NUMERICAL SIMULATION OF HOT BUOYANT SUPPLY AIR JET IN A ROOM WITH DIFFERENT OUTLETS

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1 IJRRAS 5 () Nvember 00 NUMERICAL SIMULAION OF HO BUOYAN SUPPLY AIR JE IN A ROOM IH DIFFEREN OULES Shbha Laa Sinha Mechanical Engineering Deparmen, Nainal Insiue f echnlgy, Raipur, C.G., India. shbhasinha@rediffmail.cm ABSRAC In his invesigain cnrl-vlume mehd has been used fr simulaing he indr air flw using Lam-Bremhrs lw-reynlds-number -ε urbulence mdel. he flw is cnsidered be seady, w-dimensinal and he Bussinesq s apprximain has been used fr he buyancy erm. he resuling nn-linear sysem f mmenum, energy, urbulence ineic energy and is dissipain equains have been slved n a nn-unifrm grid by SIMPLE algrihm due Paanar and SIMPLEC algrihm due Drmaal e al.. he Pwer law scheme has been used discreise he cnvecive/diffusin erms. he disribuins f velciy, emperaure, urbulen ineic energy, and dissipain f ineic energy in he rm have been presened fr Reynlds number f and fr Grashf number up 0 7 ( = 0 0 C ) fr differen lcains f inle and ule. he inle air is assumed be a higher emperaure han he walls. I has been bserved ha flw paern changes cnsiderably as Gr increases. Keywrds : urbulen flw, Lw Reynlds number - ε mdel, Rm airflws, Buyan flw, Canda effec, Occupied zne, Cmfr.. INRODUCION I has been bserved ha frm cmpuainal perspecive he airflws in rms are very cmplex. In realiy, a reasnable venilain raes, he flw is fully urbulen in supply ducs, HVAC inles/ules and dwnsream f he edges f he bsacles. Elsewhere he flw is mre liely be wealy urbulen and ime unseady wih a wide range f large small scale flw srucures where he mlecular ranspr is impran. In he cnex f heaing (r cling in warm climaes), hese flws are buyan, and in sme cases, buyancy drives he mean flw min. he presence f walls creaes s called near wall effecs, where he urbulen ranspr is significanly influenced by a slid surface. Away frm he supply air ule, he velciies and he urbulen ineic energy decrease, leading re-laminarizain f he flw in sme cases. In pracical applicains, he bsrucins wihin he rm creae gemerical cmplexiy. In realiy, ms airflws are inherenly hree-dimensinal, buyan and unseady. Due hese characerisics he airflws in rm presen a grea challenge fr he available numerical cdes and mdels. Alhugh India has he rpical weaher, even han sme par f he cunry near munains are very cld. In hse par, he cnsruced huses require venilain wih heaing fr he human cmfr. In his paper, he effec f air-cndiining wih heaing a differen lcains f ule has been discussed fr he urbulen flw.. REVIE he need f precise deerminain f airflw paern and emperaure disribuin in a rm was realized a firs by air cndiining engineers s as prvide cmfr cndiin f emperaure, relaive humidiy and air velciy hrughu he ccupied zne. Accrdingly he research n hermal cmfr and rm air mvemen sared a ASHVE/ U. S., Bureau f Mines labrary in Pisburgh, which was funded in 99. CFD was iniiaed arund 930. he cncep f urbulence was inrduced in calculain f rm airflw afer 970. Yshiawa and Yamaguchi[], presened calculain f w-dimensinal high Reynlds number flws in rm using ne equain mdel. In he same year Nielsen[] als develped a calculain prcedure based n sream funcin-vriciy apprach fr predicing w-dimensinal flw paern in a venilaed rm using w equain (- ) mdel. hereafer Nmura e al.[3], Saam e al. [4] calculaed hree-dimensinal frced and naural cnvecin flws using he - urbulence mdel wih he MAC mehd and cmpared he resuls wih mdel experimens. Ms f he rm-airflw prgrams currenly in use are based n he numerical echnique develped a Imperial Cllege by Paanar and Spalding[5]. his invlves cnrl vlume mehd fr he cnservaive frm f equains discreised ver saggered cnrl vlumes using primiive variables. Nielsen e al. [6] used a finie-vlume mehd 96

