Experimental and Numerical Investigation of Temperature Distribution in Room with Displacement Ventilation

Transcription

1 Expermenal and Numercal Invesgaon of Temperaure Dsrbuon n Room wh Dsplacemen Venlaon PETER STANKOV, Professor, Deparmen of Hydroaerodynamcs and Hydraulc Machnes, Techncal Unversy of Sofa, Bulgara JORDAN DENEV, Asssan Professor, Deparmen of Hydroaerodynamcs and Hydraulc Machnes, Techncal Unversy of Sofa, Bulgara MARTIN BARTAK, Asssan Professor, Deparmen of Envronmenal Engneerng, Czech Techncal Unversy n Prague, Czech Republc FRANTISEK DRKAL, Professor, Deparmen of Envronmenal Engneerng, Czech Techncal Unversy n Prague, Czech Republc MILOS LAIN, Asssan Professor, Deparmen of Envronmenal Engneerng, Czech Techncal Unversy n Prague, Czech Republc JAN SCHWARZER, Asssan Professor, Deparmen of Envronmenal Engneerng, Czech Techncal Unversy n Prague, Czech Republc VLADIMIR ZMRHA L, PhD Suden, Deparmen of Envronmenal Engneerng, Czech Techncal Unversy n Prague, Czech Republc ABSTRACT The paper deals wh he assessmen of resuls from an mproved form of he sandard k-ε model for buoyan room flows. Ths mproved k-ε model s based on he generalzed graden dffuson hypohess of Daly and Harlow (970). Resuls from he compuaons for hreedmensonal flow are compared wh emperaure measuremens performed by he auhors n a laboraory room wh dsplacemen venlaon. The numercal resuls show a good agreemen wh he laboraory expermens, superor o he resuls from he sandard k-ε model. The mproved k-ε model showed also a beer convergence behavour han he sandard k-ε equaon model. I s que easy o mplemen n every code.. INTRODUCTION Buoyan flows n venlaed rooms se a good challenge o urbulence modellng. A grea varey of urbulence models exs n he world of compuaonal flud dynamcs (CFD) wh dfferen levels of complexy and accuracy. Ths paper deals wh he exenson of sandard k-ε model, whch s based on he deas from more advanced algebrac flux models. The proposed mprovemen of k-ε model uses he generalzed graden dffuson hypohess (GGDH) of Daly and Harlow (970) bu unlke Ince and Launder (989) s sll based on he wall-funcons approach. As s shown n hs paper, he mproved k-ε model s que smple, numercally sable and gves accurae resuls when compared o emperaure measuremens n a laboraory room wh dsplacemen venlaon. Clma 000/Napol 00 World Congress - Napol (I), 5-8 Sepember 00

2 Frsly, he paper gves a shor heorecal descrpon of boh he sandard k-ε urbulence model and he mproved model based on he generalzed graden dffuson hypohess (GGDH). Secondly, he laboraory room wh dsplacemen venlaon s presened and he expermenal mehods used by he auhors are descrbed. Then he resuls of emperaure measuremens are compared wh hose of numercal predcons usng boh he sandard and he mproved k-ε models. Conclusons abou he accuracy and he convergence behavour of he wo modellng approaches gve useful nformaon for all hose who are no sasfed wh he use of sandard k-ε model for buoyan room flows.. THEORETICAL BACKGROUND. Sandard k-ε model of urbulence for sohermal flows The sandard k-ε model of urbulence s developed for sohermal flows and consss of he followng wo paral dfferenal equaons (summaon over repeang ndexes s assumed): - equaon for he urbulen knec energy k µ k ρu µ + = ρε () σ k P k - equaon for he dsspaon rae of urbulen knec energy ε µ ε ε ρuε µ = ( cp c ρε ) x + σ ε k where he producon erm P of he urbulen knec energy s presened by u P = ρu u Afer applyng he Boussnesq's approxmaon and rearrangemen, we oban: u P = µ u + u In he above equaons u and u are he mean velocy componens, u and u are he velocy flucuaons, µ s he dynamc vscosy, ρ s he flud densy, σ s he Prandl number. The urbulen vscosy µ s defned as µ = cµ ρk ε. The urbulence model consans are: c µ = 0.09; c =.44; c =.9; σ k =.0; σ ε =.. Smple Graden Dffuson Hypohess (SGDH) When buoyan flows are consdered, he producon erm P from eq. () s modfed o nclude also he buoyancy effecs and becomes: P u ρ u βρ θ u g u = () () (4)

