Co oupled d Heat and a Mo oisture e Trans sfer in Buildiing Co ompon nents - Implementin ng WUFI® Approach hes in ® CO OMSOL L Multiphysic cs 1* B. Nusser N , M. Teibinger1 1 Hollzforschung Austria, Divvision of Buillding Physics
*Corrresponding aauthor: Franz-G Grill-Strasse 7, 7 AT-1020 V Vienna,
[email protected] Absttract: Calculaating time deependent heatt and moissture transporrt trough buillding componnents are important taasks in the area of buillding physsics. A well known and worldwide used comm mercial softw ware for this is WUFI®. From F the scientific s poinnt of view thee restricted acccess to governing equations e is neverthelesss a wback of this ssoftware. draw In thhe present papper it is shownn how the phyysical apprroaches used in WUFI aree implementeed in COM MSOL Multiphysics® ussing the Paartial Diffe ferential Equaation interfacee. The COM MSOL moddel is evalluated with two diffe ferent bencchmarks for heat h and moiisture simulattions and WUFI W results itself. It is shown, that the COMSO OL model delivers marks goodd results in acccordance witth the benchm and with WUFII. However, slight deviattions betw ween COMSO OL and WUFII results can occur o if thhe moisture looad on the coonstruction is very highh.
In this papeer it is show wn how the physical approaches used u in WUF FI are implem mented in ® COMSOL Multiphysics M using thee Partial Differential Equation (P PDE) interfaace. The COMSOL reesults are evaluated with different benchmarks and a WUFI ressults itself.
words: heat moisture trransport, buillding Keyw physsics, timber flaat roof
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1. In ntroduction C Calculating time-dependdent heat and moissture transporrts trough building componnents are important taasks in the area of buillding physsics. Differennt approachess can be useed to investigate the loong time behaaviour of buillding ments under fluuctuating connditions [2,3,88,10]. elem Besiide calculationn programmes, which are used onlyy by scientists for research purposes, p therre are also commercial programms available. a A well wn and worldw wide used com mmercial softw ware know for calculating c thhe coupled heat h and moisture transsfer in buildding componnents is WU UFI®, deveeloped at tthe Fraunhoofer-Institute for Buildding Physics [8]. It is used u for reseearch purpposes and alsoo by designerrs for commeercial taskss. From the scientific pooint of view w the restrricted access to governiing equationns is neveertheless a draawback of WU UFI.
2. Governin ng Equation ns In the following seection the governing g equations foor the heat aand moisturee transfer trough buildiing componennts are presennted. It is also shown, how the bouundary condiitions are generated. 2.1 Transporrt processes The couppled heat annd moisture transport processes arre calculated from WUF FI in the following waay [8]: (1)
dH/dT Heatt storage capaacity in J/m³.K K dw/dφ Moisture storage ccapacity in kgg/m³ λ Therrmal conductivity in W/m.K K Dφ Liquuid conductionn coefficient inn kg/m.s δp Water vapour perm meability of th he hv psat T φ
buildding material in kg/m.s.Pa Evapporation enthaalpy of water in i J/kg Water vapour satuuration pressuure in Pa Tem mperature in K Relaative humidityy
In this approaach the temperrature and thee relative humidity are the driving pootentials. Bothh potentials aree affecting botth transport prrocesses, so they have to be deviatedd with respect to space in both equations. (3) With equationn (3) the heat and moisture transport equations cann be describedd in the follow wing way:
dp δ φ dT dp d δ φ dT withh
the heat stoorage capacity by the following f equation [3]: (4)
(5)
1
cs cw w ρs
(6) (7)
Mw hv R
Moisture sstorage capaciity in kg/m³ Liquid connduction coeffficient in kg/m m.s Liquid trannsport coefficient m²/s Liquid trannsport coefficcient for suctioon in m²/s Slope off water vaapour saturaation pressure cuurve by the Clausius-Clapeeyron relation [3] in Pa/K Molar weight of water inn kg/mol Evaporatioon heat of watter in J/kg Universal gas constant in i J/mol.K
The water vapouur permeabilityy of the buillding b the follow wing mateerial can be calculated by relattion: (9) withh
μ PL
δ φ δ φ
dp dT
dp dT T
1
(12) 0
0
2.2 Boundarry conditions The heat exchange at the building elements f surface can be calculatedd using the following relation [8]: (13)
q α Tair Tsurf
Heat flux f density inn W/m² Total heat transfer coefficient in n W/m²K Tempperature of the ambiient air Tempperature of thhe building elements surfacce
with 2,0 · 10
δ
Specific heat capaccity of dry building materrial in J/kg.K Specific heat capaccity of water in n J/kg.K Waterr content in kgg/m³ Bulk density d of the dry building material in kg//m³
Rearrange thee transport equuations (4) annd (5) into matrix notatioon, we finallyy get
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ξ Dφ Dw Dws
(11)
.