2 IJRRAS 5 () Nvember 00 fr he sluin f w-dimensinal equains fr he cnservain f mass, mmenum and energy wih he - urbulence mdel including he effec f buyancy. his sluin prcedure was hen exended by Gsman e al. [7] fr slving hree-dimensinal ishermal flw in venilaed rms. Sl venilaed enclsures fr varius psiins f sls have been invesigaed by immn e al. [8]. Ka e al. [9] exended heir earlier wr sudy he lcally balanced supply and exhaus flw wih a flw bsacle alng wih he experimenal verificain f he numerically prediced resuls. Chen e al. [0] invesigaed he indr air qualiy and hermal cmfr in an ffice under six inds f air disribuins fr summer cling cndiins. Baer e al. [] and illiam e al. [] have carried u CFD mdeling fr hree-dimensinal urbulen flw and cmpared i wih bench mar sluins. Muraami e al. [3] and Ka e al. [4] sudied he rm airflw disribuin wih and wihu buyancy using -, ASM, DSM and EVM mdels. Chen and Jiang[5] reviewed he rle f - urbulence mdel fr he predicin f rm air mvemen. 3. ASSUMPIONS USED IN MODELING Numerical mdeling fr he airflw is based n he fllwing assumpins:. Presence f hea and plluin surces have n been cnsidered.. Physical prperies such as densiy, cnduciviy ec. are assumed be cnsan. 3. Only w-dimensinal flw has been cnsidered as he inle and ule are cnsidered be exended hrughu he widh f he rm. 4. he flw is cnsidered be seady, urbulen and incmpressible under Bussinesq s apprximain. 4. PROBLEM FORMULAION he airflw and emperaure disribuin during air-cndiining wih heaing in a mdel rm have been invesigaed. he inle and ule are n ppsie walls and exend alng he full widh f he rm maing he flw essenially w-dimensinal; bsrucins wihin he rm are n cnsidered fr he sae f simpliciy. Hea surces inside he rm are n cnsidered. he cnfigurain f w-dimensinal mdel rm f 6m lengh and 3m heigh is shwn in Figs and 5 where h air a emperaure eners wih unifrm velciy U 0 while he wall emperaure is ep a w. he inle velciy U 0 and inle pening are aen as characerisic velciy and lengh respecively. he difference beween wall emperaure w and inle emperaure is used as a reference fr nn-dimensinalizain f emperaure. he fllwing dimensinless variables are inrduced nndimensinalize he Reynlds averaged frm f Navier Ses equains: u u U U, v v U, x x, y y, p p U,,,, Pr, 3 U U, w w g ( Gr 3 w), U 0 R e where Pr, Re and Gr are he Prandl number, Reynlds number and Grashf number respecively. Pr is aen as 0.7 hrughu he cmpuain. he resuling mean cnservain equains in nn-dimensinal frm can be expressed in he fllwing general frm (he superscrip and verscre have been drpped fr breviy): ( ) ( x u) x ( y v) S y 97

3 IJRRAS 5 () Nvember 00 able gives he deails f variables ф, Γυ and surce erm (Sф) fr varius cnservain equains. able: Nains fr Gverning Equains in Caresian C-rdinaes fr urbulen Flw Equain S Cninuiy 0 0 u-mmenum u v-mmenum urbulence Energy Dissipain Energy Rae Energy v p u v ( ) ( ) Re Re x x x y x p u v Gr ( ) ( ) Re Re y x y y y Re G G b Re Re Re ( fcg C f C3Gb Re Re Pr Re Pr 0 ) C Re f, G b Gr, G 3 Re y u Re x v y u v y x 5. NEAR ALL REAMEN IN RANSPOR EQUAION BASED MODELS he - urbulence mdel suggesed by Launder and Spalding [6] is n applicable in he viciniy f he slid walls where Reynlds number is small. In he lw-re versin f - mdel, he damping f he urbulence near a slid surface due mlecular viscsiy is simulaed hrugh he use f damping funcins muliplying varius erms f he ranspr equains. hese damping funcins allw a smh change f he flw variables frm he small laminar sub-layer values very near he wall he fully urbulen values away frm he wall. he damping funcins (f, f, f ) and mdel cnsans (C, C, C 3, C ) fr a lw Re - urbulence mdel suggesed by Lam and Bramhrs [7] are as fllws: f [ exp( 0.065Re )] 05 ( ), f Re f 3 Re f exp( Re ),Re,Re Re y p U,Re C , C.44, C.9, C.44,.0,.3, Pr 0.9 where Re and Re are he Reynlds number based n urbulen quaniies and disances frm he wall (y p ) respecively. In rder predic near wall characerisics Lam-Bremhrs mdel has been used hrughu he cmpuainal wr. 6. HE GEOMERY AND BOUNDARY CONDIIONS A recangular rm 6m lng and 3m high has been cnsidered. he air mvemen in he rm has been analyzed fr differen values f Re and Gr. he rm layu has been shwn in Figure and 5. he bundary cndiins are as fllws. 98

