APPLICATION OF CFD TOOLS FOR INDOOR AND OUTDOOR ENVIRONMENT DESIGN

, Volume 1, Number 1, p.14-9, 000 APPLICATION OF CFD TOOLS FOR INDOOR AND OUTDOOR ENVIRONMENT DESIGN Q. Chen and J. Srebrc Buldng Technology Program, Department of Archtecture, Massachusetts Insttute of Technology 77 Massachusetts Avenue, Cambrdge, MA 0139-4307, U.S.A. ABSTRACT Computatonal Flud Dynamcs (CFD) has become a useful tool for the study of ndoor and outdoor envronment problems. Recently, the Massachusetts Insttute of Technology (MIT) has developed several Reynolds Averaged Naver-Stokes (RANS) equaton models and Large Eddy Smulaton (LES) models to enhance the capabltes of CFD for use n ndoor and outdoor envronment desgn. The new models have been successfully used to assess buldng shape desgn, to evaluate the effectveness of natural ventlaton n buldngs, to model Volatle-Organc-Compound (VOC) emssons from buldng materals, and to calculate ndoor envronment parameters. 1. INTRODUCTION The CFD technque has become a tool for predctng engneerng flows snce the early 1970s, due to the development n computer programmng and turbulence models. CFD solves flud flow, heat transfer, and chemcal speces transport. The parameters solved, such as ar velocty, ar temperature, contamnant concentratons, relatve humdty, and turbulence quanttes, are crucal for desgnng a comfortable ndoor or outdoor envronment. Ths s because the desgn of approprate ventlaton systems and the development of control strateges requre detaled knowledge of arflow, contamnant dsperson and temperature dstrbuton n a buldng. Ths knowledge s also requred by archtects for desgnng the buldng confguraton. In the past thrty years, the CFD technque has been appled wth consderable success n buldng desgn, as revewed by Chen [1] and Murakam []. The CFD approaches are normally classfed nto three types: Drect Numercal Smulaton (DNS), Reynolds Averaged Naver-Stokes (RANS) equaton modelng, and Large Eddy Smulaton (LES). DNS solves the hghly relable Naver-Stokes equatons wthout approxmatons. Therefore, DNS requres a grd resoluton as fne as the Kolmogorov mcro-scale. Snce the Reynolds number s approxmately 10 6 for typcal wnd flow and approxmately 10 5 for ndoor arflow, the total grd number for solvng arflow n and around a buldng s approxmately 10 13. Current super computers can have a grd resoluton as fne as 51 3. The computer capacty s stll far too small to solve such a flow. Therefore, DNS cannot be used to study ndoor and outdoor envronment under a realstc condton. RANS solves ensemble-averaged Naver-Stokes equatons by usng turbulence modelng. RANS can be further dvded nto turbulent vscosty models and Reynolds-stress models. The most wdely used turbulent vscosty model s the standard k-ε model [3]. Chen [4] compared fve dfferent k-ε models for the predcton of natural, forced, and mxed convecton n rooms, as well as an mpngng et flow. These models faled to predct the ansotropc turbulence and secondary recrculaton of ndoor arflow. The Reynoldsstress models solve the transport equatons for the Reynolds stresses. Recent effort on the Reynoldsstress models focuses on how to mprove the pressure-stran correlaton. Murakam [5] used four dfferent Reynolds-stress models to calculate the reattachment lengths around a cube. All the models sgnfcantly over-predcted (40% to 90%) the lengths. Chen [6] used three dfferent Reynoldsstress model to predct ndoor arflows wth natural, forced, and mxed convecton. The performance of those models was not much better than the standard k-ε model. In addton, the models are mathematcally complex and numercally unstable. LES was developed n the early 1970s by Deardorff [7] for meteorologcal applcatons. He departed from the hypothess that the turbulent moton could be separated nto large-eddes and small-eddes. The separaton between the two does not have a sgnfcant effect on the evoluton of large-eddes. LES solves the large-eddy moton by a set of fltered equatons governng the threedmensonal, tme dependent moton. Turbulent transport approxmatons are used for small eddes whch are modeled ndependently from the flow 14

geometry. The success of LES stems from the fact that the man contrbuton to turbulent transport comes from the large-eddy moton. Thus, LES s clearly superor to RANS where the transport terms (e.g. Reynolds stresses) are treated wth full emprcsm. LES s also more realstc than DNS because LES can be performed on a large and fast workstaton. Murakam [] revewed the use of LES for arflow around buldngs. He found that LES gave the best accuracy and the standard k-ε model the worst. Very few applcatons of LES are for ndoor arflow. These applcatons nclude the predcton of forced convecton n an empty room [8-11]. The results show that LES can predct ndoor arflow, especally the turbulence level, more accurately than RANS. At present, LES needs at