BBAA VI Internatonal Colloquum on: Bluff Bodes Aerodynamcs & Applcatons lano, Italy, July, 0-4 008 NUEICAL SIULATION OF TUBULENT FLOW AOUND A BUILDING COPLEX Sungsu Lee, Choon-Bum Cho, Kyung-Soo Yang and Ha-Sun Km School of Cvl Engneerng Chungbu Natonal Unversty, Cheongu, 361-763, Chungbu, South Korea e-mal: oshua@cbnu.ac.r, hasun@cbnu.ac.r Depaprtment of echancal Engneerng Inha Unversty, Incheon, Korea Keywords: Large Eddy Smulaton, Immersed Boundary ethod, Buldngs. Abstract. Strong wnd flow around a buldng complex was numercally studed by LES. The orgnal motvaton of ths wor stemmed from the efforts to develop a rs assessment technque for wndstorm hazards. Lagrangan-averaged scale-nvarant dynamc subgrdscale model was used for turbulence modelng, and a log-law-based wall model was employed on all the sold surfaces ncludng the ground and the surface of buldngs to replace the no-slp condton. The shape of buldngs was mplemented on the Cartesan grd system by an mmersed boundary method. Key flow quanttes for the rs assessment such as mean and S values of pressure on the surface of the selected buldngs are presented. In addton, characterstcs of the velocty feld at some selected locatons vtal to safety of human bengs are also reported. 1 INTODUCTION Wnd flow around buldngs are of prme nterest n wnd engneerng, and numerous studes n computatons and experments have been performed for flow around sngle buldng. Snce Castro and obns experments[1] of pressure on a cube, the nvestgaton has deepenng for the flow around a cube, and LES and DES have been tred n computatonal wors. However, only few of studes are found for the nvestgaton of flow around a buldng complex, most of whch have been done by experments. Ths paper presents a large eddy smulaton of turbulent flow around a buldng complex usng the mmersed boundary method (IB). Due to hgh e of the wnd feld, Lagrangan Dynamc Subgrd-scale model [] s employed and wall model s appled on the surface nstead of no-slp. The complcated geometry of the buldng complex does not pose any computatonal ssues snce IB [3] allows for usage of Cartesan grds wth forcng terms n the governng equatons. 1
FOULATIONS.1 Large Eddy Smulaton Based on the mmersed boundary method and the mass forcng for contnuty by Km et al. [3], the governng equatons for ncompressble flud flow usng IB and LES are as follows; u q 0 and u uu p τ 1 u + + + f (1) t t e x and p represents pressure, q and u denote Cartesan coordnate and velocty component, respectvely. f denote mass source and momentum forcng, respectvely. s the eynolds stress to be modeled. e s eynolds number based on reference length, h and nflow velocty U. Ths study employs the Smagornsy model based on the eddy vscosty. τ ν S. () SGS ν SGS s the eddy vscosty for LES whch has the form of 1 ν SGS ( CSΔ) SS and u u S + (3) Germano[4] suggested Dynamc Subgrd-scale model n whch C S s dynamcally determned usng averagng n the homogenous drecton based on algebrac dentty between resolvable scale and subgrd scale,.e., L u u u u (4) Accordng to Llly[5], L C S ( S S S S ) Δ 4 (6) However, the flow around a buldng complex does not present such a drecton, whch results n numercal nstablty n evaluatng C S. Instead, ths study employs Lagrangan Dynamc Subgrd-scale model [] whch averages C S n the paths of flud partcles. Ths results from mnmzng the error of Germano s dentty. The Lagrangan expresson of the error and the accumulated error along the streamlne are e ( z, ) L ( z, ) C ( x, ) ( z, t ) (4) Therefore S t e z( t ), t ) e ( z( t ), t ) W ( t t dt E ( ) (5) W ( t ) s a weght functon and z () s the prevous poston of flud partcle. C S wth mnmzed E s C S L L t t L ( z( ), ) W ( t ) d ( z( ), ) W ( t ) d τ (5) (6) (7)
