Using Large Eddy Simulation to Study Airflows in and around Buildings

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1 Jang, Y., Su., M., and Chen, Q Usng large eddy smulaton to study arflows n and around buldngs, ASHRAE Transactons, 109(), Usng Large Eddy Smulaton to Study Arflows n and around Buldngs Y Jang, Ph.D. Mngde Su, Ph.D. Qngyan Chen, Ph.D. * ASHRAE Member ASHRAE Member ABSTRACT Ths nvestgaton uses three subgrd-scale models of large eddy smulaton (LES) to study arflows n and around buldngs. They are the Smagornsky model, a fltered dynamc subgrdscale model and a stmulated small-scale subgrd-scale model. For outdoor arflow that s hghly turbulent, the smple Smagornsky model s suffcent. For ndoor arflow where lamnar flow can be as mportant as turbulent one, the fltered dynamc subgrd-scale model and the stmulated small-scale subgrd-scale model are recommended. However, the computng tme requred by the fltered dynamc subgrd-scale model and the stmulated small-scale subgrd-scale model are consderably hgher than that by the Smagornsky model. Ths paper also dscusses how to set up boundary condtons for wnd and how to smulate ndoor and outdoor arflow together wth good resoluton and reasonable sze of computatonal doman for natural ventlaton studes. KEYWORDS: ar flow, ndoor ar qualty, modelng, turbulence, ventlaton 1. INTRODUCTION Study of arflows n and around buldngs helps us understand the effectveness and energy performance of ventlaton systems, ndoor ar qualty, thermal comfort, smoke dsperson, and fre development n buldngs, polluton spread n urban area, and mpact of wnd load on buldng structure systems. The propertes of buldng arflows, such as velocty, temperature, pressure, and speces concentraton, etc. are determned by supply ar, thermal buoyancy, buldng geometry and spatal arrangements, and weather condtons. Correct predcton of buldng arflows s very challengng. Measurements on a buldng ste or n a full-scale envronmental faclty can provde relable arflow dstrbutons around and nsde a buldng. Katayama et al. (1989), Fernandez and Baley (199), Dascalak et al. (1995), and Yuan (1999) have performed such measurements. However, on-ste measurements are tme consumng and the measured data are normally wth very low resoluton so that they cannot be easly generalzed. The experment n a full-scale envronmental faclty s not only tme consumng but also expensve. Furthermore, studes of arflow around a buldng often use wnd tunnels that could smulate wnd condtons. Notable studes of ths type * Y Jang was a Research Assstant at Massachusetts Insttute of Technology and now s a Mechancal Engneer, RES Engneerng Inc., Hudson, MA, Mngde Su were a Senor Post- Doctoral Assocate at Massachusetts Insttute of Technology s now wth Chrysler, Detrot, MI and Qngyan Chen s a Professor, School of Mechancal Engneerng, Purdue Unversty, West Lafayette, IN. Chen s phone: (765) , fax: (765) , emal: yanchen@purdue.edu, and malng address: 585 Purdue Mall, West Lafayette, IN

