Effect of Different Near-Wall Treatments on Indoor Airflow Simulations

Transcription

1 Journal of Appled Flud Mechancs, Vol. 5, No. 4, pp , Avalable onlne at ISSN , EISSN Effect of Dfferent Near-Wall Treatments on Indoor Arflow Smulatons N. El Gharb 1,3, R. Abs 2, A. Benzaou 3 1 Center for Renewable Energy Development, Po. Box 62 Bouzareah Algers, Algera 2 EBI, Inst. Polytech. St-Lous, PRES UPGO Unversté Pars Grand Ouest, 32 Boulevard du Port, 95094, Cergy- Pontose Cedex, France 3 Unversty of Scences and Technology Houar Boumedene(USTHB), Po. Box 32 El Ala Bab Ezzouar Algers, Algera Correspondng Author Emal: rafk.abs@yahoo.fr (Receved October 30, 2010; accepted July 4, 2011) ABSTRACT Arflow smulaton results depend on a good predcton of near wall turbulence. In ths paper a comparatve study between dfferent near wall treatments s presented. It s appled to two test cases n buldng: (1) the frst concerns flow through a long corrdor whch s smlar to that n a fully developed plane channel. Smulaton results are compared to drect numercal smulaton (DNS) data of Moser et al. (1999) for Re τ = 590 (where Re τ denotes the frcton Reynolds number defned by frcton velocty u τ, knematcs vscosty ν and the channel half-wdth δ); (2) the second case s a benchmark test for room ar dstrbuton. Smulaton results are compared to expermental data obtaned wth laser-doppler anemometry (Nelsen, 1990). Smulatons were performed wth the ad of CFD code Fluent (2005). Near wall treatments avalable n Fluent were tested: Standard Wall Functons, Non Equlbrum Wall Functon and Enhanced Wall Treatment. In each case, sutable meshes wth adequate poston of the frst near-wall node are needed. Results of near-wall mean stream wse velocty u + and turbulent knetc energy k + profles are presented, varables wth the superscrpt of + are those non dmensonal by the wall frcton velocty u τ and the knematc vscosty ν. Keywords: CFD, Arflow, Turbulence, Smulaton, Near-Wall treatment, Channel, Room. NOMENCLATURE C 1, C 2 Constant of emprcal turbulence model for k-ε one G k Generaton of k, (Nm 2 ) H Hgh,(m) k Turbulent knetc energy, (m 2 s -2 ) L Wdth, (m) R j Reynolds stress tensor, (kg m -1 s -2 ) Re Frcton Reynolds number u 0 Inlet velocty,(m s -1 ) Arbtrary fluctuatng velocty component, (m s -1 ) u Frcton velocty,(m s -1 ) x Axal coordnate, (m) Arbtrary drecton, (m) u Frcton velocty,(m s -1 ) y Radal coordnat, (m) No-dmensonal wall coordnate Greek symbols δ j Kronecker delta ε Turbulent energy dsspaton rate, (m 2 s -3 ) μ Dynamc vscosty, (kgm -1 s -1 ) μ t Turbulent vscosty, (kgm -1 s -1 ) ν Knematcs vscosty,(m 2 s -1 ) ρ Flud densty,(kgm -3 ) τ j Turbulent stress tensor, (m 2 s -2 ) τ w Wall shear stress, (kg m -1 s -2 ) Abbrevaton CFD Computatonal Flud Dynamcs DNS Drect Numercal Smulaton EWT Enhanced Wall Treatment NEWF Non-Equlbrum Wall Functon RMS Root Mean Square SWF Standard Wall Functon TKE Turbulent Knetc Energy

