# SIST EN 15026:2007

(Main)## Hygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation

## Hygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation

This standard specifies the equations to be used in a simulation method for calculating the non steady transfer of heat and moisture through building structures.

It also provides a benchmark example intended to be used for validating a simulation method claiming conformity with this standard, together with the allowed tolerances.

The equations in this standard take account of the following storage and one-dimensional transport phenomena:

- heat storage in dry building materials and absorbed water;

- heat transport by moisture-dependent thermal conduction;

- latent heat transfer by vapour diffusion;

- moisture storage by vapour sorption and capillary forces;

- moisture transport by vapour diffusion;

- moisture transport by liquid transport (surface diffusion and capillary flow).

The equations described in this standard account for the following climatic variables:

- internal and external temperature;

- internal and external humidity;

- solar and longwave radiation;

- precipitation (normal and driving rain);

- wind speed and direction.

The hygrothermal equations described in this standard shall not be applied in cases where:

- convection takes place through holes and cracks;

- two-dimensional effects play an important part (e.g. rising damp, conditions around thermal bridges, effect of gravitational forces);

• hydraulic, osmotic, electrophoretic forces are present;

daily mean temperatures in the component exceed 50 °C.

## Wärme- und feuchtetechnisches Verhalten von Bauteilen und Bauelementen - Bewertung der Feuchteübertragung durch numerische Simulation

## Performance hygrothermique des composants et parois de bâtiments - Evaluation du transfert d'humidité par simulation numérique

La présente norme spécifie les équations à utiliser dans le cadre d’une méthode de simulation pour calculer le transfert non stationnaire de chaleur et d’humidité à travers les structures des bâtiments.

Elle fournit également un exemple de référence destiné à être utilisé pour valider une méthode de simulation déclarée conforme à la présente norme, et indique les tolérances admises.

Les équations figurant dans la présente norme prennent en compte les phénomènes unidimensionnels suivants d’accumulation et de transport :

accumulation de chaleur dans les matériaux de construction secs et eau absorbée ;

transfert de chaleur par conduction thermique en fonction de l’humidité ;

transfert de chaleur latente par diffusion de vapeur ;

accumulation d’humidité par sorption de vapeur et par capillarité ;

transfert d’humidité par diffusion de vapeur ;

transfert d’humidité par transport liquide (diffusion de surface et conduction capillaire).

Les équations figurant dans la présente norme prennent en compte les variables climatiques suivantes :

température intérieure et extérieure ;

humidité intérieure et extérieure ;

rayonnement solaire et de grande longueur d’onde ;

précipitations (normales et pluie battante) ;

vitesse et direction du vent.

Les équations hygrothermiques figurant dans la présente norme ne doivent pas être appliquées lorsque :

la convection se produit par des trous et fissures ;

les effets bidimensionnels jouent un rôle important (par exemple augmentation de l’humidité, conditions autour des ponts thermiques, effet des forces gravitationnelles) ;

des forces hydrauliques, osmotiques, électrophorétiques sont présentes ;

les températures quotidiennes moyennes du composant dépassent 50 °C.

## Higrotermalno obnašanje sestavnih delov stavb in elementov stavb - Ocenjevanje prenosa vlage z numerično simulacijo

### General Information

### Relations

### Standards Content (Sample)

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Wärme- und feuchtetechnisches Verhalten von Bauteilen und Bauelementen - Bewertung der Feuchteübertragung durch numerische SimulationPerformance hygrothermique des composants et parois de bâtiments - Evaluation du transfert d'humidité par simulation numériqueHygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation91.120.30WaterproofingICS:Ta slovenski standard je istoveten z:EN 15026:2007SIST EN 15026:2007en,de01-julij-2007SIST EN 15026:2007SLOVENSKI

STANDARD

SIST EN 15026:2007

EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN 15026April 2007ICS 91.080.01 English VersionHygrothermal performance of building components and buildingelements - Assessment of moisture transfer by numericalsimulationPerformance hygrothermique des composants et parois debâtiments - Evaluation du transfert d'humidité parsimulation numériqueWärme- und feuchtetechnisches Verhalten von Bauteilenund Bauelementen - Bewertung der Feuchteübertragungdurch numerische SimulationThis European Standard was approved by CEN on 28 February 2007.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the CEN Management Centre or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as theofficial versions.CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre: rue de Stassart, 36

B-1050 Brussels© 2007 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN 15026:2007: ESIST EN 15026:2007

EN 15026:2007 (E) 2 Contents Page Foreword.3 Introduction.4 1 Scope.5 2 Normative references.6 3 Terms, definitions, symbols and units.6 3.1 Terms and definitions.6 3.2 Symbols and units.6 4 Hygrothermal equations and material properties.8 4.1 Assumptions.8 4.2 Transport of heat and moisture.9 4.3 Material properties.11 5 Boundary conditions.13 5.1 Internal conditions.13 5.2 External conditions.14 6 Documentation of input data and results.15 6.1 General.15 6.2 Problem description.15 6.3 Hygrothermal model and numerical solution.16 6.4 Calculation report.16 Annex A (normative)

