NUMERICAL DETERMINATION AND TREATMENT OF CONVECTIVE HEAT TRANSFER COEFFICIENT IN THE COUPLED BUILDING ENERGY AND CFD SIMULATION

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1 Zai, Z. and Cen, Q Numerical deerminaion and reamen of convecive ea ransfer coefficien in e coupled building energy and CF simulaion, Building and Environmen, 6(8), NUMERICAL EERMINAION AN REAMEN OF CONVECIVE HEA RANSFER COEFFICIEN IN HE COUPLE BUILING ENERGY AN CF SIMULAION Ziiang Zai * eparmen of Civil, Environmenal and Arciecural Engineering, Universiy of Colorado, UCB 48, ECO 44, Boulder, CO , USA Qingyan (Yan) Cen Ray W. Herrick Laboraories, Scool of Mecanical Engineering, Purdue Universiy, 585 Purdue Mall, Wes Lafayee, IN , USA ABSRAC e inegraion of building Energy Simulaion (ES) and Compuaional Fluid ynamics (CF) programs eliminaes many assumpions employed in e separae applicaions, resuling in more accurae predicions of building performance. is paper discusses e meods used o deermine convecive ea ransfer on inerior s of building envelope, wic is e key linkage beween ES wi CF programs. e sudy found a e size of e firs grid near a wall in CF is crucial for e correc predicion of e convecive ea. A finer grid resoluion in CF does no always lead o a more accurae soluion wen using zero-euaion urbulence models. roug numerical experimens, e paper suggess a universal firs grid size a 0.005m for naural convecion room airflows and 0.m for forced convecion indoor airflows. e invesigaion also found a negaive convecive ea ransfer coefficiens may cause divergence and insabiliy of e coupled simulaion. KEYWORS: Convecive Hea ransfer, Energy Simulaion, CF, Coupling INROUCION A building energy simulaion (ES) program predics building ermal performance, wile a compuaional fluid dynamics (CF) program calculaes deailed airflow caracers. Bo of em are imporan ools for building performance evaluaion and ave been widely used in building and sysem design pracices. Many lieraures on is opic are available, suc as ose by Clarke [], Cen [], Marin [], Cen and Srebic [4] ec. e coupling of ES and CF can ake full advanages of e individual programs and produce more accurae and complee resuls, because ey can provide complemenary boundary condiions o eac oer. For example, ES can provide inerior emperaures of building envelopes and eaing/cooling load o CF as boundary condiions wile CF can deermine accurae convecive ea fluxes for ES. e benefis of e inegraion ave been discussed in many previous sudies, suc as, by Clarke [5], Nielsen and ryggvason [6], Srebric e al. [7], Beausoleil-Morrison e al. [8], and Zai e al. [9]. In a coupled simulaion, ES calculaes e ea conducion roug building envelopes and CF deermines air movemen in an indoor space. e convecive ea ransfer on inerior s of building envelope is e mos imporan linkage o couple ese wo programs [9]. In e coupling, CF provides ES convecive ea ransfer on eac enclosure. e convecive ea ransfer calculaed by CF is igly sensiive o e numerical meods and urbulence models employed in CF. is sudy analyzes e effec of e size of e firs grid o a wall used in CF on e ea ransfer and examines ow urbulence models deermine e convecive ea ransfer. In addiion, wi radiional definiion of convecive ea ransfer coefficien, wic is based on e emperaure difference of an inerior and room air, e coefficien value can be negaive. e impac of negaive coefficien on e coupled simulaion is anoer subjec of is sudy. FACORS O NUMERICAL SOLUION OF CONVECIVE HEA RANSFER CF discreizes e compuaional domain ino many grid cells and solves e governing conservaion euaions of flow on ese grid cells. As sown in Figure (a), CF calculaes convecive ea ransfer from a rigid roug: ( - ) ρ( + ) Q A () C () p Pr were is convecive ea ransfer coefficien, A is area, is emperaure, is air emperaure a e firs grid node a is a a normal disance of o e, C p is e specific ea of air, Pr * Corresponding auor, jon.zai@colorado.edu, fax:

