Urban Dispersion Modeling: Comparison with Single-Building...

Urban Dispersion Modeling: Comparison with Single-Building Measurements

STEVE R. DIEHL, DONALD A. BURROWS, ERIC A. HENDRICKS, AND ROBERT KEITH

Advanced Engineering and Sciences, ITT Corporation, Colorado Springs, Colorado

(Manuscript received 8 September 2005, in final form 8 September 2006)

ABSTRACT

Two models have been developed to predict airflow and dispersion in urban environments. The firstmodel, the Realistic Urban Spread and Transport of Intrusive Contaminants (RUSTIC) model, is a fast-running urban airflow code that rapidly converges to a numerical solution of a modified set of the com-pressible Navier–Stokes equations. RUSTIC uses the k–� turbulence model with a buoyancy productionterm to handle atmospheric stability effects. The second model, “MESO,” is a Lagrangian particle transportand dispersion code that predicts concentrations of a released chemical or biological agent in urban or ruralareas. As a preliminary validation of the models, concentrations simulated by MESO are compared withexperimental data from wind-tunnel testing of dispersion around both a multistory rectangular building anda single-story L-shaped building. For the rectangular building, trace gas is forced out at the base of thedownwind side, whereas for the L-shaped building, trace gas is forced out of a side door in the inner cornerof the “L.” The MESO–RUSTIC combination is set up with the initial conditions of the wind-tunnelexperiment, and the steady-state concentrations simulated by the models are compared with the wind-tunnel data. For the multistory building, a dense set of detector locations was available downwind at groundlevel. For the L-shaped building, concentration data were available at three heights in a lateral plane at adistance of one building height downwind of the lee side. A favorable comparison between model simu-lations and test data is shown for both buildings.

1. Introduction

Urban airflow models have traditionally fallen intoone of two categories: 1) high-fidelity computationalfluid dynamic (CFD) models or 2) fast-running low-fidelity models. The CFD methods include large-eddysimulation models [e.g., the Finite-Element Method,Version Massively Parallel (FEM3MP; Chan andLeach 2004) and Finite-Element Flow Solver—Urban(FEFLO-URBAN; Camelli et al. 2004) models], directnumerical simulation models, and Reynolds-averagedNavier–Stokes (RANS) models [e.g., the “Fluent”(Fluent 2005) and Flame Acceleration Simulator(FLACS; Hanna 2004) models]. The CFD models at-tempt to solve for the flow at relatively high resolutionto capture eddy formation using intensive calculations,and they take significant amounts of computer time forfairly small geographic regions. These models are very

useful for examining the time-averaged structure of theflow at fairly small scales and for describing the turbu-lent shedding that occurs, but, in general, they take toolong for fast-response situations or in parametric stud-ies.

The faster-running lower-fidelity approach to airflowmodeling generally uses either empirical fittingschemes or mass-consistent flow techniques (or a com-bination of both) to generate quickly a rudimentaryestimate of the flow patterns and turbulence param-eters (most often an eddy viscosity) in the region ofinterest. The U.K. Urban Dispersion Model (UDM)code (Brook et al. 2003, Hall et al. 2003) and the Finn-ish Meteorological Institute (FMI) UDM-FMI code(Karppinen et al. 2000) are representative of this ap-proach, both using Gaussian puffs. An example of theuse of mass-consistent flow is given by Kaplan andDinar (1996). This type of modeling is useful for veryquick response situations, but the lack of fidelity re-stricts the technique to situations in which no othersolution method is practical.

