A BESTEST VALIDATION STUDY OF THE DYNAMIC GROUND-COUPLED HEAT TRANSFER MODEL USED IN ACCURATE Dng Chen CSIRO Energy Transfrmed Flagshp and CSIRO Ecsystem Scences PO Bx 56, Hghett. Vc. 390, Australa ABSTRACT Ths paper presents the grund effectve slab mdel used n AccuRate s smulatn engne fr huse energy star ratng n Australa. By cmparng AccuRate s predctns wth the results reprted n the IEA BESTEST, t s demnstrated that fr unnsulated slab-n-grund buldngs, AccuRate s grund mdel perfrms satsfactry cnsderng the balance between calculatn speed and accuracy. Ptental mprvement n AccuRate s grund mdel has als been recmmended fr further develpment. INTRODUCTION Grund-cupled heat transfer (GCHT) can cntrbute up t arund 50% f annual buldng heatng lads (Neymark et al., 2008). Despte ts sgnfcance n energy effcent buldng desgns, rapd and relable calculatn f GCHT remans a challenge fr the buldng smulatn cmmunty. Dfferences n GCHT calculatns arund 50% r hgher were reprted amng varus smulatn tls fr unnsulated slab-n-grund cnstructns (Neymark et al., 2008). The dffculty n GCHT calculatn s manly due t the lack f straghtfrward mathematcal expressns fr the three dmensnal (3D) transent grundcupled heat transfer. S far, the nly avalable 3D analytcal expressn s the steady state GCHT slutn fr a rectangular slab derved by Delsante et al. (983). Ths analytcal expressn currently prvdes the mathematcal truth standard n the Internatnal Energy Agency (IEA) Buldng Energy Smulatn Test (BESTEST) fr grund-cupled heat transfer (Neymark et al., 2008). Ideally, a cmparable analytcal 3D transent heat transfer slutn wuld clse the GCHT prblem fr ths smplest flr gemetry. Hwever, as mentned n the BESTEST reprt, such an analytcal 3D transent slutn wuld be dffcult, f nt mpssble, t derve (Neymark et al., 2008). Ths paper descrbes the frst tme n an pen lterature the grund effectve slab mdel fr the smulatn engne n AccuRate, whch s the benchmark sftware fr Natnwde Huse Energy Ratng Scheme (NatHERS) used n Australa (Delsante, 2005). The mdel was develped by Dr Delsante based n apprxmate 3D expressns cnstructed frm 2D analytcal slutns. In ths paper, the accuracy f the mdel was nvestgated usng the relevant IEA BESTEST cases. It was demnstrated that the mdel gves satsfactry steady state, transent hurly and annual heat transfer, and phase shft results. The grund effectve slab mdel prvdes a methd fr rapd dynamc GCHT calculatns. APPROXIMATE 3D EXPRESSIONS Fgure schematcally shws a tw-dmensnal (2D) slab wth wdth B n a sem-nfnte grund. By assumng the same thermal prpertes fr the slab and the sl, and lnear temperature dstrbutn alng the wall/grund nterface, Delsante et al. (983) derved an analytcal slutn fr the transent grund-cupled heat transfer wth perdc ndr and utdr temperatures at an angular frequency (/s): where 2D K K K kalbt 2 D 2Lk T T aw aw K3aW ab K3aB ab W K3aB W expjt / 4 () s the nterr grund-cupled 2D transent heat flw (W); k the thermal cnductvty (W/mK) f the grund and L the length perpendcular t the slab wdth (m) and W the wall thckness (m). a j / / 2 and j =, s the grund thermal dffusvty (m 2 /s) and t the tme (s). K and K 3 are the repeated ntegrals f the mdfed Bessel functn K 0. T and T are the ndr and utdr temperature ampltudes (C) respectvely. Bth T and T may nclude a cmplex phase term exp(j) t accunt fr the phase shft relatve t a specfed ntal start tme. - 595 -