2 is Prandl number, ρ is air densiy, is urbulence viscosiy deermined by urbulence models a e firs grid node, and is e molecular viscosiy of air. According o Euaions () and (), e convecive ea ransfer is deermined by e convecive ea ransfer coefficien and emperaure difference beween e and air a e firs grid node, and e convecive ea ransfer coefficien is deermined by effecive viscosiy of air (urbulence viscosiy plus molecular viscosiy) a e firs grid node. In order o obain accurae convecive ea ransfer, i is imporan o find is relaionsip wi e and urbulence model. Since e size of e firs grids in CF can be adjused according o e resoluion reuiremen, e convecive ea calculaed in is manner could be grid-dependen. Anoer meod is o use a prescribed disance,, o a wall and calculae convecive ea ransfer based on e air emperaure and effecive viscosiy ere, as illusraed in Figure (b). Since e is a prescribed value, is meod would eliminae e grid dependence problem. However, e convecive ea ransfer calculaed wi e second meod could be differen from a calculaed based on e informaion a e firs grid node. For example, if assuming laminar flow and, e same ea ransfer would reuire - ( - ). is implies a linear air emperaure profile in e region, wic is rue only a e very close viciniy of e for laminar flow. Suc a condiion is difficul o mee for mos indoor airflows. erefore, e calculaion of convecive ea ransfer sould use e firs meod. e uesion now is ow o avoid e grid dependence problem or wa e size of firs grids sould be for e correc predicion of convecive ea ransfer. CF eory indicaes a finer grids provide more accurae resuls [0]. is may no be rue wen using simple urbulence models. is paper discusses e grid dependence problem in e following secions by using laminar and urbulen flows over a fla plae as examples. CONVECIVE HEA RANSFER IN LAMINAR FLOWS Firs is invesigaion considers a laminar flow of forced convecion along a orizonal plae and a of naural convecion along a verical plae, as illusraed in Figure. e convecive ea ransfer compued by CF is compared wi e analyical and empirical soluions o idenify e impac of e size of firs grid on e ea ransfer. e convecive ea ransfer roug e ermal boundary layer of e plae is: k ( ) () y y 0 were k is e fluid conduciviy, is e plae emperaure, is e emperaure of e free sream ouside of e ermal boundary layer. Euaion () sows a e ea conducion is e same as e convecive ea ransfer, because ere is no fluid moion in e direcion of ea ransfer. () Forced Convecion e exac soluion of e laminar plae flow of forced convecion is [] U U (4) were is e ickness of ermal boundary layer and k ρ C p /Pr. k ρc p k (5) y Pr y e analyical soluion of e boundary layer euaions sows wen Pr, were is e ickness of velociy boundary layer. e exac soluion of e boundary layer euaions produces [] 4.9x Re x (6) were plae, U x Re x is e Reynolds number of plae flow. For example, if e velociy is 0.m/s over a 5m long

3 U L 0..5 Re L (7) e a e middle leng of e plae is 0.09m. A CF program would calculae e convecive ea ransfer from e plae as CF ρc p k (8) Pr were is e normal disance from e cener of e firs grid cell o e (alf of e cell size) and is e air emperaure a cell cener. In order o analyze possible errors associaed wi grid sizes, is sudy considers wo differen grid sizes: is smaller an and is larger an. < Wen is smaller an, e possible numerical error is Pr CF ρcp k k (9) Because e emperaure profile in e ermal boundary can be approximaed as [] (0) e relaive error of convecive ea ransfer due o en becomes k( ) ( ) ( ) Euaion () verifies a e smaller e e more accurae e calculaed convecive ea ransfer. e error of convecive ea ransfer due o is on e order of O( ) for is case. () e same analysis can be conduced wen is eual o or larger an, were. en, k( ) () Euaion () sows a e minimum error of e calculaed ea flux is one-ird of e analyical soluion in Euaion (5) as euals. e convecive ea ransfer calculaed will deviae significanly from e acual soluion if e size of firs grids is unreasonably large. () Naural Convecion For e naural convecion case, e analyical soluion sows [] ( + Pr) gβ Pr x () Wi is euaion, one can rougly esimae e scale of due o naural convecion in e middle of a m verical wall a 40 C and room air emperaure a 5 C o be 0.04m. e analyical soluion of e convecive ea ransfer for naural convecion is []

