EPA 903/9-75-019 DECEMBER, 1976 WIND TUNNEL MODELING STUDY OF THE DISPERSION OF SULFUR DIOXIDE IN SOUTHERN ALLEGHENY COUNTY, PENNSYLVANIA \] -^ f... .'. - U.S. Environmental Protection Agency Region ffl Philadelphia, F EPA Report Collection Information Resource Center US EPA Region 3 Philadelphia, PA 19107 ------- ------- I I EPA 903/9-75-019 I I I I I I I I I I I I I I I I WIND TUNNEL MODELING STUDY OF THE DISPERSION OF SULFUR DIOXIDE IN SOUTHERN ALLEGHENY COUNTY, PENNSYLVANIA Prepared by G.R. Ludwig and G.T. Skinner Li c fir' r:r> '-';-! P,-;fe'i? »\ ij>. -;c-r,iv,at!&n Resourca I!'.! C:;>:t!.ut Street Prepared for: h, jl1;;!^, PA 1SI07 U.S. Environmental Protection Agency Region HI Philadelphia, Pennsylvania 19106 December 1976 Calspan Corporation P.O. Box 235 Buffalo, New York 14221 ------- I I I I I I I I I I I f I I I I I i I ACKNOWLEDGMENT The authors wish to thank Dr. Peter Finkelstein, EPA Region III Meteorologist, who was EPA Project Officer in this work. His understanding of the problems posed by this program and his guidance and help in their solution were invaluable. We are also indebted to Mr. Harry Geary of H.E. Cramer Company Inc. and to Mr. Ron J. Cheleboski, Director of the Allegheny County Bureau of Air Pollution Control for their timely assistance in providing in- formation required for the design of both the physical model and the emission inventory model. Finally, we wish to thank Dr. William H. Snyder of the EPA Environment Sciences Research Laboratory for his suggestions on the prepara- tion of this report. 111 ------- I i i i I I i i i i I i i i i i i i i ABSTRACT This report presents the results of a wind tunnel model study to determine the ground-level SO,, concentrations in the Clairton Area of Allegheny County, produced by emissions from stationary sources within the area. The study was designed to provide data under flow conditions which correspond roughly to those which prevailed during an air pollution episode at Liberty Burough, Clairton in January 1973. The inventory of emission sources used in the tests corresponded to the estimated 1973 full-scale inventory for 49 sources which were located within the confines of the modeled area. The test program included flow visualization studies and quantitative measurements of ground-level concentrations of a tracer gas from which full- scale SO,, concentrations could be calculated. The concentration level measure- ments were performed for four wind directions. At each wind direction, three wind speeds were studied with neutrally stable flow, and for one of these a temperature inversion condition was also tested. The report presents details of the model scaling laws, the test facilities, the model, test procedures, and the experimental results. The results include measurements of the velocity and temperature profiles at several locations above the model as well as ground-level concentrations. The latter are presented in terms of full-scale SO,, concentrations. ------- I I I I I I I I I I I 1 I I I I I I I TABLE OF CONTENTS Section Page I INTRODUCTION 1 II SCALING CRITERIA 3 A. Modeling of Atmospheric Winds 4 B. Modeling of Stack Emissions 6 1. Exit Momentum Scaling 7 2. Buoyancy Scaling 9 3. Pollutant Concentration Scaling 12 C. Sampling Time 14 D. Summary 16 III TEST FACILITIES 17 A. The Atmospheric Simulation Facility 17 B. Pollutant-Concentration Measuring System 18 C. Auxiliary Equipment 22 IV WIND TUNNEL MODEL 24 A. Model Scale 24 B. Model Construction 28 C. Emission Inventory and Source Locations 29 D. Stack Emission Model 30 V DESCRIPTION OF TEST PROCEDURES 37 VI EXPERIMENTAL RESULTS AND DISCUSSION 41 A. Model Atmospheric Wind Conditions 41 1. Approaching Flow 41 2. Flow Over the Model 42 B. Flow Visualization 46 C. Ground Level Concentrations 48 1. Preliminary Near Field Test 48 2. S02 Concentrations 50 3. Summary 60 VII ------- TABLE OF CONTENTS (Cont'd) Section Page VII CONCLUDING REMARKS 62 APPENDIX A - Minimum Permissible Ground Roughness Reynolds Number 65 APPENDIX B - Table of Ground Level S02 Concentrations Calculated from Model Test Data 67 REFERENCES 127 Vlll ------- I I I I I I 1 I I I I I I I I I I I I I. INTRODUCTION This report presents the results of a model study to determine the dispersion of stack emissions over a strip of land located near the Monongahela River in the Clairton area Southeast of Pittsburgh. The objective of the study was to determine ground level concentrations of the stack effluents from steel mills and power plants which are located in the area. Both