Infiltration Heat Recovery in Building Walls: Computational Fluid Dynamics Investigations Results

Transcription

1 LBNL-534 Infltraton Heat Recovery n Buldng Walls: Computatonal Flud Dynamcs Investgatons Results Marc O. Abade, Elzabeth U. Fnlayson and Ashok J. Gadgl Lawrence Berkeley Natonal Laboratory Envronmental Energy Technologes Dvson Indoor Envronment Department Berkeley, CA 9470 August 00 Ths work was supported by the Assstant Secretary for Energy Effcency and Renewable Energy, Offce of Buldng Technology, of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.

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3 Abstract Conventonal calculatons of heatng (and coolng) loads for buldngs assume that conducton heat loss (or gan) through walls s ndependent of ar nfltraton heat loss (or gan). Durng passage through the buldng envelope, nfltratng ar substantally exchanges heat wall nsulaton leadng to partal recovery of heat conducted through the wall. The Infltraton Heat Recovery (IHR) factor was ntroduced to quantfy the heat recovery and correct the conventonal calculatons. In ths study, Computatonal Flud Dynamcs was to calculate nfltraton heat recovery under a range of dealzed condtons, specfcally to understand factors that nfluence t, and assess ts sgnfcance n buldng heat load calculatons. Ths study shows for the frst tme the mportant effect of the external boundary layers on conducton and nfltraton heat loads. Results show (under the dealzed condtons studed here) that () the nteror detals of the wall encountered n the leakage path (.e., nsulated or empty walls) do not greatly nfluence the IHR, the overall relatve locaton of the cracks (.e., nlet and outlet locatons on the wall) has the largest nfluence on the IHR magntude, () external boundary layers on the walls substantally contrbute to IHR and (3) the relatve error n heat load calculatons resultng from the use of the conventonal calculatonal method (.e., gnorng IHR) s between 3% and 3% for nfltratng flows typcally found n resdental buldngs. 3

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5 Contents. INTRODUCTION ILTRATION HEAT RECOVERY CALCULATIONS Smplfed IHR approach Energy flux through the buldng envelope Conventonal method of accountng for nfltraton energy load Infltraton Heat Recovery (IHR) calculaton of nfltraton load Combnng IHR calculatons for Infltratng and Exfltratng Walls DETAILS OF CFD INPUT FOR THE SIMULATED WALLS Wall geometry Ar propertes Densty Other propertes Sheathng propertes Ar flow model CFD SIMULATIONS Determnaton of the conducton heat flux wthout nfltraton Calculaton relablty Smulaton convergence IHR Error estmates RESULTS Insulated Wall Straght Through crack Low/Hgh and Hgh/Low cracks Empty Walls Straght Through crack Low/Hgh and Hgh/Low Cracks Concluson and future developments ILLUSTRATIVE APPLICATIONS Combnng One Infltratng and One Exfltratng Wall to Obtan a whole buldng IRH value IHR as a functon of Peclet number IHR as a functon of nfltrated ar mass flux IHR as a functon of pressure dfference across the wall Combnng One Infltratng and Three Exfltratng Walls to Obtan a whole buldng IRH value Comparson between the conventonal and actual total energy load CONCLUSION ACKNOWLEDGEMENTS

6 REFERENCES APPENDIX : WORKED EXAMPLE

7 . Introducton Conventonal heatng (and coolng) calculatons for buldngs assume that conducton heat loss (or gan) s ndependent of ar nfltraton heat loss (or gan), and that the heatng (or coolng) load s the drect summaton of these losses. The small number of studes n the lterature regardng the nfluence of nfltraton (Caffey (979), Persly (98), Sherman and Matson (993) and NIST (996)) all conclude that the combned effect of conducton and ar leakage s substantally smaller than that predcted wth conventonal calculatons. Consderng the complex analyss requred to determne the combned effects of conducton and ar leakage and the need to provde a smple engneerng calculaton procedure that can be used by practtoners, Sherman et al (000, 00) proposed that the conventonal method can be corrected by ntroducng only one coeffcent: the nfltraton heat recovery (IHR). The present study ams to calculate the nfltraton heat recovery (IHR) usng Computatonal Flud Dynamcs (CFD); specfcally to understand factors that nfluence t, and assess ts sgnfcance n buldng heat load calculatons. As shown by Sherman and Walker (00), the ntermxng between the external boundary layers and the nfltratng ar could play a role n the heat recovery. In order to test ths assumpton, we studed two confguratons: n the frst, a fxed temperature boundary condton s drectly appled to the wall surface and n the second, a fxed temperature boundary s defned n ar, some dstance away from the wall, and the exteror surface flow feld s modeled to nclude the boundary layers. Each wall comprses two sold layers (e.g., gypsum wallboard or plywood) wth space between the layers that can be flled wth nsulaton or left empty. The two sold layers have one crack each. Ar enters the wall cavty through a crack n one sold layer, traverses the space between the two layers, and leaves the wall through a crack n the opposte layer.e. the flow s undrectonal. Sx confguratons of crack locaton and nsulaton were selected to cover a wde range of potental IHR values. Three cases had nsulaton-flled walls and three had empty wall cavtes. These walls have three dfferent postons of the nlet and outlet cracks: straght through cracks, low nlet/hgh outlet and hgh nlet/low outlet. The CFD modelng ncluded a study of convergence crtera and grd geometry. In addton, uncertantes n predcted IHR values were calculated based on uncertantes n the CFD modelng and the calculaton procedure used to calculate the IHR. The IHR results for the nfltratng and exfltratng walls are presented n terms of the rato of heat transfer due to ar flow to the heat transfer due to conducton: the Peclet number. The results for nfltratng and exfltratng walls were combned to determne the overall IHR for a whole buldng that s requred to perform energy use calculatons. 7