2 1. INTRODUCTION Most people spend the majorty of ther tme ndoors, often n shared spaces, so the expectatons of the occupant for a thermally comfortable ndoor clmate have rsen. For ths reason tools are requred to determne and predct the flow characterstcs n the early desgn phase. The CFD method s often employed. For predctng room ar flow, the standard k- turbulence model has enjoyed the greatest usage (Murakam et al. (1987), Nelsen (1989), Chen et al. (1992), Weathers (1992), Haghghat et al. (1992), Chen (1995), El Gharb (2007), Sumon et al. (2008), Bahlaou et al. (2011), El Gharb et al. (2012)). However ths model s only vald for fully-developed turbulence, the flow s not solved up the wall. In addton, the wall s the most common boundary encountered n these confned flud flow problems. Therefore, to smulate ths regon the selecton of approprate near-wall treatment methods s very mportant for obtanng relable predcton results of arflows smulaton. The frst near wall treatments was developed wth k- model, we quoted: Spaldng (1961), Wolfsten (1969), Launder et al. (1974), Chen et al. (1988), Jongen (1992), Km et al. (1995). Ths nvestgaton studed two typcal ndoor arflows: (1) a flow n a fully developed plane channel, assmlated to flow through a long corrdor, (2) a forced convecton flow n a ventlated room, a benchmark test for 2D room ar dstrbuton. Flud flow near a sold wall as well as the characterstcs of turbulent flow near such structures s consdered. Smulatons wll be performed wth the ad of the commercal CFD code Fluent (2005). All dfferent near wall treatments avalable n Fluent wll be tested: Standard Wall Functons, Non Equlbrum Wall Functon and Enhanced Wall Treatment. We wll nvestgate both effects of meshes and poston of the frst near-wall node. For the frst test case smulatons results are compared to drect numercal smulaton (DNS) data of Moser et al. (1999) for Re τ = 590 (where Re τ denotes the frcton Reynolds number defned by frcton velocty u τ, knematc vscosty ν and the channel half-wdth δ). Then, for the second test case, the smulaton results are compared wth expermental data obtaned wth laser- Doppler anemometry (Nelsen, 1990). Ths one s use to measure velocty and velocty fluctuaton. 1. MODEL EQUATIONS A. Governng Equatons In ths study, arflow s modeled usng the standard k-ε model. The governng equatons are: Mass conservatve equaton: ( u ) 0 (1) x Momentum conservaton equaton: ( uv j ) p j Rj (2) x x x x j j where s the vscous stress tensor and s the turbulent Reynolds stress tensor u u j 2 uk j j x j x 3 x k R u u u u k ' ' j 2 j j t j x j x 3 Turbulent knetc energy: k k t u Gk x x k x Dsspaton rate: u x x k x 2 k t C G t 2 C1 Gk C 2 k k u u u 2 u k x x x 3 x j j j k t j j B. Near-wall Treatments (3) (4) (5) (6) (7) (8) Close to the wall, the flow s nfluenced by vscous effects. The mean velocty feld s affected through the no-slp condton that has to be satsfed at the wall. Toward the outer part of the near-wall regon, however, the turbulence s rapdly augmented by the producton of turbulence knetc energy due to the large gradents n mean velocty. Therefore, accurate representaton of the flow n the near-wall regon determnes successful predctons of wall-bounded turbulent flows. For that and because most k- and RSM turbulence models wll not predct correct near-wall behavor f ntegrated down to the wall, specal near-wall treatment s requred. Fluent near-wall treatments: Fluent offers two approaches based on the classcal theory descrbng the flow near-walls n turbulent flows, Fluent (2005), Fg. 1: a. The frst one s a sem-emprcal approach, and uses the so called "wall functon" to brdge the vscosty affected regon between the wall and the fully turbulent regon. The vscous sublayer and buffer layer regon are not resolved. Therefore, the near-wall mesh may be relatvely coarse, the frst grd pont off the wall must be postoned n the log law regon at y + >30 (the dstance beng measured n wall unts y + = yu τ ν, where u τ s the frcton velocty). Ths approach s justfed for 64