qualitative flow visualization studies and quantitative concentration level measurements were made. The model study was performed in the Calspan Atmospheric Simulation Facility (ASF). This specialized wind tunnel, which is described in the text, was designed for the specific purpose of modeling the wind in the lower atmos- phere. During the course of the current program, the ASF was modified to in- clude the capability of generating an elevated inversion layer over the model. The test program included studies under neutrally stable flow conditions and studies in the presence of the elevated inversion. The inventory of stack emissions used in the model tests corresponded to the estimated 1973 full- scale emission inventory for forty-nine of the stacks which fell within the confines of the modeled area. Tests to determine ground level SO- concentrations were performed for three wind velocities in neutral flow and one wind velocity with an elevated inversion, for each of four wind directions. In addition, the model emission inventory was operated in separate sub-groupings of sources in order to optimize the sensitivity of the concentration measurement system and at the same time allow identification of the separate contributions from various groups of stacks. In all, a total of forty tests were performed to determine ground level concentrations of SO,, under the various wind and stack combinations. ------- Each test provided quantitative concentrations of S02 at twenty ground level sampling points. In all of the tests, two of the sampling point locations were held fixed at locations corresponding to full-scale continuous monitoring stations at Glassport and Liberty Borough- The remaining eighteen sampling points were located on the basis of flow visualization studies to provide a satisfactory distribution of samples for determining overall ground level concentrations of SO . The inclusion of the two full-scale monitoring stations in the sample array for all tests allows an assessment of the effectiveness of these monitoring stations as pollution alert monitors. In the sections that follow, the scaling criteria for the model tests are presented first. This is followed by descriptions of the test facilities, the wind tunnel model, and the test procedures. Next, the experimental re- sults are presented in three steps, First, the flow conditions over the model are described and then the results of flow visualization studies are discussed briefly. Finally, the measured ground level concentrations are presented as a series of maps which show full-scale SO,, concentrations in ppm calculated from the model data and the scaling laws. Some concluding remarks on the program are presented in the final section. Two appendices are attached at the end of the report. In Appendix A, a discussion of the minimum permissible Reynolds number based on ground roughness height is presented. The ground level con- centration data are listed in tabular form in Appendix B. ------- I I I I I I I I I I I I i I I I I I I II. SCALING CRITERIA In attempting small-scale modeling of flows in the atmospheric boundary layer, care must be taken to ensure that all important features of the full-scale situation are represented in the model. Broadly speaking, these include the ambient wind environment, including both the mean and tur- bulent characteristics, as well as the local terrain. In stack emission studies such as presented here, one must also model the relevant features of the exhaust gases, namely; exit momentum, buoyancy and pollutant concentra- tion. The dynamics of such flows involve inertial, viscous and buoyancy forces, as well as turbulent transport. The scaling criteria presented here are mathematical statements of the requirement that each of these forces be present in the same relative degree in the model as in the full-scale situation. This section is divided into four parts. The scaling requirements for modeling the atmospheric wind are discussed in II-A. The additional scaling requirements for modeling of stack emissions are presented in II-B. This is followed by a discussion of sampling time for the model measurements in II-C. Finally, a summary of the scaling equations is presented in II-D. The following notation is used. C = pollutant volume concentration (He in model, SO^ in prototype) (dimensionless) Cs = volume concentration of total stack gas (dimensionless) 9 a = acceleration of gravity (meters/sec ) Ji = characteristic length (meters) ,f> = pressure (pascal = newtons/meter ) Q = mass flux of S0~ from prototype stack (kilograms/sec) t = time (sec) T = temperature (°K) u-^ = reference velocity (meters/sec) u.