3 where β s he volumerc expanson coeffcen and θ s he emperaure flucuaon. Whn he wdely used smple graden dffuson hypohess (SGDH) he urbulen hea flux n he las erm of he equaon (5) s modelled by: µ θ ρu θ = (6) σ θ where θ s he emperaure and σ θ s he urbulen Prandl number, aken as a consan. Thus he buoyan par of he urbulen producon (wh g, g usually equal o zero, g = g and x z) becomes: µ θ Pb = β g (7) σ z θ The SGDH s que smple, easy o mplemen and as shown by Nelsen (998) n some cases sgnfcanly nfluences he predced resuls. However, hs que smple equaon has he followng drawback: n he vercal shear layers drven by buoyancy he buoyan generaon would vansh, f he vercal emperaure graden becomes zero (Ince and Launder, 989). Ths apples for example o he flows n caves or rooms heaed from below n whch he emperaure dsrbuon s almos unform. A very mporan feaure for he numercal predcon of buoyan flows s he numercal sably of urbulence model. However, as saed by Nelsen (998), s known ha SGDH may produce numercal nsably and herefore commercal codes gve he possbly o exclude from he compuaons.. Generalzed Graden Dffuson Hypohess (GGDH) Accordng o hs hypohess nroduced by Daly and Harlow (970), he urbulen hea flux s calculaed from: θ ρu θ = c u u θ ρ (8) The coeffcen c θ s usually se equal o c µ σ n order o say closer o he eddyvscosy formulaon (Ince and Launder, 989). where C, ξ and η are he model consans. θ (5).4 Commens on he mproved k-ε model used n he presen sudy Generalzed graden dffuson hypohess could be vewed as he frs erm of he more comprehensve algebrac flux model descrbed by Hanalc e al. (994): k θ u ρu = + ξρ θ + ηβ ρθ (9) θ C ρu ε u u g

4 Ths algebrac flux model, besdes he conrbuon from mean velocy gradens, accouns also for he muual neracon beween he dfferen componens of urbulen hea flux and he conrbuon due o emperaure varance. Despe he fac ha GGDH s a somewha 'runcaed' verson of he las equaon, accordng o Hanalc (994) mproves subsanally he predcon of naural convecon n hgh caves. An example of a model based on GGDH s he model of Ince and Launder (989). In hs work he auhors neglec he sreamwse graden as unmporan n her wo-dmensonal sudy; herefore Hanalc and Vasc (99) call hs modfcaon he 'parally generalzed graden dffuson hypohess'. Unlke he work of Ince and Launder (989), n he presen hree-dmensonal sudy all erms of eq. (8) are reaned. Thus, n he presen work he expresson for he buoyancy producon erm wll be (consderng g and g se o zero, g = g, and for deal gas condons β = /[θ + 7.5]): θ Pb = gc u u θ ρ θ (0) and afer subsuon P b k u u T g = 0.5 µ + δ k x x ρ θ ε where δ s he Kronecker dela, equal o f =, oherwse equal o zero. In he {x, y, z} coordnaes we oban: k u w T v w T w T Pb = g 0.5 µ + + µ + + µ ρ k θ ε z z y y z z () where u, v, w are he mean velocy componens. The man reason why o use formula () for he presen mproved k-ε model s ha unlke eq. (7) gves he vercal flux drven by horzonal emperaure graden n he presence of shear sress. As s shown furher, hs mproved k-ε model shows also a superor numercal sably for he suded hree-dmensonal flow. Mos ofen he advanced algebrac flux models as well as he model of Ince and Launder (989) nclude low-re number exensons (Launder and Sharma, 974; Lam and Bremhors, 98) amng a he mproved predcon of he flow physcs n he near-wall regon. The equaons for such models nclude dampng funcons, whch are acve n he regons near he wall whle n he nernal regons he flow remans unchanged. However, such an approach requres an ncreased number of numercal pons near he wall consderably (up o 0-0 pons n he very proxmy of each wall). Ths prevens he algebrac flux models from beng used for hree-dmensonal engneerng predcons. Three-dmensonal engneerng flows sll need o use a knd of wall-funcons near he wall n order o overcome he problem wh large number of grd pons, see e.g. he work of ()