3 ndustral flows wth hgh Reynolds numbers, because t saves computatonal tme and t s suffcently precse. There are two optons for sem-emprcal approach use n Fluent code. The frst Standard Wall Functon (Launder et al. 1974) s presented as default n Fluent. It assumes equlbrum between the producton and dsspaton of turbulent knetc energy. The second Non- Equlbrum Wall Functon (Km et al. 1995) may be selected by the user. It does not assume ths equlbrum, but allows dfferng producton and dsspaton, as may be the case for flows where there s separaton and reattachment or severe pressure gradents (Fluent 2005). b. The second approach combnes a two layer model (where the vscosty affected near-wall regon s completely resolved, along the way to the vscous sublayer), together wth enhanced wall functons. Generally, t requres a very fne near-wall mesh. The frst grd pont off the wall must be from y + 1. Ths approach s more suted for low- Reynolds number flows wth complex nearwall phenomena. Although t obvously requres a greater amount of computatonal resources. (Fluent 2005). Fg. 1. Schematcs of, the wall functon approach and the two-layer approach 2. TEST CASES Arflow smulatons wth dfferent near-wall treatments are appled to two test cases: A. Channel flow The frst test case s the plane fully developed channel flow smlar to flow through a long corrdor n a buldng, Fg. 2. Smulatons results are valdated by DNS data of Moser et al. (1999) for Re τ = 590. Fg. 3. Presentaton of Nelsen s room, H=3m and L=9m. 3. RESULTS AND DISCUSSIONS A. Effect of Mesh and Frst Grd Pont To captures boundary layer properly, the mesh should be correctly generated. For turbulent flows, calculaton of the y + value of the frst node pont helps n dong that. Ths dmensonless dstance s defned as: uy y (9) v where s the frcton velocty defned as s the wall shear stress. w and For that and because the wall dstance y + s nvolved n the selecton of the approprate near-wall treatment, we do a grd test for only mesh n y drecton. The geometry of a fully developed plane channel s chosen (frst test case) and eght dfferent mesh szes are appled to select the approprate mesh sze that adapt wth near-wall treatment (wall functons or near-wall modelng). Ths s acheved by refnng the mesh, wth partcular attenton to the frst grd pont off the wall. Table 1 shows selected computatonal mesh and the correspondng wall y + values. Table 1 Dfferent mesh mesh sze frst y + mesh type (xy) mesh 1 (50010) 59 regular mesh 2 (50014) regular mesh 3 (50019) regular mesh 4 (50028) regular mesh 5 (50057) regular mesh 6 (50076) regular mesh 7 (50057) exponental law mesh 8 (50076) exponental law Fg. 2. Presentaton of the channel flow B. Room ar dstrbuton The second test case s a benchmark test (Annex 20, Nelsen, 1990) for a room ar dstrbuton, Fg. 3. The smulaton results are valdated by expermental data obtaned wth Laser-Doppler Anemometry. Non-dmensonal mean stream wse velocty profles scaled by the wall velocty u u and nondmensonal profles of turbulent knetc energy ut k k are plotted (Fgs. 4 and 5). 2 u 65

4 able to resolve the mean velocty and turbulent quanttes n that regon. 20 DNS Mesh 5 Mesh 7 Mesh 6 Mesh 8 u y + Fg.4. Comparson of non-dmensonal mean streamwse velocty profles usng coarse mesh wth wall functon (SWF), fne mesh wth near-wall modelng (EWT) The dfferent mesh confguratons and correspondng wall y + value have sgnfcant nfluence on the computed non-dmensonal mean streamwse velocty and turbulent knetc energy profles. Wth wall functons, the frst grd pont must be n the log- law regon.e y + >30. Fgures 4 and 5 show that mesh 3 seems to be the most approprate. As a test case, Fg. (6) presents turbulent knetc energy (TKE) and mean velocty profles obtaned by standard wall functon and frst grd pont at y + <30 (y + 10 for mesh 5 and y + 1 for mesh 7). It shows clearly that t s mpossble to obtan correct predctons when we use fne mesh wth wall functons. As llustrate n Fgure 6, the dstrbuton of u + and k + are sgnfcantly affected. Because wall functons use the assumpton of local equlbrum, that s not vald n the vscous affected regon.e y + <30. Wth near wall modelng the frst grd pont must be n vscous sublayer.e y + 1. Fgures 4 and 5 show that mesh 7 seems to be the most approprate. The vscosty affected near-wall regon s completely resolved. Accordng to user's gude of fluent (Fluent, 2005), wth ths modelng, we should have at least 10 cells wthn the vscosty affected near-wall regon to be Fg. 5. Comparson of non-dmensonal turbulent knetc energy profles usng coarse mesh wth wall functon (SWF), fne mesh wth near-wall modelng (EWT). B. Selecton of more approprate near wall treatment All dfferent near wall treatments avalable n Fluent were tested: Standard wall functon SWF, Non equlbrum wall functon NEWF and Enhanced wall treatment EWT. Results of mean streamwse velocty u + and turbulent knetc energy k + profles are presented n Fgs. (7) and (8). For the two test cases, channel flow and room ar dstrbuton, a fne mesh (respectvely and 45 38) was used for enhanced wall treatment EWT, whle a coarse mesh (respectvely and 45 12) was used for standard wall functon SWF and nonequlbrum wall functon NEWF. For the frst test case (plane channel flow), Fg. 7 presents smulaton results: mean streamwse velocty u + (Fg. 7) and TKE k + (Fg. 7) profles, wth DNS data of Moser et al. (1999) for Re τ =