^ = model reference wind velocity (meters/sec) measured 1.22 meters (4 feet) above model river f. = full-scale reference wind velocity (meters/sec) corresponding to u-ry,re.f (i.e., full-scale wind velocity at 2926 meters above river) ------- u.s = stack-exit velocity (meters/sec) a* = friction velocity (meters/sec); u# = CC 2 \l = volume (meters ) % = strearawise coordinate (meters) it - horizontal cross-stream coordinate (meters) z = vertical coordinate (meters) Z0 = characteristic ground roughness length (meters) 3 A = S0? (tons per year)/He (cm /min) for any stack 2 £> = kinematic viscosity (meters /sec) ^ = density (kilograms/meter ) p* = density of S0? at ambient temperature 2 f = Reynolds shear stress at the wall (pascal = newtons/meter ) 4> = volumetric flux of He from model stack (meters /sec) ( )^ = in ambient air C ), = model (. ")^ - prototype ( )s = at stack exit A. MODELING OF ATMOSPHERIC WINDS The primary constraint on modeling of atmospheric flows comes from the need to ensure that the tunnel boundary layer, formed over the rough floor, conforms to the "fully-rough wall" flow criterion. When this criterion is satisfied, the mean-velocity profile i? logarithmic, namely u = const, x 2t>q ( ) (1) U^ Z.g / where a is the mean velocity at a height z , and the characteristic roughness length of the flow, z0 , is related numerically to some average dimension of the roughness elements on the floor. Many have studied the general problem of simulating atmospheric winds in a laboratory facility. The conclusions reached in these studies are that the ratio of a typical length scale JL to the roughness length of the wind profile 2 should be matched between the model and prototype (full-scale) approaching flows: ------- I I I I I I I I I I I I I I I I I I I (2) and that the approaching model flow should be "fully rough", i.e., there should be no laminar sublayer in the tunnel boundary layer. Usually this latter criterion is satisfied when a Reynolds number based on zn and the friction velocity u^ is more than about 3: <** Z. (3) Of the two conditions, (2) and (3), it is more important to satisfy condition (3). In addition to these criteria, it is also necessary to make certain that the turbulence spectra of the tunnel flow are suitably scaled reproductions of the atmospheric flow. When these conditions are met, the wind environment in the tunnel flow is a proper representation of the atmosphere, for neutrally stable conditions. The problem of actually generating the required flow in a laboratory facility is one that has received a great deal of attention in recent years. A wide variety of approaches is available for the development of the proper flow; these involve the use of various types of roughness elements, fences, spires, and jets transverse to the flow. At Calspan, the approach that has been used is that of a matched fence/rough floor combination (see Section III). With this technique, the appropriate logarithmic mean velocity profile as well as a turbulence spectrum representative of that in the neutral atmosphere is generated. In addition to the above scaling criteria for modeling of the neutrally stable atmosphere, another relationship is required when thermally stratified flows are to be modeled. A simple derivation of the scaling between model and prototype in thermally stratified flows can be obtained as follows, with the understanding that all full-scale temperatures are measured relative to the potential temperature (i.e., 7= T '- Pz where P is the adiabatic lapse rate and T' is the absolute temperature). ------- The vertical velocity attained by unit mass of gas in a given interval of time, as a result of buoyancy, must scale with the horizontal velocity. Since the vertical acceleration is given by ^*" />«. ^ '* the velocity acquired in time interval At is Q ^ At . ' 'a, Taking the ratio of this to the reference velocity, we obtain Atm Using the time-scaling relation = -- -j^- we obtain ~AT^ ~ 7^ ~J^ i*^~ This result is equivalent to scaling based on Richardson number in a form which may be called a bulk Richardson number, B0 = uI T* . Use of ths parameter Bg for a scaling law has been discussed in Reference 1. For j practical purposes, the ratio -^ in Equation (4) is essentially unity. Thus, Equations (2), (3) and (4) constitute the scaling criteria for the flow approaching the model. Proper simulation of stack'emissions requires