J19.1 NUMERICAL SIMULATIONS OF AIRFLOWS AND TRANSPORT AND DIFFUSION FROM WIND TUNNEL TO TERRAIN SCALES

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1 J9. NUMERICAL SIMULATIONS OF AIRFLOWS AND TRANSPORT AND DIFFUSION FROM WIND TUNNEL TO TERRAIN SCALES Tetsuj Yamada Yamada Scence & Art Corporaton, Santa Fe, New Mexco. INTRODUCTION We added CFD (Computatonal Flud Dynamcs) capabltes to a three-dmensonal atmospherc model HOTMAC. The new model s referred to as ACflow where AC stands for Atmosphere to CFD. A sngle model approach has an attractve feature such that model physcs are dentcal for the CFD and atmospherc components. For example, ACflow can smulate arflows from buldng to terran scales n a seamless manner by nestng computatonal domans. Yamada (008) presented fve smulatons to demonstrate the AC modelng capabltes from wnd tunnel to atmospherc smulatons. Smulatons were conducted to llustrate the thermal effects of buldng walls on the ar flows around two () buldngs. When buldng walls were heated and cooled by the sun, ar flows around two buldngs became qute dfferent from those wthout wall heatng. Recrculaton and reattachment around buldngs no longer exsted. In general upward motons were smulated along warm walls and downward motons were smulated along cold walls. Arflows exteror and nteror of buldngs were also nvestgated. Buldng nteror flows were nfluenced by the locatons of openng (wndows and doors) and exteror flows. Exteror flows, on the other hand, were functons of local crculatons resulted from topographc varatons. We smulated durnal varatons of ar flows around a cluster of buldngs, whch were bound by the ocean and hlls. Large ctes are often located n a coastal area or n complex terran. Predcton of transport and dffuson of ar pollutants and toxc materals s of consderable nterest to the safety of the people lvng n urban areas. There were sgnfcant nteractons between ar flows generated by topographc varatons and a cluster of buldngs. Sea breeze fronts were retarded by buldngs. Wnds were calm n the courtyards. Wnds dverged n the upstream sde and converged n the downstream sde of the buldng cluster. In ths study, verfcaton studes were conducted by comparng the modeled AC results wth wnd tunnel data. Horzontal and vertcal grd spacng were decreased to the order of cm n order to resolve rectangular obstacles placed n a wnd tunnel. Reattachment dstance behnd an obstacle was compared wth wnd tunnel data and other model results. Afflated wth the ACflow s a three-dmensonal transport and dffuson code ACt&d where t&d stands for transport and dffuson. ACt&d s based on a Lagrangan random walk theory (Yamada and Bunker, 988). ACflow provdes three-dmensonal mean and turbulence dstrbutons to ACt&d. The Lagrangan model requres an ntegral tme scale whch nfluences the correlaton between the random veloctes generated n the model. The ntegral tme scale was obtaned as the rato between the modeled length scale and velocty scale. The velocty scale was the square root of the turbulence knetc energy (TKE).. MODELS The governng equatons for mean wnd, temperature, mxng rato of water vapor, and turbulence were smlar to those used by Yamada and Bunker (988). Turbulence equatons were based on the Level.5 Mellor-Yamada secondmoment turbulence-closure model (Mellor and Yamada, 974, 98). Fve prmtve equatons were solved for ensemble averaged varables: three wnd components, potental temperature, and mxng rato of water vapor. In addton, two prmtve equatons were