Benchmark example – Moisture uptake in a semi-infinite region.18 A.1 General.18 A.2 Problem description.18 A.3 Results.19 Annex B (informative)

Design of Moisture Reference Years.22 Annex C (informative)

Internal boundary conditions.23 Bibliography.24

SIST EN 15026:2007

EN 15026:2007 (E) 3 Foreword This document (EN 15026:2007) has been prepared by Technical Committee CEN/TC 89 “Thermal performance of buildings and building components”, the secretariat of which is held by SIS. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2007, and conflicting national standards shall be withdrawn at the latest by October 2007. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard : Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. SIST EN 15026:2007

EN 15026:2007 (E) 4 Introduction This standard defines the practical application of hygrothermal simulation software used to predict one-dimensional transient heat and moisture transfer in multi-layer building envelope components subjected to non steady climate conditions on either side. In contrast to the steady-state assessment of interstitial condensation by the Glaser method (as described in EN ISO 13788), transient hygrothermal simulation provides more detailed and accurate information on the risk of moisture problems within building components and on the design of remedial treatment. While the Glaser method considers only steady-state conduction of heat and vapour diffusion, the transient models covered in this standard take account of heat and moisture storage, latent heat effects, and liquid and convective transport under realistic boundary and initial conditions. The application of such models has become widely used in building practice in recent years, resulting in a significant improvement in the accuracy and reproducibility of hygrothermal simulation.

The following examples of transient, one-dimensional heat and moisture phenomena in building components can be simulated by the models covered by this standard: ƒ drying of initial construction moisture; ƒ moisture accumulation by interstitial condensation due to diffusion in winter; ƒ moisture penetration due to driving rain exposure; ƒ summer condensation due to migration of moisture from outside to inside; ƒ exterior surface condensation due to cooling by longwave radiation exchange; ƒ moisture-related heat losses by transmission and moisture evaporation. The factors relevant to hygrothermal building component simulation are summarised below. The standard starts with the description of the physical model on which hygrothermal simulation tools are based. Then the necessary input parameters and their procurement are dealt with. A benchmark case with an analytical solution is given for the assessment of numerical simulation tools. The evaluation, interpretation and documentation of the output form the last part.

Inputs

• Assembly, orientation and inclination of building components

• Hygrothermal material parameters and functions • Boundary conditions, surface transfer for internal and external climate

• Initial condition, calculation period, numerical control parameters Outputs

• Temperature and heat flux distributions and temporal variations • Water content, relative humidity and moisture flux distributions and temporal variations Post processing • Energy use, economy & ecology • Biological growth, rot and corrosion • Moisture related damage and degradation The post processing tools are not part of this standard. As far as possible references to publications dealing with these tools is given. SIST EN 15026:2007

EN 15026:2007 (E) 5 1 Scope This standard specifies the equations to be used in a simulation method for calculating the non steady transfer of heat and moisture through building structures.

It also provides a benchmark example intended to be used for validating a simulation method claiming conformity with this standard, together with the allowed tolerances. The equations in this standard take account of the following storage and one-dimensional transport phenomena: • heat storage in dry building materials and absorbed water; • heat transport by moisture-dependent thermal conduction; • latent heat transfer by vapour diffusion; • moisture storage by vapour sorption and capillary forces; • moisture transport by vapour diffusion;

• moisture transport by liquid transport (surface diffusion and capillary flow). The equations described in this standard account for the following climatic variables: • internal and external temperature; • internal and external humidity; • solar and longwave radiation; • precipitation (normal and driving rain); • wind speed and direction. The hygrothermal equations described in this standard shall not be applied in cases where: • convection takes place through holes and cracks; • two-dimensional effects play an important part (e.g. rising damp, conditions around thermal bridges, effect of gravitational forces); • hydraulic, osmotic, electrophoretic forces are present; • daily mean temperatures in the component exceed 50 °C.

