of Automotive Engineers, vol. 66., 1958, pp. 574-
595-
18. Hottel, H. C., Williams, G. C., and Bonnel1, A. H., "Application of
Well-Stirred Reactor Theory to the Prediction of Combustor Perfor-
mance", Combustion and Flame Quarterly Journal of the Combustion
Inst i tute. vol. 2, no. 1, March, 1958.
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lh
TABLES
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75
TABLE I
REFERENCE ENGINE INPUT DATA USED WITH
DIRECT-INJECTION ENGINE MODELS-
Model Parameters
Fuel Vaporization Rate Parameter (Cj) 10 DCA"~"
Fuel Burning Rate Parameter (C_) 10 DCA
^ _ 1
Dilution Rate Parameter (C^) 0.05 DCA
Heat Transfer Coefficient (C^) 0.001 1bf - ft (Engine A)
ft2 - deg R - DCA
0.010 1 bf - ft (Engine B)
ft2 - deg R - DCA
Mean Fuel Fraction at Burning (F ) 0.0636 (stoichiometric)
Fuel Fraction Increment (AF) 0.01
Minimum Fuel Fraction at Burninq (F . ) 0-0318
J min
Maximum Fuel Fraction at Burninq (F ) 0.0955
3 max
Ignition Delay (DCA) 15
Design Parameters
Cylinder Bore (B) 0-375 ft
Crank Length (R) 0.1875 ft
Compression Ratio 17:1
Clearance Volume (Vc) 0.00259 ft^/cyl inder
Inlet Manifold Pressure 1500 psfa
Inlet Air and Fuel Temperature 520 deg R
Average Wall Temperature 1200 deg R (Engine A)
1000 deg R (Engine B)
Engine Speed 3200 rpm
Injection Time 15 DCA-BTC""5'
Fuel Injection Rate 5-23 x 10~^ '
DCA - cy1i nder
Mean Injection Rate 10.^6 x 10~^ --^¦rn,
cycle - cy1i nder
The same input data were used for both reference Engines A and B except
where indicated.
DCA = degrees crank angle; BTC = before top center.
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76
TABLE I I
REFERENCE ENGINE INPUT DATA USED WITH
INDIRECT-INJECTION ENGINE MODEL
Model Parameters
Prechamber
Fuel Vaporization Rate Parameter (Cj)
Fuel Burning Rate Parameter (C^)
Dilution Rate Parameter (C^)
Heat Transfer Coefficient (C^)
Mean Fuel Fraction at Burninq (F )
3 m
Fuel Fraction Increment F)
Minimum Fuel Fraction at Burninq (F . )
3 min
Maximum Fuel Fraction at Burninq (F )
3 max'
Igni t ion Del ay (DCA)
10 DCA
10 DCA
-1
0.05 DCA
0.01 ,bl - ft
ft'
0.0636
0.005
0.0318
0.0955
11.5
deg R - DCA
Main Chamber
5 DCA"
10 DCA
0.05 DCA
0.01 lb! " ft
ft - deg R
O.O636
0.005
0.0318
0.0955
14.0
DCA
Design Parameters
Cylinder Bore (B) 0.396 ft
Crank Length (R) 0.250 ft
Compression Ratio 12:1
Clearance Volume (V_) 0.0056 ft^/cylinder
Prechamber Volume (Vp^-) 0.00168 ft /cylinder
Inlet Manifold Pressure 4000 psfa
Inlet Air Temperature 580 deg R
Inlet Fuel Temperature 520 deg R
Average Wall Temperature (both chambers) 1000 deg R
Engine Speed 2200 rpm
Fraction of Fuel Injected to Main Chamber 0.25
Injection Time 14 DCA-BTC"
Fuel Injection Rate 1.4 x 10 ^ 7-77 ; —
DCA - cy11nder
Mean Injection Rate 2.8 x 10 ^
cycle - cylinder
DCA = degrees crank angle; BTC = before top center.