least 51 megabytes of computer memory to separately study ndoor arflow or outdoor arflow only. For natural ventlaton where ndoor and outdoor arflow must be studed smultaneously, LES would requre several ggabytes of computer memory. Snce LES smulates arflow n a three-dmensonal, tmedependent manner, the computng tme needed s much longer than that by RANS. Wth a 533 MHz Alpha workstaton, a typcal run wth LES s two to three days, whle wth RANS t s only two to three hours for ndoor arflow smulaton. Although the computng costs seem to be hgh at present, the fast development n computng power wll make LES an affordable desgn tool n the near future. Ths paper wll demonstrate some efforts at the Massachusetts Insttute of Technology (MIT) to use CFD as a desgn tool for ndoor and outdoor envronment desgn.. RANS MODEL DEVELOPMENT Based on the revew above, the effort at MIT n the past few years has been to use RANS as a man desgn tool and to use LES as an advanced tool. For an ncompressble and Newtonan flow, the RANS conservaton equatons for contnuty, momentum (usng Boussensseq approxmaton for buoyancy), turbulence quanttes, energy, and chemcal speces can be generalzed as: ( ρφ) + t ( ρu Φ) = ( Γ Φ φ ) + S φ (1) The Φ, Γ φ and S φ for dfferent flows are shown n Table 1, where the standard k-ε model [3] s used..1 A Two-Layer k-ε Model Prevous studes [4,6] found that the Reynoldsstress models and low-reynolds-number models dd not perform much better than the standard k-ε model or the Re-Normalzaton Group (RNG) k-ε model but were more demandng on computng tme. Therefore, the standard k-ε model and the RNG k-ε model have been used for these studes. However, the standard k-ε model and the RNG k-ε model cannot accurately calculate the heat transfer near a wall. The data from a drect numercal smulaton from Kasag and Nshmura [1] has been used to develop a new two-layer model to solve the problem. Table 1: Values of Φ, Γ φ and S φ n Eq. (1) Equaton Φ Γ Φ, eff S Φ Contnuty Momentum T-equaton k-equaton 1 U (=1,,3) T k 0 µ+ µ t µ/σ l + µ t /σ t (µ+ µ t )/σ k 0 - P/ - ρg β(t-t 0 ) S T G-ρε +G B ε-equaton ε (µ+ µ t )/σ ε [ε (C ε1 G-C ε ρε)/k] +C ε3 G B (ε/k) Speces C (µ+ µ t )/σ c S C µ t =ρc µ k /ε G=µ t ( U / + U / ) U / G B =-g(β/c P )( µ t /σ T,t ) T/ C ε1 =1.44, C ε =1.9, C ε3 =1.44, C µ =0.09 σ l =0.7, σ t =0.9, σ k =1.0, σ ε =1.3, σ C =1.0 15

A two-layer model conssts of two turbulence models. Ths paper uses a sngle k-equaton turbulence model for near-wall flow and the standard k-ε model for flow n the outer-wall regon. The crtera to swtch from one model to the other s the y * value. If y * < y * prescrbed, the sngleequaton model apples; otherwse, the standard k-ε model wll be used. y * prescrbed = 80 seems optmum for room arflow. In the near-wall regon, where y * < 80, the new one-equaton model s used through whch k s solved by Eq. (), k + U t k = d k + P k + G k ε The eddy vscosty s calculated by Eq. (3): µ () ν t = vvl (3) and the ε by Eq. (4): ε = vvk l ε (4) Then l µ, l ε, and k vv are determned by Eqs. (5), (6) and (7) respectvely. l l µ ε (0.33 + 0.14f l )y µ = (5) 4 ] µ 1 + 5.05 10 y lε *[1.53+ 0.1fl v (1.3 + 7.5f l )y ε = 1+ (.1 + 7.88f ) / y + (0.08 + 0.035f * v *( fvv / k ) vv = y 0.4 1 exp k 400(1 0.99f where vv / k [ 1 + tanh(50 * Ar 4) ] ) lε )y (6) (7) 1 f l µ = f l ε = y (8) f vv / k [ 1 + tanh(10 * Ar 4) ] 1 = y (9) In the outer-wall regon, where y * 80, the standard k-ε model and Eqs. (10) and (11) are used: * v Dk ν = ( Dt x ν + σ ν t T ε + g β Pr t t k k ) + ν x t U ( U + ) (10) where σ k = 1.0. The ε s solved by a transport equaton Dε ν t ε = ( ν + ) Dt σε ε U U + C1ε ν t ( + ) C k ε ε + C 3ε ν t g β Pr t (11) T The eddy vscosty s calculated by the equaton, k ν t = C µ, where C µ = 0.09. The standard k-ε ε model does not need a length scale prescrpton. Ths model has been used wth success to study forced, natural, and mxed convecton flow n a room [13]. Fg. 1 shows the ar velocty and temperature profles at the center of a smulated offce wth dsplacement ventlaton. The agreement s very good n the regon close to the celng. In the regon close to the floor, some dscrepances dd occur. However, the largest dfference between the calculated temperatures and measured ones was less than 1 K, whch s about 4% of the measured temperature. Ths can be consdered a good agreement. The numercal smulaton conducted by Yuan et al. [14] used the RNG k-ε model wth wall functons to predct the flow and heat transfer. Snce wall functons would predct grd dependent heat flux and cause an unacceptable error, a prescrbed convectve heat transfer coeffcent was used to obtan the correct temperature dstrbutons. The value of the coeffcent used n ther study was calbrated by the expermental data. Ths s undesrable n a numercal predcton because the coeffcent s generally unknown. The two-layer model does not requre a prescrbed convectve heat transfer coeffcent, and thus s more favorable for numercal smulatons. The agreement between the numercal results and the measured data s acceptable but not excellent. The models used n the computaton may have some uncertantes for ndoor arflow predcton due to the assumptons made n the model development. The measurements are also not free from errors. The hot-wre anemometers used n the experment cannot accurately measure the ar velocty when t s lower than 0.1 to 0.15 ms -1. Snce the velocty level n ths case s low, the 16