Delsante et al. (983) als btaned a steady state 2D heat transfer expressn frm Equatn () by lettng 0: 2kL T T 2D B B W ln ln W W B (2) Daves (993) bserved that Equatn (2) s unsymmetrcal fr L and B snce t s tw dmensnal. Fr a rectangular slab f L B, wth the argument fr symmetry between L and B, Daves (993) cnstructed an apprxmate 3D steady state heat transfer expressn by replacng L wth (L+B) and B wth a characterstcs length LB / L B n Equatn (2). Mre generally, we may replace LB wth the flr area A, 2(L+B) by the flr permeter P, and B by a characterstc length 2A/P. Nw Equatn (2) becmes kp T T x x ln x 3D ln / (3) Here, 3D s the apprxmate 3D steady state heat transfer va the nterr grund surface; x 2 A/ WP. Results presented n Daves (993) shwed that Equatn (3) gves a maxmum errr f - 2% fr a wde range f flr dmensns n cmparsn wth the exact 3D steady state slutn f Delsante et al. (983), whch s a 7-term expressn. Usng the same argument fr symmetry between L and B, Delsante (202) cnstructed an apprxmate 3D transent GCHT expressn frm Equatn () by replacng 2L wth permeter P, and B by a characterstc length 2A/P,.e.: (3). Fr the 2D case, Equatn (4) reduces t the exact 2D transent slutn f Equatn (). GROUND EFFECTIVE SLAB MODEL Delsante (990) shwed that an expressn lke Equatn (4) can be used n buldng smulatn tls based n a frequency respnse factr methd. Fr a hmgeneus D slab f fnte thckness, the heat transfer fr perdc ndr and utdr temperatures can be descrbed as T q S S 2 T (6) S 2 S 22 q where q and q are the ampltudes f heat flws per unt area fr nterr and exterr slab surfaces respectvely. Frm Equatn (6), we have: T S T q (7) S 2 Fr buldng smulatn tls, t s desrable that the grund be represented by a D grund effectve slab (smplfed as GRES hereafter), whch allws the GCHT t be calculated by Equatn (6). By cmparng Equatn (7) wth Equatn (4), Delsante (990) fund that G S aa / P (8) S A / kp G 2 If the ndr ar flm resstances R s cnsdered, the fllwng equatns can be used t btan the grund-cupled heat transfer fr a harmnc frequency f : 3D kgpt T kaat expjt (4) T q S S 2 R T (9) S 2 S 22 0 q where Here, G aw K K K / 4 K aw K aw 2 Aa / P K32Aa / P a2 A/ P W a2 A/ P W 3 3 D 3 (5) s the apprxmate grund-cupled 3D transent heat flw (W). It can be shwn that when appraches 0, Equatn (4) reduces t the apprxmate 3D steady state heat transfer Equatn and S T T q (0) S R S Equatn (9) and the crrespndng 3D steady state cmpnent,.e., Equatn (3), have been mplemented n AccuRate s smulatn engne snce 994. In the AccuRate smulatn engne, the frequency respnse f a buldng s frst calculated ver a range f frequences. The respnse t a transent pulse s then derved frm the frequency respnses va lnear system thery (Walsh and Delsante, 983). In the exstng AccuRate engne, 2-596 -
frequency respnses at 59 frequences, gven by n39/ 2 2 / 24 2 (n =,2,,59) radans per hur are evaluated. Fr resdental buldngs, an hurly smulatn usng AccuRate ver ne year perd nrmally takes less than ne mnute. It s nted that the exstng AccuRate engne mplementatn des nt nclude the external ar flm resstance as S 2 and S 22 cannt be btaned frm Equatn (4) alne. An mprved versn f the GRES mdel whch can accunt fr the external ar flm resstance has recently been develped. The calculatns f S 2 and S 22 and the mplementatn methdlgy n buldng smulatn tls fr ths mprved GRES mdel are detaled n Chen (203). In the next sectn, the accuracy f the AccuRate GRES mdel s nvestgated usng IEA BESTEST fr grund cupled heat transfer (Neymark et al., 2008). Fr the a -seres test cases, the temperature bundary cndtns are appled drectly t the grund and the nterr slab surfaces. The b -seres test cases apply ar flm resstances t bth nterr slab and exterr grund surfaces, whle the c seres test cases were desgned wth ar flm resstance appled n the nterr