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77
TABLE I I I
PREDICTED EFFECTS OF TURBOCHARGING ON DIRECT-INJECTI ON
ENGINE PERFORMANCE AND NO EMISSION
Pa rameter
Enq i
i ne
B
C
D
E
Inlet Pressure (psia)
13-2
26.5
26.5
80.0
Inlet Temperature (deg R)
520
655
590
590
Compression Ratio
17
17
17
10
Peak Pressure (psia)
945
1 360
1440
1930
ISFC (lbm/IHP-hr)
0-325
0.262
0.253
0.166
IMEP (psi)
107
1 32
138
210
1 HP
247
306
317
486
Over-Al1 f/a
0-0375
0.0218
0.0197
0.0062
Exhaust NO (ppm)
2213
2058
1803
619
NO Emission Rate (gr/IHP-hr)
9-73
11.47
10.52
7-49
1gn i t ion Del ay (DCA)
15-0
15.0
15.0
15-0
Note: Engine configuration same as Dl reference Engine B (Table l).
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78
TABLE IV
PREDICTED EFFECTS OF PILOT INJECTION ON DIRECT-1NJECTI ON
ENGINE PERFORMANCE AND NO EMISSION
Parameter
Ref"
P ilot Fuel Quant i ty
(fraction of total) 0
Pilot Injection Time (DCA)
Main Fuel Injection Time (DCA) -15
Ignition Time (DCA) 0
I HP 247
ISFC (1bm/lHP-hr) 0-325
Exhaust NO (ppm) 3227
NO Emission Rate (gr/IHP-hr) 14.2
F
Enq i ne
G H
i
J
0.3
0-3
0.3
0.4
0.3
-35
-35
-55
-35
LTV
CO
1
_15.
-15
-15
-15
-7
-5
-8
-8
-8
0
256
256
256
257
245
0-315
0.314
0.315
0.312
0.325
3656
^507
4031
4000
3182
15-6
19-2
17-2
16.95
14.0
Reference Engine B (Table l) with ^F = 0.005*
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TABLE V
PREDICTED EFFECTS OF FUMIGATION ON DIRECT-INJECTION
ENGINE PERFORMANCE AND NO EMISSION
Pa rameter
Enq i ne
Ref-'
K
L
M
N
Quantity of Fumigated Fuel
(fraction of total)
0
0.2
0.2
0.4
0.4
Main Fuel Injection Time (DCA)
-15
-15
-15
"15
-7
1gni t ion Time (DCA)
0
-8
0
-8
0
1 HP
247
206
206
163
154
ISFC (lbm/IHP-hr)
0-325
0.389
0.391
0.492
0.52C
Exhaust NO (ppm)
3227
1003
603
214
105
NO Emission Rate (gr/IHP-hr)
14.2
5-29
3-19
1.43
0.74
Reference Engine B (Table l) with AF = 0.005-
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TABLE VI
SUMMARY OF CONTROL METHOD EFFECTIVENESS
Control Method
Turbochargi ng
Pi lot 1nject ion
Fum i gat i on
Water Injection
Exhaust Gas
Reci rculation
Exhaust Gas
Reci rculation wi th
Turbocharging and
After cool ingVf
Effect on Emission Rates (qr/bhp-hr)
NOx
Increase
Increase
Decrease
Decrease
CO
Decrease
U
Increase
N
HC
Decrease
U
Increase
N
Pa rt i culates
Decrease
U
Increase
N
Decrease
Increase
U
Increase
Decrease
Results actually dependent on extent of EGR and TC.
Code: N = little or no effect.
U = effect unknown.
-------
81
FIGURES
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82
AIR
m ,
, abm,i
m
. a
mf]
L1 QU1 D
m
V.
V
FUEL
*
BURNED
M XTURE
GASEOUS
abm,i-1
BURNED
MIXTURE
i - 1
abm, 1
BURNED
MIXTURE
1
FIGURE 1
- FLUID SYSTEMS AND MASS TRANS PORT
PROCESSES: DIRECT-INJECTION FNGINE MODEL
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83
AIR
^/"abm, i
m
abm,i-1
m
a, kl
BURNED
MIXTURE
"fb
LIQUID
FUEL
PRECHAMBER
MAIN CHAMBER
m
fg
fl.kl
AIR
GASEOUS
FUEL
m
fg.kl
BURNED
MIXTURE
i, kl
fl
m
abm, i
BURNED
MIXTURE
m
fb
LIQUID
FUEL
: >
fl r
fg
GASEOUS
FUEL
BURNED
MIXTURE
i-1
m u
y abm,
BURNED
MIXTURE
m.
bm,i-1,k1
±
m
bm,1,kl
BURNED
MIXTURE
i-1 , kl
BURNED
MIXTURE
l.kl
I
r
m
k • abm,i — 1
JL
BURNED
MIXTURE
i-1
1
™ k
. abm
BURNED
MIXTURE
1
FIGURE 2 - FLUID SYSTEMS AND MASS TRANSPORT PROCESSES:
INDIRECT-INJECT I ON ENGINE MODEL
-------
8k
< 0 >
TDC Pi ston
Pos i t i on
FIGURE 3 -
DIRECT-INJECTION ENGINE CYLINDER DESIGN VARIABLES
-------
85
f b
(9
Q. Q,
e.