4 k ( ) (4) wile e CF euaion for naural convecion is e same as Euaion (8) for forced convecion. erefore, k( ) ( ) (5) < Wen is smaller an, (6) k( ) ( ) (7) Hence, e smaller e size of firs grids, e beer e accuracy. e calculaion error of e convecive ea ransfer due o e size of firs grids () is on e order of O() for naural convecion. Since wen, Euaion (5) becomes k( ) (8) e euaion is very similar o Euaion () for forced convecion, excep a e analyical ea flux is differen. CONVECIVE HEA RANSFER IN URBULEN FLOWS e sudy on laminar flows verifies a finer grid disribuion provides more accurae soluions. However, mos indoor airflows are urbulen. e analysis for urbulen flows is more complicaed an a for laminar flow, because e accuracy of convecive ea ransfer prediced in urbulen flows depends on bo e size of firs grids and urbulence model used. is sudy as examed e accuracy by using ree zero-euaion urbulence models and differen grid resoluions for a forced convecion flow along a plae. e zero-euaion urbulence models are freuenly used in e CF simulaion for building design due o eir simpleness and efficiency. e ree zero-euaion urbulence models esed ere are: () Consan viscosiy model: () Xu s zero-euaion model []: 00 (9) U l (0) were l is e normal disance o e and U is e airflow speed a is locaion. () Prandl s zero-euaion model []: were κ 0.4 and y is e disance o e. U κ y () y e convecive ea ransfer in urbulen flows is relaed o urbulence as defined by 4

5 ρcp( + ) ( ) () Pr Pr y were is urbulence eddy viscosiy and represens Reynolds-averaged emperaure. In Euaion (), >> for e flow region away from walls, and << for e near wall region, wic is called viscous sub-layer. I is obvious a if e firs grid is locaed in e viscous sub-layer, e relaionsip beween e convecive ea ransfer prediced and e size of firs grids is similar o a for laminar flow. e ea ransfer compued does no direcly depend on e urbulence model, aloug e urbulence model does influence e velociy and emperaure profiles. According o e empirical euaion [], y 0 urbulence 0.057[(n+)(n+)/n] 0.8 Re x -0. x () were n7 for a common velociy profile in e boundary layer, urbulence for a forced convecion wi a velociy 0.m/s over a 5m long plae is urbulence 0. m (4) and sub-layer 0.5~0. urbulence 0.0~0.0m. Wen e velociy is increased o m/s, urbulence and sub-layer are reduced o 0.08m and 0.0~0.0m, respecively. e empirical soluion for e urbulen plae flow and ea ransfer gives [] Nu 0.8 / Re Pr x k (5) x x Considering e ea ransfer in e middle of e plae wi a velociy of 0.m/s, 0.8 / 0..5 / Nu L ReL Pr L k (6) As a resul, surfce ( ) 8.k( ) (7) On e oer and, wi e assumpion of Pr Pr, a CF program would calculae e ea ransfer as, CF ρcp ( + ) Pr Pr y y 0 ρc p + Pr + k (8) Since as, k( ) k( CF + ) 8. (9) Wi consan viscosiy model: k( + ) (0) Wi Xu s zero-euaion model: k( + ) () Wi Prandl s zero-euaion model: + k( ) () < 5