4 IJRRAS 5 () Nvember 00 A he lef and righ walls, ceiling and flr A he inle u 0, v 0, 0, 0, Re y p u, v 0,, 0.005, A he ule Neumann cndiins have been se fr he flw variables a ule. he ule velciy prfile is ieraively adjused saisfy verall mass cnservain equain and, where n is he direcin nrmal he uflw bundary. 7. NUMERICAL SOLUION PROCEDURE 0 n he gverning equains have been slved by using a saggered grid sysem fr he velciy cmpnens. hese equains are discreised using a cnrl vlume mehd. A Pwer law scheme is used fr he discreizain f he cnvecive and diffusin erms in he equains. he numerical scheme used herein is based n SIMPLE algrihm due Paanar[5] and SIMPLEC due Drmaal e al.[8]. Saring wih an iniial guess fr velciy and pressure disribuin, he u and v mmenum equains are slved fr all he cnrl vlumes. he velciy disribuin may n saisfy he mass cnservain equain fr each cnrl vlume since he guessed values f pressure and velciy may n be crrec. he pressure and velciies are herefre ieraively crreced s as saisfy he mass cnservain equain in each cnrl vlume. cmplee an ierain, ε and equains are slved successively. he DMA is used bain sluins f discreised linear algebraic equains. Ierain and under-relaxain are used reslve nn-lineariy. Relaxain facrs are 0.5, 0.5, 0.8, 0.4, 0.4 and 0.5 fr u, v, p,, ε and respecively. he urbulen viscsiy is under -relaxed by a facr f 0.5. Cnverged sluin is deemed have been achieved and ierains are erminaed when all he abslue residuals (nrmalized) are less han 0 5. he sluins were bained fr varius grids and fund be grid independen. he numerical sluins were cmpared wih benchmar experimenal resuls repred by Nielsen [9]. he heigh (H), lengh (L) and widh () f he es rm are m, 6m and m respecively. he inle and ule dimensins are 0.m and 0.3m respecively and exend hrughu he widh f he rm. Fig. shws a cmparisn f he hriznal velciy (U) and urbulen inensiy (I = ^0.5) a w verical crss-secins. hese experimenal resuls are a he cenral plane where he w-dimensinal numerical predicins can be cmpared wih he measured daa f hree-dimensinal case. he agreemen is bserved be very gd. A grid f in x and y direcins respecively has been used. he grid spacing was unifrmly expanded away frm he wall accrding a pwer law frmulain wih a pwer f Fine grids are needed near he walls capure he ransiin f flw frm urbulen laminar -lie near he wall. he al number f grids in x and y direcins were chsen s as ensure ha y + was f he rder f 0.5 fr he firs grid pin adjacen he wall s ha very seep gradiens f and near he wall can be reslved. his crierin is a requiremen fr he lw Re number mdel used in he presen wr..5 99

5 IJRRAS 5 () Nvember 00 Figure : Velciy Prfile (U ) and urbulen Inensiy(I ) a w differen secins 8. RESULS & DISCUSSIONS In his paper, he effecs f air-cndiining and heaing a differen lcains f inle je and ule wih differen values f Gr have been discussed. able & 3 shw he supply airflw rae, air change rae, emperaure rise crrespnding Re / Gr in he air-cndiined rm. able : Supply airflw rae (SR) and air change rae (ACH) OpeningSize(m) Re V el.(m/s) SR(m 3 /s) AC H (/hr) able 3: emperaure Rise Crrespnding Gr OpeningSize(m) Gr ( C ) Case : Inle near he flr and ule adjacen he ceiling n ppsie walls (Re=7000) In his case, inle f widh 0.m is prvided n he lef wall a 0.5m abve he flr level and ule f widh 0.5m is prvided.5m abve he flr as shwn in Fig.. he sreamline pls are shwn in Figs. 3 (a-c) fr Re=7000 and hree values f Gr, namely 0 7, and respecively. A Gr = 0 7, he main sream f warm fluid eners hrugh he inle, aaches wih he flr a x 0.9m due Canda effec, mves alng he flr, rises up near he righ wall and hen mves alng i befre leaving. One small recirculaing cell is bserved jus belw he inle a he bm-lef crner due Canda effec and a large recirculaing cell has been bserved abve he main sream. As Gr increases, he pin f aachmen shifs wards he lef wall. he inensiy f upper recirculaing zne increases wih he increase f Gr. he exen f recirculain zne n he lef-bm crner reduces wih he increase f Gr. As Gr increases (Fig. 3b), he main sream aaches wih he flr a x 0.8m, mves alng he flr and rises up suddenly due he buyancy, aaches wih he ceiling a x.7m and mves alng he ceiling wards exi. his gives rise ne mre recirculain cell in he Figure : Oule and inle lcains f he rm (Case ) 00

