Nnth Internatonal IBPSA Conference Montréal, Canada August 15-18, 5 CFD MODELLING OF BUOYANCY-DRIVEN NATURAL VENTILATION OPPOSED BY WIND Malcolm Coo 1, Yngchun J 1 and Gary Hunt 1 Insttute of Energy and Sustanable Development, De Montfort Unversty, Lecester, LE1 9BH, UK Department of Cvl and Envronmental Engneerng, Imperal College London, London, SW7 AZ, UK ABSTRACT Ths paper presents CFD smulatons of natural dsplacement ventlaton arflows n whch the buoyancy force produced by a heat source s opposed by a wnd force. Cases nvestgated focus on wndbuoyancy force relatonshps for whch a two-layer stratfcaton s mantaned. CFD predctons of the poston of the nterface separatng the two layers and the change n reduced gravty (temperature dfference) between them are compared wth the analytcal wor and salt-bath measurements of Hunt and Lnden (, 5). Comparsons are good wth only mnor dscrepances n the nterface poston and a small under-predcton of the upper layer reduced gravty. INTRODUCTION Computatonal flud dynamcs (CFD) smulaton s ncreasngly beng used to gude the development of natural ventlaton strateges n low-energy buldng desgns. Ths s partly attrbutable to a renewed nterest n natural ventlaton, but also due to the avalablty of powerful affordable des-top computers whch are able to solve the complex nonlnear equatons n CFD models wthn an acceptable tme frame. Recent wor by Coo (1998), Coo and Lomas (1998) and Coo et al. (3) has examned the applcaton of CFD to predct passve arflows n buldngs drven by nternal heat sources and more recently assstng wnd flows. The ams of ths wor have been to benchmar the CFD models through valdaton by comparson wth analytcal predctons of these flows (e.g. Lnden et al. (199), Hunt and Lnden (, 1, 5)) and expermental data taen from ther laboratory measurements. Ths benchmarng has proved successful and, thus, n addton to capturng the bul features of the flow and confrmng the governng flow parameters as dentfed by the analytcal modellng, the CFD then offers a convenent means for predctng, for example, the detaled spatal varaton of flow parameters such as ar speed and temperature whch may be crucal for comfort analyss and detaled desgn n more complex spaces. Very lttle nformaton s avalable offerng gudelnes on how best to use CFD for modelng natural ventlaton. The wor reported heren s part of an EPSRC supported proect (GR/N37346), the am of whch s to begn developng such gudelnes. The wor n ths paper bulds on prevous wor by the authors. Coo (1998) and Coo and Lomas (1998) nvestgated steady natural dsplacement ventlaton n a sngle space drven by buoyancy alone. These smulatons used an external flow doman whch enabled the arflow through the nlets and outlets to be modelled explctly wthout the need for boundary condtons at these locatons. Results agreed favourably wth analytcal predctons and expermental measurements of Lnden et al. (199). The wor compared predctons usng the standard -ε turbulence model of Launder and Spaldng (1974) wth the Renormalsaton Group (RNG) -ε turbulence model developed by Yahot et al. (199). These comparsons showed that the RNG model gave results closer to the analytcal and expermental wor due to a lower rate of entranment nto the plume. Usng some of the technques developed n ths wor, smulatons were conducted for a wnd asssted buoyancy-drven dsplacement ventlaton flow (Coo et al. 3) and compared wth analytcal wor (Hunt and Lnden 1). A fundamental dfference n the way these smulatons were modelled relatve to those reported n Coo and Lomas (1998) was the use of boundary condtons specfed drectly at the openngs