/
(10)
Water vapour permeabillity of stagnannt air Pa in kg/m.s.P Water vapour diffusion resistance facctor of the building material a prressure in Pa Ambient atmospheric
i Negllecting the ennthalpy changge caused by icing and the dependennce of the watter vapour con ntent in th he building m material pores, we can calcuulate
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αc αr
Conveective heat ttransfer coeffficient in W/m²².K Radiaation related hheat transfer coefficient in W//m².K
ong-wave To consider the radiatioon effects (lo (thermal), shhort-wave (soolar)) on thee exterior surface the equivalent e exxterior temperrature T* can be used [7].
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qe T*
Exterior heeat flux densitty in W/m² Equivalentt exterior tempperature in K
B modde to If thhe "Explicit Radiation Balance" conssider the raddiation effectss (e.g. nightttime overrcooling) is applied in WUFI, only the conv vective part of the tottal heat tran nsfer coeffficient is usedd. In thhis case, WUF FI calculates thhe convective heat transsfer coefficiennt by subtraccting 6.5 W/m m².K from m the total heatt transfer coeffficient. 6,5
⁄ ².
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To calculate c the hheat flux denssity at the extterior surfaace we use thee following reelation to consider the radiation r effeccts: (17) y the Accoording to [7] T* can be calculated by folloowing correlattion: 0
I
Is,dir gatm Is,diff Il,atm σ β
Directt solar radiatioon in W/m² Atmoospheric view factor Diffusse solar radiattion in W/m² Atmoospheric longg-wave radiation in W/m²² Stefann-Bolzmann cconstant in W//m².K4 Inclinnation of thhe building elements surfacce (90° for a vvertical wall)
To get a lineear approach of the total radiation, equation (22)) is linearised by a first-ordder Taylor series approxximation [6]. 4
,
Ie,lin T0*
Inserting equuations (20),, (21) and (24) ( into equation (199) and solve equation (18) for the equivalent ouutdoor temperaature we get: ,
a Is
Short-wavve absorptivityy Incoming short-wave solar s radiatioon in W/m² Long-wave emissivity and absorpttivity Incoming long-wave raadiation in W/m² W Long-wave emission in W/m²
ε Il Ie withh
, ,
(20) (21) (22)
3 ·
1
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4
g surfaces The moisturee flux throughh the building can be calculated in the folllowing way [8]: (26)
g β pair psurf
Vapouur diffusion fflux density in n kg/m².s Waterr vapour traansfer coeffi ficient in kg/m²².s.Pa Partiaal pressure off water vapou ur in the ambieent air in Pa Partiaal pressure off water vapou ur of the buildiing elements ssurface in Pa
with 7 · 10
,
, ,
Net radiatiion to the buiilding componnents surface in W/m²
(19)
(24)
Lineaarised long-waave emission in W/m² Equivvalent exterioor temperaturre of the previoous timestep inn K
(18)
To calculate c the net n radiation an approach from [6] iss applied, whiich is also useed in WUFI. Inn the folloowing equatioons the terresstrial radiatio on is however not conssidered. It is not necessaryy for the later on investtigated flat rooof constructionn.
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2
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3. Use U of COMS SOL Multip physics 3.1 Transport T processes T implementt the governinng equations (12) To in COMSOL C Mulltiphysics, wee use the PDE E (c) interrface. All coeefficients, exccept the diffusion, dampping and masss coefficientts respectivelyy are set to t zero. In CO OMSOL notaation we havee for eachh material layeer: (28)
0 ,
T
fficient Mass coeff Diffusion coefficient c Transport potentials Temperatuure in K Relative huumidity Transposed
32 30
Rearrrange equatiion (28) into o matrix notaation gives 11 1 21 1
12 22
MSOL resultss and the Figure 1 shoows the COM confidence inntervals (CI) of the benchmark. As can be seenn from the ggraphs, the COMSOL C results are within the conffidence intervals of the analytical solutions s foor all tim me steps investigated.
temperature in °C
da c u T RH
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4.1 EN 150266 The bencchmark accorrding to the European E Standard EN 15026 [1] deeals with the influence a RH on a specific of a step chhange in T and building matterial. Accordding to the beenchmark, the simulatioon results haave to fall within w the confidence in ntervals (± 2.5 %) of the analytical a solutions.