2 of arflow nclude those from Murakam et al. (1991) and Chonere and Munroe (1994). Wth a wnd tunnel, buldngs are scaled down but the nstrumentaton used can dsturb flow patterns and lead to accuracy problems (Murakam et al. 1991). Wth thermal buoyancy, scale models n a wnd tunnel would have problem to smulate both nertal and buoyancy forces accordng to smlarty theory. Computatonal flud dynamcs (CFD) provdes an alternatve approach to obtan detaled arflow dstrbutons n and around buldngs. CFD s becomng popular due to ts nformatve results and low labor and equpment costs, as a result of the development n turbulence modelng, and n computer graphcs, speed and capacty. There are three dfferent CFD methods: drect numercal smulaton, Reynolds-averaged Naver-Stokes (RANS) modelng, and LES. Drect numercal smulaton solves the Naver-Stokes equaton wthout approxmatons. The method requres the use of very fne grd resolutons to compute the smallest eddes n flow. To solve arflows n and around a buldng, DNS would requre at least a grd number of Current super computers can handle a grd resoluton as fne as In addton, t would take years of CPU tme n a super computer to solve a meanngful problem of arflow n and around buldngs. Therefore, the computer capacty s stll far too small and the computer speed s far too slow wth the drect numercal smulaton method. RANS modelng requres lttle computng tme and s the most commonly used method to solve engneerng arflows. To solve buldng arflows, however, RANS modelng has some key lmtatons. Frst, RANS modelng cannot accurately predct arflow around buldngs. Lakehal and Rod (1997) compared the computed results of arflow around a bluff body by usng varous RANS and LES models. They found that most RANS models had dffcultes generatng the separaton regon on the roof, whch was observed n the experment. Furthermore, the RANS models over-predct the recrculaton regon behnd the body. On the other hand, the LES models dd not encounter these problems, and ther results agreed well wth the expermental data. Secondly, the Reynolds stresses n the RANS method are unknown and have to be modeled wth a turbulence model. Chen (1995) tested a number of popular turbulence models and concluded that none of them are unversal for ndoor arflow smulaton. Buldng desgners who are not very famlar wth turbulence models have dffcultes choosng a sutable model for the desgn of buldng arflow systems. On the contrary to the RANS models, the subgrd-scale models of LES are more unversal because of the physcs of the model development, whch wll be stressed below LES method has been successfully used to solve buldng arflows n recent years (Davdson and Nelsen 1996, Emmerch and McGrattan 1998, Zhang and Chen 000, Su et al. 001, Jang and Chen 001, Jang and Chen 00, and Jang et al. 003). LES separates flow motons nto large eddes and small eddes. The method computes the large eddes n a three-dmensonal and tme dependent way whle t estmates the small eddes wth a subgrd-scale model. When the grd sze s suffcently small, the mpact of the subgrd-scale models on the flow moton s neglgble. Furthermore, the subgrd-scale models tend to be unversal because turbulent flow at very small scale seems to be sotropc. Therefore, the subgrd-scale models of LES generally contan only one or no emprcal coeffcent. Snce the flow nformaton obtaned from subgrd scales may not be as mportant as that from large scales, LES can be a general and accurate tool to study engneerng flows (Pomell 1999, and Leseur and Metas 1996). The buldng arflow n the current study s only a small porton of the atmospherc boundary layer (ABL). To smulate ABL turbulence, where the heght of the layer s typcally 1,000 meters, the grd sze s much larger than a local ntegral turbulence scale n the near wall regon. Therefore, a tradtonal

3 subgrd-scale model of LES needs to be modfed to account the mpacts of scale varatons (Porte-Agel et al., 000). Furthermore, the real ABL often contans abrupt changes of surface roughness and substantal transportatons of eddes, heat, mosture and polluton vertcally through the boundary layer. Snce t s stll unclear how the coherent structure s adusted under those condtons, such a non-equlbrum smulaton s not consdered n the current nvestgaton. Hence, ths paper wll ntroduce the LES method and dscuss the accuracy and demand for CPU tme when t s appled to study arflows n and around buldngs. The accuracy of LES s generally related to subgrd-scale models, whle the computng tme to the numercal technques.. SUBGRID-SCALE MODELS OF LARGE EDDY SIMULATION By flterng the Naver-Stokes and contnuty equatons, one would obtan the governng equatons for the large-eddy motons as u t u + = 0 1 p (u u ) = ρ u + ν τ (1) () where the bar represents grd flterng. The subgrd-scale Reynolds stresses, τ, n Equaton (1), τ = u u u u (3) are unknown and must be modeled wth a subgrd-scale model. Varous subgrd-scale models have been developed n the past thrty years. Three of them are presented n ths paper: 1. Smagornsky subgrd-scale (SS) model (Smagornsky 1963). Fltered dynamc subgrd-scale (FDS) model (Zhang and Chen 000) 3. Stmulated small-scale subgrd-scale (SSS) model (Shah and Ferzger 1995).1 Smagornsky Subgrd-Scale Model The Smagornsky subgrd-scale model (Smagornsky 1963) s the smplest subgrd-scale model, and has been wdely used snce the poneerng work by Deardorff (1970). The SS model assumes that the subgrd-scale Reynolds stress, τ, s proportonal to the stran rate tensor, 1 u u S = ( + ) (4) τ = υsgss (5) where the subgrd-scale eddy vscosty, υ SGS, s defned as 3