6 e emperaure and velociy profiles in e boundary layer are approximaed as [] U U y n () Hence, U U n (4) and CF k k + + n (5) Wi consan viscosiy model: k( + ) n 0 8. n n 8. (6) Wi Xu s zero-euaion model: k( + ) n U 8. n n 8. (7) Wi Prandl s zero-euaion model: k( + ) n κ U 8. n 8. 4 n 8. (8) Euaions (0)-() and (6)-(8) can be illusraed as Figure by using e common velociy profile of n7 and 0.m. Figure indicaes a: () e use of small firs grid wi e consan viscosiy urbulence model would increase e error in predicing e ea flux. A large firs grid seems beer an a small one. () e error in predicing e ea flux increases as e grid resoluion decreases wen e oer wo zeroeuaion models are used. A finer grid soluion is preferred wi e wo zero-euaion models. Furer analysis of Euaion (7) indicaes a CF only wen / In fac, under is condiion, e firs grid falls ino e viscous sub-layer ( sub-layer / 0.5~0.). In oer words, e firs grid sould be placed in e sub-layer so as o obain e correc ea flux. Since << in e sub-layer, Euaion (5) can be re-arranged n n + CF k k (9) k( n ) 8. (40) o acieve 0, sould be 0.0m if n7 and 0.m. e value is obained based on e simple plae flow. Real indoor airflows are more complicaed. Usually, e momenum and ermal boundary layer in room airflows are icker an ose in e plae flow. e simulaion experience from e lieraures (e.g. [4]) indicaes a 0.05m is a good value for mos indoor airflows. e following secion aemps o validae is value roug wo case sudies by using Xu s zero-euaion urbulence model. 6

7 NUMERICAL EXPERIMENS FOR WO YPICAL ROOM AIRFLOWS () Naural Convecion in a Room wi an Aspec Raio of.5:7.9 In order o define a reasonable CF grid for room airflows, is sudy firs models a naural convecion flow in a full-size room as sown in Figure 4. e room was wi a o wall on one end and a cold wall on is opposie. e room was used by Olsen e al. [5] o measure flow and ea ransfer. Olson also used a :5.5 scale pysical model conaining R4 gas. e small-scale model was geomerically similar, ad e same Reyleig number, and ad e same dimensionless side wall emperaure as e full-scale room. e measuremen found a good agreemen beween e full-scale room and e scale model in flow paerns, velociy, emperaure disribuions, and ea ransfer. is sudy is paricularly ineresed in e convecive ea ransfer a e o and cold walls and compares bo full-scale and model experimenal resuls wi e compued resuls. Figure 5 presens e convecive ea ransfer a e o and cold walls for bo e measuremen and simulaion were Nussel number is ploed as a funcion of Reyleig number. Also included in e figure is e correlaion from Bon e al. [6], Nu0.Ra /4, for enclosure flows. e Nu and Ra number are based on e emperaure difference beween e o and cold walls. e experimenal uncerainy is approximaely 0 percen for e scale model and 0 percen for e full scale room. e resuls sow a e simulaions wi e firs grid size of m agree very well wi e daa, exibiing e expeced rend of increasing Nu wi Ra. e oer firs grid sizes produce e soluions a are more deviaed from e measuremens, as illusraed in Figure 6. Noe a finer grids do no give more accurae resuls wi e zero-euaion model as analyzed. Figure 5 and 6 indicae a e firs grid size a 0.005m is reasonably good for e indoor naural convecion cases. () Forced Convecion in a Room wi an Aspec Raio of 5.5:.7:.4 e sudy furer invesigaes a forced convecion flow in an experimenal camber wi e side-wall je [7]. e configuraion of e experimenal faciliy is sown in Figure 7. e simulaion uses ree differen grid densiies: fine grid ( ,470 cells) as e firs grid size a 0.05m o wall; moderae grid ( ,880 cells) as e firs grid a 0.m; and coarse grid ( 7 5 5,60 cells) as e firs grid a 0.m. e area-averaged ea fluxes a e room enclosures are en calculaed and compared wi e measured daa, as presened in Figure 8. e resuls sow a e simulaion wi e firs grid size a m can provide reasonable soluions for suc a forced-convecion flow. is conclusion confirms a by Cen [4] wo indicaed a e firs grid size a 0.m is a good value for mos indoor airflows. NEGAIVE VERSUS CONVERGENCE AN SABILIY OF ES ES and CF programs can excange e convecive ea informaion on envelope inerior s roug differen meods. Zai e al. [8] enumeraed e possible daa excange meods and comparaively sudied eac of em roug eoreical analysis and numerical experimen. According o e sudy, e fases and mos robus meod o excange convecive ea beween ES and CF is a ES provides inerior emperaures in a room o CF wile CF reurns e convecive ea ransfer coefficiens and e air emperaures near e s o ES. In order o minimize e modificaions in ES programs a use e radiional definiion of convecion coefficien based on e emperaure difference of an inerior and room air, a correced convecive ea ransfer coefficiens, correced, raer an and, can be calculaed from CF resuls and used in ES. e correced is calculaed in CF roug: correced ( - ) A( - ) A (4) e, calculaed in CF based on e flow viscosiy (Euaion ()), is always posiive. However, correced can be negaive in some paricular cases. Figure 9 illusraes suc an example in a room wi displacemen venilaion. If assuming 4W/m C, a e floor, e ea gain from e floor Q ( floor - air ) 4W/m. If Q is represened by e emperaure difference beween conrol and floor, en Q correced ( floor - conrol ) correced (0-4) 4W/m, one would obain correced -W/m C. I may even cause e singulariy problem if conrol 0 C. Negaive may cause divergence and insabiliy of an ES simulaion. ES solves e following marix euaion for energy balance were, H (4) room 7