8 . Infltraton Heat Recovery Calculatons.. Smplfed IHR approach... Energy flux through the buldng envelope In a real buldng there are many ar flow paths through the envelope, all wth dfferent geometres and ar flows. In addton, the conducton heat transfer changes greatly dependng on whether the envelope secton of nterest s an nsulated wall cavty, a wndow, a stud, etc. All these flow paths and conducton dfferences are unknowable n any practcal sense for a real buldng. Therefore, n ths study, we took a smplfed approach n whch all the ar flow and conducton are effectvely grouped together nto sngle terms. Although the heat and mass flows n real envelopes are three-dmensonal we used a two-dmensonal model for smplcty of analyss. Ths two-dmensonal approach offers sgnfcant advantages by smplfyng CFD codng and reducng executon tme for each smulaton as well as allowng the use of smplfed analytcal calculatons. Ths dealzed approach allows the development of smple algorthms for predctng IHR and allows a systematc approach for the CFD modelng such that the effect of dfferent parameters s easly observed. Two modes of heat transfer through the buldng envelope are consdered: conducton through walls and convecton heat transfer between the nfltratng ar and the nsulaton and sold layers. Fgure llustrates these two heat-transfer modes and the physcal layout for the smplfed CFD model. The mpact of solar as well as longwave nfrared radaton on heat loads s not taken nto account n ths study. Control Volume T out m& c p T out Indoor Space T n Q 0,exf m& c p T n Q 0,nf Infltratng Wall Exfltratng Wall Fgure : Cross secton of a generc buldng envelope showng the conventonal conducton and nfltraton energy load terms. 8

9 ... Conventonal method of accountng for nfltraton energy load In the absence of nfltraton through the buldng envelope, the heat load on the buldng s purely from conducton, denoted as Q 0 = Q 0,nf + Q 0,exf. When there s nfltraton, the total heat load usng conventonal methods, Q c, s determned by addng a smple convectve term to the energy balance for the buldng that s based on the leakage rate and the ndoor and outdoor ar temperatures: Q C = Q + mc & ( T T ) 0 p n out () where Q 0 s the wall heat transfer by conducton wthout nfltraton, m& s the ar mass flux through the walls, c p s the ar heat capacty and T n and T out are the ndoor and outdoor temperatures respectvely. Ths relatonshp assumes there s no nteracton (heat transfer, mosture deposton, etc.) between the leakng ar and the buldng walls...3. Infltraton Heat Recovery (IHR) calculaton of nfltraton load In realty, there s heat transfer between the sold materal wthn the buldng walls and leakng ar as the leakng ar crosses the wall. The result s that the actual values for the conducton, the nfltraton and thus the total loads (llustrated n Fgure ) are dfferent from those predcted by the conventonal method. As ar penetrates the wall, heat transfer wth wall materal changes ts temperature. Outsde ar enters the nfltratng wall at temperature T, temperature warmer than T out because of the conducton heat transfer from the wall. By the tme t enters the room t wll be at some other temperature, whch we defned as T. Smlarly, ar enters the exfltraton wall at temperature T 3, temperature cooler than T n, and exts ths wall at temperature T 4. We show the revsed heat loads n equaton. ( T ) * 0 + mc 4 T Q = Q & p () where Q s the corrected value for the total heat load, Q 0 * s sum of the nfltratng and exfltratng wall heat transfer by conducton (note that ths s NOT the same as the conducton wthout ar flow), and T and T 4 are the nlet and outlet temperatures respectvely (agan note that n general T wll not equal T out and T 4 wll not equal T n ). 9

10 Control Volume T out mc p T T T T 3 T 4 mc p T 4 T n Q* 0,nf Q* 0,exf Fgure : Cross secton of a generc buldng envelope showng the actual conducton and nfltraton energy load terms. To determne the actual conducton heat transfer and ts nteracton wth nfltraton heat transfer requres complex analyses and calculatons that are not easly carred out. To provde a smple engneerng calculaton procedure that can be used by practtoners (based on the conventonal method gven by equaton ()), Sherman et al (000, 00) proposed that the conventonal method can be corrected by ntroducng the Infltraton Heat Recovery (IHR) factor. Ths coeffcent undertakes the nfluence of the nfltratng ar on the conducton heat transfer and wall crack temperatures. So that, ( IHR) mc ( T T ) Q = Q & 0 + p n out (3) Q Q0 IHR = (4) mc & p ( T T ) n out Note that IHR has been defned such that when the ar nfltratng through the walls does not thermally nteract wth sold components of the wall, IHR reduces to zero, and equaton (3) reduces to equaton (). Thus the IHR ncludes both the effect of temperature changes of the nfltratng and exfltratng ar, and the accompanyng changes n conducton that occur. When IHR s non-zero, equaton (3) s a convenent way of restatng equaton (). The obectve of ths study was then to take the complex flow and temperature feld results from the CFD computatons and calculate values of IHR for use n equaton (4). 0

11 .. Combnng IHR calculatons for Infltratng and Exfltratng Walls The heat exchanges through the nfltratng and exfltratng walls are calculated separately, and then combned to fnd the IHR for the whole buldng by connectng the walls wth an ndoor space whose other surfaces are adabatc. The combned effect of the two walls s evaluated by selectng an approprate control volume. In ths study, two of the 4 sdes of the control volume concde wth the exteror surfaces of nfltratng and exfltratng walls. The other two sdes are adabatc (top and bottom). Conducton and convecton (.e. nfltraton) heat transfer values are evaluated at the boundares of the control volume (Fgure 3). Adabatc wall Q m& T T out T n T out T m& Q Infltratng Wall Adabatc wall Buldng Interor Exfltratng Wall Fgure 3: Heat transfer, ar mass flows and temperatures nvolved n the IHR calculatons. The nfltraton heat recovery factors for nfltratng and exfltratng walls and how they are combned to determne whole buldng are gven by the followng equatons (based on equaton (4)). IHR IHR IHR Buldng ( Tn T ) + Q c p ( Tn Tout ) ( T Tn ) + Q c ( T T ) & c p Q0 m = (5) m& & c p Q0 m = 0 (6) m& = n = m& n = IHR m& p + n n = m& n out = IHR m& (7)