Under recent Defense Advanced Research ProjectsAgency (DARPA) sponsorship, a fast-running urban

Corresponding author address: Steve R. Diehl, Advanced En-gineering and Sciences, ITT Corporation, 5009 Centennial Blvd.,Colorado Springs, CO 80907.E-mail: [email protected]

2180 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 46

DOI: 10.1175/2006JAMC1300.1

© 2007 American Meteorological Society

JAM2573

airflow model [the Realistic Urban Spread and Trans-port of Intrusive Contaminants (RUSTIC) model] hasbeen developed. RUSTIC was created to provide amidrange solution in terms of speed and fidelity whencompared with typical CFD codes, yet with more physi-cal modeling than the fast-running mass-consistent flowcodes. In specific terms, RUSTIC represents an effortto simplify and optimize a RANS CFD method to arelatively short run-time regime, as opposed to addingrules to a fast-running model in an attempt to addressphenomena like turbulence empirically. In terms of runtime, the desire is for RUSTIC to be able to create adescription of the airflow with the turbulent kinetic en-ergy (TKE) and turbulent dissipation for a 1 km � 1 kmurban area in less than 1 h on a standard personal com-puter with accuracy that is acceptable for calculating aprediction of contaminant dispersion.

For contaminate dispersal, RUSTIC is normally runin conjunction with “MESO,” a Lagrangian tracer dis-persion code, which for urban calculations is based onthe random-walk technique of Diehl et al. (1982). Also,again under DARPA sponsorship, MESO has beenmodified to accept the 3D flow and turbulence fieldsfrom RUSTIC and has been given special featuresneeded for accurate urban (building aware) dispersionmodeling. The two codes can be used separately, whichallows a single RUSTIC solution to be used for manyMESO dispersion simulations. Because MESO runsmuch faster than RUSTIC does, the source locationand strength in MESO can be varied 1) to perform fastparameter studies, 2) for training, or 3) for identifica-tion of a threat source location.

After providing short overviews of RUSTIC andMESO, this paper outlines a preliminary validation ef-fort for the two codes using wind-tunnel data for twosingle buildings: one is a simple rectangular buildingand the other is an L-shaped building. The overview ofthe RUSTIC code is abbreviated, because greater de-tail is given in a companion article by Burrows et al.(2007). However, a brief summary of the model includ-ing a description of the numerical method can be seenin an older paper by Burrows et al. (2004a). Additionalcomparisons can be seen in another companion paperby Hendricks et al. (2007) using dispersion and meteo-rological data from Oklahoma City, Oklahoma, fromthe large Joint Urban 2003 field test. An overview ofthe field test is given by Allwine et al. (2004).

2. RUSTIC flow model overview

To simplify computation, RUSTIC combines thecontinuity and thermodynamic equations into a singlepressure tendency equation. The prognostic equation

for pressure is then written in a form with the speed ofsound c identified in a manner that allows it to begreatly reduced to permit a large time step. Experimen-tation has confirmed that the exact value of c has littleor no effect on the final velocity and turbulence fieldspredicted (Burrows et al. 2004a, 2007). RUSTIC in-cludes a k–� turbulence model (Wilcox 1998, p. 121)with a buoyancy production term for TKE, permittingthe study of atmospheric stability effects. Executionspeed is further enhanced with an expanding grid ca-pability and with the ability to allow cells far from themost turbulent regions to “coast” for n cycles wheneverthe acceleration is found to be below a preset criterion.The coasting technique, however, is still under investi-gation and was not used for this study. Solutions areobtained with finite-volume techniques based on amodified Cartesian grid structure. Although the cellsare rectangular for increased computation speed, par-tial cells are used at building edges to improve the ac-curacy.

A technique for running RUSTIC with several dif-ferent grids of increasing resolution is being developedwith the goal of providing rapid convergence to a “use-ful” solution within as short a period of time as possible.A useful solution is defined here as one that results ina dispersion prediction that is accurate to within a fac-tor of 2 with a resolution smaller than the size of thesmallest building of interest. To initialize the grid and tosupply the wind profile and turbulence energy and dis-sipation at the inflow boundary, a 1D numerical algo-rithm that contains the k–� turbulence equations is in-cluded. The algorithm computes the flow as a functionof altitude over a rough surface based on the sensibleheat flux and surface roughness. RUSTIC can be runwith an upwind heat flux that differs from the heat fluxvalue around the larger buildings.