8 H,c + N k,r N,r k,r,c +,r N k k,r NN,r N,c + N,r N,r N k Nk,r (4) N (44),in,in N,in + + +,c,c N,c room room room (45) and i is e emperaure of inerior i, i,c is e convecive ea ransfer coefficien of i, ij,r is e radiaive ea ransfer coefficien beween i and j, i,in is incoming ea o i (e.g. e conducive ea roug e envelopes), N is e oal number. erefore, /H (46) From marix eory [9], as a uniue soluion if only if H 0, i.e. H is nonsingular. H is singular if and only if e rank of n n marix H < n, wic means a a leas one row in H could be represened by e algebraic combinaion of e oers. ue o e randomness of e coefficiens in H, i is impossible o anicipae e deerminan of marix H in general. However, e energy euaion for eac (eac row in Euaion (4)), aloug conneced wi oer s, canno be deermined by energy balances of e oer s. erefore, marix H is nonsingular, regardless of e sign of. Wen ieraively solving Euaion (4) in ES, one may sill mee e insabiliy and divergence problems. Marix eory [9] proves a e marix sould possess some properies o guaranee a converged soluion. Following is a brief discussion on e issue wi Jacobi meod. Euaion (4) can be rewrien in e following manner, N,, N,N,, N,N N,N,N,N,, N N,, N, N (47) N N,, N,N, N, 0, N,N, 0, N,N N,N,N,N 0,, N (48) By ieraively solving (48), one can obain e soluion wi a prescribed accuracy. Assuming afer e m ieraion, And if is e exac soluion, i.e. m -H m- (49) -H (50) 8