12 Buldng where IHR, IHR and IHR are respectvely the nfltraton heat recovery factors for nfltratng wall and exfltratng wall and buldng respectvely; m& and m& are respectvely the ar mass flux through the nfltratng wall and exfltratng wall ; c p s the ar heat capacty, T n and T out are the ndoor and outdoor temperatures; T and T are the nfltratng wall nlet and exfltratng wall outlet temperatures; Q and Q are the heat transfers by conducton through the nfltratng wall and exfltratng wall external faces; Q 0 and Q 0 are the nfltratng wall and exfltratng wall heat transfers by conducton wthout nfltraton; and n and n are respectvely the number of nfltratng and exfltratng walls. The IHR results for the nfltratng and exfltratng walls and buldng are presented n terms of the rato of heat transfer due to ar flow to the heat transfer due to conducton: the Peclet number, Pe, defned by: mc & p Pe = (8) UA where m& s the ar mass flux through the wall (kg/s), c p s the ar heat capacty (J/kgK), U s the wall conductance (W/m K) and A s the wall surface area (m ). Usual Peclet number values found n buldngs are wthn the range If all walls of a buldng are dentcal (same UA value), IHR for a buldng can be wrtten as a functon of Peclet number: IHR Buldng = n = Pe n = IHR Pe + n = Pe n = IHR Pe (9) where IHR, IHR and nfltratng wall and exfltratng wall and buldng; Buldng IHR are the nfltraton heat recovery factors for Pe and Pe are the nfltratng wall and exfltratng wall Peclet numbers; and n and n are the number of nfltratng and exfltratng walls. If, however, the walls have dfferent UA values (e.g., owng to dfferent areas, A, or a dfferent conductance, U) then the smplfcaton presented n equaton (9) s not possble, and one must use the basc relatonshp gven n equaton (7).

13 3. Detals of CFD nput for the smulated walls 3.. Wall geometry Cross sectons representng the sx wall confguratons studed are shown n Fgure 4, together wth the wall dmensons. The walls are typcal of wood frame constructon, wth a cavty created by havng a layer of sheathng on each sde of a vertcal wooden stud. The dmensons were chosen to be typcal of resdental exteror wall constructon and the leakage locatons were chosen to llustrate the extremes of how much of the wall cavty s traversed by the nfltratng and exfltratng ar flows. 0.09m.44m 0.008m 0.0m I-ST I-LH I-HL E-ST E-LH E-HL Fgure 4: CFD Smulated Wall geometres. (Notes: I: Insulated wall, E: Empty wall, ST: Straght Through crack, LH: Low/Hgh crack, HL: Hgh/Low crack.) The three-letter notaton below each schematc s a code that succnctly descrbes the confguraton (see text below). Ar always enters the wall secton from the left crack and exts the wall secton from the rght crack. To smplfy the dscusson of the results, the walls were gven code desgnatons correspondng to ther nsulaton and ar leak locaton propertes. The frst letter n the desgnaton shows whether the wall s Insulated (I) or Empty (E). The poston of the nlet and outlet cracks s denoted wth the last two letters: Straght Through cracks (ST), Low nlet/hgh outlet (LH), and Hgh nlet/low outlet (HL). 3

14 3.. Ar propertes 3... Densty The deal gas law s used to calculate the ar densty: Mp ρ = o (0) RT where ρ s the ar densty (kg/m 3 ), M s the ar molar mass ( kg/mol), po s the atmospherc pressure (035 Pa), R s the deal gas law constant (8.34 J/molK) and T s the ar temperature (K) Other propertes All other propertes of the ar are assumed constant over the temperature range studed n ths study. The molecular vscosty s set to kg/ms, the specfc heat to 006 J/kgK and the conductvty to W/mK Sheathng propertes Sheathng propertes are those of plywood: densty s 544 kg/m 3, conductvty s 0.3 W/mK and specfc heat s 00 J/kgK Ar flow model The Low Reynolds number k-ε model s employed to calculate the turbulence n the ar flows nsde the wall cavty and outsde the sheathng. Ths model has the double advantage of () allowng the calculaton of the boundary layer along walls (the wall regon s treated the same way as the nteror flow, wth a no-slp condton mposed at the boundary; no wall law s appled) and () beng accurate for Low Reynolds flows (ncludng transtonal and lamnar flows) characterstc of ths problem. Accordng to the STARCD Methodology (999) manual, the tme-averaged basc equatons for steady, Low Reynolds number, and ncompressble buoyant flows can be wrtten n Cartesantensor form (equatons -5). Note that Ensten summaton conventon s used here and that a comma before an ndex mples dfferentaton wth respect to the coordnate of the correspondng ndex. For clarty, we expand the notaton n equaton () nto more famlar symbols. 3 Contnuty d ( ) ( ρu ) ρ U = = 0 (), = dx Momentum ( ρu U ) = P ( ρuu ) + ( ρ ρ r ) g,,, () Energy ( ρu T ) ( ρu t' ),, = (3) 4

15 ν σ k Turbulent Knetc Energy t ( ρu ) ρ ν k = + l k, + ρ( Pk + Gk ε ) (4), Turbulent Energy Dsspaton ν t ε ( ρu ε ) = ρ ν ε, ρ ( C ε P C3 εg Cε fε ), + l + k + k σ (5) ε k, Equatons 6-5 gve addtonal defntons needed to the resoluton of the prevous system of coupled equatons. uu = ν t ( U, + U, ) + k 3 (6) ν t u t' = T, σ T (7) ρ r T ρ = r T (8) k ν t = Cµ fµ ε (9) =ν U + U U (0) (,, ) P k t, G k g ρ, = ν t () ρσ T [ ] 0.098R 5. e + Rk = 9 k fµ () f R k R t = 0.3e (3) y k = (4) ν l k Rt = (5) ν l ε Where ρ and ρ are the ar densty and the reference ar densty respectvely; r U s the mean velocty n the x drecton; P s the statc pressure; T and T r are the mean temperature and reference mean temperature; u u are the Reynolds stresses; u t' are the Reynolds heat fluxes; g s the component of the gravtaton vector; k s the turbulent knetc energy; ε s the dsspaton of turbulent knetc energy; ν l and ν t are the lamnar and turbulent vscosty respectvely; σ k =. 0, σ ε =. and σ T = 0. 9 are the dffuson coeffcents of the turbulent knetc energy, ts dsspaton and the temperature respectvely; P s the stress producton of turbulent knetc energy; k G s the buoyancy k producton of turbulent knetc energy; C µ = 0. 09, C ε =. 44, C ε =. 9 and C 3 ε = 0. 0 (or.0 f G k > 0 ) are turbulent model constants; f s a functon used to modfed the model constant C ; y s the dstance to the nearest wall. ε, 5