whch consderably reduced the amount of computaton necessary. Results were agan very encouragng wth only mnor dscrepances observed between predctons and measurements. The smulatons reported n ths paper are for natural dsplacement ventlaton n whch wnd forces oppose buoyancy. Predctons of the ey features of the flow are compared wth the analytcal and expermental wor carred out by Hunt and Lnden (, 5). The paper comprses the followng sectons: analytcal and expermental wor n whch the wor of Hunt and Lnden (, 5) s summarsed; smulaton detals, where the cases nvestgated are - 7 -
defned and the CFD model presented; dscusson and results analyss; and conclusons. ANALYTICAL AND EXPERIMENTAL WORK Hunt and Lnden (, 5) consder the steady arflow and thermal stratfcaton wthn a hghlynsulated enclosure contanng a pont heat source n the centre of the floor wth openngs to the exteror ar at hgh- and low-level (Fgure 1). The upper openng s n a regon of (relatvely) postve wnd pressure and the lower openng n a regon of (relatvely) negatve wnd pressure. area a L warm ar cooler ambent ar Heat Source Fgure 1 Natural dsplacement ventlaton n a space contanng a pont heat source In the absence of wnd, Lnden et al. (199) show that warm ar rsng as a turbulent plume above the heat source stratfes the nteror ar nto two homogenous layers a warm upper and cooler lower layer. The warm upper layer drves flow out through the hgh-level openng(s) whch s replenshed by ar at ambent temperature enterng the space at lowlevel. In ths buoyancy-drven flow, a stable stratfcaton s establshed n whch the heght of the nterface, h, between the warm and ambent ar layers can be expressed as a functon a W, a L, and H. A wnd actng on the upper openng (from the rght n Fgure 1) serves to oppose the buoyancy-drven flow. Hunt and Lnden (, 5), referred to hereafter as HL, show that n ths case, multple-steady flow solutons are possble for a range of dentcal enclosure geometres, wnd speeds and heat loads. The two stable steady flows (mxng and dsplacement ventlaton) that are possble represent extremes of ventlaton strategy and reversals n flow drecton through the enclosure. The smulatons dscussed and presented n ths paper are concerned wth a range of wea opposng wnds for whch the general two-layer stratfcaton shown n fgure 1 s mantaned. Under these condtons, the leeward openng behaves as an nlet and the wndward openng as an outlet. For ths dsplacement flow case, HL derved the followng analytcal model for predctng the nterface heght, h. d c y=h area a W y=h y= WIND A H C 3 / 5 / 3 = (1) 3 ( 1 ξ d H )/ ξ 5 / CFr 1/ ( ) c where A s an effectve openng area gven by ξ 1/ A a W al Ce Cd = () H H C + d aw Ce al and where 1/ ( Δ ρ) Fr = (3) ( B H ) 1/ 3 s a Froude number used to characterse the relatve magntudes of wnd and buoyancy nduced veloctes. The emprcal constant C s a functon of entranment nto the plume (va the entranment coeffcent α) and defned as 1/ 3 6α 9α / 3 C = π. (4) 5 1 The change n buoyancy across the nterface s represented by the reduced gravty, g, of the upper layer where g 5 / 3 = ξ. (5) G H In equaton (5), the reduced gravty of the upper layer s normalsed usng the reduced gravty n the plume at the heght y=h. The reduced gravty, or buoyancy, of the upper layer s gven by Δρ g = g (6) ρ 1 where Δ ρ s the densty dfference between the upper and lower layers and ρ 1 s a reference densty (for convenence, taen to be the ambent densty). Assumng the ar n the space behaves as an deal gas, equaton (6) may be wrtten n terms of the temperature dfference, Δ T and the temperature, T 1, of the ambent layer: ΔT g = g. (7) T 1 HL verfed ther analytcal model usng salt-bath experments n whch a Perspex box wth upper and lower openngs was placed n a flume of fresh water. The heat source was represented usng an necton of brne. A wde range of values of Fr were nvestgated by varyng the wnd speed n the flume and the salnty/volume flow rate of the brne. Comparson of these expermental results wth the analytcal predctons are shown n Fgures 8-11. Note that as Fr ncreases the nterface heght descends and the buoyancy of the upper layer ncreases. - 8 -