uncertanty n the measurements of the veloctes s rather hgh. The grd number requred n the current study (5 48 8) s a lttle hgher than that used by Yuan et al. [14] (48 4 4). Ths study shows that the computng costs wth the two-layer model are slghtly hgher than those wth the RNG k-ε model. If the study used a low-reynolds-number k-ε model, t would requre at least one mllon grd ponts because there are many heated surfaces n the room. A low-reynolds-number k-ε model requres at least 0 grd ponts to correctly calculate the heat transfer from a heated/cooled sold surface. The computng effort would be tremendous. (a) Offce layout (1-nlet, -outlet, 3-person, 4-table, 5-wndow, 6-fluorescent lamps, 7-cabnet, 8-baseboard heater, 9- computer, 10-partton wall) Measurements Zero-equaton model Large eddy smulaton Two-layer model (b) Velocty profle (c) Temperature profle Fg. 1: Velocty and temperature dstrbuton at the center of an offce wth dsplacement ventlaton 17

. A Zero-Equaton Model The two-layer model can accurately calculate heat transfer near a wall, whle usng far less numercal grd ponts than low-reynolds-number models. However, the computng tme s stll too hgh when smulatng transent flow n a room. The smulaton of transent flow s mportant especally when one would lke to understand the thermal comfort and ndoor ar qualty for a few typcal days n a buldng, or obtan wnd and pressure nformaton around a buldng for outdoor comfort and natural ventlaton desgn. A sngle algebrac functon (a zero-equaton model) has been developed to express the turbulent vscosty as a functon of local mean velocty, V, and a length scale, l: ν t = 0.03874 V l (1) Fg. 1 shows the ar velocty and temperature profles at the center of a smulated offce wth dsplacement ventlaton. Although the zeroequaton model s smple, ts performance s as good as that of the two-layer model. Snce no transport equatons are solved for turbulence and the equaton can lead to a stable soluton, the computng tme wth the zero-equaton model s only a fracton of that wth the standard k- ε model. Table shows the computng tme on a Pentum II PC for an offce room wth dfferent space layouts and ventlaton systems (Fg. 1a). Although the grd s coarse, the computng tme requred s mnmal. Table : The grd number and computng tme used wth the zero-equaton model Case Infltraton Partton Dsplacement ventlaton Grd number 7 0 6 0 15 5 18 16 Computng tme [mn:sec] 6:46 6:11 4:41 The CFD program wth the zero-equaton model has further been coupled wth an energy analyss program. Ths couplng has the followng advantages: The CFD program can calculate heat transfer coeffcents and ar temperature near a wall for use n the energy smulaton program. The energy smulaton program can calculate wall surface temperature and coolng or heatng loads as boundary condtons for the CFD program. The coupled program can analyze the energy used n a buldng whle provdng detaled ndoor envronment condtons. Fg. a shows the heat extracton calculated by the combned program for a typcal wnter and summer day n a large offce wth dsplacement ventlaton. The coupled program can also determne the predcted percentage of dssatsfed people due to thermal comfort at three dfferent tmes of the day (as shown n Fg. b-d). Ths calculaton uses weather data and buldng property data as nputs. Therefore, there s no need to provde wall temperatures as boundary condtons for the CFD calculaton. Snce the CFD program provdes accurate heat transfer nformaton n buldng energy analyss, the results are more accurate. The coupled program exhbts a great potental n ndoor envronment desgn. 3. RANS MODEL APPLICATIONS Recently, RANS models have been appled to study a number of ndoor and outdoor envronment problems. The followng secton summarzes a few examples. 