. Immersed Boundary ethod The governng equatons are dscretzed by a fnte-volume method whch has the secondorder accuracy n space. The tme ntegraton s carred out by a fractonal step method n whch convecton terms are ntegrated by a 3rd order unge-kutta method and dffuson terms are by Cran-Ncolson scheme. uˆ u p ( α + β ) L( u ) + β L( uˆ u ) γ N ( u ) ζ N( u ) ( α + β ) + f (8) Δt u uˆ φ (9) Δt L and N denote dffuson and convecton operators, respectvely, and the coeffcents used n Eq. (8) are n ef. [3]. In order to evaluate the momentum forcng f n Eq. (8), approxmaton of Eq. (1) s made by usng a 3rd order unge-kutta method for convecton term and a forward Euler method for dffuson terms; U u p ( α + β ) L( u ) γ N( u ) ζ N( u ) ( α + β ) + f (10) Δt U s the velocty nsde the body, to be determned by the nterpolaton scheme descrbed above. earrangng Eq. (10) leads to the momentum forcng (8), f whch s used n Eq..3 Wall odel In LES for atmospherc boundary layer near wall boundares at hgh eynolds number, wall model n Eq. (11) can be utlzed wth the dea of average n the homogeneous drecton. log κ τ w u1 (11) log( z / zo ) κ s von Karman constant. 3 COPUTATIONAL ESULTS 3.1 Flow Around Wall-ounted Sngle Cube In order to verfy the present method, turbulent flow around wall-mounted sngle cube s smulated. Inflow turbulence s mposed usng random number to ft the longtudnal turbulence ntensty gven by a experment. The number of grd s 19x18x96 and the results are compared wth those of DES. Fg (1) compares the present streamlnes n vertcal plane wth those of DES [6], whch are very smlar to each other. Horseshoe vortex formng on the wndward surface s very smlar to each other. Comparsons of the mean pressure n Fg () show that the present results are closer to the measurements. 3
(a) [6] (b) Present Fgure. 1 Streamlnes n the vertcal center plane Fgure. Pressure coeffcents 3. Flow Around a Buldng Complex The buldng complex modeled n ths study was from Goettnger Strasse, Hanover, Germany [7] shown n Fg (3). The doman s 130m, 1640m and 300m n x,y and z drecton, respectvely, along whch 160x160x48 grd s used. Among 31 buldngs, No. 4 buldng of 30m hgh s the tallest and the geometry of all buldngs s from the study of Loua et al [7]. Detals of the buldngs are lsted n Table 1. Fgure. 3 Geometry of buldngs and computatonal doman As shown n Fg (3), Drchlet and convectve condtons are used on nlet and outlet, respectvely, whle slp condton s mposed on lateral and upper boundares. On the nlet, atmospherc boundary layer profle s gven as * u u( z) ln( z / z o ) z < 100m κ (1) u( z) 59.41m / s z 100m 4
frcton velocty u * 3.165 and roughness length zo 0. 05 are used. In addton, randomly generated turbulence s ncluded on the nlet followng Spalart [8] such that the turbulence ntensty at the heght of 30m matches 0.5 descrbed n ef. [7]. On the walls on buldngs and ground, wall model s used wth z 0. 01 as n ef. [7]. Table 1. Detals of buldngs No. Length(x) Wdth(y) Heght(z) No. Length(x) Wdth(y) Heght(z) 1 180.0 ~ 65.0 700.0 ~ 710.0 0.0 17 175.0 ~ 05.0 895.0 ~ 910.0 3.0 40.0 ~ 55.0 710.0 ~ 760.0 0.0 18 00.0 ~ 65.0 910.0 ~ 940.0 3.0 3 150.0 ~ 40.0 760.0 ~ 785.0 0.0 19 87.0 ~ 30.0 700.0 ~ 710.0 0.0 4 40.0 ~ 68.0 760.0 ~ 785.0 30.0 0 87.0 ~ 97.5 710.0 ~ 755.0 0.0 5 0.0 ~ 65.0 785.0 ~ 795.0 0.0 1 97.5 ~ 98.0 740.0 ~ 750.0 0.0 6 0.0 ~ 30.0 795.0 ~ 910.0 15.0 87.0 ~ 97.5 755.0 ~ 765.0 3.0 7 30.0 ~ 40.0 795.0 ~ 910.0 17.5 3 87.0 ~ 30.0 765.0 ~ 775.0 3.0 8 40.0 ~ 45.0 795.0 ~ 910.0 15.0 4 90.0 ~ 300.0 787.5 ~ 815.0 17.5 9 50.0 ~ 65.0 795.0 ~ 798.3 0.0 5 90.0 ~ 30.0 815.0 ~ 85.0 17.5 10 50.0 ~ 55.0 798.3 ~ 805.0 3.0 6 90.0 ~ 30.0 