STUDY OF WAKE REGION BEHIND OF ISOLATED CUBIC BUILDING.PART II: NUMERICAL SIMULATIONS

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1 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl STUDY OF WAKE REGION BEHIND OF ISOLATED CUBIC BUILDING.PART II: NUMERICAL SIMULATIONS Larsse Suzy Slva de Olvera, Julana Glcéro Dazz, Marane Gonçalves Mranda, Regnaldo Rosa Cotto de Paula, Coordenadora de Engenhara Santára e Ambental, Ifes, Vtóra ES, Brasl. Fernanda Capucho Cezana, fe.cezana@gmal.com Coordenadora de Matemátca, Ifes, Vtóra ES, Brasl. Marcos Sebastão de Paula Gomes, mspgomes@mec.puc-ro.br Departamento de Engenhara Mecânca, Puc-Ro, Ro de Janero RJ, Brasl. Abstract. Ths paper presents numercal smulaton of wnd flow around an solated cubc buldng. The numercal smulatons were carred out wth the standard and Omega Reynolds Stress turbulence models. Expermental data from wnd tunnel experments n the neutral boundary layer were used to valdate the numercal results. The Reynolds number, based on the heght of the buldng was The man purpose of the present study s to nvestgate the behavor of a wake regon formated behnd an solated cubc buldng. In addton were determned the length of reattachement ponts n the roof and near the wake regon of the body. The results showed that the DSM turbulence model was able to capture the separton and the reattachment pont on the roof of the buldng. The numercal predctons of reattachment pont n the near wake behnd of the cube obtaned wth both standard and Omega Reynolds Stress turbulence models were slghtly larger n comparson wth expermental data. Keywords: numercal smulatons, turbulence models, atmospherc boundary layer, buldng. 1. INTRODUCTION The atmospherc flow near the solated buldng s extremely complex, wth regons of ntense crculaton, turbulent movements, strongly ansotropc three-dmensonalty (Murakam, 1993). Due to the complexty of the physcal phenomena nvolved, many mathematcal models used smplfyng hypotheses n order to predct the turbulent flow around a buldng (Santos, 2000; Tomnaga, and Stathopoulos, 2010). Wth the advanced of technology and computers have been possble to mprove the complexty of mathematcal models. Therefore, many studes have been performed usng the Computatonal Flud Dynamcs (CFD) models whch are based on the fundamental equatons of transport, such as Tsuchya et al. (1997), Gao and Chow (2004) and Tomnaga and Stathopoulos (2010). The man dfference n these studes was the turbulence models that have been used to predct the turbulent flow around the obstacles. Baskaran and Kashef (1996) showed the developments of the CFD technque as a powerful tool for predcton of wnd flow around a varety of buldngs confguratons. They examned the followng confguratons: as sngle buldng flow, flow between parallel buldngs and flow around multple buldng confguratons. The authors reported to that CFD method can provde very detaled predctons of ar veloctes around buldngs. Tomnaga et al. (2008) presented comparson of CFD results usng varous revsed - turbulence models (LK model, MMK model and Durbns s revsed) and LES appled to flow around a hgh-rse scale buldng model placed wthn the surface boundary layer. The numercal predctons were compared to wnd tunnel data. The results showed that all revsed - models to capture the reverse flow on the roof, although t was a lttle larger than the expermental values. The reattachment length n near wake of buldng was larger than the expermental data. The reverse flow on the roof gven by LES showed to be close wth the experment. The overestmaton of reattachment length behnd the buldng was mproved n the LES computatons. Ths mprovement was manly because to the perodc velocty fluctuaton due to the vortex sheddng behnd the buldng was well reproduced n LES. A revew of the lterature on ths flow problem verfes that the turbulence model - was wdely used to smulate the flow around buldngs (Tomnaga and Stathopoulos, 2009; Gousseau et al. 2011). However, comparsons wth expermental data (Murakam, 1993) suggest that the models for the Dfferental Reynolds Stress (Dfferental Reynolds Stress Model - DSM) have obtaned better results than the - turbulence models. The obectve of ths study was to nvestgate the behavor of the flow around an solated cubc obstacle, especally the regon at the top of the buldng and the recrculaton regon behnd the buldng, usng two dfferent turbulence models: standard - model and Dfferental Stress Model (DSM) based on the equaton of