SIST EN 15026:2007

EN 15026:2007 (E) 6 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 12664, Thermal performance of building materials and products — Determination of thermal resistance by means of guarded hot plate and heat flow meter methods — Dry and moist products of medium and low thermal resistance EN 12667, Thermal performance of building materials and products — Determination of thermal resistance by means of guarded hot plate and heat flow meter methods — Products of high and medium thermal resistance EN 12939, Thermal performance of building materials and products — Determination of thermal resistance by means of guarded hot plate and heat flow meter methods — Thick products of high and medium thermal resistance EN ISO 7345, Thermal insulation – Physical quantities and definitions (ISO 7345:1987) prEN ISO 9346:2005, Hygrothermal performance of buildings and building materials - Mass transfer - Physical quantities and definitions (ISO/DIS 9346:2005) prEN ISO 10456, Building materials and products - Hygrothermal properties -Tabulated design values and procedures for determining declared and design thermal values (ISO/DIS 10456:2005) EN ISO 12571, Hygrothermal performance of building materials and products – Determination of hygroscopic sorption properties (ISO 12571:2000) EN ISO 12572, Hygrothermal performance of building materials and products – Determination of water vapour transmission properties (ISO 12572:2001) prEN ISO 15927-3, Hygrothermal performance of buildings - Calculation and presentation of climatic data - Part 3: Calculation of a driving rain index for vertical surfaces from hourly wind and rain data (ISO/DIS 15927-3:2006) 3 Terms, definitions, symbols and units 3.1 Terms and definitions For the purposes of this document, the terms and definitions given in prEN ISO 9346:2005 and EN ISO 7345 apply. Other terms used are defined in the relevant clauses of this standard. 3.2 Symbols and units Symbol Quantity Unit cm specific heat capacity of dry material J/(kg⋅K) cw specific heat capacity of liquid water J/(kg⋅K) Dw moisture diffusivity m2/s Esol total flux density of incident solar radiation W/m2 SIST EN 15026:2007

EN 15026:2007 (E) 7 g density of moisture flow rate kg/(m²⋅s) gp density of moisture flow rate of available water from precipitation kg/(m²⋅s) gv density of water vapour flow rate kg/(m²⋅s) gw density of liquid water flow rate kg/(m²⋅s) gw,max density of water flow rate which can be absorbed at the surface of a material

kg/(m²⋅s) h surface heat transfer coefficient W/(m2⋅K) hc convective heat transfer coefficient W/(m2⋅K) he specific latent enthalpy of evaporation or condensation J/kg hr radiative heat transfer coefficient W/(m2⋅K) K liquid conductivity s/m pa ambient atmospheric pressure Pa psuc suction pressure Pa pv partial water vapour pressure Pa pv,a partial water vapour pressure in the air Pa pv,s partial water vapour pressure at a surface Pa pv,sat saturated water vapour pressure Pa pw water pressure inside pores

Pa q density of heat flow rate W/m2 qlat density of latent heat flow rate W/m2 qsens density of sensible heat flow rate W/m2 Rw liquid moisture flow resistance of interface m/s RH2O gas constant of water vapour J/(kg⋅K) sd,s equivalent vapour diffusion thickness of a surface layer m T thermodynamic temperature K Ta air temperature of the surrounding environment K Teq equivalent temperature of the surrounding environment K SIST EN 15026:2007

EN 15026:2007 (E) 8 Tr mean radiant temperature of the surrounding environment K Tsurf surface temperature K t time s v wind speed m/s w moisture content kg/m3 x distance m αsol solar absorptance - δ0 vapour permeability of still air kg/(m⋅s⋅Pa) δp vapour permeability of material kg/(m⋅s⋅Pa) ε longwave emissivity of the external surface - λ thermal conductivity

W/(m⋅K) ϕ relative humidity - µ diffusion resistance factor - ρa density of air kg/m³ ρm density of solid matrix kg/m³ ρw density of liquid water kg/m³ σs Stefan-Boltzmann constant W/(m2⋅K4)

4 Hygrothermal equations and material properties 4.1 Assumptions The hygrothermal equations specified in the following clauses contain the following assumptions: • constant geometry, no swelling and shrinkage; • no chemical reactions are occurring;

• latent heat of sorption is equal to latent heat of condensation/evaporation;

• no change in material properties by damage or ageing; • local equilibrium between liquid and vapour without hysteresis;

• moisture storage function is not dependent on temperature; • temperature and barometric pressure gradients do not affect vapour diffusion. The development of the equations is based on the conservation of energy and moisture. The mathematical expression of the conservation laws are the balance equations. The conserved quantity changes in time, only if it is transported between neighbouring control volumes.

SIST EN 15026:2007

EN 15026:2007 (E) 9 Heat conservation shall be expressed by

()()xqqtTwcc∂+∂−=∂∂⋅⋅+⋅latsenswmmρ (1) The increase of the moisture content of a control volume shall be determined by the net inflow of moisture. The moisture flow rate equals the sum of the vapour flow rate and the flow rate of liquid water. xgtw∂∂−=∂∂ (2) lvggg+= (3) The relative humidity shall be defined by the following equation:

()Tppsatv,v=ϕ (4) The pressure acting on the water inside a building material due to the capillary forces is different from the pressure of the surrounding air. The difference is called suction. psuc = pa - pw

(5) The suction of the pore water is related to the relative humidity of the surrounding air by the Kelvin equation: psuc = -ρw RH2O T lnϕ (6) The relation between the state variables ϕ, pv, psuc, T and the moisture content of a building material is defined by the moisture storage function. The moisture storage function of a building material shall be expressed either as the moisture content as a function of suction (suction curve), w(psuc), or as the moisture content as a function of the relative humidity (sorption curve), w(ϕ).