surface nly. Further, c seres test cases have relatvely small far feld bundary dstances,.e., small F values (refer t Fgures and 2 fr the defntn f F). In ths study, all the a -seres and b -seres test cases, and ne c -seres test case were used fr valdatng AccuRate GRES mdel. Table brefs the descrptns and man parameters fr the 3 test cases. Fr all the steady state test cases, the nterr and exterr temperatures are mantaned at 30C and 0C respectvely. The hurly GCHT fr the steady state cases was btaned wth AccuRate smulatn at the end f th year when t appraches steady state. Fr test cases wth harmnc varatn n the exterr temperature, the nterr temperature s mantaned at 30C whle the exterr temperature s descrbed by the fllwng equatn (Neymark et al., 2008): (a) 2 IDay 5 T 0 6cs 365 2 IHur 4 2cs 24 () Here IDay s the day cunter frm t 365; IHur s the daly hur cunter frm t 24 wth reset t after end f a day. The hurly GCHT fr a year were btaned frm the utput f AccuRate smulatn at the th year after t appraches perdc steady state. (b) Fgure Schematc vew f a tw-dmensnal slabn-grund cnstructn wth a sem-nfnte grund: (a) Temperature ampltude dstrbutns alng the grund surface; (b) Elevatn vew. BESTEST VALIDATION STUDY IEA BESTEST Cases The IEA BESTEST fr GCHT ncludes three a - seres, nne b -seres and fve c seres test cases (Neymark et al., 2008). Results frm any GCHT mdel can be cmpared wth mathematcal truth standard based n the analytcal slutn (fr Case GC0a nly see belw) by Delsante et al. (983) and secndary mathematcal truth standard based n verfed 3D numercal mdel results. In the IEA BESTEST reprt, verfed numercal mdels fr the relevant test cases nclude TRNSYS, FLUENT and METLAB (Neymark et al., 2008). (a) (b) - 597 -
Fgure 2 Schematc vew f a three-dmensnal slabn-grund used n IEA BESTEST (Neymark et al., 2008): (a) Plan Vew; (b) Elevatn vew (E s the deep grund depth and F s the far feld bundary) Case GC0a s a 3D steady state test case fr a rectangular slab n a sem-nfnte grund cnfguratn wth lnear temperature dstrbutn alng the wall/grund nterface. The GCHT result fr Case GC0a can be cmpared aganst the 3D analytcal slutn by Delsante et al. (983). Case GC30a s als a steady state test case wth the same slab-n-grund cnfguratn as Case GC0a, except that: ) the wall/grund nterface s adabatc; ) 30 m deep grund has a unfrm temperature at 0C whch s the annual average ambent temperature; ) far feld grund 20 m away frm the external wall surface has an adabatc bundary cndtn. The rectangular slab gemetry fr Case GC30a s schematcally shwn n Fgure 2. Case GC40a s exactly the same as Case GC30a except that the exterr grund surface temperature s perdc as defned by Equatn (). Fr all the cases lsted n Table, the grund was assumed t have a unfrm thermal cnductvty f.9 W/mK, densty f 490 kg/m 3 and specfc heat at 800 J/m 3 except Case GC80b whch has a thermal cnductvty f 0.5 W/mK. Detaled descrptns f the test cases can be fund n the IEA BESTEST dcument (Neymark et al., 2008). Cmparsns f GCHT Results Table 2 cmpares the predcted grund-cupled steady state heat transfer and steady perdc annual heat transfer results frm the AccuRate GRES mdel and thse reprted n the IEA BESTEST frm analytcal slutn by Delsante et al. (983) and verfed 3D numercal mdels (Neymark et al., 2008). It was fund that AccuRate GRES mdel gves predcted flr heat transfer wthn % frm the analytcal slutn and the averages f verfed numercal mdel results except test cases GC50b and GC55b. Fr all the test cases lsted n Table except test Case GC0a, unfrm temperature f 0 C s appled at the deep grund bundary. Due t the