3.1 Buldng Shape Desgn Wnd s a frend to a buldng because t can naturally ventlate the buldng to provde a comfortable and healthy ndoor envronment as well as to save energy. The conventonal desgn approach often gnores opportuntes for nnovaton that can condton buldngs at lower costs or wth hgher ar qualty and acceptable thermal comfort level, usually by means of passve coolng or natural ventlaton. On the other hand, the wnd can be an enemy to the buldng because t can cause dscomfort to pedestrans f the wnd speed around the buldng s too hgh. If the ar temperature n the wnter s low, the chllng effect of the wnd could be so strong that pedestrans cannot walk comfortably and safely. Therefore, t s essental to reduce the wnd speed around buldngs. A CFD program can be used to calculate arflow dstrbuton around buldngs. Ths flow dstrbuton provdes valuable nformaton for the desgn of natural ventlaton and a comfortable outdoor envronment. Fg. 3a shows the prelmnary ste desgn (Scheme I) of an apartment buldng complex n Beng. The desgn uses 16 hgh-rse buldngs rangng from 33 to 90 m hgh. The buldng ste has a prevalng wnd from the north n the wnter. Wth ths desgn, the wnd speed at a heght of 1.5 m above the ground n secton 1-1 s around 8 9ms -1 (Grade 5) as shown n Fg. 4a. Ths s too hgh to be acceptable even for a short stay n the wnter. The reason s that the 18

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wnd can pass freely through the lnear arrangement of the buldngs. Furthermore, the CFD calculaton shows that at a heght of 30 m, the wnd speed among most of the buldngs s 910 ms -1, and at a heght of 70 m, the wnd speed s above 1 ms -1 (Grade 6). The hgh wnd speed leads to excessvely hgh nfltraton n the wnter and dffcultes n usng the wnd for natural ventlaton n the summer. Therefore, the buldng ste should be redesgned, and the heght of the buldngs should be reduced. Based on the arflow dstrbuton for Scheme I, Scheme II was developed, as shown n Fg. 3b. Scheme II used a lower buldng heght rangng from 0 to 60 m to reduce wnter nfltraton wthout compromsng the populaton densty. The mproved desgn protects the buldngs from the north wnd n the wnter by usng relatvely hgh buldngs n the north. Fg. 4b shows that the dscomfort problem s greatly reduced n Scheme II, but there are stll some problems. For example, n entrances A, B, and C, the wnd speed s very hgh because of the lnear arrangement. Staggerng the entrances can easly solve ths problem. Moreover, natural ventlaton n summer may not be effectve n Scheme II. As shown n Fg. 3b, more than half of the buldngs have long sdes facng east and west, such as Buldngs 1-8. Snce the prevalng wnd n the summer s from the south n ths ste, the buldngs wth the long sdes facng east and west may not be able to take advantage of natural ventlaton, such as cross ventlaton. In addton, the orentaton s not good for passve heatng desgn and t s dffcult to shade the buldngs from strong solar radaton n the summer. Therefore, Scheme III was fnally developed as shown n Fg. 3c. The low-rse buldngs are now tlted 45 o, thus havng the long sde facng southeast and north-west. In Scheme III, both the outdoor thermal comfort and natural ventlaton are consdered. Fg. 4c shows that the hgh-rse buldngs on the north sde can block the hgh wnd from the north n wnter. As a result, the wnd speed at the ste s small. Although, at entrances A and B, the wnd speeds are relatvely hgh (about 710 ms -1 ), the mpact on the pedestrans comfort s small, snce these entrances for cars. In the summer, the south wnd prevals on the ste. Fg. 4d shows that the wnd speed around most of the buldngs at 1.5 m above the ground s above 1.0 ms -1. Ths wnd speed s suffcently hgh for natural ventlaton. The tlted buldng arrangement helps to ntroduce more wnd nto the ste. Furthermore, the staggered arrangement prevents the front buldngs from blockng the wnds. Therefore, Scheme III provdes good outdoor thermal comfort and potental to use natural ventlaton. (a) Orgnal desgn (Scheme I) (b) Frst mproved desgn (Scheme II) (c) Fnal desgn (Scheme III) Fg. 3: Three desgns for the apartment buldng complex 0

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3. Evaluaton of Natural Ventlaton Performance A CFD program has also been used to evaluate the performance of natural ventlaton desgn n a buldng. The most mportant evaluaton crteron s the ar temperature n the buldng. By usng the concept of couplng a CFD program wth an energy smulaton program, the ar temperature can be determned. In ths study, a generc apartment buldng n Beng wth heavy concrete floor and celng slabs was nvestgated. Accordng to the clmate data analyss, nght coolng seems to be a good natural ventlaton strategy. The buldng envelope s opened to allow natural ventlaton durng the nght hours when outdoor ar temperature s lower than 3.3 VOC Emsson Studes The CFD technque can study not only the dstrbuton of flow, temperature, and chemcal speces n room ar, but also the heat and mass transfer n sold materals. Ths s especally useful for ndoor ar qualty studes. For example, numerous feld and laboratory studes have found that commonly used buldng materals, such as wood products, floor coverngs (carpet, vnyl), wall coverngs (wallpaper, fabrc), celng materals (acoustc tles, subfloors), and nsulaton materals (fberglass, rgd foam) emt a varety of volatle organc compounds (VOCs). Emssons from