that additional scaling criteria be satisfied. These are discussed below. B. MODELING OF STACK EMISSIONS There are three aspects to be considered regarding the scaling laws for stack emissions. These are: (1) Exit momentum scaling (2) Buoyancy scaling (3) Pollutant concentration scaling ------- I I I I I I I I I I I I I I I I I I I Since the current literature contains various opinions as to the proper form of the appropriate scaling laws (see for example, Reference 5), it is relevant to discuss these laws in greater detail. In the following dis- cussion, it is a basic assumption that the model is scaled geometrically and that the distribution of eddies and eddy sizes is correctly modeled to scale (in a statistical sense) in the ASF. Then, since all properties of the flow are determined by the turbulent mixing, all other properties of the flow such as mean-velocity profile, Reynolds stress distribution, spectral energy dis- tributions, and (in the case of stratified flow) deviations from the potential temperature will be correctly scaled. That this is so in the ASF has been 2-4 demonstrated by extensive measurements in pilot studies, which formed the basis for design of the ASF, and also during calibration of the ASF itself. 1 . Exit Momentum Scaling Near the exit of a stack, the velocity and direction of motion of any small volume of the plume depends on the ratio of the horizontal momentum given to it by that portion of it which came from the ambient wind, to the vertical momentum contributed by the stack gas. This is true in the early part of the mixing process, before buoyancy has had time to contribute signi- ficant vertical momentum. Since any model motion must correspond to a possible full-scale motion, the above momentum ratio must be the same in model and full- scale. The ambient air in the small volume may have come from different levels with, therefore, different velocities. However, these can all be expressed in terms of the momentum per unit volume at some reference height where the velocity is a.^ , since the fractions of gas that come from all levels, and from the stack, must be the same in the model and in full-scale. Thus, the momentum scaling near the stack exit requires that This result can equally well be derived by considering the average direction and momentum at any cross -section of the plume. The surface enclosing all the mixing region is denoted by A. The cross-section B is bounded by the surface A. The stack exit surface is C. ------- The flux of horizontal momentum, $fl , entering the plume through A must flow out through B. Likewise, the flux of vertical momentum, (j) , entering via the stack must also flow out through B. The ratio $c / (j>fl must be the same in the model and in full scale. v- A Writing u(z) for the velocity at any height z , n Also, u. (z) can be functionally related to the reference velocity, u. as follows Thus, For correspondence between model and full-scale, the surface integral must be expressible in the form r r / / (f(z) n)\f(z)\dfi = const. I3- J Ja where J! is a characteristic length. The flux of vertical momentum is simply Ps Thus, the momentum ratio becomes ------- I I I I I I I I I I I I I I I I I I Hence, for correspondence between the model, ( ) w, > an-d the full-scale prototype, C ) ^ , we must have Am *L ^ = P*+ "5% ^ - -2 n2 2- D* Pa.U-a.r~ * Pa. ^a^b * + where we have assumed /oaryi - p ** P 'a. ft JL " Since -r^- = -^ the relation becomes, as A P* U-*^ Pa. ^a-p 2. Buoyancy Scaling As the plume from a stack diffuses downstream, its motion must become buoyancy dominated. The velocity and direction of motion of any small volume, AV , is determined by the ratio Stream momentum in AV Buoyancy momentum in A V In a volume AV of the plume, a fraction C is stack gas and a fraction (1-C ) is entrained air. The entrained air may have originated at many different heights, but its velocity will be some function of position and time and may be written as a function of the reference velocity u.^ , Thus, Stream Momentum in A I/ = AV (1-C ) /oa u.a /, ( X , u , z , t ) The buoyancy momentum in the volume AV is calculated as the impulse delivered by buoyancy to the fraction C in its travel to the location (x, y, z) at time t. If we consider A V small enough, then all of the fraction C may be considered as having traversed the same route. The time taken to traverse this route may be written as a space and time function of the charac- teristic time scale, J./U.