SIMULATION DETAILS Cases Investgated The geometry used n the CFD smulatons comprsed two openngs at hgh level and two openngs at low level (Fgure ). The flow was drven by a horzontal heat source n the centre of the floor and the nfluence of a lght, steady wnd (gvng small Fr) actng on the upper openngs nvestgated. The openngs were all of equal area and postoned symmetrcally about a plane through the centre of the heat source. The aspect rato of the enclosure consdered s the same as that used by HL n ther salt-bath experments, although the scale s a factor of 1 greater. 1.5m 1.5m.7m gauze (thcness =.5m).8m.95m Heat source 5 5 d c =.m.5m Fgure Geometry nvestgated n CFD smulatons In order to prevent the momentum of the ncomng ar nfluencng the behavour of the buoyant plume, a fne gauze was placed between the low-level nlets and the heat source. Such a devce was used both n the CFD smulatons and n the salt-bath experments. Steady-state flows were nvestgated for the operatng condtons shown n Table 1. Table 1 Operatng condtons for CFD smulatons OPERATING CONDITIONS Δ Fr A =.18m or A =.77m 3 Q = 1W ( B =.75 1 m 4 s -3 ) Ambent temperature = 15 C.51.115.5.3 3 4 5 CFD Model The software used for ths wor was CFX4, verson 4.4 (1). Ths s a multbloc code n whch geometres are defned usng one or more topologcally rectangular blocs. Each bloc s covered wth a mesh and the governng equatons are solved usng the fnte volume method (Versteeg and Malalaseera, 1995). The Governng Equatons The code solves the followng conservaton equatons for mass, momentum and enthalpy for a steady, ncompressble turbulent flow: u = (8) u ( u u ) p ( ) ρ = δ + μ + μ + + ρg CP (1) t u ( ) λ μ t He ρu He + = He (9) The Boussnesq approxmaton s appled n whch the densty n the momentum equaton s wrtten as [ β( T )] ρ = ρ 1 T. (11) The turbulent vscosty μ t s determned usng a twoequaton -ε model. Based on the fndngs of prevous wor (Coo, 1998, Coo and Lomas, 1998) the RNG -ε turbulence model of Yahot et al. (199) was employed. The transport equatons for turbulent netc energy and turbulent netc energy dsspaton ε for ths model are as follows: where ( ) μ t ρu μ + = P + G ρε ( ρu ε) ( C C ) 1 1RNG. (1) μ t ε = x μ + x ε (13) ε ε P Cρ u ( ) u u P = μ + μt + (14) G ( μ + μ ) T t = βg (15) He ( 1 η η ) η C 1RNG = (16) 3 1+ β η - 9 -
P 1 / η = (17) μ ε η = 4.38, β =. 15, C 1 = 1.4 and C = 1.68. The turbulent vscosty μ t s gven by where C =. 85. μ μt = Cμρ (18) ε The governng equatons were dscretsed usng hybrd dfferencng, except the mass equaton where central dfferencng was used, and solved on a colocated grd. Pressure and velocty are coupled usng the SIMPLEC technque wth the Rhe-Chow nterpolaton algorthm (1983) to prevent decouplng due to the co-located grd. The followng underrelaxaton factors were used: mass ~ 1. (no underrelaxaton); momentum ~.65; enthalpy ~ 1.; ~.7; and ε ~.7. To ncrease the stablty of the soluton process and ad convergence, false tme-steps of.1s were mposed on all three momentum equatons. Ths form of under-relaxaton taes nto account the tme scale over whch