5 Fg. 6. Standard wall functon usng fne mesh non-dmensonal mean stream wse velocty profles non-dmensonal turbulent knetc energy profles On the one hand, standard SWF and non equlbrum NEWF wall functons need a coarse mesh (Fg. 1.a). The frst node should be at y + >30. Fgure (7) shows that standard SWF and Non equlbrum NEWF wall functons predct well velocty profles for y + >30 and TKE profles for y + >60. However, these near wall treatments are not able to provde detals about velocty and TKE n the vscous and buffer layers. If these treatments are used, t s possble to provde an accurate descrpton of TKE by an analytcal equaton and velocty by solvng an ordnary dfferental equaton ODE (Abs, 2009). These treatments could be therefore assocated to ths smple and effcent analytcal method. On the other hand, enhanced wall treatment EWT needs a fnest mesh n the vscous sublayer (Fg. 1). Fg. 7. comparson between predcted profles usng standard k-ε model wth dfferent wall treatments and DNS data for test case 1 plane channel flow. mean stremwse velocty, turbulent knetc energy The frst node should be at about y+ 1. Fgure (7) shows that the velocty profle s more accurate and well predcted even n the vscous and buffer layers than that standard SWF and non equlbrum NEWF wall functons. However, TKE s underestmated (Fg. 7). Ths has no effect on velocty profle but can provde an underestmated eddy vscosty/dffusvty whch could be nvolved n predcted partcles concentratons. In order to nvestgate the effect of standard k-ε model on the TKE profle whch s underestmated by EWT (Fg. 7.b), a comparson wth an advanced RANS models; Re-Normalsaton Group RNG k-ε model (Yakhot et al. 1992), s done. Fgure (8) shows that RNG k-ε model provdes a very small mprovement for velocty and TKE. Snce the dfference s neglgble, the underestmaton of TKE seems therefore not related to the used turbulence model but assocated to the near wall treatment. 67

6 Fg. 8. Comparson between predcted profles usng standard and RNG k-ε models wth enhanced wall treatmant EWT and DNS data for test case 1 plane channel flow. mean stremwse velocty, turbulent knetc energy The second test case (benchmark test for a room ar dstrbuton), presents smulaton results: mean velocty u + (Fg. 9 and 9(c)) and turbulence ntensty (Fg. 9 and 9(d)), wth expermental data obtaned by laser- Doppler anemometry (Nelsen, 1990). Fgures 9 and 9(c) present mean velocty u + respectvely at x=3m (1/3 L) and x=6m (2/3 L) whle Fgs. 9 and 8(d) present turbulence ntensty u respectvely at x=3m and x=6m. Fgures (9) show that for 0< y/h<0.2 and 0.8< y/h<1, wall functons ( SWF and NEWF ) ddn t provde values, only EWT provdes results. Ths s due to the requred mesh and frst near wall node. Predcted mean velocty profles wth the dfferent nearwall treatments are qute smlar (Fgs. 9, 9(c)) for 0.2 <y/h<0.8. However, EWT provdes veloctes near the walls (where wall functons are unable to provde values) but needs more computaton tme. More mportant scatter s shown for RMS fluctuaton veloctes at x=3m (Fg. 9). All near-wall treatments fal to predct RMS fluctuaton veloctes for 0.2 <y/h<0.5. NEWF seems to be the less accurate. In contrast, at x=6m (Fg. 9(d)) wall functons seem more accurate for 0.6 <y/h<0.8. (c) (d) Fg. 9. Comparson between predcted profles usng standard k-ε model wth dfferent wall treatments and expermental data for test case 2 benchmark test for a room ar dstrbuton. mean velocty at x=3m, RMS fluctuaton velocty at x=3m, (c) mean velocty at x=6m, (d) RMS fluctuaton velocty at x=6m. 68