the buldng materals are mportant to ndoor ar qualty because of ther large surface area and permanent exposure to ndoor ar. 38 36 34 3 30 8 6 4 0 18 1 May 31 June 30 July 31 August 31 September 30 Fg. 5: Daly maxmum ar temperature n the lvng room wth nght coolng (dark gray) and outsde (lght gray) n Beng. the ndoor ar temperature; the buldng structure s then cooled down. Durng the daytme, when the outdoor temperature becomes hgher than the ndoor ar temperature, the buldng envelope s closed. The cooled structure then absorbs the nternal heat to mantan a comfortable ndoor envronment. A CFD program was used to calculate the ar exchange rate n the buldng wth nght coolng whle an energy smulaton program was used to determne the ar temperature. Fg. 5 shows the calculated ndoor ar temperature and the correspondng outdoor ar temperature n the warm season. The ar temperature n the lvng room s 3.9 K lower than the outsde ar temperature, although there are nternal heat gans. Consder a materal source that has one surface exposed to the ar. VOC emssons from ths source nclude the mass transfer n three dfferent regons: The sold materal The materal-ar nterface The bulk ar For a dry materal wth homogeneous dffusvty, the followng dffuson model has been used to descrbe the VOC mass transport wthn the materal: C t m = (D m C m ) (13)

C (ug/m 3 ) At the materal-ar nterface, a VOC phase change occurs from the materal sde to the ar sde. For low concentratons, the equlbrum condton at the materal-ar nterface may be descrbed by: C m = K ma C a (14) Then Eq. (1) s used to calculate the ar velocty dstrbuton and the VOC mass transfer from the materal-ar nterface to the ambent ar. Recently, dfferent specmens of partcleboard have been studed wth the above mentoned model for ther VOC emssons. Ths approach uses the followng parameters to descrbe emsson characterstcs: the ntal VOC concentratons n the materal (C 0 ), the sold-phase dffuson coeffcent (D m ), the materal-ar partton coeffcent (K ma ), and the age of the materal (AGE). These parameters were obtaned by fttng the predcted VOC concentratons wth the smallscale chamber data. 5000 4000 3000 000 1000 Data Smulaton Fg. 6 compares the predcted maor VOC concentratons and the data measured form a small test chamber. The results show that predetermnng the K ma and AGE and adustng the D m and C 0 can acheve a farly good agreement of VOC concentratons between the expermental data and model predcton. The nvestgaton has found that dfferent parrameters have dfferent mpacts on emssons. The emsson rate s proportonal to C 0. D m nfluences bothe short-term and long-term emssons. A hgher D m results n a hgher ntal emsson rate and a faster decay rate. On the other hand, K ma and AGE affect only the short-term emssons of the partcleboard, havng vrtually no mpact on long-term emssons. 4. LES STUDIES The above examples show that the RANS models are useful for ndoor and outdoor envronment desgn. However, these models have too many coeffcents to be tuned n order to obtan a correct soluton. Even for an experenced CFD user, t s dffcult to select a sutable turbulence model and ts coeffcents. On the other hand, LES has only one or no emprcal coeffcent; thus t sounds superor to the RANS models. Therefore, LES has been used for the study of ndoor and outdoor envronment. 0 0 0 40 60 80 100 Tme (h) (a) TVOC LES requres the separaton of small-eddes from large-eddes wth a flter. For smplcty, the followng secton uses a one-dmensonal notaton. The fltered velocty s C (ug/m 3 ) C (ug/m 3 ) 100 800 400 800 600 400 00 Data Smulaton 0 0 0 40 60 80 100 Tme (h) 0 (b) Hexanal Data Smulaton 0 0 40 60 80 100 Tme (h) (c) α.pnene Fg. 6: Comparson of measured and smulated VOC concentratons emtted from the partcle board ' ' u = G(x,x )u (x) dx (15) where G(x, x ) s a flter functon. The flter functon s large only when G (x, x ) s less than the flter wdth, a length scale over whch the averagng s performed. The flow eddes larger than the flter wdth are large-eddes, and those smaller than the wdth are small-eddes. Ths paper uses a box flter,.e. 1 ( x ) G(x ) =, (16) 0 ( x > ) Wth the fnte volume method, t seems natural to defne the flter wdth, 3 = ( x1 x x 3 ), as an average over a grd volume. 1 3