^ . ------- Thus, the buoyancy force on A V = A V Cg g ( fls - p^ ) and it has acted for a time = £ (x, y, z, t) J-/u-A producing the ? Buoyancy Momentum in AV = Al/C5 Q (ps - p^ f (Z,u,z,t)-~ Q *C 0 0- Thus, the ratio _ 2 /, Stream Momentum in A V _ _ 1-CS A, a^ f, (Xt y,z,t) Buoyancy Momentum in A I/ £s fyOs ~ p^) aji -f.^2, c/,z , t,> Since the model motion must be a possible full-scale prototype motion, this ratio must be the same in the model and prototype at corresponding points in space and time. Furthermore, the functions f and -f2 must have the same numerical values in the model and prototype at corresponding points in space and time because they are geometrical functions of the scaled motion. Thus, the scaling relationship becomes '- Csn Pa. "a ' ~ C^p Pa. "2+ Generally, where buoyancy dominates C << 1 and the relation can be written - X r r_S-rn Csn ' ~^T ^ (7) To find a relation for the ratio of the stack-gas concentration in the model to that in the prototype, we may simply observe that stack-gas concentration must be proportional to stack exit velocity and, far downstream, inversely proportional to stream velocity. Thus More formally, we may again consider a cross section, B, of the plume - say, a vertical cross section. The flux of stack gas through B must equal the flux emanating from the stack. That is e. where the bar denotes time averaging. 10 ------- I I I I I I I I I I I I I I I I I I I Again, writing C and u. as functions of some reference concentration and velocity = usfis Invoking the necessary correspondence between model and full scale, and noting Z vr1 ^ Sy" ^ that // f, dB is proportional to J. , since and n H we have S-jb as before. Finally, combining equations (7) and (8), the following equation is obtained, P 7 - In practice, this equation is usually combined with the momentum scaling equation (6) to give a 2. 'fie 5W , _ UO) leading finally to JL (lOa) This equation determines the model stack density for any choice of the parameter 1. = - Ordinarily, it is not necessary to scale the volumetric (or mass) flux at the stack exit, and no further restriction need be imposed on the scaling of the dynamics of the plume. Equation (9) can be shown to be in agreement with the buoyant plume rise re- lation recommended by Briggs (Reference 6, equations 4.19c and 4.32) and with the relation for touchdown point of negatively buoyant plumes advanced in Reference 7 (equation 6.3). Moreover, the maximum plume rise of negatively buoyant plumes (Reference 7, equation 6.2) scales in accordance with equations (6) and (9) above. 11 ------- Equation (10) indicates that the wind velocity over the model must be reduced in proportion to the square root of the geometric scale ratio between the model and full-scale. In many situations, it is necessary to model relatively large areas and the geometric scale ratio must be chosen so that the area will fit in the wind tunnel. This may require values of J.^/Jl^ which are very small, say on the order of 1/2000. Then, it becomes desirable to increase the values of the other terms in Equation (10) so that the re- quired model wind velocities do not become so small that Equation (3) cannot be satisfied. This is done using highly buoyant gas mixtures for the model stack effluents. It can readily be seen from Equation (10) that a decrease in psrr< will increase u.^^ for given values of the other variables. In other words, the buoyancy and inertial forces must not only be in the proper ratio, but must be large enough in absolute terms to keep the influence of molecular viscosity negligible, and satisfy Equation (3). This results in an envelope or "window" of experimental conditions within which one must operate to simu- late the full-scale flow properly. 3. Pollutant Concentration Scaling The inventory for full scale stack emissions usually gives pollutant fluxes in mass/unit time. In the model we deal with He fluxes in volume/unit time. For any stack let the full-scale mass flux of SO be Q and the model volume flux of He be ^ . The density of SO at ambient temperature A very simple derivation of the concentration scaling law can be obtained as follows. At some instant mark a cross section of the plume, A. Let a short time, t, pass and observe the new position of the cross section, B. A volume, V, is contained between A and B. Since the model motion must be a possible full-scale motion, we can loo< at this same picture on both scales and say the following. 