835.0 ~ 845.0 17.5 11 50.0 ~ 55.0 805.0 ~ 840.0 0.0 7 90.0 ~ 30.5 845.0 ~ 880.0 17.5 1 55.0 ~ 65.0 798.3 ~ 840.0 0.0 8 90.0 ~ 30.0 880.0 ~ 895.0 17.5 13 45.0 ~ 65.0 840.0 ~ 850.0 0.0 9 90.0 ~ 300.0 910.0 ~ 940.0 0.0 14 50.0 ~ 65.0 850.0 ~ 880.0 0.0 30 45.0 ~ 50.0 795.0 ~ 840.0 15.0 15 45.0 ~ 65.0 880.0 ~ 910.0 0.0 31 45.0 ~ 50.0 850.0 ~ 880.0 15.0 16 150.0 ~ 180.0 880.0 ~ 895.0 3.0 o Fg (4) compares the present results wth Loua et al [6] for the averaged of velocty at the heght of pedestran. The present computatons well smulate the horseshoe vortex formed n front of the wndward walls as well as the ncrease wnd velocty through urban canyons whle Loua et al [6] dd not. Fgure 4. Comparson of averaged velocty feld at pedestran level (Present on left, Loua et al [7] on rght) 5
Fg (5) shows the magntude of horzontal velocty feld at the heght of pedestran whch may be of mportance to the safety of pedestrans as well as the generaton of wnd-borne debrs. It shows that the speeds are twce the nlet velocty n some regon and very hgh along the asle n front of No. 0 buldng. The vertcal velocty n Fg (5) shows that strong upwnd s formed around No. 16, 17 and 18 buldngs resultng n strong vortex. Fgure 5. Averaged magntude of horzontal speed (left) and vertcal velocty (rght) at z1.5m Fg (6) dsplays S of pressure dstrbuton at z1.5m, whch shows the strong vortex around No. 16, 17 buldngs results n large S of the fluctuatng pressure. The rght fgure n Fg (6) shows S on the vertcal plane around the regon. Fgure 6. S of fluctuatng pressure on horzontal and vertcal planes 4 CONCLUSION A practcal method to smulate the wnd flow of hgh e around buldngs has long been pursued n the wnd engneerng communty. Hndered by computatonal capacty and/or numercal dffcultes, wnd flow around a buldng complex has been studed mostly by experments. 6
Ths study presents a computatonal method for wnd flow around a buldng complex. LES s employed to smulate the wnd flow of hgh e wth wall functon. Conflcts between complcated geometry and grd are resolved by usng IB. Well-nown problem of flow around wall-mounted sngle cube demonstrates the valdty of the present method based on Lagrangan Dynamc Subgrd-scale model. A buldng complex of 31 buldngs s modeled and wnd flow s smulated. The present method shows that wnd flow around the complex can be well predcted and t can be used on practcal purposes. EFEENCES [1] I. P. Casto, I. P and obns A. G., The Flow Around a Surface-mounted Cube n Unform and Turbulent Streams, J. Flud ech., Vol. 79, part, 1977, pp. 307-335. [] C. eneveau, T.S. Lund and W.H. Cabot, A Lagrangan Dynamc Subgrd-scale odel of Turbulence, J. Flud ech., Vol. 319, 1996, pp. 353-385. [3] J. Km, D. Km and H. Cho, An Immersed-Boundary Fnte-Volume ethod for Smulatons of flow n Complex Geometres, J. Comp. Phys., Vol. 171, 001, pp. 13-150. [4]. Germano, U. Pomell, P. on and W.H. Cabot, A Dynamc Subgrd-Scale Eddy Vscosty odel, Phys. Fluds, Vol. 3, 1990, pp. 1760-1765. [5] a Llly, D. K., "A proposed modfcaton of the Germano subgrd-scale closure method", Phys. Fluds, Vol. 4, 199, pp. 633-635. [6].P. Wlson, S.E. Haupt, L.J. Pelter and.f. Kunz, Detached Eddy Smulaton of Atmospherc Flow about a Surface ounted Cube at Hgh eynolds Number, Proceedngs of FEDS006, 006, July 17-0, am, FL. [7] P. Loua,. Ketzel, P. Sahm, E. Gulloteau, E., oussopoulos, N., Sn, J. -F., estayer, P. G. and Berowcz,., CFD Intercomparson Exercse wthn TAPOS European esearch Networ", The 7th Conference on Envronmental Scence and Technology, Ermoupols, Syros, Greece. 001, pp. 67-75. [8] Spalart, P., "Drect Smulaton of a Turbulent Boundary Layer up to e1410", J. Flud ech., Vol. 187, 1988, pp. 61-98. 7