16 Buchanan and Sherman (000) showed that n all realstc cases of ar nfltraton through an nsulated wall, the ar and nsulaton temperatures can be assumed to be n local equlbrum. As a consequence, the temperatures of ar and nsulaton are not solved separately n the present calculatons and the nsulaton s treated as a homogeneous porous medum. The ar flow calculatons are based on the standard Darcy law. The set of equatons for the nsulated regons s the followng: Contnuty ( ρ ) 0 (6) U =, Momentum ρν l U = P (7), K Energy U T, ( λeffectvet, ), = (8) where K s the medum s permeablty (0-8 m ) and λ effectve s the effectve medum s conductvty based on the sold medum s conductvty (0.04 W/mK) and the medum s porosty (0.99). STAR-CD allows the possblty to take the turbulence effect nto account on the heat calculatons at the nterface ar/porous medum. Tests showed that ths effect s neglgble n the present study because of the small sze of the wall cracks. 6

17 4. CFD smulatons CFD smulatons were performed wth the commercal code STAR-CD, for each of the sx wall confguratons, for both nfltratng and exfltratng flows, and for a range of ar flows and pressure dfferences. The buldng control volume shown n Fgure (made up of one nfltratng and one exfltratng wall) s never smulated n a sngle CFD run, rather the total heat load on t s determned by combnng the results of smulatons performed for sngle walls. For a heated house n a cold envronment, there wll be a thermal boundary layer of warm ar rsng on the outdoor surfaces of the walls. Sherman and Walker (00) descrbed the possble predomnant role of such ar boundary layers (along the faces of the wall) n the heat recovery process. Ths layer, they ponted out, would contrbute to the nfltratng ar flow enterng through the cracks, reducng nfltraton heat load. The cool ar emergng on the ndoor sde of the wall wll be entraned n the downward movng cool boundary layer, and thus reduce conducton heat loss from wall surface. H o Outlet T cold T hot T hot T cold H Inlet Inlet Outlet L left L wall L rght Infltratng Wall Fgure 5: Inlet/outlet locatons. Exfltratng Wall To examne ths effect, two dfferent problems are studed. The frst case s wth no boundary layers n whch a sngle wall s modeled wth temperatures mposed drectly on ts surfaces (no flm resstance was appled to represent the boundary layer resstance). The second case adds the external boundary layers to the smulaton. Fgure 5 llustrates the extenson of the computatonal doman, one on each sde of the wall, and shows the 7

18 nlet/outlet locaton for both the nfltratng and exfltratng walls and for the computatonal space boundary. Ths computaton of external flow feld s lmted to dmensons presented n Table referrng to Fgure 5. These addtonal spaces (referred to as cavty n the next sectons) are large enough that the boundary layer flows on the wall faces are largely unaffected by the CFD computatonal space boundares, and small enough that the ncrease n CFD computatonal tme s acceptable. The mass flow of ar through the walls s controlled by pressure dfferentals between the nlet and outlet boundares of the CFD computaton space. A postve pressure s created at the nlet and the outlet pressure s set to zero. Inlet and outlet boundares are located at the faces of the external wall crack for the no boundary layer (NB) case. For the boundary layer (B) case, the left and rght cavty szes and nlet/outlet szes and locatons have all been optmzed by performng successve smulatons to fulfll the followng goals: The man goal s to assure the formaton of an unperturbed ascendng or descendng ar boundary layer on the wall. Cavty szes were ncreased suffcently to avod the ar flows at the nlet and the outlet of the computatonal doman from dsturbng the boundary layers formed on the wall surfaces. Ths was partcularly true of the nlet sde, snce a et forms from the ncomng ar and sgnfcantly modfes the boundary layer. The nlet sze was also ncreased to reduce the velocty of ar enterng the external cavty through the nlet, to reduce the dsturbance of the wall boundary layers. Ths ncrease n nlet sze was lmted by the formaton of two-way flows at the CFD boundary, f the nlet became too large. The calculatons were found to dverge for small outlet cavtes (case of the nfltratng wall) because the pressure cannot be controlled and ncreases n the outlet cavty as the smulaton progresses. As a remedy, cavty sze was ncreased and the outlet locaton was modfed to allow an easer ar ext. Ths elmnated the dvergence problem. Table summarzes the geometres we found to optmze the CFD code performance. The slght dfference between the nlet/outlet heghts wthn columns H and Ho arses from a small dfference n the mesh spacng. Table : External Cavty characterstcs for the boundary layer cases. L left L rght H (m) H o (m) ST L wall L wall LH / HL 7 L wall 3 L wall

