FINITE ELEMENT MODELLING OF COUPLED HEAT AND MOISTURE TRANSFER IN TYPICAL EARTH-SHELTERED BUILDING ENVELOPE

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1 Eeent Internationa IBPSA Conference Gasgow, Scotand Juy 7-3, 9 FINIE ELEMEN MODELLING OF COUPLED HEA AND MOISURE RANSFER IN YPICAL EARH-SHELERED BUILDING ENVELOPE Xibin Ma 1, Baoyi Ceng 1, Jinfeng Mao 1, Wenjie Liu, Dongyi Zi 1 1 Engineering Institution of Engineering Corps, PLA Uniersity of Science and ecnoogy Nanjing, 17, P.R. Cina, xibina@gai.co Inestigation and Design Institute of Guangzou Miitary Region Air Force Guangzou, 515, P.R. Cina, newewin@gai.co ABSRAC It is necessary to do researc on te eat and oisture transfer in te eart-setered buiding for getting a better underground enironent. Based on Piips and De Vries and Zang s teory (Piip et a., 1957; Zang et a., 6), tis paper estabises a detaied -D transient ateatica ode to understand te eat and oisture transfer exacty in te eart-setered buiding eneope and te surrounding sois. A genera FEM (Finite Eeent Metod) software is adopted to soe te igy noninear goerning equations. e nuerica siuation sowed tat te existence of waterproof ayer akes te teperature fied continuous and te oisture fied discontinuous. e resuts ay afford te basis of eat and oisture oad cacuation for te eart-setered buiding. INRODUCION Wit te deeopent of econoy and society, te underground space is expored widey in Cina to enarge te urban space (Carody et a., 198; ong, 5; Qian et a., 7). Howeer, oisture is one of te ost iportant factors iiting an eart-setered buiding s serice ife. Moisture daage as been identified as one of te ain reasons for buiding eneope deterioration. More recenty recognized are te potentia serious eat azards of oud and oter organiss wic fouris in buidings and constructions wit excessie oisture (Geing, 1997). erefore, it is necessary to do researc on te eat and oisture transfer in te eart-setered buidings for getting a better underground enironent. For decades, any researcers ae deoted to te work of odeing of eat and oisture transfer in ground buiding eneope (Straube et a., 1). As eary as 196s, Luiko (Luiko, 1966) as firsty proposed a ateatica ode for siutaneous eat and ass (oisture) transfer in buiding porous aterias. e conseration equations incude te ass, te oentu and te energy conseration equations. e constitutie equations are described by Darcy s aw, Fick s aw and Fourier s aw. Howeer, te soutions are eiter nuerica or copicated inoing copex eigenaues. Cary and ayor (Cary et a., 196; Cary et a., 196) uses irreersibe terodynaics to describe te interactions of te forces and fuxes inoed. A ecanistic approac based on pysica odes of te penoenoogica processes tat occur in te soi was estabised by Piips and De Vries (Piip et a., 1957; De Vries, 1958). Witaker (Witaker, 1973; Witaker, 1977; Witaker, 198) aeraged te transport equation on a representatie eeentary oue (REV) at te continuu ee and obtained te goerning equations in a iger ee. is odeing etod oercoes te odeing difficuty tat porous edia are eterogeneous. But te transport coefficients of te ode can not be get easiy witout te copex experients. ese odes ae been adopted widey by any researcers (Deru, 1; Lu, ; Lu, ; Janssen et a., 4; Qin et a., 6). According to te odes of Piip, De Vries, Luiko and Witaker, Liu (Liu et a., 1995; Liu et a., 1998) deeoped te utipysics-pase cange-diffuse ode recenty wic based on te Naier-Stokes equation. is ode as seen fied ariabes. Besides, tere are ore odes estabised by te researcers wordwide (oas, 1987; Pedersen, 199; Matsuoto et a., 1997; Mendes et a., ; dos Santos et a., 6; ariku et a., 6). Copared to te eat and oisture researc in te ground buidings, te iterature referred to eartsetered buiding is iited. Ogura anaysed te eat and oisture beaiour in underground space by quasiinearized etod (Ogura et a., 1999). Zang ad presented a ateatica ode wic described wit teperature and reatie uidity as driing potentia for couped eat and oisture transfer in porous wa aterias. is ode coud ake te discontinuity on te oisture content profie continuous. Howeer, bot te odes did not take te infuence of te waterproof ayer into consideration and te quasiinearized etod coud not refect te eat and oisture ariations actuay. en te purpose of tis paper is to carify te eat and oisture beaiour in te eart-setered buiding eneope under te natura condition. PHYSICAL AND MAHEMAICAL MODEL o anayse te couped eat and oisture transfer in te eneope of te typica eart-setered buiding,