9 I can be easily seen, upon subracion, a Hence m --H ( m- -) H ( m- -)(-) m H m ( 0 -) (5) lim m ( m ) 0 if lim H ' m 0 (5) m In oer words, a necessary and sufficien condiion for e convergence of e Jacobi meod is a H m ends o zero as m ends o infinie. Suc a limi occurs if e specral radius of H is less an uni. For e momen, a sufficien condiion can be since H < (5) H m H m (54) From marix eory, a sufficien condiion wen H is less an uniy is o saisfy e following condiion N j j i i,j i, i <, i,,.., N (55) Wi posiive values, e elemens in e marix H of Euaion (4) always saisfy N j N i,c + ij,r > ij, r (56) wic makes H a diagonal dominan marix, assuring a ere exiss a uniue soluion for e vecor. Wen i,c is negaive, Euaions (55) or (56) may no be saisfied, wic could cause divergence and insabiliy during a calculaion. e divergence and insabiliy may no always occur, since saisfying Euaion (55) is only a sufficien condiion. In general, e larger e real siuaion depars from Euaion (55) (i.e. e larger negaive i,c ), e iger e probabiliy of divergence and insabiliy. CONCLUSIONS In a coupled simulaion of ES and CF, CF provides convecive ea ransfer on inerior s of building envelope o ES. Accurae predicion of e convecive ea ransfer by CF is crucial o e accuracy of building energy calculaion. e size of firs grid o an inerior and urbulence model in CF are mos imporan o e calculaion of convecive ea ransfer. e convecive ea ransfer deermined from e firs grid cell, raer an from a prescribed locaion, sould be used in e coupled simulaion. is invesigaion found a e calculaed convecive ea ransfer depends on e size of firs grids by analyzing laminar flows of forced and naural convecion over a fla plae. e error of convecive ea ransfer due o e size of firs grids () is on e order of O( ) for laminar forced convecion and O() for naural convecion. is sudy furer discussed e combined effec of e size of firs grids and urbulence model on e convecive ea ransfer. ree zero-euaion models ave been used: e cosan viscosiy model, Xu s model, and e Prandle mixing leng model. A finer grid disribuion in CF does no always lead o a more accurae soluion wen e consan viscosiy urbulence model is used or wen e firs grid is in e sub-layer boundary wi e oer zero-euaion urbulence models. Based on e eoreical analysis and numerical experimenaion, e sudy suggess a universal firs grid size of 0.005m for indoor naural convecion airflows and 0.m for indoor forced convecion airflows. is invesigaion also found a e convecive ea ransfer coefficiens, using radiional definiion for building energy simulaion, could become negaive for room wi srong emperaure sraificaion, suc as wi displacemen venilaion. e eoreical analysis sows a a negaive convecive ea ransfer coefficien may cause divergence and insabiliy in energy simulaion. j j i 9

10 REFERENCES. Clarke J.A. Energy simulaion in building design. Adam Hilger, Brisol, Cen Q. Compuaional fluid dynamics for HVAC successes and failures. ASHRAE ransacions 997; 0(): Marin P. CF in e real world. ASHRAE Journal 999; : Cen Q. and Srebic J. Applicaion of CF ools for indoor and oudoor environmen design. In. Journal on Arciecural Science 000; (): Clarke J.A., empser W.M., and Negrao C.O.R. e implemenaion of a compuaional fluid dynamics algorim wiin e ESP-r sysem. Proc. Building Simulaion 995, 66-75, Madison, USA, In. Building Performance Simulaion Associaion. 6. Nielsen P.V. and ryggvason. Compuaional fluid dynamics and building energy performance simulaion. Proc. Roomven 998,, 0-07, Sockolm Sweden. 7. Srebric J., Cen Q., and Glicksman L.G. A coupled airflow-and-energy simulaion program for indoor ermal environmenal sudies. ASHRAE ransacions 000; 06(): Beausoleil-Morrison I. e al. Furer developmens in e conflaion of CF and building simulaion. Seven Inernaional IBPSA Conference 00 (BS00),, 65-74, Rio de Janeiro, Brazil. 9. Zai Z., Cen Q., Haves P. and Klems J.H. On approaces o couple energy simulaion and compuaional fluid dynamics programs. Building and Environmen 00; 7: Paankar S.V. Numerical ea ransfer and fluid flow. New York: Hemispere/ McGraw-Hill, Lienard J. A ea ransfer exbook (rd ediion). Massacuses Insiue of ecnology, Cambridge, MA, Xu W. New urbulence models for indoor airflow simulaion. P.. esis, eparmen of Arciecure, Massacuses Insiue of ecnology, Cambridge, MA, Prandl L. Uber die ausgebildee urbulenz. ZAMM 95; 5: Cen Q. Indoor airflow, air ualiy and energy consumpion of buildings. P.. esis, elf Universiy of ecnology, e Neerlands, Olson.A., Glicksman L.R. and Ferm H.M. Seady-sae naural convecion in empy and pariioned enclosures a ig Rayleig numbers. ASME J. Hea ransfer, 990; : Bon M.S., Kirkparick A.. and Olson.A. Experimenal sudy of ree dimensional laminar convecion a ig Reyleig number. ASME Journal of Hea ransfer 984; 06: Fiser.E. An experimenal invesigaion of mixed convecion ea ransfer in a recangular enclosure. P.. esis, Universiy of Illinois a Urbana-Campaign, USA, Zai Z. and Cen Q. Soluion caracers of ieraive coupling beween energy simulaion and CF programs. Energy and Buildings 00; 5(5): Assem S.. Advanced marix eory for scieniss and engineers, Abacus Press, Gordon and Breac Science Publisers, 99. 0

