CoCoCOB. N1Hol*Cor Abstmoisare physcommthe sto drawIn thapprCOMDiffemodbencand WIt is goodand betwif thhigh Keywphys

1. InC

moisare physinveelemBesionlyalso knowfor ctransdeveBuildpurptasksrestrneve

oupledomponOMSOLNusser1*, M. lzforschung rresponding a

tract: Calculasture transporimportant ta

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wback of this she present paproaches used MSOL Multferential Equadel is evalchmarks for hWUFI results shown, that

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words: heat sics, timber fla

ntroduction Calculating sture transporimportant ta

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ments under fluide calculationy by scientists

commercial wn and worldwcalculating thsfer in buildeloped at tding Physics

poses and alsos. From the ricted access ertheless a dra

d Heat anents - L MultTeibinger1 Austria, Div

author: Franz-G

ating time dert trough builasks in the

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in WUFI areiphysics® us

ation interfaceluated with heat and moiitself. the COMSO

ccordance witI. However,

OL and WUFIoad on the co

moisture trat roof

time-dependrts trough buiasks in the nt approachesong time behauctuating conn programmefor research pprogramms a

wide used comhe coupled hding componthe Fraunho [8]. It is uo by designer

scientific poto governi

awback of WU

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ependent heatlding componarea of builworldwide

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s can be useaviour of builnditions [2,3,8s, which are purposes, theravailable. Ammercial softwheat and moinents is WUofer-Institute used for resers for commeoint of viewing equation

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In this papeapproaches uCOMSOL MDifferential COMSOL rebenchmarks a

2. GoverninIn the

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2.1 TransporThe coup

processes arfollowing wa

dH/dT Heatdw/dφ  Moiλ TherDφ Liquδp Wat buildhv Evappsat WatT Temφ Rela In this approahumidity are potentials areso they have in both equat

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Equation (Pesults are evand WUFI res

ng Equationfollowing se

or the heat aing componenhow the bou

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t storage capasture storage crmal conductiuid conductioner vapour permding material poration enthaer vapour satu

mperature in Kative humidity

ach the temperthe driving po

e affecting botto be deviatedions.

n (3) the heatn be described

Buildiproach

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physical mented in e Partial ace. The

different

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transport FI in the

(1)

(2)

K g/m³ K n kg/m.s he

in J/kg ure in Pa

e relative h rocesses, to space

(3)

transport wing way:

         

         with

ξ Dφ Dw Dws

Mw hv R The materelat

with

δ μ PL Negland in th

                        

δ φd

                        h

Moisture sLiquid conLiquid tranLiquid tranm²/s

Slope ofpressure curelation [3Molar weiEvaporatioUniversal

water vapouerial can be tion:

h

2,0 · 10 .

Water vapin kg/m.s.PWater vapof the builAmbient a

lecting the enthe dependen

he building m

δ φdpdT

             

dpdT

      

storage capacinduction coeffnsport coefficnsport coeffic

f water vaurve by the C] in Pa/K ght of water in

on heat of watgas constant i

ur permeabilitycalculated b

. /

our permeabilPa our diffusion ding material

atmospheric pr

nthalpy changnce of the watmaterial pores,

ity in kg/m³ficient in kg/mient m²/s

cient for suctio

apour saturalausius-Clape

n kg/mol ter in J/kg in J/mol.K

y of the builby the follow

lity of stagnan

resistance fac

ressure in Pa

ge caused by iter vapour con we can calcu

(4)

(5)

(6)

(7)

(8)

m.s

on in

ation eyron

lding wing

(9)

(10)

nt air

ctor

icing ntent ulate

the heat stoequation [3]:

cs Speci matercw Speciw Waterρs Bulk d in kg/ Rearrange thematrix notatio

δ φ

δ φdpdT

2.2 BoundarThe heat

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q Heat fα Total Tair TempTsurf Temp surfac with

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orage capaci

1

fic heat capacrial in J/kg.K fic heat capacr content in kgdensity of the/m³

e transport equon, we finally

dpdT

T1

0

ry conditionsexchange at be calculated

flux density inheat transfer

perature of perature of thce

ective heat t².K ation related h/m².K

the radiatiohort-wave (soequivalent ex7].