3. MESO Lagrangian tracer model overview

To model transport and dispersion of contaminants,RUSTIC flow and turbulence fields are passed toMESO, which is based on Lagrangian tracer tech-niques. MESO has been primarily sponsored by theNaval Surface Warfare Center Dahlgren Division forgeneral-purpose “rural” transport and dispersion appli-cations and can ingest 3D forecast predictions. For non-urban dispersion predictions, MESO contains a sophis-ticated convective boundary layer model and uses thestochastic Lagrangian tracer technique of Franzese etal. (1999) for unstable conditions and Luhar and Britter(1989) for stable conditions.

New urban capabilities have been recently added toMESO under DARPA sponsorship. Tracer techniques

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have a number of advantages over standard grid advec-tion methods. One is the reduction of advection errorsin highly sheared flow, which is very important whenusing coarse grid cells to reduce run time. Another isthe elimination of artificial diffusion, which is of par-ticular importance for biological agents that can causefatalities even with extremely small quantities. A thirdadvantage is the ability to handle large size distribu-tions and droplet settling naturally. MESO contains afull suite of tools for handling chemical and biologicalagents, including droplet evaporation and surfaceevaporation.

Of particular importance for small biological par-ticles, MESO contains a state-of-the-art model for es-timating the rate of particle deposition includingcanopy “filtration.” The model, which is based on si-militude curve fits (Seinfeld and Pandis 1998; Slinn1977), is a function of particle size and density, surfacecharacteristics, surface layer meteorological conditions,and vegetation characteristics. Each ground cell of theflow grid can have its own surface/vegetation qualities,including canopy type, a condition that allows the depo-sition rate to be modeled on a cell-by-cell basis. Theprimary limitation of the model is the assumption thatthe boundary layer is fully developed, implying a longupwind fetch that is seldom the case in an urban setting.As yet, MESO does not model chemical reactions orsurface absorption.

MESO also includes a sophisticated heat flux algo-rithm that uses the heat budget at the surface/canopy toestimate the sensible heat flux. The algorithm also com-putes the Obukhov length L and the friction velocityu*, which are needed for estimating the deposition. Forurban runs the heat flux model ignores the turbulencepredicted by RUSTIC and instead computes its ownsurface-layer properties based on the local flow speedand surface type. The heat flux model, which is basedon an iteration technique similar to that of van Uldenand Holtslag (1983), has been found to reproduce ac-curately the 24-h heat flux histories taken during theFirst International Satellite Land Surface ClimatologyProject Field Experiment (FIFE) field trials (Strebel etal. 1998) in the Kansas prairie. The model accuracy islimited, however, by the fact that MESO–RUSTICdoes not yet take into account shading behind thebuildings. This limitation will be corrected in the nearfuture. For urban simulations, the output of the heatflux model is only used to compute particle deposition,and the dispersion is computed with the turbulence pre-dicted by RUSTIC.

To move tracers with the flow, MESO first deter-mines the cell in which the tracer is located. MESO usesa grid that is offset by one-half of a RUSTIC cell such

that each of the eight corners of the MESO cell has itsown velocity vector. The tracer velocity is then esti-mated by interpolating among the eight corners of thecell. The interpolation scheme assumes the flow is de-tached at the building edges and corners. To improvethe flow accuracy around corners and in tight eddies,the tracers are advanced with a predictor–corrector nu-merical scheme. When one or more of the eight cornersis located inside a building, boundary conditions are setto force the flow normal to the surface to be zero.

MESO includes a terrain-tracking capability to pre-vent tracers from artificially depositing or impactingbuilding walls as a result of advection errors. This is ofparticular importance in turbulent flow in which thetracers are also moved in a stochastic manner. Theground surface, which is defined by a terrain gridpassed to MESO from RUSTIC, includes the buildingsthemselves. In other words, MESO treats the buildingsas ground elevation changes. For tracers that are mov-ing toward the surface and reside within a vertical dis-tance of one cell height from the surface, the normalcomponent of the velocity is linearly interpolated tozero at the surface from the first adjacent node. Thus,the closer to the surface that the tracer resides, themore parallel its flow vector becomes to the surface.Based on numerical studies with urban geometries, thisapproach has been found to affect the predicted con-centrations by only a few percent or less over the re-gions of the plume with concentrations above 10% ofthe peak value.