FIGURE k
- DIRECT-INJECTION ENGINE COMBUSTION
CYCLE AND MASS TRANSPORT PROCESSES
-------
86
V,
Precombus t i on
Chambe r
Ma i n
Chamoer
Top Dead Center
(TDC) Positi on
FIGURE 5 - INDIRECT-INJECTION ENGINE CYLINDER DESIGN VARIABLES
-------
1^0-
120.
100-
80
60
*40-
0)
-O
E
to
sz
LJ
c
ru
0)
20-
0L
30
C71
0)
"O
rsj
o
— (U
fD
u
a>
CL
E
0)
25
20
15
E
a.
Q_
c
o
c
u
u
c
o
LJ
O
z
u
o
JD
E
_c
o
c
HJ
0)
10
5^
Tempera ture
Eng. A
Pressure
Eng. A
Eng. B
[NO]
Eng. A
Eng. B
0 10 20 30 *t0
Crank Position (degrees from top center)
FIGURE 6 - MEAN CHAMBER GAS PROPERTIES, D IRECT-INJECTI ON REFERENCE ENGINES
-------
at.n
Total Charge
(mean properties)
Crank Angle (deg)
System 3
i r—i 1 i r
t.c. ^0 80
F/F
=r=M
Crank Angle (deg)
System 18
st
F/F
st
*»
r
80
T
°R
F/Fst
[NO]
ppm
"4000
"2.0
"^000
"2000
"1.0
" 2000
-0
•0
0
T
°R
F/Fst
.—,e
-ifOOO
- 2.0
- **ooo
-2000
-1.0
- 2000
-0
-0
L 0
T
°R
F/F
st
[no]
ppm
-6000
-A000
- 2.0
1 1 1
O
o
o
-2000
- 1.0
- 0
- 0
-0
System 1
88
Crank Angle (deg)
System h
Crank Angle (deg)
System ^0
¦ F/F
st
I I r—
t.c. *40
I 1 I
t.c. ^0
Crank Angle (deg) Crank Angle (deg)
FIGURE 7 -•PREDICTED PERFORMANCE OF THE REFERENCE DIRECT-INJECTI ON ENGINE
80
-------
-Ol SFC
or
On
\
s
ofNol
f HP'
HP
-600
-J^oo
-200
i
10
1
20
1-0
Fuel Vaporization Rate Parameter (DCA)
0'
A-
o.6s
0. 10
Dilution Rate Parameter (DCA ')
ISFC O-
I HP A-
M?
I
0.5
I
1-5
IHP-hr
h 0.3
0.2
I SFC
1 hm.
[noI
¦ppm
" 2000
0. 1
- 1000
89
—O— \—O O- I SFC
& —I HP
\
1-0
1
20
0 10
Fuel Burning Rate Parameter (DCA)
I HP I SFC [no]
HP
) hn
-600
1HP-hr
-0.3
-OlSFC
¦0[no]
-'~OO
-0.2
-A 1 HP
-200
-0. 1
•0
¦0
- 2000 q—O
- 1000
AI HP
I HP ISFC
5 0.605 0?01
Heat Transfer Coeff. Ct2-°R-DO})
HP
1 hn
-600
1HP-hr
-0.3
¦ <400
-0.2
-200
-0.1
•0
-0
ppm
- 2000
-OlSFC
\
—AI HP
- 1000
k)
1 1 1
0 0.01 0.02
Fuel Fraction Increment
Mean Fuel Fraction at Burning (F /F )
m st
FIGURE 3 - SENSITIVITY OF PREDICTED DIRECT-INJECTI ON ENGINE PERFORMANCE TO MODEL PARAMETERS
-------
LEGEND
T [no]
V J
^OOO
3000
2000
1000
Cu rve
(0
(2)
0 -,ES
Heat Transfer
Coeff i c i en t
(lbf-ft/ft2-R-DCA)
0.010
0.010
0.001
0
Wal1 Temperature
Mean Cylinder Temperature
11 on
T
0
t. c.