relatvely shallw deep grund depth fr Case GC50b (large flr area) and Case GC55b (shallw deep grund depth), there are substantal cre heat transfer drectly nt the deep grund frm these tw cases. The analytcal slutn presented n ths study assumes a sem-nfnte grund and thus cannt be used fr GCHT calculatn fr Cases GC50b and GC55b. Therefre, Case GC50b and Case GC55b were excluded n the remanng valdatn study n ths paper. It shuld als be nted that all the cases n Table except Case GC0a assume adabatc bundary cndtn at the wall/grund nterface. Hagentft (996) shwed that fr nrmal buldng dmensns, the apprxmatn f adabatc walls gves a 5-0% hgher heat lss than gven by a lnear temperature drp under the walls. Cnsequently, these tw dfferences n the mdel assumptns explan that n general, the estmated heat transfer frm the AccuRate GRES mdel were slghtly lwer than the averages f the verfed numercal mdel results fr cases wth n r very small ar flm resstances,.e., Cases GC30a, GC30b, GC40a, GC40b, GC45b and GC80b. When there are realstc ar flm resstances appled n the grund surfaces,.e., Cases GC40c, GC60b, GC65b and GC70b, the GRES mdel slghtly verpredcts the grund-cupled heat transfer. The reasn s that the GRES mdel des nt accunt fr the varyng heat transfer rate and mplctly assumes unfrm heat transfer rate alng the grund surface by usng Equatn (6) r (9). Ths s nt an ssue when the grund surface temperatures are knwn and are drectly used n calculatng the grund-cupled heat transfer snce Equatn (6) tgether wth Equatn (8) are exact representatns f Equatn (4). Equatn (3) s als the drect representatn fr the steady state heat transfer calculatn. Hwever, ths treatment can reduce the calculatn accuracy when there are realstc ar flm resstances abve the grund surfaces. Due t the shrt path, the grundcupled heat transfer rate near the wall edges s relatvely hgh r the lcal thermal resstance f the grund s relatvely small. The ar flm resstance reduces heat transfer mre effectvely at lcatns near the wall edges than thse away frm the walls. The net mpact f gnrng the lcal heat transfer nn-unfrmty s an verestmatn f the ttal GCHT. Ths s als demnstrated by the peak-hur heat transfer results n Table 3 fr Case GC70b whch has realstc ar flm resstances n bth the nterr and exterr grund surfaces. The GRES mdel verpredcts 2.2% n the peak hur heat transfer n cmparsn wth the verfed numercal mdels. It shuld be nted that the AccuRate GRES mdel des nt accunt fr the external ar flm resstance, whch can als cntrbutes t the GCHT ver-predctn fr Case 70b. Wth the same reasn, the GRES mdel ver-predcts slghtly fr Case GC40c. Fr all the ther test cases, the maxmum dfference n peakhur heat transfer between the GRES mdel and the verfed numercal mdels s -8.2% whch s manly caused by the dfferences n the steady state cmpnents due t bundary cndtn dfferences. Table 4 cmpares the phase shft results frm the AccuRate GRES mdel and the verfed numercal mdels fr harmnc temperature varatn test cases. The phase shft s defned as the dfference between the hur wth the cldest ambent temperature and the hur wth the hghest heatng lad. It was fund that the GRES mdel gves satsfactry phase shft predctns whch are wthn 7 days f thse - 598 -