To model urban dispersion, each tracer undergoesnumerous random-walk excursions in each coordinatedirection as the tracers travel with the flow. As dis-cussed in detail by Diehl et al. (1982), the random-walktechnique satisfies the well-mixed condition, which ineffect means there is no artificial drifting of the tracersin areas of high diffusion gradients. For improved ac-curacy, the diffusivity K between cells is modeled withlinear segments rather than as a series of step changes.Although stochastic in nature, the random-walkmethod is in effect a gradient transfer process. For ex-ample, at the limit of large numbers of tracers, the ver-tical random-walk movements in each RUSTIC layerresult in a tracer flux F(z) of the form

F �z� � ��K0 � K1z��z, �1�

where � is the tracer concentration and the diffusivityK0 � K1z is a linear function of the height z, with theconstants K0 and K1 chosen so that a linear change inthe diffusivity smoothly spans between each RUSTICgrid value. Thus, with 3D RUSTIC flow fields, MESOpredictions are numerical solutions to the 3D advec-


tion–diffusion equation. As shown by Diehl et al.(1982), a linear diffusivity of this form requires tracerrandom-walk movements given by

��z� � 2�t�K0 � K1z� � ��tK1�2�1�2 � �tK1, �2�

where the sign is determined by a random-bit gen-erator and �t is the time step. Even though each traceris independent of the others, by integrating to deter-mine the flux across a boundary it can be shown thatEq. (2) will, in the limit of an infinite number of tracers,give the flux F(z) in Eq. (1). If near a surface where K0

is zero, the negative sign generates movements towardthe surface that are much smaller than those producedby the positive sign. In fact, as a tracer becomes pro-gressively closer to the surface the negative movementsgo to zero.

As shown in Fig. 1, the vertical diffusivity predictedby RUSTIC is modeled as a series of connected lineardiffusivity segments, which is much more accurate thana series of step changes between levels. Small abnormalnet fluxes can, however, occur near junctions if the par-ticle movements are not handled correctly. As illus-trated in Fig. 2, this problem is easily resolved by ex-tending the adjoining diffusivities, K and K , at thejunction at z0 to levels z1 and z2 above and below z0.These levels correspond to the maximum distance fromwhich tracers above and below z0 can penetrate thejunction at each time step. The heights of z1 and z2 aregiven by

z1 � z0 � 2�t�K0 � K1z0��1�2 and

z2 � z0 � 2�t�K0 � K1z0��1�2. �3�

These expressions for z1 and z2 could as easily havebeen written using K 0 � K 1z0 instead of K0 � K1z0

because at z0 the two are equal. Tracers in the overlapregion above z0 are moved upward according to K butare moved downward according to K. The converse isrequired for tracers in the overlap region below z0. Ifone assumes that the time step �t is sufficiently smallthat the overlap regions do not extend more than half-way across the layer, the resulting flux F(z) is strictlyproportional to the concentration gradient. Even with-out the overlap regions, the net drift at cell junctions issmall relative to the treatment of diffusivity in a step-wise manner.

For the random-bit sequence needed for Eq. (2), thenumerical method of Press et al. (1988) is used, basedon the work of Watson (1962). Because the random bitscan be obtained in a numerically fast manner, the ran-dom-walk movements in general take less computertime than do other stochastic techniques that require anormally distributed random-number generator. [See,e.g., Marsaglia and Bray (1964), McGrath and Irving(1975), and Luhar and Britter (1989).] Furthermore,when a tracer nears a surface where the diffusivity goestoward zero, the technique does not require a smalltime step. For the random-walk method, the time stepcriteria is �t � �z2/(8Kmax), where �z is the layerthickness and Kmax is the maximum diffusivity in thelayer. The random-walk step size is usually smaller thanthe advection step, which is limited to one-half of thetravel time across a RUSTIC cell. Many stochasticLagrangian models set the time step to a small fractionof the Lagrangian time scale, which becomes very smallnear the surface as the dissipation becomes very large.[See, e.g., Luhar and Britter (1989).] Thus, tracers canin effect become trapped near the surface, eating up

FIG. 1. Linear diffusivity segments used to model the diffusivityprofile predicted by the RUSTIC flow code.