2 solved for turbulence: one for TKE and the other for a turbulence length scale (Yamada, 983). The hydrostatc equlbrum s a good approxmaton n the atmosphere. On the other hand, ar flows around buldngs are not n the hydrostatc equlbrum. Pressure varatons are generated by changes n wnd speeds, and the resulted pressure gradents subsequently affect wnd dstrbutons. We adopted the HSMAC (Hghly Smplfed Marker and Cell) method (Hrt and Cox, 97) for non-hydrostatc pressure computaton because the method s smple yet effcent. The method s equvalent to solvng a Posson equaton, whch s commonly used n non-hydrostatc atmospherc models. Boundary condtons for the ensemble and turbulence varables were dscussed n detal n Yamada and Bunker (988). The temperature n the sol layer was obtaned by numercally ntegratng a heat conducton equaton. Approprate boundary condtons for the sol temperature equaton were the heat energy balance at the ground and specfcaton of the sol temperature at a certan dstance below the surface, where temperature was constant durng the ntegraton perod. The surface heat energy balance was composed of solar radaton, longwave radaton, sensble heat, latent heat, and sol heat fluxes. Lateral boundary values for all predcted varables were obtaned by ntegratng the correspondng governng equatons, except that varatons n the horzontal drectons were all neglected. The upper level boundary values were specfed and these values were ncorporated nto the governng equatons through four-dmensonal data assmlaton or a nudgng method (Kao and Yamada, 988). Temperatures of buldng walls and roofs were computed by solvng a one-dmensonal heat conducton equaton n the drecton perpendcular to the walls and roofs. One boundary condton was a heat energy balance equaton at the outer sdes of walls and roofs. Another boundary condton was the room temperatures specfed at the nner sdes of the walls. Mellor-Yamada turbulence closure equatons were n three-dmensonal where dervatves n x, y, and z (vertcal) drectons were ncluded. HOTMAC adopted the boundary layer approxmaton where dervatves n x and y drectons were neglected n comparson wth those n z drecton. The boundary layer approxmaton was vald for mesoscale smulatons where horzontal grd spacng was sgnfcantly larger than the vertcal grd spacng. Consequently, horzontal dervatves became neglgble n comparson wth those n the vertcal drecton. The producton terms n the TKE and length scale equatons should nclude horzontal dervatves for CFD smulatons. The producton terms n the horzontal and vertcal drectons are n the same order of magntudes snce the horzontal and vertcal grd spacng are comparatve. Turbulence fluxes n the standard k-e models were modeled by the followng down-gradent relatonshps. u u j = ν ( t j + j ) () Ths method s known to overestmate TKE at the mpngng area of the buldng walls. Varous approaches were proposed to mtgate the ssue (e.g.,tomnaga et al, 008). In the present study, the followng relatonshps were used. w u v u w v () ( = γ (3) = w ) q = γ q γ = 0. (4) Relatonshps (3) and (4) were obtaned by the Level model of Mellor and Yamada (98). The TKE equaton ncludes the followng producton terms whch are related to mpngement: P k V W = uu vv ww KK y z V = ( w u ) + ( w v ) KK y (5)

3 where the mass conservaton equaton was used to elmnate W / z n the frst lne. The producton terms ncluded many other terms whch were modeled by the down-gradent relatonshp () and ncluded n AC. Here only the terms related to mpngement were dscussed. Murakam (000) dentfed that the cause of the TKE overestmaton: the mpngement terms became very large f they were modeled by usng the down-gradent relatonshp. Murakam also dscussed varous proposals to mtgate the ssue. In ths study, the down- gradent relatonshp was not used to model the mpngement terms. Instead, we used the Mellor-Yamada Level relatonshps as n (3). Substtutng an assumpton () nto (5), the mpngement terms became V P k = ( w u )( + ) KK y (6) W = (3γ ) q KK z W = 0.334q KK z where relatonshps (3) and (4) and the mass conservaton equaton were used. Note that the coeffcent of the mpngement terms n the frst lne of (6) s the dfference between the two turbulence components. If the flow were n sotropc, the coeffcent became zero and so dd the mpngement terms. The fnal form of (6) became ndependent of horzontal dervatves whch assured symmetry of the model results for varous wnd drectons. Ths feature was dscussed n the next secton. 