Wth the flter, t s possble to derve the governng conservaton equatons for momentum (Naver- Stokes equatons), mass contnuty, and energy. The fltered Naver-Stokes equatons for an ncompressble flow are: u + t x τ x 1 P u (u u ) = + υ ρ x x x + g β(t T ) 0 where the subgrd Reynolds stresses are (17) τ = u u u u (18) u u s unknown and needs to be modeled. In order to close the equatons, the subgrd Reynolds stresses can be modeled usng the Smagornsky model [15]. τ = C S S (19) 1 1 u u where S = (S S), S = ( + ) x x C = C s, C s = 0.1 0.5. However, the Smagornsky model coeffcent C s an emprcal coeffcent that depends on flow. Ideally, C should be determned as a functon of flow through a Dynamc Subgrd-scale Model (DSM) [16]. DSM calculates the model coeffcent by relatng the subgrd scale Reynolds stresses to two dfferent flter szes. Snce the Reynolds stresses vary wth tme and locaton, the resultng model coeffcent s therefore also a functon of tme and locaton. DSM uses an explct test flter, G, wth a flter wdth of ( = ) [16] to determne the turbulent stresses on the test flter ( G flter). T = u u uu (0) The frst term on the rght sde of Eq. (0) cannot be determned drectly, lke the one n Eq. (18). However, substtutng Eq. (0) and Eq. (18) wth a test flter can elmnate the terms T τ = L (1), where L = uu uu The resolved turbulent stresses, L, n Eq. (1) can be calculated explctly. Wth the defnton of the Smagornsky model, the DSM coeffcent C can be determned. However, the DSM requres averagng the coeffcent over a homogeneous flow drecton (statstcal homogenety) snce the coeffcent fluctuates sgnfcantly. The averagng procedure can dampen large fluctuatons of C often encountered n a flow predcton. Ths procedure gves good results for smple flows wth at least one homogeneous drecton, such as a turbulent channel flow. However, t cannot be used for a flow wthout a homogeneous drecton, such as room arflow. Another approach by Meneveau et al. [17] used a Lagrangan dynamc model. Ths model s sutable for nhomogeneous flows and the results look encouragng. The model needs an addtonal parameter, the Lagrangan averagng tme, whch must be prescrbed. Addtonal tests are requred to establsh how to calculate ths parameter [18]. Therefore, a DSM model s beng developed that calculates an ndoor arflow wthout a homogeneous flow drecton. 4.1 Fltered Dynamc Sub-Grd Scale Model (FDSM) Note that all of the terms n Eq. (1) are related to the test flter ( ). The model coeffcent C obtaned wth Eq. (1) should be vald for the test flter ( ). Snce the subgrd scale Reynolds stresses, τ, are defned wth the grd flter ( ), the model coeffcent C should be related to the grd flter ( ). Ths can be done by applyng a grd flter to Eq. (1) to yeld T τ = L () In order to obtan a new model coeffcent from Eq. (), the τ and the T n Eq. () are modeled by usng the Smagornsky model or the mxed model [19]. However, ths modelng leads to an error n satsfyng Eq. (): e = L C α + C τ β = L CM (3) T S S where α =, β = S S, and M = α β. 4

We have used the least-square approach to obtan the model coeffcent, C n Eq. (3), as suggested by Llly [0] and Ghosal et al. [1]. At any gven pont n a space, x, the e s a functon of the C. In order to obtan an optmal C, the e should be ntegrated over the entre flow doman wth a smooth functon, because the square of the resdual, e e, may have locally volent changes. The ntegrated square of the error functon, (C), s E (C) = G f (x, x' ) e(x' ) e(x' ) d x' (4) where G f (x, x' ) s a smooth functon. By substtutng Eq. (3) nto Eq.(4), Eq. (4) reads: E (C) = Gf (x, x' )(L CM) d x' (5) Snce the least square condton for Eq. (4) s E (C) = 0, the optmal model coeffcent C s C obtaned as: G f (x, x') LMd x' C = (6) G (x, x') M M d x' f The C s clearly 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 (Eq. (16)) may be the most convenent ( G f (x, x' ) = G(x, x' ) ). The flter can be ether a grd flter or a test flter LM C = M M (wth the grd flter ) (7) or M M L C = (wth the test flter ) (8) M Eqs. (7) and (8) are now defned as the fltered dynamc subgrd scale model (FDSM). The FDSM G has the grd flter n Eq. (7), and the FDSM T has the test flter n Eq. (8). The functon of the grd flter s to average the coeffcent and to smooth the large fluctuaton of the coeffcent. The flter technque wll lead to a stable numercal soluton. The FDSM can be consdered as a smple model compared wth those proposed by Ghosal et al. [1] and Meneveau et al. [17]. The model can be used for flow wthout a homogenous drecton. E The FDSM G or FDSM T can also be locally negatve. Accordng to Pomell et al. [], a negatve C ndcates a negatve eddy vscosty and mples an energy transfer from small scales to the resolved scales or backscatter. However, the negatve C can also lead to a numercal nstablty. In order to avod the nstablty, the present nvestgaton uses C = Max (0.0, Eq.