4 1 1 SGS = ( CSGSΔ) (S S) = CΔ (S S) υ (6) The Smagornsky constant, C SGS, ranges from 0.1 to 0. determned by flow types, and the model coeffcent, C, s the square of C SGS. The SS model s an adaptaton of the mxng length model of RANS modelng to the subgrd-scale model of LES.. Fltered Dynamc Subgrd-Scale Model The SS model requres a pror specfcaton of the model coeffcent, C, and a dampng functon must be used to account for near wall effects. It s dffcult to specfy the model coeffcent n advance and the coeffcent may not be a constant. In order to solve the problem, Germano et al. (1991) developed a subgrd-scale model wth a dynamc procedure, whch s usually called a dynamc model. Ths model can determne the coeffcent as a functon of tme and locaton. The dynamc model has no prescrbed coeffcent, s physcally sound, and therefore s very attractve. The orgnal dynamc model s computatonally unstable. The least square approach provded by Llly (199) s wdely adapted to stablze the soluton. The dynamc subgrd-scale model has the key features of proper asymptotc behavor near walls and the subgrd-scale eddy vscosty can vansh n the regons of lamnar flow. However, ths dynamc subgrd-scale model can stll lead to numercal nstablty f the subgrd-scale eddy vscosty remans negatve for too long. To overcome ths dffculty, Germano et al. (1991) averaged the flow varables over a homogenous drecton. For a channel flow, t s possble to dentfy the homogeneous drecton. For arflows n buldngs, there s no homogeneous drecton. To stablze the calculaton, Zhang and Chen (000) ntroduced a fltered dynamc subgrd-scale model. In the FDS model, a local average procedure replaces the average procedure over a homogeneous drecton. Ths method s dfferent from the local averagng procedure proposed by Zang et al. (1993). As ponted out by Zhang and Chen (000), although Zang et al. s (1993) method can effectvely reduce the fluctuaton for low-reynolds number cavty flow, Zang et al. s (1993) method does not work for ndoor arflow that does not have a homogeneous drecton. Therefore, we use the FDS model proposed by Zhang and Chen (000). The model coeffcent, C, n the FDS model s calculated as follows: Gf ( x, x' ) LMd x' C = (7) Gf ( x, x' ) MMd x' where ~ ~ L = ~ u u u u (8) M = α β ~ (9) ~ α = Δ ~ S S ~ (10) β = Δ S S (11) ~ ~ and ~ stands for an explct test flter wth a flter wdth of Δ ( Δ = Δ) and G f ( x, x' ) s a smooth functon. 4

5 The C s obvously a functon of tme and space, and t can be appled to nhomogeneous flows. The smooth functon G f ( x, x' ) should be chosen for the entre flow doman and may depend on the turbulent scales. Although the smooth functon can be n many forms, a box flter may be the most convenent ( G f ( x, x') = G( x, x' ) ). Equaton (7) ndcates that C can be negatve that mples the flow energy from small scales s transferred to the resolved large scales. However, the negatve C can lead to numercal nstablty. In order to avod the nstablty, the present nvestgaton sets C = max (0.0, Equaton (7))..3 Stmulated Small-Scale Subgrd-Scale Model Most of subgrd-scale models, such as the SS and FDS models, are eddy vscosty models, whch apply Boussnesq hypothess to calculate the eddy vscosty. A non-eddy vscosty model, named as stmulated small-scale subgrd-scale model, was developed by Shah and Ferzger (1995). Ths method attempts to obtan the unresolved parameters by usng mathematcal and/or physcal methods based on statstcal theory or DNS data, whch s the reason to be called as stmulated. The method apples successve nverson of a Taylor seres expanson to represent the unknown full velocty n terms of the fltered velocty and ths seres expanson model s of scale-smlarty form. The SSS model calculates the subgrd stresses from * * * * τ = u u u u (1) The SSS model expands varables, such as veloctes, wth Taylor seres, so that the unknown subgrd-scale stresses can be computed. * ( x x ) * d u d u u (x) = u + + (x x ) + (13) d x d x By neglectng the thrd-order and hgher-order terms and replacng the dervatves wth central dfferencng ones, ths equaton becomes * * * * * * u + 1 u 1 ( x x ) u + 1 u + u 1 u(x) = u + (x x ) + (14) h h Su et al. (001) gave a detaled mathematcal explanaton about ths model. 3. NUMERICAL METHODS Ths secton dscusses the numercal scheme employed for solvng the governng equatons wth approprate boundary condtons. Snce ths nvestgaton nvolves natural ventlaton, how to effectvely calculate both ndoor and outdoor arflows wll also be addressed n ths secton. 3.1 Numercal schemes Wth the subgrd-scale models, the present study uses the smplfed marker and cell method (Harlow and Welch 1965) to solve the governng equatons of LES. In order to correlate the momentum equaton and the contnuty equaton, the smplfed marker and cell method frst * 5