19 Table summarzes the cases studed to examne the effects of the boundary layer. Converged computatons for a total of 9 confguratons are reported ncludng all nsulated wall confguratons. Only a lmted number of smulatons for empty wall confguratons are reported. We present results for No Boundary layer (NB) cases and a few results for cases ncludng the boundary layers (B). All NB confguratons have the same set of pressure dfferentals across the wall (noted as P n Tables and 3). Fewer smulatons are reported for the confguraton wth boundary layer (B) because of lmtatons mposed by convergence nstablty and needs for large amounts of smulaton tme. Table : Summary of confguratons smulated to nvestgate boundary layer effects. ST LH HL NB I P P P P P P E P P P P P P B I P P3 P4 P4 P5 P5 E P Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, E: Empty wall, ST: Straght Through crack, LH: Low/Hgh crack, HL: Hgh/Low crack, : ltratng wall, : ltratng wall, and P (=,, 6): Pressure dfferental mposed across wall cracks (see Table 3 for values). Table 3: Pressure gradents (Pa) between wall cracks ndcated n Table. P P P3 P4 P5 P Determnaton of the conducton heat flux wthout nfltraton The IHR calculaton requres the evaluaton of the conducton heat flux when there s no nfltraton ar flow through the wall, and only natural convecton ar flows nduced by the temperature gradent wthn the studed doman are taken nto account. In the absence of any nfltraton, heat transfer across the wall, commonly treated as pure conducton, actually ncludes the effects of convectve ar currents set up nsde the wall cavty. To evaluate ths zero nfltraton heat flux the nlet/outlet boundares were replaced by sold walls. As an llustratve example, Fgure 6 presents the temperature, velocty and pressure felds near the exteror and n the nteror of an Insulated wall confguraton, for zero nfltraton. 9

20 B A L left L wall L rght Temperature (K) B-I-zero-nf Velocty Magntude (m/s) B-I-zero-nf Relatve Pressure (Pa) NB-I-zero-nf Fgure 6: Temperature, velocty and pressure felds for zero nfltraton near the exteror and n the nteror of an nsulated wall. 0

21 The temperature feld shows a quas-unform temperature n the two cavtes wth a small gradent due to the change n elevaton. The boundary layer effects can be seen close to the sold wall boundares, sotherms are not exactly vertcal contrary to the case wth mposed temperature at the wall external faces. Our goal was that the boundary layers on the vertcal boundares of the computatonal doman must not nterfere wth the boundary layers on the exteror of the wall secton. The velocty feld clearly llustrates that we have met our goal. The external ar boundary layers on the wall surfaces are well developed, the boundary layers start wth a zero velocty magntude at the left cavty s bottom rght hand corner (zone A n Fgure 6) and reach a maxmum velocty of 0. m/s. Note that, as we ntended, the ar flow comng from the opposte walls at the left cavty s bottom left hand corner (zone B n Fgure 6) does not perturb the ar boundary layer. Smlar observatons can be made for rght cavty s ar flow. The last llustraton n Fgure 6 shows the vertcal pressure gradent n the wall due to buoyancy effects. Ths pressure gradent between the two cracks for the low/hgh (LH) and hgh/low (HL) confguratons exsts even f there s no mposed ar flow. When examnng IHR as a functon of pressure dfference across the leaks, a pressure shft equal to ths pure conducton pressure gradent wll be subtracted so the pressure dfference s ust the forced convecton pressure dfference.

22 4.. Calculaton relablty 4... Smulaton convergence The boundary layer (B) and non-boundary layer (NB) confguratons were studed as two dfferent problems. It was easer to acheve a good and quck convergence for the confguraton wthout boundary layers. It was possble to obtan resduals for all varables (velocty, pressure, turbulent knetc energy, turbulent energy dsspaton and temperature) lower than 0-6 n 0-0 mnutes usng one processor on a Slcon Graphcs Orgn 000 server (called LORAX n the rest of ths text), wth processors, 000 MB of RAM and a 00 GB external hard drve. Ths convergence level was not obtaned for one confguraton and one mposed pressure gradent: the NB-E-ST- at.0 Pa. Ths falure to converge s lnked to a physcal change of the ar flow at or near ths partcular pressure gradent. Ths s most lkely a case where no steady state stuaton exsts or there are multple stable solutons to the ar flow and heat transfer. Fgure 7 llustrates the ar flow structures and turbulence ntensty nsde an empty wall wth a straght-through crack as a functon of pressure gradent spannng ths poor convergence case. Ths fgure llustrates a central porton of the wall (rather than ts complete heght) n order to make t easer to see the ar flow structure. Note that color scale s not the same for every case, color s only used to dentfy the turbulent structures. In the zero nfltraton case (0.0 Pa), ar gets cold near the left face and descends whle t gets hot near the rght face and rses. As a consequence a clockwse loop s created. For low-pressure gradents (below.0 Pa), the loop s cut nto two clockwse loops and the turbulence n the regon near the crack s small compared to that n the loops. For pressure gradents closer to.0, calculaton convergence cannot be acheved. Tests show that ths nstablty occurs for pressure gradents between 0.8 and. Pa. We beleve that the cause of ths unstable ar flow les n the appearance of two new loops near to the crack. For pressure gradent of.0, the ar flow through the cracks s strong and cuts the thermal flow wthn the wall cavty n two regons. These two loops can also be seen at hgher pressure gradents. The confguraton wth boundary layers s much more dffcult to smulate because accountng for the external ar boundary layer makes the problem much more complex. Numerous geometrcal adustments (e.g. enlargng the left cavty or changng nlet/outlet szes and locatons) and calculaton methods (e.g. usng zero nfltraton converged soluton or prevous converged soluton for ntalzaton) were necessary to obtan results. It s dffcult to acheve a good convergence everywhere n the doman, partcularly n the center of the cavtes and at the nlet boundary regon. The method to assess a good convergence for ths confguraton was to look for and confrm well developed boundary layers n the near wall regons. The smulatons were also tme consumng and each took a mnmum of 4 hours usng one processor on LORAX. Good convergence was harder to acheve wth the lowest pressure gradents, and relablty of the results for low pressure gradents s worse than for hgher pressure gradents. Ths s because t s dffcult to model very small ar flows (low veloctes and low overall knetc energy), when much of the flow feld s close to resoluton lmt of the CFD code.