2 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl 2. METHODS 2.1 The Wnd Tunnel Experments The flow consdered n ths work was nvestgated n open return wnd tunnel wth test secton of 2.0 m 0.5 m 0.5 m of the Energy Laboratory of Ifes, Vtora, Brazl. Wood spres (0.379 m) and roughness elements (cubcal wooden blocks of m) were nstalled upwnd of test area of the wnd tunnel n order to generate a neutral atmospherc boundary layer (Irwn, 1981). The mean streamwse velocty has the followng power law profle: U U z p y (1) where = 0.30 m s the atmospherc boundary layer thckness. In ths work the velocty profle was ft wth p = 0.20, whch corresponds to the velocty profle over flat terran wth low buldngs (Blessman, 1988). The scale model buldng conssts of a cubc block of heght H b = 0.10 m. Fg. 1 shows a schematc three dmensonal flow around cubc buldng used for these wnd tunnel experments. 2.2 Governng Equatons Fgure 1. Sketches of the expermental flow feld analyzed n ths study. The governng equatons for the atmospherc flow n the neutral condtons of an ncompressble and Newtonan steady-state flud wth constant vscosty,, based on the Reynolds-averaged Naver-Stokes approach are: u x 0 u u u u x x = x p 2 u 3 x k k u x u x (1) (2) where u and u are the fluctuatng and mean veloctes n the x -drecton ( =1, 2, 3); p s the dynamc pressure and ' s the densty of the flud. The knematc Reynolds stress uu represents the turbulent fluxes of momentum. In ths present work t were used the standard - model (Jones and Launder, 1972) and DSM based on the equaton of Wlcox (1988) for turbulence closurethe k- turbulence models and DSM dffer precsely n the treatment of ths term. 2.2 Numercal Methods A commercal CFD code (ANSYS CFX 13.0) was used to calculate the velocty feld around buldng. The code solves three-dmensonal Reynolds-average Naver-Stokes (RANS) equaton usng a UPWIND scheme. The computatonal doman was extended up to a dstance of 3.0H b upwnd of the obstacle, 8.0H b downwnd (x 1 = 12.0H b ), 2.5H b n each crosswnd drecton (x 3 /2), and 5.0H b n the vertcal drecton (x 2 ). In order to evaluate the mesh senstvty, three non-unform meshes were tested: 100,000 nodes (coarse mesh), 200,000 nodes (regular mesh) and 400,000 nodes (fne mesh). The varaton of the mean vertcal velocty profle at