ty by the f

city of dry bui

city of water ing/m³ dry building

uations (4) any get

0

the building d using the f

n W/m² coefficient in

the ambihe building

transfer coeff

heat transfer c

on effects (loolar)) on thexterior temper

following

(11)

lding

n J/kg.K

material

nd (5) into

(12)

elements following

(13)

n W/m²K ient air elements

(14)

ficient in

oefficient

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,

,

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0

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ve absorptivityshort-wave s

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e emission in

,

ty in W/m²perature in K

Balance" mods (e.g. nightWUFI, only tal heat tran

he convective cting 6.5 W/mfficient.

sity at the extelation to con

calculated by

ilding compon

an approach ed in WUFI. Instrial radiationot necessary

of construction

y solar radiatio

and absorptadiation in WW/m²

(15)

de to ttime

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heat m².K

(16)

terior sider

(17)

y the

(18)

nents

from n the

on is y for n.

(19)

on in

tivity W/m²

(20) (21)

(22)

Is,dir Directgatm AtmoIs,diff DiffusIl,atm Atmo W/m²σ Stefanβ Inclin surfac To get a lineequation (22)series approx ,

Ie,lin LineaT0* Equiv previo Inserting equequation (19equivalent ou

The moisturecan be calcul

g Vapouβ Water kg/m²pair Partia ambiepsurf Partia buildi with

7 · 10

2

t solar radiatioospheric view se solar radiat

ospheric long² n-Bolzmann cnation of thce (90° for a v

ear approach ) is linearised ximation [6].

4

arised long-wavalent exterioous timestep in

uations (20),9) and solve utdoor tempera

,

e flux throughated in the fol

ur diffusion fr vapour tra².s.Pa al pressure ofent air in Pa al pressure ofing elements s

on in W/m² factor tion in W/m² g-wave radi

constant in W/he building vertical wall)

of the total by a first-ord

ave emission or temperaturn K

, (21) and (equation (18ature we get:

,

, 3

·  14

h the buildingllowing way [

flux density inansfer coeffi

f water vapou

f water vapousurface in Pa

(23)

ation in

/m².K4 elements

radiation, der Taylor

(24)

in W/m² re of the

(24) into ) for the

(25)

g surfaces 8]:

(26)

n kg/m².s ficient in

ur in the

ur of the

(27)

3. U3.1 T

Tin Cinterdampset teach

da c u T RH T Reargive 1121

        

The can b A ggoveCOM

3.3 MB

databcoefvalulog1

4. MI

COMdiffetranssimu

Use of COMSTransport prTo implement

COMSOL Mulrface. All coeping and masto zero. In COh material laye

0,

Mass coeffDiffusion cTransport TemperatuRelative huTranspose

rrange equatis

1 121 22

                  

coefficients be taken from

good descriperning equatiMSOL Multip

Material dataBasically, thebase can be

fficients one hes to enable 0(3E-9)).

Model verificIn the followiMSOL simuerent benchmsport simululations.

SOL Multipocesses t the governinltiphysics, we

efficients, excss coefficientOMSOL notaer:

0

fficient coefficient potentials

ure in K umidity d

ion (28) into

11 1221 22

c11,…,c22 am equation (12)

tion how toions for isothysics can be

a e material daused, but fohas to use slinear interp

cation ing section thlations are

marks for helations and

physics

ng equations e use the PDEcept the diffuts respectivelyation we have

o matrix nota

22

and da11,…,d).

o implement thermal casefound in [11]

ata of the Wor liquid transemi logarithm

polation (e.g.

he results of compared

eat and moid with W

(12) E (c) sion, y are e for

(28)

(29)

ation

(30)

da22

the s in ].

WUFI sport mical

60 |

1-D with sture

WUFI

4.1 EN 15026The benc

Standard ENof a step chbuilding matthe simulatioconfidence insolutions. Figure 1 shoconfidence incan be seenresults are wanalytical sinvestigated.

Figure 1: COmoisture conteas associated csolution accorcertain time ste

4.2 HAMSTAThis ben

simulation is HAMSTADcondensationmaterials in shows the moisture seainsulation lay

018

20

22

24

26

28

30

32

0.0040

60

80

100

120

140

tem

pera

ture

in °C

mc

in k

g/m

³

6 chmark accor 15026 [1] de

hange in T aterial. Accordon results hantervals (± 2.

ows the COMntervals (CI)

n from the githin the confsolutions fo

OMSOL resulent (mc) of the confidence interding to the ENeps

AD nchmark for a result of th[4]. It dea

n on the conan insulated calculated f

aling, a load yer at the in

1 2

0.02 0.04

distance from

rding to the Eeals with the and RH on ading to the beave to fall w5 %) of the a

MSOL resultsof the bench

graphs, the Cfidence intervor all tim

lts for temperbuilding mater

erval (CI) of thN 15026 benc

r heat and he internationals with the ntact surfaceflat roof [5].

flat roof wibearing laye

nterior side.