28 26 24 22 20 18
11 21
12 2 22 2
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140
0
1
2
3.3 Material M dataa B Basically, thee material daata of the WUFI W datab base can be used, but foor liquid transsport coeffficients one hhas to use semi logarithm mical values to enable linear interppolation (e.g. 60 | log10(3E-9)).
4. Model M verificcation I the followiing section thhe results of 1-D In COM MSOL simulations are compared with diffeerent benchm marks for heeat and moisture transsport simullations andd with WUFI W simu ulations.
mc in kg/m³
A good g description how too implement the goveerning equatiions for isotthermal cases in COM MSOL Multiphysics can be found in [11]].
4
5
COMSOL 365 5 days COMSOL 30 days d COMSOL 7 daays EN 15026 CI
120
The coefficients c11,…,c22 and a da11,…,da22 can be b taken from m equation (12)).
3
100 80 60 40 0.00
0.02
0.04
0.06
0.08
0.10
distance from m surface in m Figure 1: CO OMSOL resullts for temperrature and moisture conteent (mc) of the building materrial as well as associated confidence c inteerval (CI) of thhe analytic solution accorrding to the EN N 15026 benchmark for certain time steeps
4.2 HAMSTA AD This bennchmark forr heat and moisture simulation is a result of thhe international project HAMSTAD [4]. It deaals with the internal condensationn on the conntact surfacee of two materials in an insulated flat roof [5]. Figure 2 shows the calculated fflat roof wiith outer moisture seaaling, a load bearing layeer and an insulation layyer at the innterior side. The load
Figure 2: Construction details for f the HAMS STAD benchhmark [5]
Figuure 3 shows the COMSO OL results off the moissture content of o material A and B in the first simu ulated year and a the corrresponding mean m value and connfidence inntervals of the MSTAD bencchmark. It iss shown, thatt the HAM COM MSOL results are withinn the confiddence interrvals and closee to the meann values. The same s holdds for materiall A in the fiftth year, which h can be seen s in Figuree 4. The moisture content for mateerial B in the fifth year staays at a veryy low levell and thereforee it is not indiicated here.
14
mc material A in kg/m²
beariing material A is capillaryy active whilee the insullation materiaal B is capillaary non-activee and has a thermal connductivity 50 times as higgh as c and stteady mateerial A. A trannsient outer climate statee indoor clim mate were used u as bounndary cond ditions.
COMSOL HAMSTAD D mean HAMSTAD D CI
13
12
11
10 04
05
simulaated years
Figure 4: COM MSOL results ffor moisture coontent (mc) of material A as well as meean value and confidence c interval (CI) of o the HAMSTA AD benchmarkk [5] in the fifth simulatedd year
4.3 WUFI To comppare COMSO OL results witth WUFI results, we calculated c a flat roof witth vapour tight sealing and wooden ccladding at the exterior 5 side (Figure 5).
mc material A in kg/m²
15 COMSOL HAMSTAD meann HAMSTAD CI 14
13
Figure 5: Constructionn COMSOL/WU UFI comparisonn
for
the
We investigaated two versioons of the flat roof: Version 1: airtight a and suun exposed Version 2: not n airtight andd temporarily shaded
12
mc material B in kg/m²
details
0.5 0.4 0.3 0.2 0.1 0.0 00
01
simulated years y Figure 3: COMSOL L results for mooisture content (mc) of material m A andd B as well as a mean valuee and confiidence interval (CI) of the HAMS STAD benchhmark [5] in the first simulatedd year
ditions for With versionn 2 we create critical cond timber flat rooofs [9]. Figure 6 inddicates the m moisture content of the softwood andd the whole rooof element during d the simulated yeears. The mooisture contennt of the softwood is expressed in % of water (mass) ( of the oven-dry mass of the softwood. Ass one can MSOL results and the WUF FI results see, the COM are nearly iddentical in veersion 1. In version v 2 where the moisture m conttent of the softwood exceeds the critical vaalue of 20 %, % slight SOL and WUFI results deviations beetween COMS occur. The maximum m abssolute deviation at the highest moistture content iss + 5.7 % for softwood and + 6.8 % for f the whole construction.
v1 COMS SOL v2 COMS SOL
CO OMSOL WUFI W
50 0 -50 -100 -150 1 Jan 100
20
2 Jan
3 Jan
4 Jan
5 Jaan
6 Jan
2 Jul
3 Jul
4 Jul
5 Juul
6 Jul
0
15
qe in W/m²
mc softwood in %
25
v1 WU UFI v2 WU UFI
100
qe in W/m²
Figuure 7 shows the exterior heat flux dennsity simu ulated by COMSOL and WUFI W for thee flat rooff version 1 in January and July in the tenth t year. Deviations aare hardly visiible in the graaphs, e heat fluxes of botth simulationss are the exterior nearlly identical.