11 Figure Illusraion of e grid, cell, node, and disance o e in CF Figure Laminar plae flows of forced and naural convecion Figure Impac of urbulence model and firs grid size on e error of convecive ea ransfer prediced by CF Figure 4 Configuraion of e experimen [5] Figure 5 Comparison of simulaed ea ransfer a enclosures wi e daa from [5] Figure 6 Influence of firs CF grid size on e calculaion of Nu a Ra Figure 7 Scemaic of experimenal faciliy [7] Figure 8 Comparison of simulaed ea flux a enclosures wi e measuremen Figure 9 Illusraion of negaive

12 (a) (b) Figure Illusraion of e grid, cell, node, and disance o e in CF

13 U, L (a) convecion (b) naural convecion forced Figure Laminar plae flows of forced and naural convecion

14 90 Consan Viscosiy Model d/k*d (m) d/(k*d) Xu's Zero-Euaion Model (m) Figure Impac of and firs grid size on convecive ea by CF d/(k*d) Prandl's Zero-Euaion Model urbulence model e error of ransfer prediced (m) 4

15 Figure 4 Configuraion of e experimen (Olson e al. 990) 5

16 Nu E+0.5E+0.0E+0.5E+0.0E+0.5E+0 Ra CF- Firs Grid 0.005m: o wall CF- Firs Grid 0.005m: cold wall CF- Firs Grid 0.00m: o wall CF- Firs Grid 0.00m: cold wall Empirical Correlaion (Bon e al. 984) Model experimen (Olson e al. 990): o wall Full-scale experimen (Olson e al. 990): o wall Model experimen (Olson e al. 990): cool wall Full-scale experimen (Olson e al. 990): cold Figure 5 Comparison of simulaed ea ransfer a enclosures wi e daa from Olsen e al. (990). 6

17 (NuCF-Nuexp)/Nuexp Ho wall Cold wall Firs CF Grid (m) Figure 6 Influence of firs CF grid size on e calculaion of Nu a Ra

18 Figure 7 Scemaic of experimenal faciliy (Fiser 995) 8

19 Surface Hea Flux (W/m) Experimen CF-CoarseGrid: 0.m CF-ModeraeGrid: 0.m CF-FineGrid: 0.05m -5 Floor Lower level walls Middle level walls Upper level walls Ceiling Figure 8 Comparison of simulaed ea flux a enclosures wi e measuremen 9

20 conrol 4 C Figure 9 Illusraion of negaive air 9 C floor 0 C 0