3. SIMULATIONS. Wnd Tunnel Model Smulaton Wnd tunnel experments were conducted under well controlled condtons (n comparson wth feld campagns) and extensve measurements were avalable for verfcaton of model results. We selected three cases from the wnd tunnel experments reported n Tomnaga et al. (008). A frst smulaton was conducted n a computatonal doman of 00 cm x 50 cm x 00 cm (vertcal) wth horzontal grd spacng of cm. The vertcal grd spacng was cm for the frst 30 cm from the ground and ncreased gradually to the top of computatonal doman. A model buldng of 0 cm (W) x 0 cm (D) x 0 cm (H) was placed along the centerlne of the computatonal doman (:: block). Inflow boundary values of wnds and TKE were specfed by the measurements. Steady state solutons were obtaned when boundary condtons were kept constant and ntegraton contnued untl flow felds became vsbly unchanged. Fgure shows wnd drecton (arrows) and wnd speed (color) dstrbutons n a vertcal cross secton along the centerlne of the computatonal doman. There was upward moton at the leadng edge of the buldng, whch resulted n separaton and recrculaton of ar flows along the roof. Separaton of ar flows also occurred at the rear sde of the buldng. The modeled characterstcs of recrculaton and reattachment were n good qualtatve agreement wth wnd tunnel data. Fg. : The modeled wnd dstrbutons n a vertcal cross secton along the centerlne of the computatonal doman A second smulaton was conducted n a computatonal doman of 00 cm cube where a block of 0 cm (W) x 5 cm (D) x 0 cm (H) (4:4: block) was placed along the centerlne of the computatonal doman. Horzontal and vertcal grd spacng were the same as for the frst case. Inflow boundary condtons were specfed from the measurements. Fgure shows wnd drecton (arrows) and wnd speed (color) dstrbutons n a vertcal cross secton along the centerlne of the computatonal doman. The reattachment dstance was sgnfcantly larger than the counterpart of the frst case because the block was twce wder.

4 Inflow wnd drectons were vared by 90 degrees to test symmetry of the model results. Fgure 4 and 5 shows the modeled wnd speed and TKE dstrbutons at cm above the floor for varous wnd drectons. Both wnd and TKE dstrbutons were approxmately symmetrc. Slghtly better results were obtaned for TKE than wnd speed. The areas of asymmetry are manly n the area where wnd speeds were very small (blue color). Fg. : The modeled wnd dstrbutons n a vertcal cross secton along the centerlne of the computatonal doman Table shows comparson of the reattachment dstance from the back sde of a block among varous models and wnd tunnel measurements. :: block (cm) wnd tunnel 4 38 LES :4: block (cm) k-e k-l (AC) 7 40 Table : Comparson of reattachment dstance between wnd tunnel measurements and varous models. The model results except AC were from Archtectural Insttute of Japan (007) Fg. 4: Modeled wnd speed dstrbutons for nflow wnd drectons of 45, 35, 5, and 35 degrees (clock wse from upper-left mage) A thrd smulaton was conducted n a computatonal doman of 00 cm x 00 cm x 00 cm (vertcal) where nne blocks of 0 cm cube were placed except the center one whose heght was 0 cm (Fg. 3). Fg.3: Computatonal doman of 00 cm x 00 cm x 00 cm (vertcal). Horzontal grd spacng was cm. Vertcal grd spacng was cm for the frst 50 cm and ncreased wth heght. Fg. 5: Modeled TKE dstrbutons for nflow wnd drectons of 45, 35, 5, and 35 degrees (clock wse from upper-left mage). Lagrangan Integral Tme ACt&d s based on Lagrangan random partcle algorthm.