10
-100 -200 -300
total mc in kg/m³
5 -400 1 Jul
2 2.5
simulattion period Figure 7: Exterrior heat flux ddensity of versio on 1 in the tenth year
2 2.0 1.5
5. Conclusioon
1.0
This papeer describes thhe governing equations which are necessary n to implement th he WUFI approaches in COMSO OL Multiphysics and m It is sho own, that evaluate the so created model. the COMSO OL model dellivers good results r in accordance with w two diffferent benchm marks for heat and moissture simulatioons. The accordannce of COMS SOL and WUF FI results is good as well. Howevver, slight deviations d between COM MSOL and W WUFI results can c occur if the moistuure load on thhe constructioon is very high.
00.5 00
01
02
03
04
05
06
07
08
09 9
10
simulated years y Figure 6: COMS SOL and WUFI results forr the mc) of the softw wood and of thee total moisture content (m roof construction c for both calculateed versions
6. Referencces [1]
EN 150026: Hygrotherrmal performan nce of buildinng components aand building ellements Assessm ment of moisturre transfer by numerical n simulation.(2007-06-001)
[2]
Bednarr, T.: Beurteilunng des feuchte- und wärmeetechnischen Veerhaltens von Bauteilen und Geebäuden. Weiterentwicklung der d Meßund Reechenverfahren.. Dissertation. Technical T Univerrsity Vienna, Auustria. (2000)
[3]
C.-E.: HAMSTA AD. WP2: Modeeling. Hagentoft, C Reference ddocument basic modelling physsics. Version 4, Chalmers C Univeersity of Technologyy, Gothenburg, Sweden. S (2001))
[4]
Hagentoft, C C.-E.: HAMSTA AD - Final repoort: Methodology gy of HAM-Moddeling, Report RR 02:8. Chalm mers University of Technology, Gothenburg, Sweden. (20002)
[5]
C.-E.; et al.: Asssessment Methood of Hagentoft, C Numerical Prediction P Moddels for Combined Heat, Air annd Moisture Traansfer in Buildiing Componentss: Benchmarks for f Onedimensionall Cases. In: Jouurnal of Thermaal Envelope annd Building Science, Vol. 27, No. N 4, P. 327–3552. (2004)
[6]
Kehrer, M.; Schmidt, T.: Radiation R Effectss On Exterior Surrfaces. In: Proceedings of the 8th 8 Symposium m on Building Ph hysics in the Noordic Countries. Report R R-189. Copenhagen, C Denmark , P P. 207–212. (20 008)
[7]
Koch, H.; Peechinger, U.: Möglichkeiten M zuur Berücksichtiigung von Sonnnen- und Wärmestrahhlungseinflüssen n auf Gebäudeobeerflächen. In: GesundheitssIngenieur, Voll. 98, No. 10, P.. 265–280. (1977)
[8]
Künzel, H. M.: M Simultaneoous Heat and Moisture Trransport in Buillding Componennts. One- and tw wo-dimensional calculation usiing simple param meters. Disserttation, Universitty Stuttgart, Geermany. (1994))
[9]
Nusser, B.: F Flachgeneigte hölzerne h Dachkonstruuktionen. System manalysen undd neue Ansätze zur Planung hygrissch robuster flachgeneigtter hölzerner Dachkonstruktio D onen unter Beachhtung konvektiveer Feuchteeintrräge und temporäärer Beschattunngssituationen. Dissertationn. Technical Unniversity Viennaa, Austria. (2012)
[10]
Schijndel, J.. A. W. M. van: Integrated Heeat Air and Moiisture Modelingg and Simulatioon. Dissertationn. Technical Unniversity Eindhooven, The Netherllands. (2007)
[11]
Williams Poortal, N.: Evaluaation of heat annd moisture indduced stress andd strain of histooric building maaterials and arteefacts. MasterThesis. Challmers Universitty of Technologgy, Gothenburg, Sweden. (2011)