5 Chkamoo e al. (99). Therefore, n order o brng he presen model as close o he needs of praccal engneers as possble, he sandard log-law wall-funcons approach of Launder and Spaldng (974) are reaned.. NUMERICAL PROCEDURE In he presen nvesgaon a new verson of he compuaonal flud dynamcs (CFD) par of he ESP-r (Energy Sysems Performance - research) sofware s ulzed. The ESP-r sofware s developed for he purposes of he buldngs energy performance analyss and he compuaonal flud dynamcs par s added o enlarge s possbles for negraed smulaon ogeher wh he dealed ar flows n rooms (Beausolel-Morrson e al., 00). The CFD par uses he fne volume numercal mehod for he dscrezaon of he paral dfferenal equaons on srucured saggered numercal grds. The model ncludes he equaons for emperaure, he equaons for he hree velocy componens and for he pressure correcon segregaed by he SIMPLEC algorhm. The k-e urbulence model s used ogeher wh he wall-funcons approach for he boundary condons on rgd walls. Radaon beween walls s no aken no accoun n he presen sudy. 4. DESCRIPTION OF LABORATORY EXPERIMENTS 4. Tes Room The measuremens were performed n a es room 4. m long,.6 m wde and m hgh wh dsplacemen ype of venlaon. The supply ar openng 0. m x 0. m was placed symmercally on he wes wall havng he boom edge on he floor level. A specal lemnscae-shaped nle nozzle was desgned n order o oban nle velocy profles as unform as possble. The oule poson was on he wes wall.05 m above he floor. z y 4, m Fgure : Schemac drawng of he es room (hea sources shown hached),6 m,0 m

6 The es room was nsulaed on he exernal surface n order o mnmze he hea ransfer hrough he room envelope. Three elecrc heang shees were nsalled on he wo longer walls and on he wall oppose o he ar supply (see Fg. ). Addonal hermal nsulaon was appled beween he room walls and heang sources. 4. Expermenal condons The es room was placed n a bgger ar-condoned enclosure provdng requred exernal condons for he expermens. Dfferen locaons of he surroundng enclosure were ndvdually venlaed and heaed by 4 heaers and 0 fans n order o oban he room walls as adabac as possble accordng o he local ar emperaures n he room (quas-adabac walls). Ths occurred o be very dffcul for he floor, whch s parly cooled by suppled ar. The average nle velocy (over he nle secon) was 0.84 m/s, yeldng he venlaon rae of 4 ach. The emperaure of suppled ar was 0 C wh flucuaons ±0.5 C. The heang oupu of elecrc shees was 40 W/m, whch gves oupu 68 W n oal for he hree heaers. 4. Mehod and nsrumenaon The emperaure profles were measured on vercal lnes, each of hem havng measurng pons. Up o four vercal mul-pon probes wh negave hermsors (NTC) were used a a me. The NTC probes were of.4 mm dameer and havng a shor me consan (0 s). Expermenal daa were colleced n one-mnue perods by he daa acquson un Ahlborn ALMEMO The radaon error n ar emperaure measuremens was found neglgble; here were no dfferences observed n measuremens wh and whou reflecve screens. The reason s n low surface emperaures of he heang panels (0 o 40 C) compared o he ar emperaures and n small-szed NTC sensors. The emperaures were measured a 4 pons n hree vercal planes, ou of hem 68 pons (8 vercal lnes) n he mddle longudnal plane and he res (4 vercal lnes) on boh sdes of hs plane. 4.4 Resuls and dscusson The resuls from smulaon are avalable a any pon of he D numercal grd whle he measured daa were obaned only n hree vercal planes. The man par of measured pons were placed n he mddle longudnal plane because he bgges dfferences beween suppled ar emperaure and nner ar emperaure can be observed n hs plane. Hence hese resuls from hs plane were used for he comparsons beween he measured and numercally smulaed daa as hey are gven n he followng Fgures o 4. The emperaure profles presened n Fg. 5 are seleced from dfferen vercal planes o show ha he conclusons are vald no only for he mddle plane. Consderng he emperaure profles shown n he Fgure 5 boh numercal mehods show a very good agreemen wh he expermenally measured daa. However, he generalzed graden dffuson hypohess (GGDH) follows beer he measuremens n erms of overall emperaure fled paern (see Fgures o 4). The smple graden dffuson hypohess (SGDH) produces emperaure srafcaon, whch s dfferen from ha n he laboraory expermen. GGDH provdes also slghly beer convergence gvng he resduals of he order of 0-4 (excep for energy) afer 6000 eraons whle SGDH gave he resduals of he order of 0 -.