6 solves the momentum equatons wthout the pressure term. So the velocty obtaned, u *, s a pseudo-velocty. * u u τ + (u )δ u ) = ν + g β(θ θ0 (15) t Subtractng Equaton (1) from Equaton (15) yelds * (u u ) 1 p = (16) t ρ Then, by dfferentatng both sdes of Equaton (16) and usng Equaton (), we have * u 1 p ( ) = (17) t ρ Equaton (17) s a Posson equaton. Ths nvestgaton apples a strong-mplct procedure (Stone 1968) or a fast Fourer transformaton method to solve the Posson equaton. The fast Fourer transformaton method requres less computng tme than the strong-mplct method. But currently t requres a unform grd dstrbuton along at least one drecton. Ths stuaton works for some buldng arflows. However, for most arflows around and nsde buldngs, the grds along all three drectons are normally non-unformly dstrbuted due to the strongly nhomogeneous characterstcs of the arflows and buldng geometry. Therefore, the fast Fourer transformaton method needs to be further mproved before beng used as a general method to solve the Posson equaton. 3. Boundary Condtons Boundary condtons, ncludng the treatments of walls, and nflow and outflow condtons, are needed to close the equaton. They are dscussed n ths secton. If a no-slp boundary condton s used for the arflows around and nsde buldngs, a large number of fne grds close to the walls are needed, whch s not practcal at present due to lmtatons on computer capacty. Therefore, a macroscopc boundary condton, a wall model, has to be ntroduced nto the arflow study n buldngs. The current study uses the wall model suggested by Werner and Wengle (1991). Ths model can be appled to both fully developed turbulent regons and regons of unsteady lamnar flow, whch are common n arflows around and nsde buldngs. When applyng LES to study arflow around buldngs, the boundary condtons at open boundares, whch nclude nflow and outflow condtons, are complex due to the effects of up and down-stream obstacles, free stream turbulence, etc. The nflow condtons are wth or wthout wnd. For the stuaton wthout wnd, there are no nertal forces to the open boundary and only buoyancy forces drve the ar movement nsde the computatonal doman. Therefore, a zero-gradent condton can be appled at the boundary. If the computatonal doman s large enough, a symmetrcal or non-slp condton can also be adopted. Wth wnd, the technque for generatng a realstc wnd at the nflow boundary s very mportant. Two mportant ssues have to be addressed n ths wnd smulaton: the fluctuatons of wnd speed and wnd drecton. The smplest method to smulate wnd fluctuaton s to store the tme hstory of velocty fluctuatons gven from a prelmnary LES computaton (Werner and Wengle 1991 and Shah 1998). However, ths method requres extra computng costs to generate a seres of transent flow felds and a large amount of memory to store the data. The current 6