3 4

0.06 0.0

COMSOL 365 COMSOL 30 d COMSOL 7 da EN 15026 CI

m surface in m

European influence

a specific enchmark, within the analytical

s and the mark. As

COMSOL als of the

me steps

rature and rial as well he analytic hmark for

moisture al project

internal e of two

Figure 2 ith outer er and an The load

5

8 0.10

5 daysdaysays

beariinsulhas matestatecond

Figubench

FigumoissimuvaluHAMCOMinterholdbe smatelevel

Figuof mconfibench

mc

mat

eria

l A in

kg/

m²

mc

mat

eria

l B in

kg/

m²

ing material Alation materiaa thermal con

erial A. A trane indoor climditions.

re 2: Construhmark [5]

ure 3 shows sture content oulated year ae and con

MSTAD bencMSOL resultrvals and closeds for materialseen in Figureerial B in the l and therefore

re 3: COMSOLmaterial A andidence intervhmark [5] in th

12

13

14

15

000.0

0.1

0.2

0.3

0.4

0.5

A is capillaryal B is capillanductivity 50nsient outer c

mate were u

ction details f

the COMSOof material Aand the corrnfidence inchmark. It iss are withine to the meanl A in the fifte 4. The mo fifth year stae it is not indi

L results for mod B as well aal (CI) of e first simulated

simulated y

y active whileary non-active times as hig

climate and stused as boun

for the HAMS

OL results ofA and B in the

responding mntervals of s shown, thatn the confidn values. The sth year, whichisture contenays at a veryicated here.

oisture content as mean value

the HAMSd year

COMSOLHAMSTAD meanHAMSTAD CI

years

e the e and gh as teady ndary

STAD

f the first

mean the

t the dence same h can t for

y low

(mc)

e and STAD

01

n

Figure 4: COMof material A interval (CI) ofifth simulated

4.3 WUFI To comp

results, we ctight sealing side (Figure 5

Figure 5:COMSOL/WU

We investigaVersion 1: aVersion 2: n With versiontimber flat roFigure 6 indsoftwood andsimulated yesoftwood is the oven-dry see, the COMare nearly idwhere the mexceeds the deviations beoccur. The mhighest moistand + 6.8 % f

0410

11

12

13

14

mc

mat

eria

l A in

kg/

m²

MSOL results fas well as me

of the HAMSTAd year

pare COMSOcalculated a and wooden c5).

ConstructionUFI comparison

ated two versioairtight and sunot airtight and

n 2 we create oofs [9]. dicates the md the whole roears. The moexpressed in mass of the

MSOL results dentical in vemoisture cont

critical vaetween COMSmaximum absture content isfor the whole

simula

for moisture coean value and cAD benchmark

OL results witflat roof witcladding at th

n details n

ons of the flat un exposed d temporarily

critical cond

moisture conteoof element doisture conten% of water (softwood. Asand the WUF

ersion 1. In vtent of the

alue of 20 %SOL and WUsolute deviatis + 5.7 % for construction.

ated years

COMSOL HAMSTAD HAMSTAD

ontent (mc) confidence

k [5] in the

th WUFI th vapour e exterior

for the

roof:

shaded

ditions for

nt of the during the nt of the (mass) of s one can FI results version 2 softwood

%, slight FI results on at the softwood

05

D meanD CI

Figusimuroof yearthe enearl

Figumoisroof c

0

2

2

mc

softw

ood

in %

tota

l mc

in k

g/m

³

ure 7 shows ulated by COf version 1 in . Deviations aexterior heat ly identical.

re 6: COMSture content (mconstruction fo

5

10

15

20

25

00 01 020.5

1.0

1.5

2.0

2.5

the exterior MSOL and WJanuary and

are hardly visifluxes of bot

SOL and WUmc) of the softw

r both calculate

03 04 05

v1 COMS v2 COMS

simulated y

heat flux denWUFI for the

July in the tible in the grath simulations

FI results forwood and of theed versions

06 07 08 09

SOL v1 WUSOL v2 WU

years

nsity e flat tenth aphs, s are

r the e total

9 10

UFIUFI

Figure 7: Extertenth year

5. ConclusioThis pape

which are napproaches evaluate the the COMSOaccordance wheat and moisThe accordanis good as between COMif the moistuhigh.