3 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl 1.0H b and 3.0H b downwnd dstance of wndward buldng face showed lttle dfference between the three mesh szes. It was confrmed that the predctons results wth - turbulence model dd not change sgnfcantly wth mesh sze. Therefore, all smulatons were performed usng the regular mesh, Fg. 2. In ths case the mnmum cell wdth was H b /12. Fgure 2. 3D non-unform regular mesh for wnd flow smulaton around a cubc buldng. 2.3 Boundary condtons of the computatonal flow In the nlet the vertcal and lateral veloctes are consdered to be equal zero and the component n the man drecton was gven by equaton (1). 0, 025 U, where U Hb Hb s the velocty at the top of the buldng. The value of the dsspaton of turbulent knetc energy can be obtaned The nlet boundary condton for the turbulent knetc energy was gven by 2 3. RESULTS 3/2 C by the expresson 1/2 1/2 du, where l C l dz and C = 0,09 (Murakam, 1993). Symmetry boundary condton n central plane of the cube was mposed, because n ths case exsts a symmetrcal nature of the flow and the equatons were solved only n one half of the doman. The outflow boundary condtons the dffuson fluxes for all flow parameters n the drecton normal were assumed to be zero. Therefore outflow velocty and pressure gradent were consstent wth a fully developed flow assumpton. At the lateral face and at the top of the computatonal doman was set to free-slp condtons. At the ground surface and at the buldng surfaces the velocty was set to zero by the non-slp condton. The results of the numercal smulatons of the flow around cubc buldng are presented. The flow structure n the vcnty of the cube was analyzed for a Reynolds number of , based on buldng heght H b and wnd velocty at the buldng heght, U H = 2.30 m/s. Fgures 3 and 4 show the expermental results of the flow n front and behnd the cubc buldng, respectvely. Fg. 5 shows the sde vew pattern of the computed ar flow n the vcnty of cubc buldng wth two turbulence models nvestgated. In all fgures the velocty felds can be analyzed wthn three dfferent regons: frontal regon, roof of the buldng and the recrculaton bubble behnd the body. Qualtatvely varous features of the flow were correctly captured by record of the mages and numercal smulatons wth the two dfferent turbulence models. In frontal face of the buldng the flud flow towards the ground and return n the opposte drecton to the man flow. Ths nteracton between the ncdent flow and reverse flow generated the standng vortex near the ground. In the Fgs. 3 and 5, was observed that the expermental and all numercal smulatons clearly predcted the recrculaton regon behnd the obstacle. It was evdent that the results obtaned by flow vsualzaton and computed flow, across DSM model based on the equaton of, were able to show the separaton and the reattachment pont of the boundary layer on the roof of the buldng (Fgs. 3 and 5). However, the standard κ-ε fals to represent ths phenomenon accurately. The numercal smulaton usng κ-ε can not to predct the separaton regon. 1

4 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl Fgure 3. Sde vew of the ncdent flow around cubc buldng. Fgure 4. Sde vew of the flow n near wake behnd the cubc buldng. (a) (b) Fgure 5. Sde vew of the computed ar flow around cubc buldng: (a) standard - model and (b) DSM based on the equaton of Fgure 6 shows the computed ar flow around cubc n x-z plane at the y = H b /2 wth the standard - model and DSM based on the equaton of turbulence models. The topology of the flow patterns wth both models showed that there were two symmetrcal recrculaton downstream of the buldng behnd the backs faces.

5 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl (a) (b) Fgure 6. Computed ar flow around cubc n x-z plane at the y = H b /2: (a) standard - model and (c) DSM based on the equaton of Fgure 7 show the dfference between computed streamlne around cubc buldng wth the standard - model and DSM based on the equaton of turbulence models. The DSM turbulence model was able to capture the vortex sheddng n the regon of the separated flow feld behnd the obstacle a as show the Fg. 7. (a) (b) Fgure 7. Streamlne around cubc buldng: (a) standard - model and (b) DSM based on the equaton of Table 1 shows the comparson of reattachment lengths on the roof (x R /H b ) of the cube obtaned by experments and numercal smulatons. These results showed that numercal predctons wth standard - turbulence model was not able to capture the reverse flow on the roof. Tomnaga et al. (2009) ponted out that the overestmaton of n the standard - model contrbute to the large mxng effects produced by the eddy vscosty whch not reproduce the reverse flow on the roof. The results compared here, show the applcablty of DSM based on the equaton of the flow feld around a buldng was good. However, ths model overestmates the reattachment length on the roof.