5 x ( t + Δt) = U = U + u, p x ( t) + U Δt, p u ( t + Δt) = au ( t) + bσ ξ + δ ( a) t u ( σ ), 3 Lx u cube. Concentraton dstrbutons were obtaned wth the modeled and a constant tme scale. As seen from Fg. 7, concentraton dstrbutons are smlar f approprate constant value was selected. An optmum value was selected by performng several tral smulatons. a = exp( Δt / ), b = ( a ) / t Lx t s the Lagrangan ntegral tme. AC used Lx constant values for the Lagrangan ntegral tme as lsted n Table. Tme scale TKE mesoscale (s) buldng (s) wnd tunnel (s) Tab le : Typcal values of Lagra ngan tme scale used n AC for mesoscale, buldng, and wnd tunnel smulatons, resplectvely Fgure 6 shows the modeled TKE, length scale, and tme scale for a :: block n the vertcal cross secton along the centerlne of the computatonal doman. Concentraton dstrbutons wth the modeled tme scale Concentraton dstrbutons wth a constant tme scale Fg. 7: The modeled tme scale, TKE, and concentraton dstrbutons. Concentraton dstrbutons were obtaned wth the modeled tme scale (left) and a constant tme scale (rght). The dmenson of the buldng was a 30 m cube. The modeled tme scale represented the tme scale n the vertcal drecton. The same numercal values were used for the horzontal drectons, because the horzontal and vertcal grd spacng was dentcal (4 m). It was antcpated that horzontal tme scale could be obtaned by multplyng the grd spacng rato to the modeled tme scale. Ths assumpton need to be tested n the future. 4. SUMMARY TKE (m**/s**) Length scale (m) l = ql / q Tme scale (sec) t = l / sqrt (tke) Fg. 6: The modeled TKE, length scale, and tme scale for a :: block n the vertcal cross secton along the centerlne of the computatonal doman The modeled tme scale n Fg. 6 shows dstrbutons nversely proportonal to TKE. In other words tme scale became relatvely small where TKE was large. Fgure 7 shows the modeled tme scale, TKE, and concentraton dstrbutons for a buldng of 30 m ACflow was mproved by ncludng not only the producton terms n the vertcal but also n the horzontal drectons n the turbulence knetc energy and length scale equatons. Arflows around rectangular blocks of dfferent dmensons n a wnd tunnel were smulated wth horzontal grd spacng of cm. Reattachment dstance behnd blocks was n good agreement wth those predctedby the standard k-e model, but was larger n comparson wth wnd tunnel data. The Lagrangan ntegral tme was determned as the rato of the length scale to the square root of TKE. Ths approach removed ambguty assocated n selectng an optmum constant value by tral and error to match the computed wth the observed concentraton dstrbutons.

6 The Lagrangan ntegral tme n the horzontal drectons were proposed to be proportonal to the tme scale n the vertcal drecton multpled by the grd spacng rato. Ths assumpton remaned to be tested n the future. REFERENCES Archtectural Insttute of Japan, 007: Gudebook for Practcal Applcatons of CFD to Pedestran Wnd Envronment around Buldngs, 07pp (n Japanese). Yamada, T., 008: Numercal smulatons of arflows and transport of arborne materals n the exteror and nteror of buldngs n complex terran, Amercan Met. Soc. Annual meetng, New Orleans. Yamada, T., and S. Bunker, 988: Development of a Nested Grd, Second Moment Turbulence Closure Model and Applcaton to the 98 ASCOT Brush Creek Data Smulaton. Journal of Appled Meteorology, 7, Hrt, C.W., and J. L. Cox, 97: Calculatng Three-Dmensonal Flows around Structures and over Rough Terran. J. of Computatonal Phys., 0, Kao, C.-Y. J. and Yamada, T., 988: Use of the CAPTEX Data for Evaluaton of a Long-Range Transport Numercal Model wth a Four- Dmensonal Data Assmlaton Technque, Monthly Weather Revew, 6, pp Mellor, G. L., and T. Yamada, 974: A Herarchy of Turbulence Closure Models for Planetary Boundary Layers. J. of Atmos. Sc., 3, Mellor, G. L., and T. Yamada, 98: Development of a Turbulence Closure Model for Geophyscal Flud Problems. Rev. Geophys. Space Phys., 0, Murakam, S., 000: Computatonal Envronment Desgn for Indoor and Outdoor Clmates. The Unversty of Tokyo Press, 443pp (n Japanese). Tomnaga, Y., A. Mochda, R. Yoshe, H. Kataoka, T. Nozu, M. Yoshkawa, and T. Shrasawa, 008: AJI gudelnes for practcal applcatons of CFD to pedestran wnd envronment around buldngs. J. Wnd Eng. and Industral Aerodynamcs, 96, Yamada, T., 983: Smulatons of Nocturnal Dranage Flows by a q l Turbulence Closure Model. J. of Atmos. Sc., 40, Yamada, T., 004: Mergng CFD and Atmospherc Modelng Capabltes to Smulate Arflows and Dsperson n Urban Areas. Computatonal Flud Dynamcs Journal, 3 ():47,