FIG. 2. Junction between two diffusivity segments.


CPU time. To solve this problem, various model devel-opers have limited the time step to a finite value; how-ever, this occasionally results in tracer penetration ofthe ground surface. Thus, various schemes have beensuggested to “reflect” tracers back above the surface ina manner that does not overly distort the underlyingphysics. For example, Thomson and Montgomery(1994) suggest a method that relates the reflected ve-locity to the incident velocity and the normal velocitydistribution.

For horizontal diffusivity, standard interpolationtechniques are used to compute the diffusivity in anarbitrary location in a cell based on the values at theeight corners. First, horizontal diffusivity values are es-timated by vertical interpolation at the tracer height atthe four horizontal corners. Next, as shown in Fig. 3,interpolation in both x and y produces the diffusivitiesKx1, Kx2, Ky1, and Ky2 on the lines intersecting at thetracer location, which are then used to interpolate adiffusivity value at the tracer location and to estimatethe horizontal diffusivity gradients. For example,

�K

�x�

�Kx2 � Kx1�

�x, �4�

and, in the spirit of Eq. (2), the tracer random-walkmotion in the x direction is computed using

��x� � �2�tK � ��tdK

dx ��1�2

� �t�K

�x. �5�

As is done for the velocities, when one of the corners islocated inside a building, the diffusivity in the buildingis set to a value that forces the diffusivity to zero at thesurface.

In contrast to the vertical random-walk movements,overlap regions near diffusivity junctions have not been

included for the horizontal tracer movements. How-ever, the net artificial flux decreases as the size of theoverlap region decreases, which is a function of the timestep. To limit the problem, the horizontal time step iskept small in comparison with the vertical time step.Numerical experimentation has shown that the drift er-ror is often small relative to the statistical fluctuationsfrom the use of a finite number of tracers. Furthermore,it can be argued that the drift only occurs where thegradients are high near building walls. Additional re-search is under way to find a more numerically efficientsolution to the problem. As will be shown in the nexttwo sections, in its current form the model does a re-spectable job of matching experimental data.

4. Comparison with wind-tunnel data for arectangular building

For this dispersion comparison, the wind-tunnelsetup represented a midsized rectangular structure thatresembles a multistory building with a parking garageat the base. A full description of the experiment andresults, listed as case A1-5, could be found at the Com-pilation of Experimental Data for Validation of Micro-scale Dispersion Models (CEDVAL) Internet sitemaintained by Hamburg University (Schatzmann2005). Although the wind-tunnel building was at 1/200scale, the model represents a full-scale height of 25 mwith a frontal width of 30 m and a thickness of 20 m.The boundary layer flow in the tunnel corresponded toa surface roughness of 0.14 m and a friction velocity of0.377 m s�1, yielding a wind velocity at the roof heightof 5 m s�1. On the downwind side of the building arefour openings of size 4.6 m2 that are emission sourceswith a flow rate of 3 m s�1.

The building was modeled with cubic cells 1 m in sizeout to 20 m away from the building in each horizontaldirection, at which point the grid was then expanded.Prior to expanding vertically, the cell dimensions wereheld at 1 m in size until a height of 40 m. The totalnumber of cells was 527 904 and required 112 min ofCPU time on a 2.2-GHz Pentium IV processor forRUSTIC to reach convergence. For the MESO simu-lation, 20 000 tracers were employed, requiring about 4min of CPU time on a 2.8-GHz Pentium IV. Because ofstatistical fluctuations, the MESO results have a nor-malized rms error of about 5% in the central body ofthe plume near the buildings. The error estimate wasbased on a series of runs, each with 20 000 tracers butwith a different starting seed for the random-numbergenerator.