6 IJRRAS 5 () Nvember 00 righ par f he rm and he upper recirculain cell ges squeezed wards he lef side f he main sream. he inensiy and exen f he lef side recirculain cell decrease and hse f righ side recirculain cell increases as Gr increases. A Gr = (Fig. 3c), buyancy frce becmes s large ha he main sream des n aach wih he flr, insead i aaches wih he lef wall, rises alng i and mves alng he ceiling wards he exi. he lef recirculain cell cmpleely vanishes. he inensiy and exen f recirculain cell belw he main sream increase. he isherms fr his case are shwn in Figs. 3 (d-f ). he emperaure variain is significan alng he primary flw. he emperaure prfile near he flr is similar ha f wall je. emperaure is unifrm in he upper recirculary regin a Gr = 0 7. As Gr increases.5 0 7, he emperaure variain is lie he wall je near he flr and her isherms fllw he main sream which aaches wih he ceiling. A Gr = 5 0 7, he emperaure variain is very seep alng he lef wall and he main sream, a nd is bserved be unifrm in ms f he rm. he variain f he Nussel number, alng he walls, flr and ceiling is shwn in Figs. 4 (a-b) fr Gr = 0 7. he Nussel number has been fund be maximum near he lwer lip f he inle, ha is, a he beginning f recirculain cell due Canda effec n he lef wall. In his zne, hea ransfer rae is large due he presence f he shear layer and he enrainmen. On he righ wall, he Nussel number is larger in cmparisn ha a he lef wall since he heaed main sream mves alng i fr Gr = 0 7. he highes value f he Nussel number has been bserved a he pin f aachmen n he flr a x 0.8m because f large emperaure gradien near he sagnain pin. As he main sream mves alng he flr, he Nussel number reduces in he wall je due increasing hicness f hermal bundary layer. he flw is frm he righ he lef alng he ceiling. here will be a hermal bundary layer n he ceiling. he Nussel number n he ceiling decreases frm righ lef as he hicness f bundary layer increases. he Nussel number increases n bh he walls, ceiling and flr as Gr increases. (a) SC (Gr=0 7 ) (d) C (Gr=0 7 ) (b) SC (Gr= ) (e) C (Gr= ) 0

7 IJRRAS 5 () Nvember 00 (c) SC (Gr=5 0 7 ) (f ) C (Gr=5 0 7 ) Figure 3: Cnurs f sreamlines Re=7000 and ACH=.4/hr (Case ). (a) NUV (Gr=0 7 ) (b) NUH (Gr=0 7 ) Figure 4: Variain f Nussel number alng he walls, flr and ceiling fr Re=7000 and ACH=.4/hr(Case ). 8. Case : Inle and ule bh near he flr n ppsie walls (Re=7000) In his case, he inle and he ule bh f widh 0.m are prvided n he lef and righ walls a heigh f 0.5m abve he flr level as shwn in Fig. 5. Figure 5: Oule and inle lcains f he rm (Case ) 0