the varables evolve and the local cell sze. Further detals can be found n Coo (1998). The mesh used for the CFD smulatons was a hexahedral mesh comprsng 68, elements wth smaller cells located around the gauze and wthn the regon of the thermal plume (fgure 3). Fgure 3 Hexahedral mesh structure used for CFD smulatons Boundary Condtons In the CFD model, only half of the geometry was modelled explctly. Ths was done usng a vertcal symmetry plane passng through the centre of the heat source, mdway between the openngs. All other surfaces of the enclosure (except the heat source) were modelled as adabatc. The heat source was represented usng a constant heat flux of 4Wm - 3 over a source area of.5 1 m. The gauze used for absorbng momentum from the ncomng ar was modelled usng a porous medum boundary condton whch enables resstances to arflow to be mposed. Resstances were specfed usng a volume porosty of.5 together wth a resstance vector of (3, 3, 3)Nm -1 per m 3 s -1 of flow at the level of the nlet. Above ths level, the resstance was reduced to (15, 15, 15)Nm -1 per m 3 s -1 of flow. At the nlet and outlet openngs, constant pressures were mposed to represent the wnd force. The values of pressure used were calculated such that the dfference between them gave the requred value of Δ for the Froude number under consderaton (Equaton 3). Dscusson and ustfcaton for adoptng ths approach to specfyng boundary condtons at openngs can be found n Coo et al. (3). To account for dsspatve losses and the contracton assocated wth the flow through the nlet and outlet openngs, the physcal nlet and outlet areas n the CFD model were reduced by the coeffcents of expanson (C e ) and dscharge (C d ) respectvely. In ths wor, both coeffcents tae the value.6. DISCUSSION AND RESULTS ANALYSIS Convergence was taen to be when the enthalpy resdual (unts of Watts) fell below 1% of the heat nput nto the space. Typcally, ths was acheved after about 5 teratons. A typcal arflow pattern and typcal temperature dstrbutons are shown n fgures 4-7. The velocty vectors (Fgure 4) clearly show the rsng plume above the heat source. Ths plume transports buoyant ar nto the upper zone of the space where a steady buoyant layer forms of unform temperature. Fgures 5-7 llustrate the ncrease n the depth and temperature of the upper layer as Fr ncreases. As the opposng wnd s wea, buoyancy domnates and for the cases shown the buoyant layer s able to drve a flow out through the upper openng nto the wnd. Fresh ambent ar enters at low level and the twolayer stratfcaton s mantaned for a range of wnd speeds. These flows are qualtatvely smlar to those obtaned for the assstng flow smulatons (Coo et al. 3). However, for gven Fr and A values, the wnd-opposed smulatons predct a lower nterface - 1 -
heght and hgher temperature (reduced gravty) n the upper layer. Ths s n eepng wth the analytcal predctons and the expermental results of HL and Hunt and Lnden (1). Fgure 7 CFD predcton of temperature dstrbuton ( A =.18m, Fr = 4) Quanttatve results comparng the CFD predctons wth the analytcal and expermental wor are shown n fgures 8-11. Favourable agreement was acheved for the varaton of nterface heght and reduced gravty wth Fr for both A values nvestgated. Fgure 4 CFD predcton of velocty vectors ( A =.18m, Fr = 3) Fgure 5 CFD predcton of temperature dstrbuton ( A =.18m, Fr = ) Fgure 6 CFD predcton of temperature dstrbuton ( A =.18m, Fr = 3) The varaton of nterface heght wth Fr shows a small over-predcton at low Fr whch gradually becomes a small under-predcton as Fr ncreases (Fgures 8 and 9). These small dcrepances may be caused