7 study uses random fluctuatons supermposed on a mean velocty profle at the nlet. The fluctuatons are constructed to be of the same magntude as the real wnd. It s observed that wnd drecton changes over tme and ts hstogram exhbts some rules (Ntta 1990). Followng these rules, Jang and Chen (00) successfully used LES to smulate the drectonal fluctuaton of wnd around and across buldngs. The treatment of an outflow boundary condton s also mportant. The boundary condton at the ext should cause a mnmal nfluence on the upstream and should permt eddes n the flow to ext the doman wthout any adverse effect on the flow feld nsde the computatonal doman. The current nvestgaton uses the zero-gradent condton that has been used successfully for a long tme. 3.3 Determnaton of Computatonal Doman When usng LES to study arflows both nsde and outsde of a buldng, such as natural ventlaton, the computatonal doman must be large enough to capture macro-scale outdoor arflow and the grd resoluton must be hgh enough to obtan detaled mcro-scale ndoor arflow. However, f the doman s too large, the computng tme wll be ncreased sgnfcantly. Ths s partcularly true when Cartesan coordnate system s used. To save computng tme whle ensurng detaled ndoor arflow nformaton, t s better to separate ndoor and outdoor calculatons. When smulatng macro-scale outdoor arflow, buldngs can be treated as sold blocks wthout openngs, such as wndows. Ths s because the sze of buldng openngs s normally less than 1/6 of the total facade area and the effect of the openngs on the outdoor arflow dstrbutons can be neglected (Vckery and Karakatsans 1987). The grd dstrbuton n ths outdoor flow smulaton can therefore be relatvely coarse so that a large computatonal doman can be covered. Ths would lead to an error of less than 5%. The separaton of ndoor and outdoor arflow calculatons can reduce the computng tme sgnfcantly and makes t possble to use LES to study a large-scale mult-buldng ste. 4. RESULTS AND DISCUSSION In ths secton, the subgrd-scale models of LES are used to study both ndoor and outdoor arflows. The examples of ndoor arflows are natural, forced, and mxed convecton, whch are common stuatons nsde a buldng. The results are then compared wth expermental data to evaluate the model performance. 4.1 Natural Convecton n a Room To study ndoor arflow drven by buoyancy forces, the arflow crculated wthn a cold and a warm wall s nvestgated. Although ths cavty type s not a real ndoor condton, the arflow characterstcs are very smlar to those nsde a room. Therefore, ths case can be regarded as an ndoor arflow drven by buoyancy forces. Detaled ar velocty, temperature, turbulence energy, and heat transfer were measured by Cheesewrght et al. (1986). Fgure 1 shows the arflow dstrbutons along the mddle heght of the cavty. The RANS modelng wth the standard k-ε model s also used as a comparson. The fgure shows that the two subgrd-scale models gave good results for mean veloctes and temperatures. However, the 7

8 SS model predcted much too small turbulence knetc energy than the expermental data. The results computed wth the FDS model were n better agreement wth the expermental data. (a) Mean velocty (b) Mean temperature (c) Turbulence knetc energy Fgure 1. Comparson of the computed arflow dstrbutons along the md secton of the walls wth the expermental data (Cheesewrght et a. 1986). Squares: Experment, Sold lnes: RANS modelng wth the k-ε model, Dotted lnes: SS model wth C SGS = 0.16, Dashed lnes: FDS model. 4. Forced convecton n a Room The LES models have also been appled to study a forced convecton flow n a room. The velocty was measured by Nelsen et al. (1978) wth a laser Doppler anemometer. Ths case represents a smple but typcal ndoor ventlaton stuaton. Fgure shows the computed arflow pattern n the md-secton. Besdes a large recrculaton n the center of the room, there s a small eddy n the upper rght corner, whch was also observed n the experment. Fgure 3 shows the comparson wth measured data for the mean ar velocty, represented by U, and the fluctuatng ar velocty, represented by ur. The FDS and SSS models perform slghtly better than the SS model. Ths suggests that for ndoor arflow cases, n whch walls normally have sgnfcant effects and both turbulent and lamnar flows exst, the SS model may not be approprate. Fgure. The computed mean velocty n the mddle secton of the room (LES wth SS model). 8