2 tis paper takes an underground buiding in Nanjing (Cina) as an exape, as depicted in Figure 1. e engt (L), wit (W), eigt () and te arc eigt ( 1 ) is 5, 6, 5.3 and 1.5, separatey. e distance between te soi surface and te top of te buiding is 1.5 and te tickness of te eneope is.5 (Suppose te tickness in te different area of te eneope is sae). H Ω Y W Ω1 Figure 1 Cross-section of typica saow buried underground engineering X d+ Before te ateatica odeing, tere are soe assuptions. Hoogeneous and isotropic porous edia (eneope and te surrounding soi) wit no distension and contraction is considered. Loca tera equiibriu is satisfied trougout te porous edia. Capiary pressure on te interfaces of te different ateria ayers is equa, i.e. te ydrauic continuous. e oisture absorption and desorption progress is isotera witout considering te infuence of te capiary ysteresis. e engt of te buiding is reatie ong copared to te wit and eigt, te two diensiona is adopted. e drie potentia for te iquid water in te porous ateria and te water apor is density gradient and capiary pressure gradient. 1 e waterproof ayre can stop te ositure transfer copetey. e tera paraeters are constants for gien ateria. ere is no eat or oisture source in te eneope and te surrounding sois. As te Piips and De Vries ode (Piip et a., 1957) was adopted wordwide and te erit of Zang s ode (Zang et a., 6), te couped eat and oisture transfer ode in tis paper is deried according to te two. Based on te assuption aboe, te goerning equations describing te eat and oisture transfer in te eneope and te surrounding sois are as foows. c keff (1) Were k eff D D L () L D p, sat k 1 R R (3) D p, sat D R D R (4) D p, sat L D D Rn 1 R R (5) D in Equation (4) is deterined by Equation (6) (Vaen, 1998), D, sat D (6) R e eaning of te sybos and notations used in te equations are gien in te Noencature. e upper surface of te pysica doain is exposed to soar and ong-wae radiations, conection eat and oisture transfer. is way, for Y, te boundary condition becoes keff Y s o I Y (7) 4 4 L Y sky s o Y and te ass baance is written as D D (8) s o Y e eat and oisture baance on is described as k eff Y i i i i L i i (9) D D (1) e interface 1 represents te waterproof ayer, so te eat is continuous wie te oisture coud not transfer fro it. e boundary is D D (11) soi 1 D D (1) eneope 1 (13) soi eneope

3 roug te ode of natura soi teperature fied, te dept forua of te constant teperature ayer was deduced by Liu et a. (Liu et a., 7). So in te dept of H, it is supposed tat te water tabe is tere and te teperature is constant. As a resut, te eat and oisture condition in tis ayer in Nanjing (Cina) is written as (Liu et a., 7) Y K (14) 9% (15) Y If it is sufficient far away fro te eneope, te eat and oisture transfer can no onger infuence te soi teperature profie, were is defined as te adiabatic and ipereabe. Wen it refers to te deterination of, it is anoter probe. It coes true ony in teory. Howeer, it is unreaistic in te nuerica siuation in any siuations (Adjai et a., 1998; dos Santos et a., 3) is adopted ere. Syetry reduces te odeing doain to af of te ode. It gets a syetry boundary on X. SIMULAION e goerning equations were soed using COMSOL Mutipysics (COMSOL AB, 8). COMSOL Mutipysics is a powerfu interactie enironent for odeing and soing a kinds of scientific and engineering probes based on partia differentia equations (PDEs). Wit tis software you can easiy extend conentiona odes for one type of pysics into utipysics odes tat soe couped pysics penoena and do so siutaneousy. e software runs te finite eeent anaysis togeter wit adaptie esing and error contro using a ariety of nuerica soers. Suppose te ateria of te eneope consists of concrete, and te sois surrounding te underground buiding is ade of ie rock. e teropysica paraeters of te are isted in abe 1. abe 1 eropysica paraeters of te buiding aterias and te sois (Ma et a., 1986) MAERIAL LIME ROCK CONCREE [kg/ 3 ] 17 c [J/(kg K)] K [W/( K)] D [ /s] e CSWD, Cinese Standard Weater Data, (Cina Meteoroogica Bureau Ciate Inforation Center Ciate Data Office et a., 5) for te city of Nanjing was used, wit a constant conection eat transfer coefficient of 15 and 8.14 W/( K) for s and i (Yuan, 5), an absorptiity of.5 (dos Santos et a., 3) and eissiity of.9 (Liu et a., 1983). Figure -Figure 5 present te annua ariation of teperature, reatie uidity, orizonta goba irradiation and equiaent sky teperature in Nanjing. Outdoor teperature /C Reatie uidity /% orizonta goba irradiation /(W ) ie / Figure Annua ariation of te dry bub teperature Nanjing (Cina) for CSWD ie / Figure 3 Annua ariation of reatie uidity Nanjing (Cina) for CSWD ie / Figure 4 Annua ariation of orizonta goba irradiance Nanjing (Cina) for CSWD e approxiate expression of ass conection coefficient is deterined by (Gabrait, 199) (16)