by dfferent rates of entranment nto the CFD plume compared wth that assumed n the analytcal wor. Varyng rates of entranment may be brought about by the turbulence model employed or the performance of the gauze. Also note that the CFD predctons shown on the graph denote the md-pont of a temperature transton zone between the ambent lower layer and the warmer layer above. The varaton n the extent of ths transton zone vares between smulatons whch gves rse to a small spread n h/h values. The CFD predcted nterface heght for Fr=5 s notceably under-predcted (Fgure 8). In ths case, some nflow was observed n the smulatons through the wndward openngs. HL show that the transton from mxng ventlaton to dsplacement ventlaton occurs when the nternal Froude number F=Fr(A/H)1/3=31//1/3 ( 1.375). They fnd that a value of F=Fc>1.375 s requred to mae the transton from dsplacement to mxng ventlaton as n ths case wor has to be done to brea down the exstng thermal stratfcaton. The parameter F s a rato of the wnd-nduced and buoyancy-nduced veloctes wthn the enclosure and, hence, we refer to t as the nternal Froude number. Wth Fr=5, A =.18m and H=.5m we have Fr(A/H)1/3=1.368 whch s wthn 1% of Fc and, thereby, accounts for the wea nflow observed and the onset of a transton. CFD predctons of the reduced gravty varaton wth Fr show a small under-predcton relatve to the analytcal and expermental wor (Fgures 1 and - 11 -
11). Ths may agan be due to dfferng rates of entranment. The authors are now nvestgatng ths phenomenon by comparng the CFD-predcted plume propertes (volume and buoyancy fluxes) wth those determned by plume theory (Morton et al. 1956) around whch the theoretcal model of HL s based. h/h 1..8.6.4 Analytcal Model Experment CFD g' /G' H 1. 11. 1. 9. 8. 7. 6. 5. 4. 3.. 1. Analytcal Model Experment CFD.. 1.. 3. 4. 5. 6. 7. 8. 9. 1. Fr Fgure 11 Varaton of reduced gravty wth Froude number Fr ( A =.77m )... 1.. 3. 4. 5. 6. 7. 8. 9. Fr Fgure 8 Varaton of nterface heght wth Froude number Fr ( A =.18m ) h/h 1..8.6.4. Analytcal Model Experment CFD.. 1.. 3. 4. 5. 6. 7. 8. 9. Fr Fgure 9 Varaton of nterface heght wth Froude number Fr ( A =.77m ) g' /G' H 1. 11. 1. 9. 8. 7. 6. 5. 4. Analytcal Model 3. Experment. CFD 1... 1.. 3. 4. 5. 6. 7. 8. 9. 1. Fr Fgure 1 Varaton of reduced gravty wth Froude number Fr ( A =.18m ) CONCLUSIONS CFD technques have successfully been employed to model buoyancy-drven dsplacement ventlaton n whch wnd forces oppose the flow. Favourable agreement was acheved n comparsons wth analytcal predctons and expermental measurements. Small dscrepances n the nterface heght separatng the warm stratfed ar from the cooler ambent layer below are attrbuted to dfferences n the plume behavour and performance of the gauze used for nhbtng horzontal momentum. Dfferences n plume structure may also be the cause of an under-predcton n the reduced gravty of the upper layer, although t should be noted that these dfferences are small. A heat nput, room geometry and wnd pressure drop correspondng to a Froude number wthn 1% of the theoretcal value of F c =Fr(A /H ) 1/3 =3 1/ / 1/3 ( 1.375) dentfed by Hunt and Lnden (5) resulted n wea nflow through the wndward openng. Ths nflow opposed the outflowng buoyant ar and sgnfed the onset of a transton from a dsplacement to a mxng flow. Transtons between the flow regmes s complex and wll be the subect of further CFD modellng wor. The results n ths paper and those n Coo et al. (3) wll begn to form the bass for generatng gudelnes on how to model natural ventlaton usng computatonal flud dynamcs. ACKNOWLEDGMENT The wor reported here s wor n progress and s part of an EPSRC supported proect (GR/N37346) to establsh gudelnes on how best to model natural ventlaton flows usng CFD. The support of the EPSRC s gratefully acnowledged. - 1 -