9 Fgure 3. Comparson of the computed mean and fluctuaton velocty profles wth the expermental data (Nelsen et al. 1978) at x=1 secton. Dots: expermental data, Trangles: SS model wth 66x18x34 grds, Dot-dash lnes: SS model wth grds, Dash lnes: FDS model wth grds, Sold lnes: SSS model wth grds. The dstrbutons of the model coeffcent, C, can show how the FDS model produces good results. Fg. 4 llustrates that C s small both near the walls and n the regons of lamnar flow, whch correctly represents the physcs of flow motons. Fg. 4. Dstrbutons of the mean model coeffcent, C, at the mddle secton of the room 4.3 Mxed Convecton n a Room The mxed convecton studed s the arflow n a room wth dsplacement ventlaton. Yuan et al. (1999) performed detaled expermental measurements on the dstrbutons of ar velocty, ar temperature, and contamnant concentraton by usng a tracer-gas (SF 6 ). In the experment, cool ar was suppled through a dffuser n the lower part of a room and warm ar was exhausted at the celng level. The room has two occupants, two PCs, overhead lghtng, and furnture. Fgure 5 shows the mean arflow pattern n the md-secton of the room obtaned wth the SSS model of LES. Because of the buoyancy effect, the cold ar from the dffuser moved rapdly downwards along the floor. The mean arflow pattern showed a large but weak recrculaton n the lower part of the room. In the upper part of the room, there were some recrculatons caused 9

10 by the thermal plumes from heated obects, such as PCs, occupants, and overhead lghts. The computed arflow pattern was smlar to that observed n the measurement. Fgure 6 compares the computed mean ar velocty, temperature, and SF 6 concentraton wth the expermental data n the center of the room. The results ndcate that the three subgrd-scale models performed slghtly dfferent from each other. A model may work better than the others n one locaton but poorer n another. Fgure 5. The mean arflow pattern n the md-secton of the offce (LES wth SSS model). 10

11 Fgure 6. Comparson of the computed profle of ar velocty, temperature, and SF 6 concentraton to the expermental data (Yuan et al. 1999) n the center of the room. The vertcal coordnate s dmensonless room heght, VEL s ar velocty (m/s), T s normalzed ar temperature, and ce s normalzed SF 6. (ce=(c-c s )/(-c s ), c s =0.4 ppm, where c s s the tracer gas concentraton at the source). Dots: expermental data, Dashed-dotted lnes, SS model, Sold lnes: FDS model, Dashed lnes: SSS model. The performance of dfferent subgrd-scale models to smulate ndoor arflow can be summarzed n Table 1. Please note that Reynolds numbers are computed based on the nlet heght and nlet velocty and Raylegh numbers are computed based on the temperature dfference between the cold and the warm walls, the heght of the walls and the dstance between the two walls. It shows that n terms of accuracy, the SS performs farly well n most regons as FDS and SSS model. The computng tme requred by the FDS model s 0% more than that by the SS model because t needs to calculate the coeffcent C. Although t s mathematcally sound, the SSS model needs twce as long computng tme as the FDS model. Table 1. Performance comparson wth dfferent subgrd-scale models of LES Natural convecton Forced convecton Mxed convecton SS model FDS model SS model FDS model SSS model SS model FDS model SSS model Reynolds N/A N/A 5,000 5,000 5, number Raylegh.5x x10 10 N/A N/A N/A N/A N/A N/A number Grd number 69,19 69,19 99,00 99,00 99, Tme step x10-4 x (second) 11