Position in Cycle (DCA)
+ 100
FIGURE 9 -
SENSITIVITY OF PREDICTED NO EMISSION RATE TO HEAT TRANSFER PARAMETERS
vn
o
-------
I SFC
N0|
I HP
H*
i 1 1
0 0.0025 0.005
Clearance Volume (ft3)
I HP I SFC [no] [no] *
HP
1 bm
ppm
- 600
IHP-hr
-0.3
-2000
-^00
¦0.2
-1000
•200
¦0. 1
-0
- 0
-0
_1L
91
IHP-hr
10
O— I SFC
0?\ 2!jOO
(^ng i ne Speed (rpm)
5000
I HP
HP
- 600
-i+oo
-200
r
"I
SFC
I hm
IHP-hr
^0.3
0.2
-0. 1
0 L 0
ppm
2000
SFC
- 1000
0 5000 10000
2
Effective Inlet Pressure (lbf/ft )
IHP-hr \
£ I HP
J NO
-kO -20 0 +io
Injection Time (DCA from t.^'c.)
I HP ISFC NO
I SFC
4 I HP
0.6
1.2 x 10
-5
[no] [no] *
ppm qr
HP
1 bm
ppm 1
"600
IHP-hr
"0.3
" 2000 "
-^00
-0.2
- 1000
-200
-0. 1
-0
-0
- 0
IHP-hr
10
- 5
-------
92
100
50
0 J
6000-
l»O00
0
1 2000
0 ->
2000 -
1000'
~ "S Prechamber Pressure
Main Chamber Pressure
100
-50
0
t.c.
Crank Angle (deg)
I
50
100
A
/ \
/ \
A Prechamber Temperature
Main Chamber Temperature
I—
¦100
I I I
-50 0 50
t.c.
Crank Angle (deg)
100
I \Prechamber Concentration
I \
I \
Average Concentration
I ¦ /Main Chamber Concentration
0-1
0
t.c.
Crank Angle (deg)
FIGURE 11 - PREDICTED PERFORMANCE OF THE REFERENCE I NO IRECT-INJECTI ON ENGINE
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93
Main Chamber Only
o— — — — —q-
I HP
ISFC
[no]
-O I SFC
Prechamber Only
i n> r5
Fuel Vaporization Parameter (OCA)
HP
- 600
1 hm
.^P-hr .
¦400
-0.2 -
"200
-0.1 -
- 0
-0
ppm
Main Chamber
3000 r> —o I SFC
Both Chambers
I HP
[no]
I HP ISFC
[no]
5 10 15
Burning Rate Parameter (DCA)
HP
Ibm
ppm
IHP-hr
0 O——O ISFC
- 600
-0.3
O
O
O
t>
l>
- 400
-0.2
-2000
Onl y —v
t
\
1
I
- 200
-0.1
-1000
jS' Both Chambers
1— —r - 1 >
- 0
-0
-0
Main Chamber
Both Chambers
0.05
0. 1
-I,
Dilution Rate Parameters (DCA )
Prechamber Main Chamber I SFC I HP [no]'
0 0.005 /..--0.01
Heat Transfer Coeff. c
I HP
ISFC [no]
\\ft3-°R-DCA
1.0
1.3
1.0
1.3
1.0 0.295 378 1275
1.0 0.289 384 898'
0.75 0.295 376 1099
0.75 0^289 384 638
HP
1 bm
-600
IHP-hr
-0.3
- 400
-0.2
- 200
-0.1
-0
•0
ppm
-Ol SFC
.2000
-1000
Mean Fuel Fraction at Burning (F /F )
3 m st
0 0.005 0.01
Fuel Fraction Increment
FIGURE 12 - SENSITIVITY OF PREDICTED INDIRECT-INJECTI ON ENGINE PERFORMANCE TO MODEL PARAMETERS
-------
I HP
ISFC
0.005
0.0075 0.01
Clearance Volume (ft,!)
