Influence of a Refurbishing on an Old Residential building's Wall in Paris in Summer: Mass and Heat Transfer Approach

K. Azos-Diaz1*, B. Tremeac1, F. Simon2, D. Corgier2 and C. Marvillet1

1Laboratoire de Chimique Moléculaire, Génie des Procédés Chimique et Energétique, (EA21), CNAM, Paris, France2MANASLU Ing. , Savoie Technolac, Le Bourget du Lac, France*Corresponding author: 292, rue Saint-Martin 75141 Paris cedex 03, France, karina.azos_diaz@cnam.fr

Abstract: The implementation of thermalinsulation in old residential building walls couldcompromise the hygrothermal behavior of thiskind of construction. A bad installation ofinsulation, especially when it is place inside,could compromise the health of the wall withaccumulation of moisture in the interfaces of twomaterials during cold periods. In summer time,insulation could have consequences on thequality of indoor air conditions. Thus, theevaluation of heat and mass transfer through thewall is an important and critical task. The aim ofthis study is to evaluate through a hygrothermaltime-dependent 2D-model, the behavior of twokinds of multilayered renovated walls.Modelings are made under real externalconditions (for a building located in Paris).COMSOL Multiphysics® is the modeling tooladopted, with the PDE interface which allowsthe coupling of mass and heat equations.

Keywords: Mass transfer, Heat transfer,Moisture, refurbishing, multi-layered wall

1. Introduction

Old buildings, like in Paris, were built withuninsulated thick walls made of porous materialswith high thermal inertia, giving to thesebuildings a thermal potential in the quality ofindoor conditions during summer time. Besidesthis thermal characteristic, the materials used inold buildings are mostly hygroscopic, whichmeans that they are materials that absorb andrelease water vapor from the indoor air. Thus,walls in old buildings moderate the amplitude ofthe indoor relative humidity. These mechanismsalso participate in the improvement of the indoorair quality and are energy saving, meanly insummer time.

French thermal regulation and the Factor 4approach have resulted in the implementation of

thermal insulation to reduce energy consumptionduring winter.

From an installation point of view, thermalinsulation poses two major difficulties. When itis put inside, the living area surface is reduced.And when it is put outside, thermal insulationimplementation is in most cases restricted,because a very large part of the old buildings inParis are classified, and facades must bepreserved.

From a hygrothermal point of view, theproperties and the behavior of old buildings areaffected by the installation of thermal insulationdevices, mainly when they are placed inside. Forthis reason, it is important to evaluate heat andmass transfer through the old wall withinsulation.

As mentioned before, most building materialsare porous, with a solid matrix and pores. In thiskind of media, the main mechanisms ofmoisture transfer are vapor diffusion (linked toFick's law) and liquid conduction of water(linked to Darcy's law). Thus, every material hasan isothermal curve that covers the hygroscopicand capillary region. The isothermal curve is ahygric property which shows the moisturecontent in the material as a function of relativehumidity (Figure 1).

To assess the implications of insulation measuresin old buildings, modeling time-dependent heatand mass (moisture) transfer through the wallbecomes an important task. The aim of thisstudy is to evaluate the hygrothermal behavior ofa 2D-multilayered renovated wall, for two kindsof configurations: outside and inside thermalinsulation, under real external conditions (for abuilding located in Paris). COMSOLmultiphysics is a modeling tool which allowscoupling heat and mass transfer equations

Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge

through coefficients in the non-linear PartialDifferential Equation (PDE) module [7, 1, 8].

2. State of the art

In physics buildings, heat and moisture transferprocesses are described by means of amacroscopic model based on the conservativeenergy and mass governing equations, wheretemperature gradients and the moisture variationare the driving forces [9, 6, 2, 4]. Hence, themoisture variation in the mass transport equationcould be described in terms of vapor pressure,moisture content or relative humidity [2, 4].

Figure 1. Equilibrium moisture content of limestone

Dos Santos et al. developed a heat, air andmoisture transfer model (HAMT) that predictsthe behavior of a building component and theeffect of mass transport over the thermal flux [2].Künzel proposes a method which connects thevapor pressure with the relative humidity, inorder to ensure continuity at the interfaces in amultilayered component [4]. WUFI is acommercial software developed by Fraunhofer-institut based on Kunzel's model that simulates2D dynamic heat and mass transfer forconstruction elements. However, this softwarerestricts access to governing equations and doesnot allow changes to specific calculationparameters [7, 8]. In this field, other simplifiedlumped approaches have been developed,including the effective moisture penetrationdepth model (EMPD). This model is used tocalculate the hygrothermal behavior of materialsassuming that only a thin layer near the indoorsurface, known as humidity buffer, interacts withthe indoor air. Therefore there are no exchangesbetween outside and inside [3].