4 e oisture absorption and desorption process ines for concrete and ie rock are proided wit te foowing equations (Ma et a., 1986; Pei et a., 1999),.39 w (17) 4 3 w (18) Figure 6 eperature profie of te eart-setered buiding eneope and te surrounding sois at te tie of years 3 Sky teperature /K ie / Figure 5 Annua ariation of te equiaence sky teperature Nanjing (Cina) for CSWD RESULS AND DISCUSSIONS In tis nuerica siuation, te finite eeent etod is triange and 945 es points, 176 eeents were used. ake 15: on Juy t, wic is te tie of outdoor axia teperature (37. C), as te initia tie for te siuation. For initia condition for te soi, a teperature of 17.5 C and a reatie uidity of 5% were utiized. Wie for te eneope, teperature of 17.5 C and a reatie uidity of 9%. Suppose te underground space is air-conditioned by te HVAC syste, and te teperature and reatie uity aintains 6 C and 6%, separatey. e siuation period is year (175 ours) and tie step is 1 our (Wang, 7). Figure 7 Reatie uidity profie of te eartsetered buiding eneope and te surrounding sois at te tie of years Figure 6 and Figure 7 present te teperature and reatie uidity spatia distributions at 14: on Juy t. It is possibe to notice in Figure 6 tat te existance of te eart-setered buiding ad infuenced te soi s teperature distribution a ot. For te indoor air ae a constant teperature of 6 C, te eat is tranfered fro te eneope to te soi in suer. Wie te waterproof ayer ad not affect te eat transfer progess on te interface of te eneope and te rock, it did effect te oisture transfer (see in Figure 7). Note tat in Figure 7, te eft coorbar is for te rock and te rigt one for te eneope. After a woe year, te oisture ad absorped by te upper ay of soi in tis siuation. Due to te waterproof ayer, te oisture in te sois didn t transfer to te eneope, and te oisture in te eneope ad been transferred into te indoor enironent afer construction. 6.5 Heat fux q/(w ) Heat fux ie / Moisture fux Figure 8 Variation of te eat and oisture fux on te wa of te eart-setered buiding Moisture fux /(g 1 )

5 Figure 8 sows te ariation of te eat and oisture fux on te wa of te eart-setered buiding. e oisture fux aries siiary wit te eat fux. e axiu oisture fux in tis siuation is 3.3g/( ) and it fuctuates between.1-.3 g/( ), Wic eets te experienta resuts of 1.7g/( ) and.1 g/( ) in Cina (Editoria Group, 1983). So te odes in tis paper is aidated based on te assuption tat te waterproof ayre can stop te ositure transfer copetey. Moisture fux /(g 1 ) Ceiing Wa Foor ie / Figure 9 Variation of te oisture fux in te ceiing, foor and wa of te eart-setered buiding Heat fux q/(w ) Couped eat and oisture Heat ony ie / Figure 1 Coparison of te eat fux by te ode in tis paper and te eat transfer ony ode e difference of oisture fux in te ceiing, foor and wa of te eart-setered buiding is depicted in Figure 9. e oisture fux on te ceiing fuctuated ore tan te one on te foor or wa. It ay due to te infuence of te aiation of outdoor eteoroogic parateters. Figure 1 copares te eat fux on te surface of te underground engineering eneope based on te couped eat and oisture transfer ode and eat transfer ode, separatey. e ean reatie error during te siuation is 11.4%. Sen did an an inestigation of transient, two-diensiona couped eat and oisture fow in sois (Sen, 1986), resuts fro te couped ode were copared to resuts obtained wen te goerning equations were decouped. For te sand siuation, a 9% greater wa eat oss during te winter and aost a 5% increase in suer eat gain occurred due to couping. Due to te ack of teropysica paraeters of te buiding aterias, ony te ie rock and concrete were studied in tis paper. Howeer, bot te resuts indicates tat te coupe eat and oisture transfer ode soud be considered in soe cases. CONCLUSION Based on te teory of Piips and De Vries and Zang s ode, tis paper buit a ateatica ode to anayze te couped eat and oisture transfer in te eneope of eart-setered buiding and te surrounding sois. e COMSOL Mutipysics was utiized to soe te goerning equations in te porous aterias. e software coud coupe te teperature fied wit te oisture fied and soe te noninear probe effectiey. It ay be concude fro te resuts tat, 1. e waterproof ayer coud preent te oisture tranfering between te eneope and te surrounding sois, wie te teperature fied is sti coutinuous. e ateatica ode coud describe te couped eat and oisture transfer in te different porous ateria siutaneousy and independenty.. e oisture fux in te wa, ceiing and foor of te eart-setered buiding is different. Of te tree, oisture fux in te ceiing is te biggest. Becasuse te eat transfer in te ceiing is affected by te ourdoor eteoroogic parateters ore. Accordingy, te oisture transfer is infuenced by te teprature. 3. e coupe eat and oisture transfer ode soud be considered in soe cases wen do inestigation of eat transfer in te porous aterias. e researc ay refect te eat and oisture transfer in te underground engineering eneope and te surrounding sois objectiey and te resuts coud afford te basis of eat and oisture oad cacuation for underground engineering. As te resuts were obtained by te nuerica siuation, it is necessary to do erification and anaysis by bot te experients in te ab and fied test furter. ACKNOWLEDGEMEN e financia support fro Cina Nationa Cii Air Defense Office (Project NO. ZC13K3) is gratefuy acknowedged. REFERENCES Adjai, M. H., M. Daies and J. Litter reediensiona eart-contact eat fows: A

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