7 Ar emperaures: SGDH 0,0 0,4 0,8,,6,0,4,8,,6 4,0 X [m] Fgure : Ar emperaures numercally smulaed usng he smple graden dffuson hypohess (SGDH); resuls n he mddle longudnal plane. Ar emperaures: GGDH 0,0 0,4 0,8,,6,0,4,8,,6 4,0 X [m] Fgure : Ar emperaures numercally smulaed usng he generalzed graden dffuson hypohess (GGDH); resuls n he mddle longudnal plane.,8,4,0,6, 0,8 0,4 0,0,8,4,0,6, 0,8 0,4 0,0 Z [m] Z [m] Temperaure [ C] Temperaure [ C]

8 Ar emperaures: measured 0,0 0,4 0,8,,6,0,4,8,,6 4,0 X Fgure 4: Ar emperaures measured n he es room; resuls n he mddle longudnal plane. Z [m] Temperaure profles comparson X =.5 Y = 0.55 (0.6) Measuremen SGDH GGDH Temperaure [ C] Fgure 5: Ar emperaure profles: comparson beween he wo numercal mehods and he measured daa (seleced vercal lnes) Z [m] Temperaure profles comparson X =.975 Y =.8 Measuremen SGDH GGDH Temperaure [ C] Z [m] ,8 Temperaure [ C],4,0,6 Z, 0,8 0,4 0, Temperaure profles comparson X =.7665 Y =.5 (.55) Measuremen SGDH GGDH Temperaure [ C]

9 5. CONCLUSIONS An mproved k-e model for buoyan flows s nroduced and esed for venlaed rooms. The mproved model, based on he GGDH s compuaonally more sable han he sandard k- e model. I gves beer resuls whch are closer o he expermens for a hree-dmensonal room flow wh dsplacemen venlaon. I s very smple o upgrade he sandard k-e model o he nroduced mproved form: all wha s requred from he user s he use of equaon (), nsead of he equaon (7). Based on he more correc resuls and he mos sable numercal behavour he auhors made he concluson ha hs mproved model wll become sandard for he new verson of he CFD (Compuaonal Flud Dynamcs) code used for buldngs energy analyss as par of he ESP-r (Energy Sysems Program-research) sofware. 6. ACKNOWLEDGEMENTS Ths work was made wh he fnancal suppor from he European Comsson (INCO Coperncus proec ERB IC5 CT989 05) and he Czech Mnsry of Educaon (proec MSM 00000). REFERENCES Chkamoo, T., Murakam, S. and Kao, S. 99. Numercal smulaon of velocy and emperaure felds whn arum based on modfed k-ε model ncorporang dampng effec due o hermal srafcaon. Proc. of Inernaonal Symposum on Room Ar Convecon and Venlaon Effecveness. Tokyo, Japan. Beausolel-Morrson, I., Clarke, J. A., Denev, J., Macdonald, I. A., Melkov, A., Sankov, P. 00. Furher developmens n he conflaon of CFD and buldng smulaon. Proc.of 7 h Inernaonal IBPSA Conference Buldng Smulaon 00. Ro de Janero, Brasl. Daly, B. J. and Harlow, F. H Phys. Fluds, vol., 64 Hanalc, K. and Vasc, S. 99. Compuaon of urbulen naural convecon n recangular enclosures wh an algebrac flux model. In. J. Hea Mass Transfer, 6 (4), pp Hanalc, K Achevemens and lmaons n modellng and compuaon of buoyan urbulen flows and hea ransfer. Proceedngs of he 0h Inernaonal Hea Transfer Conference, Vol., pp. -8, Brghon, UK. Hanalc, K., Keneres, S. and Durs, F Numercal sudy of naural convecon n paroned -dmensonal enclosures a ransonal Raylegh numbers. In. Symposum on Turbulence, Hea and Mass Transfer, Lsbon, Porugal

10 Ince, N. Z. and Launder, B. E On he compuaon of buoyancy-drven urbulen flows n recangular enclosures. In. J. Hea and Flud Flow, 0 (), pp Lam, C.K.G. and K.A. Bremhors 98 `Modfed form of he k-e model for predcng wall urbulence, J. of Fluds Engng, 0, Launder, B. E. and Spaldng, D. B The numercal compuaon of urbulen flows. Compuer Mehods n Appled Mechancs and Engneerng, (), pp , reprned n specal ssue (990) Launder, B.E. and B.I. Sharma 974 `Applcaon of he energy-dsspaon model of urbulence o he calculaon of flow near a spnnng dsc' Leers n Hea and Mass Transfer,, -8 Nelsen, P Turbulence models for predcon of room arflow. n: Room Ar Movemen Compuaon - lecure course a he CFD Cenre for Eengneerng Predcon and Desgn, pp. 75-9, Techncal Unversy of Sofa, Bulgara. Nurnberg, G., Wood, P. and Shoukr, M Expermenal and numercal urbulen buoyan flows n an enclosure. Proceedngs of he 0h Inernaonal Hea Transfer Conference, Vol. 7, pp. 9-4, Brghon, UK.