In this paper, heat and moisture transport modelis expressed by means of partial derivativesequations, where gradient temperature andrelative humidity variation are the driving forces.

3. Hygrothermal Model

The following partial differential equations(PDE) describe respectively heat and moisturetransfer through a multilayered wall:

(1)

(2)

Temperature T and relative humidity φ are thedependent variables in equations (1) and (2),hence the spatial derivative of φPsat term mustbe expressed in terms of T and φ [1]:

(3)

In (2), the first term on the right side of theequation is linked to Darcy's law and the secondterm is linked to Fick's law which describesvapor and liquid transport respectively. Equation(3) describes the vapor diffusion term linked to avapor diffusion coefficient δp as a hygricproperty of material. In building physics, theterm linked to gravity effects on Darcy's law isdisregarded.

The pressure vapor saturation is calculated as afunction of temperature by the followingempirical expression [4]:

(4)

With:

The enthalpy of a system is the sum of sensitiveand latent enthalpies:

(5)

Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge

Thus, the heat storage capacity dH/dT in (1)depends on the heat capacity of the solid media(dry material) and the heat capacity of themoisture stocked in its pores:

(6)

Substituting equations (3) and (6) into (1) and (2)yields :

(7)

(8)

With:

ξ=dw/dφ, Dφ=Dw.ξ and δp=δ/μ

4. Study cases

Figure 2. Case studies a) Case 1 outside polystyreneinsulation, b) Case 2 inside mineral wool insulation

4.1. Description and hypotheses

In this paper, two cases are modeled. In caseone, outside Polystyrene insulation andlimestone are modeled, and in case two, insidemineral wool insulation and limestone are

modeled (Figure 2). In both cases we assumethat two layers are homogeneous with perfectcontact between them, which means that contactresistance is neglected.

We have simplified two cases putting only twolayers. In reality a renovated wall has multipleslayers like mortar and plaster, that participate inheat and mass transfer process. Furthermore, oldbuilding walls built with limestone have small aircavities inside them.

As known, thermal conductivity λi is a materialthermal property that change depending on themoisture content stocked in its pores. In thisstudy we assume that has λi a constant value. InTable 1, some hygrothermal properties areshown.

Table 1. Material hygrothermal properties

4.2. Boundary conditions

The heat flux and mass flow exchanged betweenair and building element surfaces, arerespectively described by the followingrelationship as a third kind boundary condition:

(9)

(10)

Ti et Pvi are conditions from outside and insideair. This data is provided from measurementstaken inside of an old renovated apartment inParis during a summer day. External conditionshave been taken from météo-Paris weather datawebsite[10]. Indoor air temperature have beentaken own project data (Figure 3). Heat transfercoefficient hi and mass transfer coefficient βi aretaken as a constant value from [4]:

Indoor h_in = 17 [W/m2K]

Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge

β_in = 75*10-9 [kg/m2sPa]

Outdoor h_out = 17 [W/m2K]β_out = 75*10-9 [kg/m2sPa]

Figure 3 Indoor and external air temperaturetemperature in Paris during 25th July 2014

5. Use of COMSOL Multiphysics

COMSOL is a multiphysics commercialsoftware, based on the finite element method(FEM) which allows coupling between differentphysics.

The solutions of equations (7) and (8) are solvedsimultaneously in COMSOL 4.4. multiphysicsPDE's interface. These PDE's equations aredescribe and thereby coupled to be modeled. Thegeneric form (11) offers the possibility to replaceeach term in the governing equation bycoefficients, as shown below:

(11)

With:

The boundary conditions in COMSOL areexpressed in the following manner:

(12)

g is the heat flux and mass flow exchangebetween air and walls surfaces, hi and βi from (9)and (10) respectively.

The spatial discretization, then the mesh of themodel, is selected based on length scalegoverning physical phenomena modeled. In heattransfer and mass transport particularly,significant exchanges occurs on the surface or onthe interfaces between materials. For this reason,we have chosen an extra-fine mesh alongboundaries and fine mesh for the rest of themodel. In this study, spatial discretization isbuild using triangular mesh.

6. Results

Modelling has been performed for one hot dayduring 25th July 2014 in Paris. Figure 3 andFigure 4 show temperature and relative humidityevolution at 6 different hours in this particularday, where outdoor temperature and relativehumidity are important.

Figure 4 and Figure 6a show temperatureevolution in materials. We observe thatlimestone damps down the daily temperaturevariation. This is explained by fact that limestonehas a high heat capacity. Thus, an important aheat flow is required to cool down or heat up thematerial by one degree.