Figure 4 shows the results of a RUSTIC simulation

FIG. 3. Horizontal interpolation of the diffusivity between thecorners of a cell.


for flow around the structure in which cells on thedownwind side have been set up as sources of addi-tional flow. Surface vectors at a height of 2 m and iso-surfaces of TKE are plotted. The effluent openingswere modeled with not only the correct flow rate, butalso with estimated values of the TKE and dissipation,as determined from a simple 1D numerical channelflow model containing the k–� turbulence model. Theflow near the surface at the rear corners is apparentlydisrupted by the flow out of the rear openings, prevent-ing the formation of large corner eddies. A comparisonbetween dispersion measurements and data is shown inFig. 5 at heights of 2 and 7 m. Here, the dimensionlessconcentration K* is plotted, defined by normalizing theconcentration by Q/(uh2), where Q is the sourcestrength, h is the building height, and u is the windspeed at z � h. The diffusivity K for the simulation wasset to K � 2.5k/�, where � is the dissipation coefficientin the k–� turbulence model. More will be said aboutthis choice for K in the next section.

For the main plume located behind the structure, thecomparison between the measurements and the model

simulations is within a factor of 2 or better. For a givencontour, both the width and length of the plumes are ofsimilar size. At a height of 2 m, the regions of similarcontour value are approximately the same length, butthe model underpredicts the plume width. At both lev-els the model underpredicts the degree to which theeffluent is pushed upwind along the sides of the build-ing. This is likely the result of the use of cells that aretoo large in this region to allow correct simulation ofthe narrow eddies along the sides of the buildings. Theresults could be improved with finer cells in this region.Nevertheless, the model simulated the movement ofeffluent roughly halfway upwind along the buildingwalls. The inability to handle correctly the dispersionalong the sides of the structure might also be linked tothe fact that the plume is too narrow downwind. Themodel did a respectable job of simulating the change insize and shape of the high-concentration region (red)between the 2- and 7-m levels at the rear of the build-ing. In other words, even though the release was nearground level, the model simulated the relatively highvalues of concentration at the 7-m level.

FIG. 4. Simulated surface flow and 3D isocontours of TKE (m2 s�2) around the CEDVALA1-5 rectangular building. (Vectors at the four emission sources represent 3 m s�1, and thegreen TKE region is 1–2 m2 s�2.)


Fig 4 live 4/C

5. Comparison with wind-tunnel data for anL-shaped building

For this comparison, the wind-tunnel setup was the“Project EMU” A1 case as described by Cowan et al.(1997) and by Castro et al. (1999). Project EMU was astudy funded by the European Union to assess CFDsolution variability. For case A1, an L-shaped buildingwith an inner side door was placed in a boundary layerflow with a surface roughness z0 of 0.12 m. Althoughthe model was tested at 1/200 scale, only full-scale val-ues will be given here. As shown in Fig. 6, the full-scalebuilding was 10 m in height with the wind directionhead on toward the long end of the building. The windspeed at a height of 10 m was 5 m s�1. Flow was also

FIG. 5. Comparison between (left) measured and (right) simulated dimensionless concentration K* for a rectangular building witheffluent holes near ground on the lee side. The comparison is shown at two heights: (bottom) 2 and (top) 7 m. Measurements wereavailable only at the locations of the colored squares.

FIG. 6. The L-shaped building geometry used in EMUwind-tunnel test A1.


Fig 5 live 4/C

forced out of the door at 1 m s�1 with a trace gas addedto allow dispersion estimates downwind of the building.Because the door was fairly large, 4 m wide � 5 m high,the door flow had a substantial influence on the flow.

To investigate the effect of grid size on the results,three simulations were made using cell sizes in the re-gion of the building of 0.75, 1.0, and 1.5 m. For each ofthe three cases, the cell size was slowly increased in alldirections away from the building, creating a domainsize approximately 100 m upwind of the building, 170 mdownwind of the building, and 100 m on either side.The horizontal grid for the 1.0-m case is shown in Fig.7. In the vertical direction, the cells were held constantin size up to the height of the roof and then expandedup to a height of over 40 m. Near the ground, the ver-tical cell sizes were 0.4, 0.4, and 1.0 m corresponding tothe minimum horizontal cell sizes of 0.75, 1.0, and 1.5m, respectively. For the 1.0-m case the total number ofcells was 108 � 94 � 43 and required 67 min on a2.2-GHz Pentium IV processor for RUSTIC to reachconvergence.