12 Computng tme (hours) st order Accuracy nd order Accuracy 3 1 Computed on an Alpha workstaton wth a sngle 164 processor Mean velocty, temperature, and contamnant concentraton, etc. 3 Turbulent knetc energy, fluctuatng velocty and temperature, etc. 4.4 Arflows n and around a Buldng The SS and FDS models have been further appled to calculate arflow n and around a buldng for a natural ventlaton study. Ths study also used a wnd tunnel to measure detaled arflow around and wthn a smple, cubc, buldng-lke model. Two-dmensonal mean and fluctuatng velocty components were measured by usng a laser Doppler anemometer. The pressure dstrbutons along the model surface were also measured. The Reynolds number studed s based on the velocty at the buldng heght n the nlet of the computatonal doman. Both of a coarse mesh, , and a fne mesh, , were used. It was found that the computed results wth the coarse mesh are generally n good agreement wth the expermental data. For example, the dstrbutons of the mean and fluctuatng veloctes close to buldng openngs were properly predcted wth the coarse mesh and the ventlaton rate can be calculated correctly. Therefore, to study natural, the coarse mesh s adopted. However, to nvestgate the flow dstrbuton n some specal regons, such as above the buldng roof, the fne mesh provded better results than the coarse mesh. For the coarse mesh, the correspondng CPU tme used s 150 hours for the SS model and 190 hours for the FDS model. For the fne mesh, the CPU tme s more than three tmes longer than that requred by the coarse grd due to the ncreased grd number and reduced tme step sze. The measurements were conducted for several cases, such as the buldng has an openng n the wndward drecton, n the leeward drecton, n the sdewalls, etc. LES has been used to smulate all of those cases. Here, the measured and computed veloctes n sngle-sded ventlaton wth an openng n leeward wall are presented. Fgure 7 shows the locatons where the computed results from LES are compared wth the measured data. Fgure 8 shows that the mean veloctes computed from LES are generally n good agreement wth the expermental data. The dfference between the expermental data and the LES results s less than 5% n most regons. Ths ndcates that LES can be used to study wnd-drven arflows around and wthn a buldng wth excellent accuracy. Fgure 8 also llustrates that the results from both SS model and FDS model are almost the same. By analyzng the magntudes of dfferent terms n the momentum equaton, we found that the contrbuton of the subgrd-scale stresses to the man flow moton s much smaller than that of the resolved (large-scale) stresses n most regons around the block. Therefore, most energy s contaned n the large eddes, whch play a more mportant role than the small eddes. Snce both the SS and FDS models can drectly solve the large-eddy motons, they are able to provde accurate flow results. In the current study, although the buldng model s not a blockage, most of the arflows outsde of the buldng model are fully or nearly fully developed turbulent flows, 1

13 whch are very smlar to the arflows around a blockage. Hence, the computatonal results from the two subgrd-scale models are almost the same n most of the flow doman. Wnd -H/5 0 H/ H+H/ Fgure 7. The locaton where comparson of the LES results wth expermental data was made n the md-secton (The thck lnes represent the buldng model and the ground). (a) Mean velocty dstrbutons (b) Fluctuatng velocty dstrbutons 13

14 Fgure 8. Comparson of LES results of mean and fluctuaton ar velocty n horzontal drecton for sngle-sded, leeward ventlaton. Dots: expermental data; Sold lne: SS model; Dotted lne: FDS model. (U ref s the reference velocty at the buldng heght and H n front of the buldng.) 5. CONCLUSIONS Three subgrd-scale models of LES have been used to study arflows n and around buldngs. For outdoor arflow cases, the SS model works farly well snce the flows are fully turbulent. For cases where lamnar phenomenon s as mportant as turbulent one, such as ndoor arflows, the SS model performs poorly n some regons and the FDS and SSS models can gve a much better result. Although the SSS model s mathematcally sounded, t requres longer computng tme than the other two models. Therefore, the SS model s recommended for outdoor arflow and FDS or SSS model for ndoor arflow and combned ndoor and outdoor arflows. When applyng LES to study natural ventlaton, t s better to separate the ndoor arflow and outdoor arflow smulatons. The separaton helps to ensure that the computatonal doman s suffcently large to accurately smulate upstream condtons and the grd resoluton for ndoor arflow s suffcently fne to obtan detaled flow nformaton. ACKNOWLEDGMENTS Ths work s supported by the U.S. Natonal Scence Foundaton under grant CMS NOMENCLATURE C model coeffcent S stran rate tensor (1/s) C SGS Smagornsky model constant t tme (s) G f smooth functon u ar velocty (m/s) h grd sze u, u ar velocty components n the x H buldng heght (m) and x drectons (m/s) L ~ u u ~ u ~ = u u * u at x M β ~ * = α u pseudo-velocty p ar pressure (Pa) x, x coordnates n and drectons (m) Greek Symbols = Δ ~ S ~ S ~ ν SGS subgrd-scale eddy vscosty (m /s) α β = Δ S S ρ ar densty (kg/m 3 ) Δ flter wdth (m) ρ p partcle densty (kg/m 3 ) 14

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