23 Crack centerlne 0.6 m 0.0 Pa 0. Pa 0.0 Pa 0.50 Pa. Pa.0 Pa Fgure 7: Turbulent structures n the wall cavty (NB-E-ST-). For clarty, only the central secton of the wall s shown enlarged IHR Error estmates Ths secton s dedcated to the evaluaton of uncertantes n predcted IHR values. Calculatons are based on the calculaton procedure used to calculate the IHR (equatons (5) and (6)) and on the uncertantes n the CFD modelng. Results show that IHR values can be obtaned wth reasonable accuracy (lower than 0%) only for Peclet numbers hgher than 0.. Error propagaton s used to combne random errors of CFD parameters to get an estmate for the total error. It s used n stuatons where one doesn t have the luxury or ablty to measure the same thng several tmes and thereby estmate the random error on one s fnal result drectly. 3

24 4 Error propagaton can also be used to combne several ndependent sources of random error on the same measurement. The random error calculaton prncples are the followng. Let f, g and h be three functons. Functon f s obtaned from functons g and h. Then the random error on f, f, s a functon of the random errors on g, g, and h, h, dependng on the functonal dependence of f on g and h as follows: h g f + = ( ) ( ) ( ) h g f + = (9) h g f = + = h h g g f f (30) ag f = g a f = (3) Applyng these rules to equatons (5) and (6), the random errors for the nfltratng and exfltratng walls are gven by: ( ) + + = m m Q Q m Q T T T IHR out n & & & m m Q Q m Q & & & (3) ( ) + + = m m Q Q m Q T T T IHR out n & & & m m Q Q m Q & & & (33) The man dffculty les n the determnaton of the random error for the varables evaluated by CFD calculatons. Precson of the results depends on the specfed varable. Fractonal uncertantes, ( f f ), are lower than: for temperature and conducton and for mass flow. Accuracy of the CFD results depends on a host of other feature of the smulaton, such as adequacy of the turbulence model, adequacy of grd geometry and so on. Lookng only at the CFD convergence error can not capture these errors from model msfts. Experment comparsons are necessary for good estmaton of errors from model msfts. Snce we do not have an estmate of error from model msft, we use the CFD convergence error as the mnmum estmate of error. Actual errors are probably several tmes larger.

25 Reasonable absolute uncertanty ( f ) estmaton based on typcal results s gven below: 3 - T = 5 0 K 6 - Q = Q0 = 5 0 W 4 - m & = 5 0 kg / s Fgure 8 presents the IHR random error for nfltratng confguratons as a functon of Peclet number. IHR Absolute Error NB-I-ST- NB-I-LH- NB-I-HL- B-I-ST- B-I-LH- B-I-HL Pe Fgure 8: Absolute random error as a functon of Peclet number. (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, ST: Straght Through crack, LH: Low/Hgh crack, HL: Hgh/Low crack, : ltratng wall.) The separaton n Fgure 8 between the curves for no boundary (NB) and boundary (B) cases s due to the change n wall conducton value. Because of the boundary layers, the wall conductance value n case B s lower than the no boundary (NB) one. Note that even f the random error decreases rapdly wth an ncrease of the Peclet number, uncertanty s very hgh for Peclet number lower than 0.. As an example, IHR uncertanty s 50% for Peclet number 0.0 and decreases to 0% for Peclet number 0.. Thus IHR values can be obtaned wth reasonable accuracy (0%) only for Peclet numbers hgher than 0.. 5

26 5. Results 5.. Insulated Wall 5... Straght Through crack NB-I-ST- NB-I-ST- B-I-ST- B-I-ST- 0.6 IHR Pe Fgure 9: IHR results for Insulated walls, wth Straght Through leaks (I-ST). (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, ST: Straght Through crack, : ltratng wall, : ltratng wall.) Fgure 9 shows all the CFD results for the straght through crack cases. The vertcal lnes ndcate the uncertanty lmts dscussed earler. Ponts wth no vsble lnes mean that the uncertanty lmts are smaller than the sze of the ponts used n the fgure. IHR values ncrease towards 0.5 as Peclet number decreases. Ths s consstent wth the lmtng value of 0.5 for low-peclet numbers as suggested from the analytcal approach of Sherman and Walker (00). At a gven Peclet number, the IHR values are hgher for the nfltratng wall than for the exfltratng wall. Ths tendency s observed for all walls wth no boundary layers (NB). Results for the walls wth boundary layers (referred to n the rest of the text as the boundary layers (B) case) follow the same trends. IHR values are larger by about 0. than for the no boundary layers case (NB). Ths shows that the effect of the external ar boundary layer on the IHR s sgnfcant. For the nfltratng wall (gven the nsde warm and the outsde cold), the added heat recovery s the result of the ar enterng the wall from the outdoor warm boundary layer, whch s at a hgher temperature than the cold ambent ar. On the room sde, the cooler ar enterng through the leak enters the ndoor 6

27 cool boundary layer and acts to reduce conducton losses through the wall. The same effects also occur for the exfltratng wall. The CFD code encountered a convergence problem for the B-I-ST- confguraton at hgh-peclet number (for Peclet number close to 3). Addtonal smulatons were conducted to address ths problem: calculatons were performed usng more teratons, convergence crtera were tghtened and pressure boundary condtons were replaced by velocty boundary condtons to avod two-way flows at the doman boundares. None of these modfcatons were able to address the convergence problem for ths case at hgh Peclet numbers Low/Hgh and Hgh/Low cracks NB-I-LH- NB-I-LH- B-I-LH- B-I-LH- 0.6 IHR Pe Fgure 0: IHR results for Insulated walls and ar flowng from Low to Hgh leaks (I-LH). (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, LH: Low/Hgh crack, : ltratng wall, : ltratng wall.) The results for these geometres are shown n Fgure 0, together wth vertcal lnes showng the uncertanty estmates. As for the straght through case, IHR values for nfltratng wall are hgher than those for exfltratng wall and the dfference remans about the same for the entre Peclet number range. Also, as n the prevous case, results are consstent wth a lmt value of 0.5 for low-peclet number. Predcted errors are hgher than for the straght through (ST) confguraton. The hgh flow resstance of the longer ar flow path lengths for these cases leads to very low nfltrated ar mass flux. 7