8 IJRRAS 5 () Nvember 00 he sreamline pls are shwn in Figs. 6 (a-c) fr Re=7000 a hree values f Gr, namely, 0 6, 0 7 and he main sream eners hrugh he inle, aaches wih he flr a x m due Canda effec, mves alng he flr and slighly rises up befre leaving. One small recirculaing cell jus belw he inle a he bm-lef crner and ne large recirculaing cell abve he main sream have been bserved. he magniude f upper recirculaing zne increases wih he increase f Gr. he exen f small recirculaing cell reduces wih he increase f Gr. A Gr = 0 7 (Fig. 6 b), he sreamline labelled.0 aaches wih he ceiling insead f he righ wall and a par f he main sream rises wards he ceiling and hen drps dwn alng he warm righ wall befre leaving. his is due he srng effec f buyancy. A Gr = (Fig. 6 c), he main sream direcly rises up alng he lef wall afer enering he rm, mves alng he ceiling and he righ wall subsequenly befre leaving. he Canda effec disappears due he prminen effec f buyancy. Only ne recirculain cell has been bserved belw he main sream. he isherms fr his case are shwn in Figs. 6 (d-f ). he isherms reveal prfiles similar hse fr free je near he inle wih a small hermal penial cre f unifrm emperaure, wall je afer aachmen and unifrm emperaure disribuin in he circulain regin. he emperaure drps a faser rae in sream-wise direcin a higher values f Gr. he emperaure disribuin becmes seeper near he lef wall and unifrm in ms f he rm a higher values f Gr. he variain f he Nussel number alng he walls, flr and ceiling is shwn in Figs. 7 (a-f ). (a) SC (Gr=0 6 ) (d) C (Gr=0 6 ) (b) SC (Gr=0 7 ) (e) C (Gr=0 7 ) 03

9 IJRRAS 5 () Nvember 00 (c) SC (Gr= ) (f ) C (Gr= ) Figure 6: Cnurs f sreamlines and emperaures fr Re=7000 and ACH=.4/hr (Case). he Nussel number has been fund be maximum ( 0.0) near he lwer lip f he inle. I has he high values in recirculain regin near he lef wall. In his zne, hea ransfer rae is large due he shear layer and he enrainmen. he Nussel number is bserved be larger n he righ wall han ha n he lef wall fr Gr < A Gr =.5 0 7, he Nussel number (a) NUV (Gr=0 6 ) (d) NUH (Gr=0 6 ) (b) NUV (Gr=0 7 ) (e) NUH (Gr=0 7 ) 04

10 IJRRAS 5 () Nvember 00 (c) NUV (Gr= ) (f ) NUH (Gr= ) Figure 7: Variain f Nussel number alng he walls, flr and ceiling fr Re=7000 and ACH=.4/hr (Case ). increases drasically n he lef wall due he sudden change in he sreamline paern. he highes value f he Nussel number has been bserved a he pin f aachmen n he flr a x m because f large emperaure gradien near he sagnain pin. As he main sream mves alng he flr, he Nussel number reduces slighly in he wall je due increasing hicness f bundary layer. he flw is frm he righ he lef alng he ceiling. here will be a hermal bundary layer n he ceiling. he Nussel number n he ceiling decreases frm righ lef as he hicness f bundary layer increases. he Nussel number increases n bh he walls, ceiling and flr as Gr increases. he Nussel number n he ceiling fr Gr = 0 7, increases up x 4.5m due he high enrainmen and hen i reduces near he righ wall. he Nussel number n he flr fr Gr =.5 0 7, is smaller han ha fr lwer values f Gr and remains alms cnsan hrughu he flr. he Nussel number n he ceiling decreases frm lef righ as he main sream mves alng i a Gr = he emperaure difference and velciy bh are large n lef par f he ceiling, which gives rise larger value f he Nussel number. 9. CONCLUSIONS In bh f he cases, recirculain znes have been bserved n eiher side f he main sream. In Case, where he inle is near he flr and ule is adjacen he ceiling n he ppsie wall, he fluid direcly rises afer enry hrugh he inle a Gr/Re 0.5. In Case where bh, he inle and he ule are 0.5m abve he flr respecively, fluid direcly rises afer enering in he rm a Gr/Re 0.. he emperaure variain is fund be significan alng he primary flw. he primary flw exhibis a hermal penial cre. emperaure is fund be alms unifrm in he recirculain znes. Sharp emperaure gradiens have been bserved near he walls. he isherm essenially fllw he pah f he main sream. he lengh f hermal penial cre reduces as Gr increases. he maximum value f Nussel number ccurs a he pin f aachmen where he sagnain f flw ccurs alng he walls, ceiling and flr depending upn he pah f he main sream, Canda effec and effec f buyancy. 05