6. Referenc[1] EN 150

buildinAssessmsimula

[2] Bednarwärmeund Geund ReUniver

1 Jan-150

-100

-50

0

50

100

1 Jul-400

-300

-200

-100

0

100

q e in W

/m²

q e in W

/m²

rior heat flux d

on er describes thnecessary to

in COMSOso created m

OL model delwith two diffsture simulationce of COMS

well. HowevMSOL and Wure load on th

ces 026: Hygrotherng components ament of moisturtion.(2007-06-0

r, T.: Beurteilunetechnischen Veebäuden. Weiteechenverfahren.rsity Vienna, Au

2 Jan 3 Jan

2 Jul 3 Jul

simulat

density of versio

he governing implement th

OL Multiphymodel. It is sho

livers good rferent benchmons.

SOL and WUFver, slight d

WUFI results che constructio

rmal performanand building elre transfer by n01)

ng des feuchte- erhaltens von Brentwicklung d. Dissertation. Tustria. (2000)

4 Jan 5 Ja

4 Jul 5 Ju

CO W

tion period on 1 in the

equations he WUFI sics and own, that results in marks for

FI results deviations can occur

on is very

nce of lements - numerical

und auteilen

der Meß- Technical

an 6 Jan

ul 6 Jul

OMSOLWUFI

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

Hagentoft, CReference dVersion 4, CTechnology

Hagentoft, CMethodology02:8. ChalmGothenburg

Hagentoft, CNumerical PHeat, Air anComponentsdimensionalEnvelope an4, P. 327–35

Kehrer, M.; Exterior SurSymposium Countries. RDenmark , P

Koch, H.; PeBerücksichtiWärmestrahGebäudeobeGesundheits265–280. (1

Künzel, H. MMoisture TrOne- and twsimple paramStuttgart, Ge

Nusser, B.: FDachkonstruAnsätze zur flachgeneigtunter Beachund temporäDissertationAustria. (20

Schijndel, J.Air and MoiDissertationThe Netherl

Williams Pomoisture indbuilding maThesis. ChalGothenburg

C.-E.: HAMSTAdocument basic Chalmers Univey, Gothenburg, S

C.-E.: HAMSTAgy of HAM-Modmers University

, Sweden. (200

C.-E.; et al.: AssPrediction Modnd Moisture Tras: Benchmarks fl Cases. In: Jound Building Sci52. (2004)

Schmidt, T.: Rrfaces. In: Proc

m on Building PhReport R-189. CP. 207–212. (20

echinger, U.: Migung von Sonn

hlungseinflüssenerflächen. In: sIngenieur, Vol977)

M.: Simultaneoransport in Builwo-dimensional meters. Dissertermany. (1994)

Flachgeneigte huktionen. SystemPlanung hygrister hölzerner D

htung konvektiveärer Beschattunn. Technical Un12)

. A. W. M. vanisture Modeling

n. Technical Unlands. (2007)

ortal, N.: Evaluaduced stress andaterials and artelmers Universit, Sweden. (201

AD. WP2: Modemodelling phys

ersity of Sweden. (2001)

AD - Final repodeling, Report Rof Technology

02)

sessment Methodels for Combinansfer in Buildifor One-

urnal of Thermaence, Vol. 27, N

Radiation Effectseedings of the 8hysics in the NoCopenhagen, 008)

Möglichkeiten zunen- und n auf

l. 98, No. 10, P.

ous Heat and lding Componencalculation usi

tation, Universit)

hölzerne manalysen und sch robuster

Dachkonstruktioer Feuchteeintrngssituationen. niversity Vienna

: Integrated Heg and Simulationiversity Eindho

ation of heat and strain of histoefacts. Master-ty of Technolog1)

eling. sics.

)

ort: R-,

od of ed

ing

al No.

s On 8th ordic

ur

.

nts. ing ty

d neue

onen räge

a,

eat on. oven,

nd oric

gy,