Figure 8 shows the simulated velocity vectors for the1.0-m cell case at 2.5 m above the ground after the flowhas reached steady state. Also shown at this level areTKE contours (m2 s�2). As expected, the TKE valuesare high in the strong shear regions at the front cornersand weak in the slow eddies behind the building. TheTKE is also moderately high well away from the build-ing because of the boundary layer. Two eddies can beseen at the rear of the structure, with the stronger of thetwo coming off the far rear corner. Although not shownin this particular figure, a relatively strong eddy alsoforms at the rear corner of the roof.

Streamlines are shown for a series of starting loca-

tions at the door. Although the streamlines would sug-gest that most material is carried over the roof ratherthan around the building, as will be shown, a significantamount of the trace gas goes out around because of theturbulence. A few of the streamlines follow small ed-dies in the region of the door that carries them to thefront of the building prior to flowing over the roof. Atabout one building height behind the structure, many ofthe streamlines curve back toward the building in thesmall rear eddy. Even a small difference in the startinglocation can result in an entirely different path relativeto its neighbors. However, the turbulence is sufficientlystrong to disrupt the path of a tracer along any givenstreamline.

A contour plot of simulated dimensionless concen-tration K* is shown in Fig. 9, again for the 1.0-m cellsize. For the simulation, a series of 20 Gaussian-shapedclusters were released 0.5 m from the door in a patternfour across and five high. Improving the fidelity of thedoor source to an even greater degree was found tohave little effect on the concentrations. As seen in thefigure, turbulent eddies near the inside corner by theeffluent source carry trace gas upwind to near the frontend of the structure. Primarily because of turbulencecreated at both upwind corners on the door side, tracegas at low levels is carried well away from the buildingside section.

For this same simulation, a plot of measured versussimulated concentration is shown in Fig. 10 for threedifferent scaled heights z/h. The measurements weretaken in a plane directly behind the building at a down-wind distance x/h � 1. The crosswind distance has alsobeen normalized by the building height. Thus, as indi-cated in the diagram in the upper-right corner of theplot, the location y/h � �1 aligns with the long wall ofthe building, and y/h � �1 aligns with the small wall ofthe side extension. At all three altitudes, the peak valueon the simulated curves is within about 30% of the peakvalue of the test data. The main difference betweenthe simulated and measured values is for the simulatedz/h � 0.16 curve, which does not extend as far out fromthe building toward negative y as the measured curvedoes. The MESO dispersion simulations were madewith 30 000 tracers, resulting in a normalized rms errorof about 5% in the region of the peak concentration.

The diffusivity K used in this calculation was set toK � (k/�)/Sct, where k/� is the kinematic eddy viscosityin the k–� turbulence model, as simulated by RUSTICfor each cell. A value for the turbulent Schmidt numberSct of 0.4 was found to give the best overall comparisonto the data, and is the same value that was used for therectangular building. Although a more standard valuefor Sct is about 0.7, Riddle et al. (2004) found for at-

FIG. 7. Inner region of the grid used for RUSTIC flow simulationsfor EMU case A1. Smallest cells are 1 m � 1 m in size.


mospheric flow that an even smaller value of 0.3 gavethe best results with a CFD code containing the k–�model. Increasing values of K do not substantiallywiden the peaks, suggesting the effect of the higherdiffusivity primarily reduces the residence time of thetracers circulating in eddies behind the building. Asomewhat lower value for Sct than that found by otherinvestigators might be in part the result of lower artifi-cial diffusion due to the use of tracers.

The smaller values of Sct needed here to improve thecomparison to measurements might be simply compen-sating for artificially low values of k simulated by thek–� turbulence model when used for urban geometries.For example, Lien and Yee (2004) and Lien et al.(2004) reported that CFD models using the standardk–� as well as modified k–� models often underpre-dicted k by a factor of 1.5–2.0 for urban flow. Burrowset al. (2004b) also noted that RUSTIC underpredictsTKE near ground level by roughly a factor of 2 relativeto urban measurements; however, this may also be dueto the presence of large-scale atmospheric turbulence inthe measurements.