(7) or (8)). We have appled the FDSM for mxed convecton flow n a room, as shown n Fg. 7a. Blay et al. [3] measured the ar velocty, temperature, and turbulent energy dstrbutons for ths case. The geometry of the test rg was H = 1.04 m, L = 1.04 m, and D = 0.7 m. Ths test rg s a scale-model of a room and has a homogeneous drecton (the depth drecton) so that the DSM can also be used. The nlet heght, h n, was 0.018 m, the supply ar velocty, U n, was 0.57 ms -1, and the supply ar temperature, T n, was 15 C. The outlet heght was 0.04 m. The test rg used a floor heatng system wth a floor temperature, T f, of 35 o C. All other wall temperatures were 15 o C. The correspondng β gh n (Tf Tn ) Archmedes number ( Ar = ) was U 0.0036, and the Reynolds number ( = U n h n Re ) ν was 678. The computatons used a non-slp velocty condton for all the walls. The meshes employed were 6 6 1 for the heght (x), wdth (y), and depth (z) drectons. Fgs. 7b and 7c show the measured mean ar velocty dstrbuton and the averaged ar velocty dstrbuton usng the FDSM G. The measured and computed arflow patterns are almost the same. The LES smulaton shows a small re-crculaton n the left-bottom corner, but not n the experment. It s not clear whether ths s due to nsuffcent fne measurng ponts or due to the numercal model used. Fg. 8 further compares the predcted mean ar velocty, temperature, and turbulent energy dstrbutons usng the DSM, FDSM G, and FDSM T wth the expermental data at two center sectons (at x = 0.50 m and y = 0.50 m). Fg. 8a shows that the three subgrd scale models gve very smlar ar velocty profles. The FDSM G performed slghtly better than the others. The predcted velocty profles agree reasonably well wth the expermental data. However, Fgs. 8b ndcates that the predcted ar temperature usng the three models s about 1.5 K hgher than the measured one, though the shape of the predcted temperature profles s the same as n 5

the measured one. The models may overpredct the heat transfer from the floor or underpredct the heat transfer to the other walls. Snce no detaled measurements on the heat transfer were avalable, t s dffcult to dentfy the actual cause of these dscrepances. Perhaps the subgrd scale Prandtl number was not correctly modeled for the buoyancy effect. Fg. 8c llustrates the computed turbulent energy (k 1/ ={(u +v +w )/} 1/ ) profles at secton x = 0.50 m and the comparson wth the correspondng expermental data. The performance of the FDSM G and DSM n predctng the turbulence energy dstrbuton was good, whle the performance of the FDSM T was poor. (a) room geometry (a) average velocty ' (b) average velocty vectors obtaned from the experment [3] (b) average temperature (c) average velocty vectors computed by the FDSM G Fg. 7: The predcted and measured mxed convecton flow n a room (c) average turbulent energy (k 1/ ) Fg. 8: Comparson of the predcted and measured 4. results LES on Applcatons the center sectons (X=0.50m) 6

We have used LES to further study complcated ndoor and outdoor envronment problems. For example, Fg. 1 shows that an LES program can successfully calculate the ar velocty and temperature n an offce wth dsplacement ventlaton. The LES smulaton provdes more nformaton than the RANS modelng, such as power spectrum of turbulence. The power spectrum of turbulence can be a very mportant comfort parameter. Our applcaton of LES for outdoor arflow smulaton can be found n another paper [4]. Unfortunately, the computng tme needed for LES s much hgher than that for RANS modelng. At present, LES can only be performed n powerful workstatons and super computers. Only smple LES can be done on a hgh end PC. 5. CONCLUDING REMARKS Ths paper summarzes some recent studes on ndoor and outdoor envronment problems conducted at the Massachusetts Insttute of Technology by usng CFD tools. Our effort focuses not only on the development of RANS and LES models for ndoor and outdoor envronment studes but also on ther applcatons for complcated and practcal problems. The CFD tools are powerful for solvng the problems, although they need skllful users, as well as large and fast computers. The two-layer turbulence model enables us to predct accurate heat transfer on a wall. The computng tme needed s slghtly hgher than that by the standard k-ε model but much lower than that by a low-reynolds number k-ε model. The zero-equaton turbulence model can sgnfcantly reduce computng costs. For a smple room, the computng tme needed s ust a few mnutes for a steady-state soluton on a PC. The couplng of a CFD program wth the zero-equaton model wth an energy smulaton program can be used more accurately and nformatvely for buldng energy analyss and ndoor envronment desgn. The CFD program s a powerful tool to predct arflow n and around buldngs to desgn a thermally comfortable ndoor or outdoor envronment. Archtects and engneers can work together to desgn buldngs that sheld wnter wnd and allow summer natural ventlaton. The software developed can further evaluate the performance of natural ventlaton n a buldng. The CFD tool can be extended to nclude VOC dffuson n buldng materals and mass transfer at sold-ar nterfaces. Ths tool can then be used to predct VOC emssons from the buldng materals and ndoor ar qualty n the room. A new dynamc subgrd-scale model has been developed to predct ndoor arflow wthout a homogenous flow drecton. The model uses two dfferent flters to obtan the model coeffcent as a functon of space and tme. The model can accurately