12 ------- I I I I I I I I I I I I I I I I I I I The transient times between A and B are not the same for the two scales. They are related as follows. a. (12) where UL^ is the reference velocity, and J- is a characteristic length. The volumes, V, also differ 3 J p 1 3 ' w> (13) The average concentration of SO- in the prototype volume is given by p" (14) Note that, since we are primarily concerned with the far field where the plume ;k is near ambient temperature, we use the SO density, p , at ambient temperature. The average concentration of He in the model volume is given by V (15) Equations (12) through (15) can be used to obtain the ratio c. /cyn . Since the initial cross section, A, was completely arbitrary, this ratio must also hold for all values of C^/C^ at corresponding points in model and prototype. Thus, a, (16) 13 ------- Equation (16) is written in a form consistent with the relaxation of the volumetric (or mass) flux modeling law, as mentioned following Equation (11), and thus may seem unfamiliar at first. C. SAMPLING TIME A final discussion, regarding the comparison of model results with full scale, relates to the well-known fact that in full-scale the averaging time has a distinct effect on the measured concentrations. This is not the case in model tests in the ASF. The model results correspond to short-time averaged full-scale measurements, taken over not more than 10 or 15 minutes in most cases. Briefly, what is involved here is the following. The frequency spectrum of wind gusts in full-scale always shows a null, or near null, in the Q range 1 to 3 cycles per hour. Thus, it is theoretically correct to separate the spectrum into two parts at a frequency in that range, and deal with phenomena associated with each part separately. In the ASF the high-frequency portion related to the ground-induced turbulence is fully simulated. The low-frequency portion related to meandering of the wind, diurnal fluctuations, passage of weather systems, annual changes, and so on, must be considered separately. In particular, a correction ' ' for meandering of the wind can be applied if necessary, to compare with longer term averaging. Thus, since the effective full-scale averaging time is independent of model averaging times, one can choose the model averaging time to provide data which are repeatable to within a specified accuracy. The model averaging times required to obtain a given accuracy can be estimated from statistical considerations as described in the following paragraphs. However, as noted above, the data so obtained will cor- respond to full-scale data measured over not more than 10 to 15 minutes. For a statistically stationary process one can form an average of any quantity by taking N independent samples, adding their values and dividing by N. If one were to do this many times, one would obtain a distribution of average values having some standard deviation from the true mean. The ratio of this -1/2 standard deviation to the true mean value is approximately N , in most cases. This ratio may be regarded as a typical fractional error in a quantity measured by averaging N independent samples. Thus, to keep this error within 10% of the mean requires about 100 samples; to keep it within 1% requires about 10,003 samples. 14 ------- I I I I I I I I I I I I I I I I I I I We have stressed that the samples must be independent. That means that that the system (the air flow around the model in the ASF) must "forget" what it was doing in the time span between samples -- an independent sample can be obtained once the correlation with the last value has essentially vanished. Now we do not actually sample at long intervals, as indicated above. We generally deal with continuous data or with digitized data taken at a high sampling rate. However, we are still essentially bound by the same rules, and to estimate the required averaging time we can proceed along the following lines. The model is immersed in a boundary layer of thickness, cT , typically about 1 meter. The velocity, Uref , near the top of the boundary layer may be anything from roughly 1 to 25 meters per second. The biggest eddies in the turbulent flow essentially span the boundary layer, so that we are not assured of an independent turbulence picture until the boundary layer has moved a distance of about 6" . We can say that most of the boundary layer moves at a velocity close to U-ref , so we can take "independent" samples at a rate U-re!r/6' per second. We can now construct an equation which relates the sampling time, t, required to obtain a given fractional error, a~ , to the tunnel reference velocity, U-ref . From the above discussion, 7 rf. ' |