6 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl Table 1. Reattachment lengths on the roof of the cube Authors x R / Hb Experment (present work) 0.24 Standard - model (present work) - DSM model (present work) 0.31 Experment (Lm et al., 2009) 0.20 LES (Lm et al., 2009) 0.85 Table 2 shows the comparson of reattachment lengths behnd of the cube obtaned by varous experments and numercal smulatons. The x W /H b obtaned expermentally n the present work showed good agreement wth others experments, performed to by Murakam et al. (1990) and L and Meroney (1983). The numercal predctons of x W /H b obtaned wth standard - turbulence and DSM were slghtly larger n comparson wth those for experments. Table 2. Reattachment lengths behnd the cubc buldng. Authors x W / Hb Experment (present work) 1.08 Standard - model (present work) 1.1 DSM model (present work) 1.3 Experment (Murakam et al., 1990) 1.2 Experment (L and Meroney, 1983) CONCLUSIONS In ths work numercal smulatons were used to nvestgate de wnd flow n the vcnty of the cubc buldng and the results were compared wth wnd tunnel experments. From the precedng dscussons, the followng concluson can be made: 1. The numercal smulatons reproduced the standng vortex n frontal face of the buldng lke wnd tunnel experments. 2. The DSM turbulence model was able to capture the separaton and the reattachment pont of the boundary layer on the roof of the buldng. However, the standard turbulence model has problems n predctng the reattachment pont on the top of the obstacle, because ths model fals to predct the separaton regon. 3. The numercal predctons of reattachment pont n the near wake behnd of the cube obtaned wth standard - turbulence and DSM were slghtly larger n comparson wth expermental results. 5. REFERENCES ANSYS CFX 13, Solver Manual, CFX Internatonal, AEA Technology, UK. Baskarn, A. and Kashef, A., Investgaton of ar flow around buldngs usng computatonal flud dynamcs technques. Engneerng Structures, Vol. 18, pp Gao, Y. and Chow, W.K., Numercal studes on ar flow around a cube. Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 93, pp Gousseau, P., Blocken, B. e Hest, G. J. F. V., CFD smulaton of pollutant dsperson around solated buldngs: On the role of convectve and turbulent mass fluxes n the predcton accuracy. Journal of Hazardous Materals, Vol. 194, pp Jones, W. P. e Launder, B. E., The predcton of lamnarzaton wth two-equaton model of turbulence. Internatonal Journal of Heat and Mass Transfer, Vol. 15. pp L, W. and Meroney, R.N., 1983a. Gas Dsperson near a cubcal model buldng, Part I, concentraton measurements. Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 12, pp Lm, H. C., Thomas, T.G. and Castro, I. P., Flow around a cube n a turbulent boundary layer: LES and experment. Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 97, pp Murakam S., Mochda A. and Yoshhko H Examnng the k-e Model by Means of a Wnd Tunnel Test and Large Eddy Smulaton of the Turbulence Structure Around a Cube. Journal of Wnd Engneerng and Industral Aerodynamcs, Vol.35, pp Murakam, S., Comparson of varous turbulence appled to a bluff body. Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 46, pp

7 Proceedngs of ENCIT 2012 Copyrght 2012 by ABCM 14 th Brazlan Congress of Thermal Scences and Engneerng November 18-22, 2012, Ro de Janero, RJ, Brazl Patankar, S., Numercal Heat Transfer and Flud Flow. Hemsphere Publshng Corporaton, Second Edton, USA. Santos, J.M., Flow and Dsperson Around Isolated Buldngs. Ph.D. Thess, Department of Chemcal Engneerng, Unversty of Manchester, England. Tomnaga, Y., Mochdab, A., Murakam, S. and Sawak, S., Comparson of varous revsed - models and LES appled to flow around a hgh-rse buldng model wth 1:1:2 shape placed wthn the surface boundary layer. Journal of Wnd and Engneerng Industral Aerodynamcs, Vol. 96, pp Tomnaga, Y. and Stathopoulos, T., Numercal smulaton of dsperson around an solated cubc buldng: Comparson of varous types of models. Atmospherc Envronment, Vol. 43, pp Tomnaga, Y. and Stathopoulos, T., Numercal smulaton of dsperson around an solated cubc buldng: Model evaluaton of RANS and LES. Buldng and Envronment, Vol 45, pp Tsuchya, M., Murakm, S., Mochda, A., Kondo, K., and Ishda, Y., Development of a new - model for flow and pressure felds around bluff body. Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 67&68, pp Yakhot, V., Orszag, S.A., Thangam, S., Gatsk, T.B. & Spezale, C.G., Development of turbulence models for shear flows by a double expanson technque. Physcs of Fluds A, Vol. 4, pp Wlcox, D.C., Mutscale model for turbulent flows. AIAA Journal, Vol RESPONSIBILITY NOTICE The authors are the only responsble for the prnted materal ncluded n ths paper.