predct flow n a room wth a heated floor and n an offce wth dsplacement ventlaton. Although the computng costs wth LES are hgh at present, the computed results are very nformatve. NOMENCLATURE Ar Archmedes number Ar y local Archmedes number, gβ Ty n / U C contamnant concentraton C coeffcent for subgrd scale model (C=Cs ) C 1ε, C ε, C 3ε constants used n the ε equaton C m VOC concentraton n the sold materal Cs Smagornsky model coeffcent C µ constant used for calculatng ν t D room depth D m dffuson coeffcent of the VOC n the sold materal d k dffuson of turbulent knetc energy E (C) ntegrated square of the error functon e error functon for C f lµ, f lε, f vv functons used n the one-equaton model G(x ) flter functon G test flter G grd flter G f (x,x ) smooth functon over x G k gravty producton of turbulent knetc energy, βg u t g component of the gravtaton vector H room heght h heght K ma dmensonless materal-ar partton coeffcent. k turbulent knetc energy, u u / L room wdth L L = uu uu l, l µ, l ε characterstc lengths P k shear producton of the turbulent knetc energy, u u U Pr t turbulent Prandtl number p grd fltered pressure Ra Raylegh number Re Reynolds number S Φ source term for Φ T mean temperature T f floor temperature turbulent stress on the test flter T 7

t tme U, U component and of the mean velocty U, V, W mean velocty component n the x, y and z drecton u, v fluctuatng velocty component n the x, y drecton u, u velocty component n x and x drecton u, u grd fltered velocty component n x and x drecton u test fltered veloctes x, x spatal coordnate n the and drecton x, y, z spatal coordnate y n normal dstance to the nearest wall y * dmensonless wall dstance, k / ν Greek symbols β thermal expanson coeffcent Γ Φ effectve dffuson coeffcent for Φ flter sze test flter sze grd flter sze ε turbulent energy dsspaton ν knematc vscocty ν t turbulent vscocty ρ ar densty σ k, σ ε Prandtl number of k and ε τ tme Φ = 1 for mass contnuty Φ = u ( = 1,, and 3) for three components of momentum (u,v,w) Φ = T for temperature Φ = C for concentratons Subscrpts, spatal coordnate ndces n nlet t turbulent quanttes ACKNOWLEDGEMENT The authors would lke to thank the contrbutons from ther colleagues at MIT (n alphabetcal order): Mr. G. Carrlho-da-Graça, Prof. L.R. Glcksman, Ms. Y. Jang, Prof. L.K. Norford, Prof. A.M. Scott, Dr. M. Su, Dr. W. Xu, Dr. X. Yang, Dr. X. Yuan, and Dr. W. Zhang. Ths work s supported by the U.S. Natonal Scence Foundaton under grants CMS-963864 and CMS-9877118, by ASHRAE through contracts RP-97 and RP-949, and by the V. Kahn- Rasmussen Foundaton, the Center for Indoor Ar Research, and the Archlfe Research Foundaton. y n REFERENCES 1. Q. Chen, Computatonal flud dynamcs for HVAC: successes and falures, ASHRAE Transactons, Vol. 103, No. 1, pp. 178-187 (1997).. S. Murakam, Overvew of turbulence models appled n CWE-1997, J. Wnd Engneerng and Industral Aerodynamcs, Vol. 74-76, pp. 1-4 (1998). 3. B.E. Launder and D.B. Spaldng, The numercal computaton of turbulent flows, Computer Method n Appled Mechancs and Energy, Vol. 3, pp. 69-89 (1974). 4. Q. Chen, Comparson of dfferent k-ε models for ndoor arflow computatons, Numercal Heat Transfer, Part B: Fundamentals, Vol. 8, pp. 353-369 (1995). 5. S. Murakam, Comparson of varous turbulence models appled to a bluff body, J. Wnd Engneerng and Industral Aerodynamcs, Vol. 46-47, pp. 1-36 (1993). 6. Q. Chen, Predcton of room ar moton by Reynolds-stress models, Buldng and Envronment, Vol. 31, No. 3, pp. 33-44 (1996). 7. J.W. Deardorff, A three-dmensonal numercal study of turbulent channel flow at large Reynolds numbers, J. Flud Mechancs, Vol. 41, p. 453 (1970). 8. L. Davdson and P.V. Nelsen, Large eddy smulatons of the flow n a three-dmensonal ventlated room, Proc. of Roomvent 96, Yokohama, Japan, Vol., pp. 161-168 (1996). 9. L. Davdson and P.V. Nelsen, A study of low- Reynolds number effects n back-facng step flow usng large eddy smulaton, Proc. of Roomvent 98, Stockholm, Sweden, Vol. 1, pp. 15-13 (1998). 10. S. Emmerch and K. McGrattan Applcaton of a large eddy smulaton model to study room arflow, ASHRAE Transactons, Vol. 104, No. 1 (1998). 11. W. Zhang and Q. Chen, Large eddy smulaton of ndoor arflow wth a fltered dynamc subgrd scale model, Accepted by Int. J. Heat Mass Transfer (000). 1. N. Kasag and M. Nshmura, Drect numercal smulaton of combned forced and natural convecton n a vertcal plane channel, Int. J. Heat and Flud Flow, Vol. 18, pp. 88-99 (1997). 13. W. Xu, New turbulence models for ndoor arflow smulaton, Ph.D. Thess, Department of Archtecture, Massachusetts Insttute of Technology, Cambrdge, MA (1998). 14. X. Yuan, Q. Chen, L.R. Glcksman, Y. Hu and X. Yang, Measurements and computatons of room arflow wth dsplacement ventlaton, ASHRAE Transactons, Vol. 105, No. 1, pp. 340-35 (1999). 8

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