FIG. 8. Flow vectors and TKE (m2 s�2) contours at a height of 2.5 m as simulated byRUSTIC for the L-shaped building. (Only every other vector is shown along the wind direc-tion.) The flow was 5 m s�1 at the roof level with a boundary layer corresponding to z0 � 0.12m. Also shown are streamlines originating at various locations at the door.

FIG. 9. Dimensionless concentration K* simulated byMESO–RUSTIC near the ground (z /h � 0.16).


Fig 8 9 live 4/C

A comparison between the simulated and measuredconcentrations for the 1.5-m cell size is shown in Fig. 11.As the cell size is increased, the near-ground concen-tration increases and the roof-level concentration de-creases. The reverse is true for the 0.75-m grid. It isapparent that the artificial diffusion produced by ad-vection through the larger cells plays a significant rolein the simulations. For the L-shaped building, Cowan etal. (1997) likewise reported that a smaller cell size madethe simulations grow worse in comparison with experi-ment and suggested that artificial diffusion might beresponsible for improving the simulations. Because the

design goal for RUSTIC is a fast-running medium-accuracy tool, setting the various coefficients for diffu-sion of momentum, k, and � as a function of cell sizeand flow curvature is under consideration for urbansimulations. Table 1 lists the computer time needed foreach of the three simulations of the L-shaped buildingat the three different cell sizes based on a 2.2-GHzPentium IV processor.

Current research is involved with investigating theeffects on dispersion-related improvements to the k–�turbulence model. In its standard form, the k–� turbu-lence model overestimates the TKE in the vicinity of a

FIG. 11. As in Fig. 10, but with simulations made using the 1.5-m grid.

FIG. 10. Comparison between measured and simulated trace gas concentrations at a distanceof one building height h behind the L-shaped building. The simulations were based on thestandard k–� turbulence model with the 1.0-m grid. The curves represent normalized con-centration data for MESO–RUSTIC (no symbols) and for measured data (no symbols) takenin a downwind plane (x /h � 1 behind the building) at three heights: z/h � 0.16 (blue), z/h �1.02 (magenta), and z /h � 1.47 (teal).


Fig 10 11 live 4/C

stagnation point in front of a wall. This was investigatedby Durbin (1996) as the stagnation point anomaly, witha solution to the problem later refined by Medic andDurbin (2002). Burrows et al. (2007) found better com-parisons to urban measurements with both the adjust-ment to handle the stagnation point problem and smalladjustments to the coefficients in the k–� model. Pre-liminary results for the 1-m grid indicate that thesemodifications do not necessarily improve the dispersionfor the L-shaped building. In particular, the dispersionnear the ground still does not extend out away from thebuilding wing (toward –y) as far as the measurements,and at the roof level the peak concentration is overpre-dicted by almost a factor of 2.

6. Conclusions

The RUSTIC and MESO models were designed togenerate predictions many times faster than typicalCFD codes with accuracy on the order of a factor of 2.For the two buildings modeled for this study, the codesolutions match the overall features of the dispersiondata reasonably well—in particular in view of the com-plicated emission source geometries and conditions.Particularly satisfying was the modeling showing 1) ef-fluent moving up the back wall of the rectangular build-ing, 2) agreement with experiment in the high-concen-tration region at the rear of the rectangular building,and 3) the rough agreement of the relative amount ofeffluent going over the L-shaped building as opposed togoing around it. Less satisfying is the result that thesimulated curve for the z/h � 0.16 level does not extendas far out from the L-shaped building as the measuredvalues do and that the results are sensitive to the modelcell size. Additional research is needed to resolve thesensitivity to cell size and to understand better the needfor a small Schmidt number Sct to obtain good com-parison to measurements. Even though some compro-mises were made to decrease model run time, the mod-els appear comparable in accuracy to other RANS CFDmodels.

Acknowledgments. This effort was sponsored by theDefense Advanced Research Projects Agency underContract SPO700-98-D-4000.

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