predcted by the average f the verfed numercal mdels. Fgures 3 and 4 cmpare the hurly heat transfer results fr test Cases GC40a and GC40c respectvely. The hurly grund-cupled heat transfer results predcted by the GRES mdel are n satsfactry agreement wth thse by the verfed numercal mdels and le between the results by varus buldng smulatn tls. It was demnstrated that despte the defcences n the GRES mdel n terms f nt cnsderng external ar flm resstance and the mplct assumptn f unfrm heat transfer rate, the gd agreement fr the IEA BESTEST cases suggests that the AccuRate GRES mdel can prvde fast and satsfactry GCHT calculatns fr unnsulated slab-n-grund cnstructns. Further mprvement n the AccuRate GRES mdel s pssble by addressng these tw defcences. An mprved GRES mdel whch takes nt accunt the external ar flm resstance has been reprted n anther submssn (Chen, 203). CONCLUSION Ths paper presents AccuRate s grund effectve slab mdel fr GCHT calculatns fr unnsulated slabn-grund cnstructns. By cmparng predctns frm the AccuRate GRES mdel wth the results reprted n the IEA BESTEST, t was demnstrated that fr unnsulated slab-n-grund buldngs, the AccuRate GRES mdel perfrms satsfactry n the GCHT calculatns cnsderng the balance between calculatn speed and accuracy. Ptental mprvement n AccuRate s grund mdel was als dscussed fr future develpment. Dynamc calculatn fr nsulated slab-n-grund s mre challenge and future research s requred n analytcal slutns fr nsulated slab-n-grund. NOMENCLATURE a = j / / 2 A = flr area B = flr wdth E = deep grund bundary dstance F = far feld bundary dstance h = grund surface heat transfer ceffcent IDay = day cunter frm t 365 IHur = daly hur cunter frm t 24 k = thermal cnductvty f the grund L = buldng length P = flr permeter = steady-state heat flw q q t T T W = transent heat flw = ndr ampltude f heat flux = utdr ampltude f heat flux = tme = ndr temperature ampltude = utdr temperature ampltude = wall thckness 2 A / WP x = Symbls Subscrpts = angular frequency = grund thermal dffusvty = nterr = exterr ACKNOWLEDGEMENT The study was c-funded by Australan State and Terrtry gvernment, and the Department f Clmate Change and Energy Effcency, Australan Federal Gvernment. The authr wuld lke t thank Dr Angel Delsante s generus supprt and advce durng ths study. REFERENCES Delsante, A.E., Is the new generatn f buldng energy ratng sftware up t the task? - A revew f AccuRate. ABCB Cnference Buldng Australa s Future 2005, Surfers Paradse, Australa, -5 September 2005. Chen, D. Dynamc Three-Dmensnal Heat Transfer Calculatn fr Unnsulated Slab-n-grund Cnstructns, Energy and Buldngs, n prntng, 203. Daves, M.G. Heat lss frm a sld grund flr. Buldng and Envrnment 28 (993):347-359. Delsante, A.E., Stkes, A.N., Walsh, P.J. Applcatn f Furer Transfrms t Perdc Heat Flw nt the Grund under a Buldng, Internatnal Jurnal f Heat Mass Transfer 26() (983) 2-32. Delsante, A.E. A cmparsn between measured and calculated heat lsses thrugh a slab-n-grund flr, Buldng and Envrnment 25 (990) 25-3. Delsante, A.E. prvate cmmuncatn, 202. Hagentft, C.E. Heat lsses and temperature n the grund under a buldng wth and wthut grund water flw-i. Infnte grund water flw rate. Buldng and Envrnment 3() (996): 3-. Neymark, J., Judkff, R., Beauslel-Mrrsn, I., BenNakh, A., Crwley, M., Deru, M., Hennnger, R., Rbbernk, H., Thrntn, J., Wjsman, A., Wtte, M. Internatnal Energy Agency Buldng Energy Smulatn Test and Dagnstc Methd (IEA BESTEST) In-Depth Dagnstc Cases fr Grund Cupled Heat Transfer Related t Slab-n-Grade Cnstructn, NREL/TP-550-43388. Glden, Clrad, USA: Natnal Renewable Energy Labratry, 2008. Walsh, P.J., Delsante, A.E. Calculatn f the thermal behavur f mult-zne buldngs, Energy and Buldngs 5 (983) 23-242. - 599 -