7 At x=3m, EWT provdes accurate velocty (Fg. 9) and RMS (Fg. 9) for 0.8 < y/h < 1. However, t under-predcts velocty for 0 < y/h < 0.2 (Fg. 9). At the opposte, at x=6m veloctes obtaned by EWT are well predcted for 0 < y/h < 0.2 (Fg. 9(c)) whle they are under-predcted for 0.8 < y/h< 1. These observatons suggest that the flow s well predcted near the nlet and the outlet. At 3m, the flow s well predcted n the upper part (nlet), whle at 6m the flow s better descrbed n the lower part (outlet). Ths could be related to recrculaton zones whch are not well descrbed n these smulatons. 4. CONCLUSIONS Arflow smulatons wth dfferent near-wall treatments were appled to two test cases. The frst test case, s the fully developed plane channel flow, smlar to a flow through a long corrdor n a buldng, smulaton results:.e. mean stream wse velocty and TKE profles, were compared to DNS data for Re τ = 590. Standard SWF and non equlbrum NEWF wall functons need a coarse mesh. The frst node should be at y + >30. SWF and NEWF wall functons predct well velocty profles for y + >30 and TKE profles for y + >60. However, they are not able to provde detals about velocty and TKE n the vscous and buffer layers. Enhanced wall treatment EWT needs a fnest mesh n the vscous sublayer. The frst node should be at about y + 1. Velocty profle s more accurate and well predcted even n the vscous and buffer layers. TKE s underestmated; ths could provde an underestmated eddy vscosty/dffusvty and therefore could have an effect on predcted temperature and partcles concentraton. Smulatons do not show any dfference between standard and RNG k-ε models. The underestmated TKE seems therefore assocated to near wall treatments. For the second test case, whch s a benchmark one for a room ar dstrbuton, smulaton results for mean velocty and turbulence ntensty (at x/l=1/3 and 2/3) were compared to expermental data. No values obtaned for all smulatons, by wall functons (SWF and NEWF) n the case of 0< y/h<0.2 and 0.8< y/h<1, only EWT provdes results. Ths s due to the requred mesh and frst near wall node. Predcted mean velocty profles wth dfferent near-wall treatments are qute smlar for 0.2 <y/h<0.8. However, EWT provdes veloctes near the walls where the wall functons are unable to provde values. At x=3m (x/l=1/3), all near-wall treatments fal to predct measured RMS veloctes u for 0.2 < y/h < 0.5. EWT provdes accurate velocty and RMS for 0.8 < y/h < 1. However, t under-predcts velocty for 0 < y/h < 0.2. At the opposte, for x=6m (x/l=2/3), veloctes obtaned by EWT are well predcted for 0 < y/h < 0.2 whle they are under-predcted for 0.8 < y/h < 1. These observatons suggest that the flow s well predcted n the upper part at x=3m (nlet), whle t s better descrbed n the lower part at x=6m (outlet). Ths seems to be n relaton wth recrculaton zones, whch are not well descrbed. More advanced models wth adequate near-wall treatments are needed for an effcent smulaton of ndoor arflow dstrbuton. In our future work, we wll access Low Reynolds Number models. REFERENCES Abs R. (2009). A smple eddy vscosty formulaton for turbulent boundary layers near smooth walls, C. R. Mecanque, Elsever, 337, Bahlaou A., A. Raj, M. Hasnaou, C. Ouard, M. Naïm and T. Makayss (2011). Heght Partton Effect on Combned Mxed Convecton and Surface Radaton n a Vented Rectangular Cavty, Journal of Appled Flud Dynamcs, 4(1), Chen H. C. and V. C. Patel (1988). Near-Wall Turbulence Models for Complex Flows Includng Separaton. AIAA Journal, 26(6), Chen Q (1995). Comparson of Dfferent k-ε Models for Indoor Ar Flow Computatons, Numercal Heat Transfer, 28, part B, pp Chen Q. and Z. Jang (1992). Sgnfcant questons n predctng room ar moton, ASHRAE Transactons, 98( 1), Chen Q. and Z. Jang (1992). Ar supply method and ndoor envronment, Indoor envronment, 1, El Gharb N. (2007). Modélsaton et smulaton du transfert de chaleur et de masse dans un espace confné : applcaton au condtonnement d ar d une salle de chrurge, mémore de magstère en physque opton Energétque et Mécanque des Fludes, USTHB, Alger. El Gharb N., Benzaou A., Khall E.E., Kameel R., (2012). Analyss of ndoor ar qualty n surgcal operatng rooms usng expermental and numercal nvestgatons, Mechancs & Industry, 13(2), Fluent Inc. (2005). Fluent 6.2 user s gude. Haghghat F, Z. Jang, J. C. Y. Wang and F. Allard (1992). Ar Movement n Buldngs Usng Computatonal Flud Dynamcs, Transactons of the ASME, 114, Jongen T. (1992). Smulaton and modelng of turbulent ncompressble flows, PhD thess, EPF Lausanne, Lausanne, Swtzerland. Kader B. (1993). Temperature and Concentraton Profles n Fully Turbulent Boundary Layers. Int. J. Heat Mass Transfer, 24(9), Km S.E. and D. Choudhury (1995). A Near-Wall Treatment Usng Wall Functons Senstzed to Pressure Gradent, ASME FED, 217, Separated and Complex Flows, ASME. Launder B. E. and D. B. Spaldng (1974). The Numercal Computaton of Turbulent Flows, Computer Methods n Appled Mechancs and Engneerng, 3,

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