NOMENCLATURE A effectve openng area (m ) a L leeward openng area (m ) a W wndward openng area (m ) B source buoyancy flux (m 4 s -3 ) C emprcal constant (-) C 1 emprcal constant (-) C emprcal constant (-) C μ emprcal constant (-) C d coeffcent of dscharge (-) C e coeffcent of expanson (-) C P specfc heat capacty (J g -1 K -1 ) d c heght between top of enclosure and mddle of upper openng (m) F nternal Froude number (-) F c crtcal nternal Froude number (-) Fr Froude number (-) G reduced gravty n plume at heght H (ms - ) H g reduced gravty of warm upper layer (ms - ) g acceleraton due to gravty (ms - ) H heght of the enclosure (m) h depth of layer at ambent temperature (m) He enthalpy (J g -1 ) turbulent netc energy (m s - ) p modfed pressure = p + g x 3 ρ ρ (Pa) Q strength of heat source (W) T temperature (K) T reference temperature used n CFX (K) u velocty vector, = (u, v, w) (ms -1 ) x poston vector (m) α entranment coeffcent (-) β coeffcent of thermal expanson (K -1 ) β emprcal constant Δ pressure drop between wndward and leeward openngs (Pa) δ Kronecer delta, = 1 f =, = f ε rate of dsspaton of turbulent netc energy (m s -3 ) η o emprcal constant (-) λ conductvty (Wm -1 K -1 ) μ dynamc vscosty (gm -1 s -1 ) μ t turbulent (eddy) vscosty (gm -1 s -1 ) ρ ar densty (gm -3 ) ρ reference densty used n CFX (gm -3 ) ε turbulent Prandtl number for ε (=.7179 n RNG -ε model) (-) He turbulent Prandtl number for enthalpy (=.9 n RNG -ε model (-) turbulent Prandtl number for (= 1. n RNG -ε model) (-) ξ = h H, normalsed nterface heght (-) REFERENCES CFX 1. User Gude Verson 4.4, CFX Internatonal, Harwell, UK. Coo, M. J. 1998. An evaluaton of Computatonal Flud Dynamcs for Modellng Buoyancy-drven Dsplacement Ventlaton, PhD Thess, De Montfort Unversty, Lecester, 3pp. Coo, M.J. and Lomas, K.J. 1998. Buoyancy-drven dsplacement ventlaton flows: Evaluaton of two eddy vscosty models for predcton, Buldng Servces Engneerng Research and Technology, Vol. 19, No. 1, pp.15-1. Coo, M. J., J, Y. and Hunt, G. R. 3. CFD modellng of natural ventlaton: combned wnd and buoyancy forces, Internatonal Journal of Ventlaton, Vol. 1, No. 3, pp.169-179. Hunt, G. R. and Lnden, P. F. Multple steady arflows and hysteress when wnd opposes buoyancy. Ar Infltraton Revew, 1, no., March. Hunt, G.R. and Lnden, P.F. 1 Steady-state flows n an enclosure ventlated by buoyancy forces asssted by wnd. J. Flud Mech., Vol. 46, pp. 355-386. Hunt, G. R. and Lnden, P. F. 5 Dsplacement and mxng ventlaton drven opposng wnd and buoyancy. J. Flud Mech. Vol. 57, pp. 7-55. Launder, B.E. and Spaldng, D.B. 1974. The numercal computaton of turbulent flows, Computer Methods n Appled Mechancs and Engneerng, Vol. 3, pp.69-89. Lnden, P.F., Lane-Serff, G.F., and Smeed, D.A. 199. Emptyng fllng boxes: the flud mechancs of natural ventlaton, J. Flud Mech., Vol. 1, pp.39-335. Morton, B.R., Taylor, G.I. and Turner, J.S. 1956. Turbulent gravtatonal convecton from mantaned and nstantaneous sources, Proc. R. Soc. London, A 34, pp. 1-3. Versteeg, H.K. and Malalaseera W. 1995. An ntroducton to Computatonal Flud Dynamcs the fnte volume method, Longman, New Yor, 57pp., ISBN -58-1884-5. Yahot, V., Orszag, S.A., Thangham, S., Gats, T.B. and Spezale, C.G. 199. Development of turbulence models for shear flows by a double expanson technque, Phys. Fluds A, Vol. 4, No. 7, pp. 151-15. - 13 -
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