I HP
2000
4000
6000
Effective Inlet Pressure (Ibf/ft )
I HP
HP
_0 ISFC
i i i r
0.5 1.0 2.0 3-0 x 10
Injection Rate .Ibm
-5
ISFC [no] [no] *
9^
HP
1 bm
ppm
-600
1HP-hr
- 0.3
-3000
-400
-0.2
- 2000
-200
- 0.1
- 1000
-0
- 0
- 0
^
IHP-hr
10
jlSFC
I HP
¦ 5
[no] *
1500 2000 2500
Engine Speed (rpm)
ISFC [NOl [NO] ^qr
HP
"600
1 bm
ppm
- 3000
-1 HP-hr
0.3
-400
1
< o
ro
- 2000
-200
- 0.1
- 1000
-0
-0
-0 lo
I HP-hr
ISFC
- 10
[NO]*
I HP
•[no]
-25 -12.5 0
Injection Time (DCA from t.c.)
1SFCH rNd*
1 bm
ppm
-600
1 HP-hr
- 0.3
- 3000
-400
- 0.2
- 2000
.200
. o; I
- 1000
-0
-0
- 0
I HP-hr
-10:
- 5-
0.01 0.02 0.03
Over-All Fuel-Air Ratio
FIGURE 13 - SENSITIVITY 0^ PR EVICTED IND IRECT-1NJECTI ON FNHINF PFR FORMANT f to nF
-------
95
r-
20
kO
I SFC
60
Prechamber Volume
(per cent of clearance volume)
1 HP ISFC
[no] [no
HP
1 hm
ppm
-600
1 HP-hr
•0.3
¦3000
o
o
-3*
i
•0.2
•2000'
-200
-0. 1
-1000
-0
-0
- 0 ¦
- 10
qr
IHP-hr
*
I r
1 NO'
Q 1 1
0 25 50
Fuel Injected to Main Chamber
(per cent of total)
FIGURE 13 -
SENSITIVITY OF PREDICTED INDIRECT-INJECTI ON ENGINE PERFORMANCE TO DESIGN PARAMETERS
(continued!
-------
96
NOMENCLATURE
-------
97
NOMENCLATURE
Symbols Descr i pt i on
A Area
B Cy1i nder bore
C Constant, specified model parameter
Cp Specific heat at constant pressure
F Mass fraction of fuel
h Enthalpy
IMEP Indicated mean effective pressure
ISFC Indicated specific fuel consumption
K Polytropic index; reaction rate
parameter
Fraction of fuel injected into main
chamber (IDI engine)
L Connecting rod length
M Molecular weight
m Mass
m Instantaneous mass flow rate
N Engine speed
n Polytropic exponent
[no] no concent rat i on
P Pressure
Q. Heat transfer rate to wall
R Crank length; gas constant
r Rate of NO formation
T Temperature
V Volume
V Clearance volume
c
x Number of revolutions per power
stroke
o(, Ratio of NO mass fraction to
equilibrium NO mass fraction
£• Internal energy
Un i ts
sq ft
ft
lbf-ft per slug deg R
lbf-ft per slug
1bf per sq ft
lbm fuel per IHP hr
ft
slug per slug mole
s 1 ug
s1ug per sec
rpm
Mass fraction
1bf per sq ft
lbf-ft per deg crank
angle (DCA)
ft; lbf-ft per slug
deg R
slug per DCA
deg R
cu ft
cu ft
lbf-ft per slug
-------
98
Symbols Descr ipt ion Units
q Crank angle position (0=0 at TDC) DCA
Fluid density slug per cu ft
Ignition delay msec
^j> Equivalence ratio
Subscr i pts
1 Precombustion chamber
2 Main chamber
a Air-residual gas mixture
abm Dilution air in burned mixture
bm Burned mixture
eb End of combustion
fb Final burning; fuel burning
fbm Fuel in burned mixture
fg Gaseous fuel
fl Liquid fuel
h Homogeneous mixture
i Number of crank angle increments;
burned mass system
i g Ign i t i on
in Fuel injection
i, j Crank angle interval or system formed during interval
k, 1 Chamber notation in indirect in-
jection engine, k or 1 = I for
precombustion chamber, k or 1 =2
for main chamber
m Mean value
s Stoichiometric
vc Valve closure
vo Valve opening
w Wa 11
Superscr i pts
o In i t i al va1ue
Mean value
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