28 Results for the boundary case (B) follow the same trend, wth IHR values about 0. hgher than for the no boundary case (NB). Values have more scatter for low-peclet number but are close to 0.5. Convergence problems appeared for the boundary case (B) at the hghest Peclet numbers as they dd for the straght through confguraton (ST). Fgure presents the results for NB-HL confguraton that are very smlar to the NB-LH confguraton. IHR results for NB-I-HL- and B-I-HL confguratons are greater than the theoretcal maxmum 0.5 for low-peclet numbers. At these low-peclet number the estmated mnmum errors encompass a range ncludng the theoretcal 0.5 lmt for IHR. However, the data show dstnct trends to IHR hgher than 0.5 rather than havng more scatter ndcatve of randomness. These trends therefore ndcate some sort of addtonal systematc uncertanty n the CFD results NB-I-HL- NB-I-HL- B-I-HL- B-I-HL- 0.6 IHR Pe Fgure : IHR results for Insulated walls and ar flowng from Hgh to Low leaks (I-HL). (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, HL: Hgh/Low crack, : ltratng wall, : ltratng wall.) 5.. Empty Walls IHR results for an empty wall presented below are for no boundary cases (NB), except for the straght through confguraton (ST) where approxmated values based on not-fully-converged computatons are shown for boundary case (B). 8

29 5... Straght Through crack Because of the low flow resstance of straght through cracks, the applcaton of typcal nfltraton pressure dfferences leads to hgh Peclet numbers and correspondngly low IHR. Fgure llustrates that IHR values for nfltratng wall are hgher than for exfltratng wall. Converged solutons could not be found for all cases of NB confguraton. At lower Peclet numbers for the nfltratng wall we found that two-way flows appeared at the cracks and IHR values for Peclet number lower than 0.5 could not be obtaned due to nstablty n the CFD calculatons. Good convergence was reached for the exfltratng case for the full range of Peclet number values. Smulatons for the boundary layer (B) case also showed two-way flows at the cracks for Peclet number close to 0.5. Because of these nstabltes and lmted tme, only three IHR results are avalable. Note that the presence of the boundary layers has an effect on IHR smlar to that for the nsulated confguraton: about a 0. ncrease n IHR value wth the external ar boundary layer (B) taken nto account, compared to the NB cases NB-E-ST- NB-E-ST- B-E-ST IHR Pe Fgure : IHR results for Empty walls for Straght Through leaks (E-ST). (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, E: Empty wall, ST: Straght Through crack, : ltratng wall, : ltratng wall.) 9

30 5... Low/Hgh and Hgh/Low Cracks NB-E-LH- NB-E-LH- NB-E-HL- NB-E-HL- 0.6 IHR Pe Fgure 3: IHR results for Empty walls for Low-Hgh and Hgh-Low leaks (E-LH & E-HL). (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), E: Empty wall, LH: Low/Hgh crack, HL: Hgh/Low crack, : ltratng wall, : ltratng wall.) Results for empty walls wth Peclet number hgher than one, present the same trend for both nfltratng and exfltratng walls and low/hgh (LH) and hgh/low (HL) confguratons. As expected, the IHR values are hgher than those for straght through confguraton (ST) lke those for nsulated walls. Also, as expected, overall the IHR values for empty walls are slghtly lower than correspondng values for nsulated walls. 30

31 5.3. Concluson and future developments Buchanan and Sherman (000) concluded that the nteror detals of the wall encountered n the leakage path (.e. nsulated or empty walls) do not have a great effect on the heat recovery f external boundary layers are gnored. The overall crack geometry (.e. straght through (ST) or low/hgh (LH) and hgh/low (HL) confguratons) s the key factor. Ths study confrms ther observatons and shows the mportant effect of the external boundary layers on conducton and nfltraton heat loads. Comparson between no boundary (NB) and boundary (B) confguratons shows that the effect of the boundary layers on the heat recovery s very mportant (t typcally ncreases IHR by 0.). Note that ths effect s hgher for the ST confguraton than for the low/hgh (LH) and hgh/low (HL) confguratons. In the low/hgh (LH) and hgh/low (HL) confguratons, the ar temperature at the outlet crack s close to the ar boundary layer temperature because the transt tme of ar nsde the wall s long. As a consequence, the leakng ar does not substantally change the boundary layer temperature. Even f the effect of the ntermxng between the external boundary layers and the nfltratng ar s ust located on the half of the wall heght for the straght through confguraton (ST), the temperature dfference s hgher and thus ts effect becomes predomnant. The Smplfed Infltraton Heat Recovery Model (proposed by Sherman and Walker 00) should be modfed to take ths effect nto account at least for the straght through confguraton (ST). Ths study covered a large range of mportant factors, nevertheless addtonal work s requred to develop a better understandng of IHR: - Some CFD results have to be recalculated. Ths ncludes all results that do not follow the trends observed n other data:.e., the last ponts of the B-I-LH and B-I-HL confguratons. Convergence crtera may have to be tghtened for these cases or usng mposed mass flux as boundary condtons nstead of mposed pressure may correct ths problem. - The present database has to be completed. Addtonal smulatons are necessary for the B-I-LH/HL confguraton (hgher Peclet number) and the Empty wall confguraton (lower Peclet number) to fll the Peclet number range. B-E confguraton remans to be studed. - External ar boundary layer effect can be examned for the straght through confguraton (ST) by preventng the spread of nfltrated ar nsde the entre wall. Ths can be accomplshed by lnng the crack and the wall-passage wth adabatc surfaces to connect the crack. - Horzontal flow confguratons (.e. floor and celng) have to be studed. These addtonal smulatons can be performed wth the exstng STAR-CD geometry and models. There s no need to create new meshes (except for the horzontal confguratons). 3