11 IJRRAS 5 () Nvember NOAIONS G Accelerain due graviy G, Gb Generain due KE and buyancy respecively urbulen ineic energy Pressure urbulen Prandl number K E P Pr SC,C u Velciy in x- direcin uτ Fricin velciy(τw/ρ) Sreamline and emperaure Cnur emperaure v Verical velciy x, y Linear dimensins n abscissa and rdinae yp Minimum disance beween he wall and adjacen grid y + Nn-dimensinalized y disance (yuτ/ ν) Gree Symbls α hermal diffusiviy Γυ Effecive diffusiviy β Cefficien f hermal expansin Difference beween inle and wall emperaure µ Dynamic Viscsiy µ urbulen viscsiy ρ ν τw σ, σ υ Mass densiy Kinemaic viscsiy Shear sress a he wall KE dissipain rae Empirical cnsans f urbulence fr urbulen energy and energy dissipain rae Dependen variable. REFERENCES []. Yashiava, A. and Yamaguchi, K., Numerical Analysis f Indr Air Flws, Japanese Sciey f Heaing-Cling Air Cndiining and Saniary Engineering (J.S.H.A.S.E.) in Japanese, 974, 48. []. Nielsen, P. V., Flws in Air Cndiined Rm, Ph D hesis, echnical Universiy f Denmar, 974. [3]. Nmura,., Masu, Y., Kaizua, M., Saam, Y. and End, K., Numerical Sudy f Rm Air Disribuin-Par 3, Archiecural Insiuin f Japan (in Japanese), 975, 38. [4]. Saam, Y., Masu, Y., Nmura,. and Kamaa, M., Numerical Predicin f hree-dimensinal hermal Cnvecin by means f -Equain urbulence Mdel, Prceedings f Annual Meeing f Archiecural Insiuin f Japan (in Japanese), 978. [5]. Paanar, S. V., Numerical Hea ransfer and Fluid Flw, McGraw Hill, ashingn, 980. [6]. Nielsen, P.V., Resiv, A. and hielaw, J.H., Buyancy Affeced Flws in Venilaed Rms, Numerical Hea ransfer, 979,, 5-7. [7]. Gsman, A.D., Nielsen, P.V., Resi, A. and hielaw, J.H., he Flw Prperies f Rms wih Small Venilain Openings, Jurnal f Fluid Engineering, Sep.980, 0, [8]. immns, M.B. and Albrigh, L.D., Experimenal and Numerical Sudy f Air Mvemen in Sl Venilaed Enclsures, ASHRAE rans., Par, 980, -40. [9]. Ka, S., Muraami, S. and Nagan, S., Numerical Sudy f Diffusin in a Rm wih a Lcally Balanced Supply Exhaus Air Flw Rae Sysem, ASHRAE rans., Par, 99, 98, [0]. Chen, Q., Mser, A. and Suer, P., A Numerical Sudy f Indr Air Qualiy and hermal Cmfr under Six Kinds f Air Diffusin, ASHRAE rans., Par, 99, 98, []. Baer, A.J., illiams, P.. and Kels, R. M., Numerical Calculain f Rm Air Min-Par : Mah, Physics and CFD Mdeling, ASHRAE rans., Par, 994, 00, []. illiams, P.., Baer, A.J. and Kels, R. M., Numerical Calculain f Rm Air Min-Par 3: hree-dimensinal, CFD Simulain f a Full Scale Rm Air Experimen, ASHRAE rans., Par, 994, 00, [3]. Muraami, S., Ka, S. and Oa, R., Cmparisn f Numerical Predicins f Hriznal Nn-ishermal Je in a Rm wih hree urbulence Mdels- -, EVM, ASM and DSM, ASHRAE rans., Par, 994, 00, [4]. Ka, S., Muraami, S. and Knd, Y., Numerical Simulain f w-dimensinal Rm Airflw wih and wihu Buyancy by Means f ASM, ASHRAE rans., Par, 994, 00, [5]. Chen, Q and Jiang, Z., Significan Quesins in Predicing Rm Air Min, ASHRAE rans., Par, 99,, [6]. Launder, B.E. and Spalding, D.B., Mahemaical Mdels f urbulence, Academic Press, 97. [7]. Lam, C.K.G. and Bremhrs, K., A Mdified Frm f he - Mdel fr Predicing all urbulence, Jurnal f Fluid Engineering, 98, 03, [8]. Van Drmal, J.P. and Raihby, G.D., Enhancemen f he SIMPLE Mehd fr Predicing Incmpressible Fluid Flw, Numerical Hea ransfer, 984, 7, [9]. Nielsen, P.V., Specificain f a w-dimensinal es Case, Inernainal Energy Agency, Energy Cnservain in Buildings and Cmmuniy Sysems, Annexure 0: Air Flw Paern ihin Buildings, -5 (Nvember 990), ISSN R