Table Input parameters fr grund cuplng n-depth dagnstc test cases, adapted frm (Neymark et al., 2008) Case Descrptn Dynamc GC0a Analytcal Base Case GC30a GC30b GC40a GC40b Cmparatve Base Case fr a -seres Cmparatve Base Case fr b -seres Harmnc varatn Harmnc varatn Harmnc varatn Slab Dmen. (m m) h ** (W/m 2 K) steady 2 2 Drect temp* steady 2 2 Drect temp h ** (W/m 2 K) Drect temp Drect temp Grund Depth (m) Far-Feld Bundary (m) Cnd. (W/mK) Cmments nfnte nfnte.9 Lner temperature fr wall/grund nterface 30 20.9 Adabatc wall/grund nterface steady 2 2 00 00 5 5.9 harmnc 2 2 Drect Drect 30 20.9 temp temp harmnc 2 2 00 00 5 5.9 GC40c harmnc 2 2 7.95 Drect 5 8.9 Realstc temp nterr flm resstance GC45b Aspect Rat harmnc 36 4 00 00 5 5.9 GC50b Large Slab harmnc 80 80 00 00 5 5.9 Hgh cre heat transfer fractn GC55b Shallw Deep harmnc 2 2 00 00 2 5.9 Shallw deep Grund Temp grund. Hgh cre heat transfer GC60b h steady 2 2 7.95 00 5 5.9 Realstc nterr flm resstance GC65b h and h steady 2 2 7.95.95 5 5.9 Realstc flm resstances GC70b GC80b Harmnc, h and h Grund Cnductvty harmnc 2 2 7.95.95 5 5.9 Realstc flm resstances harmnc 2 2 00 00 5 5 0.5 * temperature appled drectly t the grund surface; ** h and h are the nterr and the exterr grund surface heat transfer ceffcents. - 600 -
Table 2 Cmparsn f flr heat transfer frm the GRES mdel, CSIRO analytcal slutn and verfed numercal mdels (Neymark et al., 2008) Flr Heat Transfer Analytcal Slutn CSIRO (Delsante et al., 983) TRNSYS TESS Verfed Numercal Mdels FLUENT PAAET MATLAB DIT AccuRate GRES CSIRO Dff. Between GRES and.a. Mean (%) GC0a, Steady State (W) 2433 2427 2425 2432 2403 -.0% GC30a, Steady State (W) 2642 2585 2695 2403-9.0% GC30b, Steady State (W) 2533 2504 2570 2367-6.6% GC40a, Steady Perdc (kwh/annual) 23033 2276 23609 2064-9.0% GC40b, Steady Perdc (kwh/annual) 22099 2932 2253 20754-6.4% GC40c, Steady Perdc (kwh/annual) 8649 8598 8873 8892.0% GC45b, Steady Perdc (kwh/annual) 32758 32456 33483 3066-6.8% GC50b, Steady Perdc (kwh/annual) 277923 277988 2848 200572-28.% GC55b, Steady Perdc (kwh/annual) 35075 34879 3549 20754-4.0% GC60b, Steady State (W) 23 204 228 256 2.0% GC65b, Steady State (W) 994 99 2004 256 8.0% GC70b, Steady Perdc (kwh/annual) 7396 7434 7552 8892.0% GC80b, Steady Perdc (kwh/annual) 6029 5939 65 5387.2-0.8% *.A. Mean s the average f verfed numercal mdel results. Table 3 Cmparsn f annual peak-hur flr heat transfer results between the GRES mdel and verfed numercal mdels (Neymark et al., 2008) Annual Peak-hur Flr Heat Transfer (W) Verfed Numercal Mdels TRNSYS TESS FLUENT PAAET MATLAB DIT AccuRate GRES CSIRO GC40a 3087 3042 374 2846-8.2% GC40b 294 294 3002 2834-4.0% GC40c 2454 2444 2487 2539 3.2% GC45b 4444 4396 455 4230-5.2% GC70b 2254 2259 2276 2539 2.2% GC80b 776 763 794 750.3-3.5% Dff. Between GRES and.a. Mean (%) Table 4 Cmparsn f the phase shft (hurs) fr flr peak heat transfer results between the GRES mdel and verfed numercal mdels (Neymark et al., 2008) Phase Shft fr Flr Cnductn Peak (hurs) Verfed Numercal Mdels TRNSYS TESS FLUENT PAAET MATLAB DIT AccuRate GRES CSIRO GC40a (kwh/annual) 46 46 46 432 6 GC40b (kwh/annual) 47 465 44 49-22 GC40c (kwh/annual) 562 562 538 50-52 GC45b (kwh/annual) 47 44 44 396-37 GC70b (kwh/annual) 660 659 660 50-59 GC80b (kwh/annual) 568 59 567 48-57 Dff. Between GRES and.a. Mean (hurs) - 60 -
3300 300 AccuRate GRES Flr Cnductn (W) 2900 2700 2500 2300 200 900 700 500 0 000 2000 3000 4000 5000 6000 7000 8000 9000 Hur TRNSYS FLUENT MATLAB GHT AccuRate GRES Fgure 3. Cmparsn f predcted grund-cupled heat transfer fr test Case GC40a 2900 2700 AccuRate GRES Flr Cnductn (W) 2500 2300 200 900 700 500 0 000 2000 3000 4000 5000 6000 7000 8000 9000 Hur TRNSYS FLUENT MATLAB VA4 EnergyPlus ESP-r-BASESIMP BASECALC AccuRate GRES Fgure 4. Cmparsn f predcted grund-cupled heat transfer fr test Case GC40c - 602 -