32 6. Illustratve Applcatons Ths secton descrbes how to apply the prevous results to evaluate the Infltraton Heat Recovery effect for a partcular buldng (a detaled example s gven n Appendx ). We llustrate ths wth two cases, where nfltraton s caused by external wnd ncdent normal to one wall of a square buldng. The frst case s the smplest way of representng ar leaks n one buldng and has only one nfltratng and one exfltratng wall. The second case s a lttle more realstc, wth partcpaton from all four walls. However, no ar leaks are consdered through the roof and floor for both cases. The studed buldng has a square footprnt, and all four vertcal walls have the same area and crack confguratons. In both cases, wnd pressure s assumed unform over any gven wall. 6.. Combnng One Infltratng and One Exfltratng Wall to Obtan a whole buldng IRH value Fgure 4 presents a plan vew of the frst case. Outdoor ar enters the buldng through the upwnd wall (wall ) and leaves t by the opposte wall (wall ). Infltratng and exfltratng ar mass fluxes are equal. Wnd Wall Wall Fgure 4: Case plan vew. For one nfltratng and one exfltratng walls equaton (9) leads to: IHR Buldng = IHR + IHR (34) Buldng where IHR, IHR and IHR are the nfltraton heat recovery factors for nfltratng and exfltratng walls and buldng. Snce the two walls are otherwse dentcal (area, nsulaton propertes and nsulaton thckness), the nfltratng and exfltratng flow wll have dentcal Peclet numbers. IHR for a buldng at a fxed Peclet number s then the drect summaton of IHR for nfltratng and exfltratng walls at the same Peclet number. 3

33 The IHR values for a whole buldng are calculated by combnng the heat flows for an nfltratng and exfltratng walls. The followng secton summarzes trends n IHR values as functons of Peclet number, nfltrated ar mass flux, and pressure dfference across the wall. Only relable IHR values are presented, others, whch wll need further nvestgaton, are excluded from plots for clarty IHR as a functon of Peclet number Buchanan and Sherman (00) showed that Peclet number as defned by equaton (7) s a useful ndependent varable to present IHR results because t collapses the data showng the unversal trends. Whatever the wall type (nsulated or empty), the results show that low/hgh (LH) and hgh/low (HL) values are smlar whch ndcates that the problem s symmetrc. For Peclet number hgher than 0., IHR values are hgher for LH/HL confguraton than for straght through (ST) one. IHR values for straght through (ST) confguraton decrease faster than those for low/hgh (LH) and hgh/low (HL) confguraton wth ncreasng Peclet numbers. IHR Typcal buldng range NB-I-ST NB-I-LH NB-I-HL B-I-ST B-I-LH B-I-HL NB-E-ST NB-E-LH NB-E-HL Pe Fgure 5: IHR as a functon of Peclet number. (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, E: Empty wall, ST: Straght Through crack, LH: Low/Hgh crack, HL: Hgh/Low crack.) Note that for the no boundary cases (NB), trends for nsulated and empty walls look smlar. The NB-I-LH/NB-I-HL and NB-E-LH/NB-E-HL curves are smlar and the 33

34 empty wall results appear to be an extenson of the nsulated wall results for hgher Peclet number. For vertcal walls, IHR occurs not only va the drect heat exchange between the leakng ar-stream and conductng nsulaton wthn the wall, but also sgnfcantly va the partcpaton of boundary layers on the outdoor and ndoor wall surfaces n the nfltraton or exfltraton. In Fgure 5, the IHR values for boundary layer cases seem to follow a sngle curve, ndependent of crack locatons (.e., at extremes of the wall or straght through). The IHR values for straght through cracks appear as a contnuaton of the low/hgh leakage results ust at hgher Peclet number IHR as a functon of nfltrated ar mass flux For almost all buldng engneers, the Peclet number of a buldng wall s somewhat non-ntutve concept. So, we present our IHR results n more famlar terms. Fgure 6 shows IHR results as a functon of ar mass flux (kg/s per meter of wall length). Common values for ar mass flux range from to 0.00 kg/s.m. Trends dsplayed n Fgure 6 appear smlar to those n Fgure 5, for dependence of IHR results on the Peclet number. The dfference between IHR results for NB-I-LH/HL and B-I-LH/HL s slghtly smaller than n the prevous graph, and the empty cavty results are shfted away from those for nsulated walls due to the hgher mass fluxes n the former.. IHR Typcal buldng range NB-I-ST NB-I-LH NB-I-HL B-I-ST B-I-LH B-I-HL NB-E-ST NB-E-LH NB-E-HL Mass Flux per m-wall (kg/s) Fgure 6: IHR as a functon of nfltrated ar mass flux per meter of wall. (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, E: Empty wall, ST: Straght Through crack, LH: Low/Hgh crack, HL: Hgh/Low crack.) 34

35 6..3. IHR as a functon of pressure dfference across the wall We now examne IHR values as a functon of pressure dfference across the wall. Ths has the advantage of vewng results for the same envronmental condtons (wnd and stack nduced pressures). Typcal ndoor/outdoor pressure dfferences for resdental buldngs are wthn the range 0. 0 Pa. The results shown n Fgure 7 show that IHR values for low/hgh (LH) and hgh/low (HL) confguratons are always greater than the ST confguraton. Consderng a typcal pressure dfference for a buldng for the no boundary layer (NB) case: IHR effect s zero for E-ST confguraton, wthn for I-ST, between for E- LH/HL, and has ts hghest values for the I-LH/HL ( ). Infltraton heat recovery s most sgnfcant for nsulated walls wth long ar flow path lengths (I-LH/HL walls) wthn the walls. As n the prevous dscussons, the external ar boundary layer effect s more mportant for the I-ST than for I-LH/HL, and IHR values ncrease when external boundary layer effects are taken nto account. IHR values reach 0.6 for I-ST and.0 for I- LH/HL. IHR Typcal buldng range NB-I-ST NB-I-LH NB-I-HL B-I-ST B-I-LH B-I-HL NB-E-ST NB-E-LH NB-E-HL Pressure dfference across the wall (Pa) Fgure 7: IHR as a functon of pressure dfference across the wall. (Notes: NB: No ar Boundary layers (temperature mposed drectly on wall surfaces), B: ar Boundary layers are ncluded n the smulaton, I: Insulated wall, E: Empty wall, ST: Straght Through crack, LH: Low/Hgh crack, HL: Hgh/Low crack.) 35