Figure 4. 2D modelling. Temperature Dependentvariable evolution

Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge

Figure 5. 2D modelling. Relative humidity Dependentvariable evolution

In mass transfer (Figure 5 et Figure 6b) themodelling duration seems to be too short toassess moisture effect at the interfaces of twomaterials. Moisture transport for this period oftime remains a surface phenomenon: changes areobserved in thin layer 5 centimeters depth. Thus,it could be interesting to model mass transferover a long period with more important externalvariations.

(a)

(b)

Figure 6. Temperature (a) and relative humidity (b)evolution at 0,50 meters from the ground

7. Conclusions

This paper describes the process to model heatand moisture transfer in a multilayered wallusing the COMSOL PDE module. In thisinterface, the mathematical model can be easilyintegrated by predefined coefficients that allowcoupling between governing equations.

In mass transfer phenomena, more studies intime are required, because with one day data isdifficult to evaluate moisture effect in interfacesbetween materials. Moreover, initial conditionsare primary information on modeling, they couldaffect moisture and heat transfer results. Thus, itis important to build scenarios with differentpossible initial conditions over the same internaland external air conditions.

This study is a part of a project that aims toassess the impact of refurbishment measures inold buildings in Paris. One of the purposes is tointeract between different scales in simulations,from the building component to a wholebuilding. Thus, results obtained from modellingin COMSOL will be used in a simulationsoftware that allows hygrothermal and dynamicbuilding simulation during one year. Results willbe also compared with literature and discuss.

8. References

[1] Bianchi Janetti, M., Ochs, F. and Feist, W.,On the Conservation of Mass and Energy inHygrothermal Numerical Simulation withCOMSOL Multiphysics, 13th Conference ofInternational Building Performance SimulationAssociation, Chamberry (2013)

[2] Dos Santos G. H. and Mendes, N. Heat, airand moisture transfer through hollow porousblock, International Journal of Heat and MassTransfer, 52: 2390-2398 (2009)

[3] Janssens, A., Woloszyn, M., Rode, C., Sasic-Kalagasidis, A., and De Paepe, M. FromEMPDE to CFD – Overview of differentapproaches for heat air and moisture modeling inIEA Annex 41. IEA ECBCS Annex 41 (2008)

[4] Künzel, H. Simultaneous Heat and MoistureTransport in Building Components. Dissertation,Fraunhofer Institute of Building Physics (1995)

Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge

[5] Kwiatkowsky, J., Woloszyn, M. and Roux,J.J. Modelling of hysteresis influence on masstransfer in building materials. Building andEnvironment, 44: 633-642 (2009)

[6] Mendes, N. and Philippi, P. A method forpredicting heat and moisture transfer throughmultilayered walls based on temperature andmoisture content gradients. InternationalJournal of Heat and Mass Transfer, 48 :37-51(2005)

[7] Nusser, B. and Teibinger, M., Coupled Heatand Moisture Transfer in Building Components –Implementing WUFI Approaches in COMSOLMultiphysics, COMSOL Conference in Milan(2012)

[8] Ozolins, A., Jacovics, A. and Ratnieks, A.,Moisture Risk in Multi-layered Walls –Comparison of COMSOL Multiphysics andWUFI Plus Models with Experimental Results,COMSOL Conference in Rotterdam (2013)

[9] Philip, J. and De Vries, D. Moisturemovement in porous materials under temperaturegradients. Transactions American GeophysicalUnion, 38 :222-232 (1957)

[10] Weather data Météo Paris website. dataretrieved 26th July 2014 from http://www.meteo-paris.com/ile-de-france/station-meteo-paris.html.

10. Nomenclature

cps Heat capacity at constant pressure of solid media [J/kgK]

cpw Heat capacity at constant pressure of vapor water [J/kgK]

H Enthalpy [J/m3]

hi Convective and radiative transfer coefficient [W/m2K]

h_in Inside convective and radiative transfer coefficient [W/m2K]

h_out Inside convective and radiative transfer coefficient [W/m2K]

hv Evaporation enthalpy of water [J/kg]

Dφ Liquid conduction coefficient [kg/ms]

Dw Liquid transport coefficient [m2/s]

g Heat flux and mass flow from COMSOL boundary conditions

gh Heat flux [W/m2]

gm Moisture flow [kg/m2s]

psat Water vapor saturation pressure [Pa]

pv Water vapor pressure [Pa]

T Temperature [K]

w Moisture content [kg/m3]

Greek Symbols

β Water vapor transfer coefficient [kg/m2sPa]

δp Water vapor permeability of material [kg/msPa]

δ Water vapor permeability of stagnant air [kg/msPa]

φ Relative humidity

λ Heat conductivity of material [W/mK]

ξ Moisture storage capacity [kg/m3]

ρs Bulk density of the dry material[kg/m3]

μ Water vapor diffusion resistance factor of building material [-]

Excerpt from the Proceedings of the 2014 COMSOL Conference in Cambridge