4.2 Transport of heat and moisture 4.2.1 Heat transport 4.2.1.1 Heat transport inside materials Heat transport shall be composed of sensible and latent components. Sensible heat transport shall be calculated with Fourier’s law with a thermal conductivity which depends on moisture content.

xTwq∂∂⋅−=)(sensλ (7) Latent heat transport shall be calculated by the following equation: velatghq= (8) 4.2.1.2 Heat transport across boundaries The heat flow from the surrounding environment into the construction consists of convection, shortwave radiation from the sun and longwave radiation exchange with sky and surrounding surfaces.

SIST EN 15026:2007

EN 15026:2007 (E) 10

Sensible heat flow from each surrounding environment to the building envelope shall be given by: ()surfeqsensTThq−= (9) The heat transfer coefficient and the equivalent temperature are: rchhh+= (10) ()()rarsolsolaeq1hTTEhTT−++=α (11) The radiative and convective heat exchanges are represented by an equivalent temperature. Other means of accounting for these effects may be used.

If the surface temperature is known it can be used as a boundary condition.

Latent heat flow to and from the boundaries is proportional to the vapour flow rate at the surfaces (see 4.2.2). 4.2.2 Moisture transport 4.2.2.1 Moisture transport inside materials Moisture is transported by capillary forces and diffusion. The transport equations shall be formulated using the partial vapour pressure and the suction as the driving potentials. wvggg+= (12) ()xpg∂∂=v0v1δϕµ (13) ()xppKg∂∂=sucsucw (14) The temperature dependence of the liquid conductivity may be neglected.

NOTE For the liquid transport alternative potentials such as relative humidity, moisture content and temperature may be used, if the transport coefficients are transformed and the interfaces between two materials are handled in such a way that the suction and the partial vapour pressure are still continuous functions across the interface. 4.2.2.2 Moisture transport across material interfaces

Internal interfaces The details of the contact between two layers of building materials can have a large influence on the liquid moisture transport. Additional coatings, such as adhesives, can also modify the diffusive moisture transport.

Small air gaps between materials and the modification of pore structure at material interfaces, because of chemical reaction products, reduce the capillary water transport across the interface. The influence of the interface on the liquid moisture flow may be described by a moisture resistance, Rw, which is defined by: wsucwûRpg= (15) SIST EN 15026:2007

EN 15026:2007 (E) 11 External interfaces Coatings and paints can cause additional resistance for water uptake and drying. The impact on diffusion can be described by an additional moisture resistance at the surface, sd,s//0, defined by:

()sv,av,sd,0vppsg−=δ (16) where sd,s is the equivalent vapour diffusion thickness of the interface, in m. The uptake of driving rain is limited by the amount of water which can be absorbed by the material at the surface: ∂∂=xpKgsucmaxw, (17) so that: gw = min(gp, gw,max) (18) where gp is the water available for absorption from precipitation. 4.3 Material properties 4.3.1

**...**

SLOVENSKI OSIST prEN 15026:2004

PREDSTANDARD

oct 2004

Hygrothermal performance of building components and building elements -

Assessment of moisture transfer by numerical simulation

ICS 91.120.30 Referenčna številka

OSIST prEN 15026:2004(en)

© Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

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EUROPEAN STANDARD

DRAFT

prEN 15026

NORME EUROPÉENNE

EUROPÄISCHE NORM

August 2004

ICS

English version

Hygrothermal performance of building components and building

elements - Assessment of moisture transfer by numerical

simulation

Performance hygrothermique des composants et parois de Wärme- und feuchtetechnisches Verhalten von Bauteilen

bâtiments - Evaluation du transfert d'humidité par und Bauelementen - Bewertung der Feuchteübertragung

simulation numérique durch numerische Simulation

This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee CEN/TC 89.

If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations which

stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other language

made by translation under the responsibility of a CEN member into its own language and notified to the Management Centre has the same

status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,

Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,

Slovenia, Spain, Sweden, Switzerland and United Kingdom.

Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without notice and

shall not be referred to as a European Standard.

EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: rue de Stassart, 36 B-1050 Brussels

© 2004 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 15026:2004: E

worldwide for CEN national Members.

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prEN 15026:2004 (E)

Contents Page

Foreword.3

Introduction .4

1 Scope .6

2 Normative references .7

3 Definitions, symbols and units.7

4 Model components and material properties .9

5 Boundary conditions.14

6 Benchmark example – Moisture uptake in a semi-infinite region .16

7 Documentation of input data and results.19

Annex A (informative) Design of Moisture Reference Years .22

Annex B (informative) Internal boundary conditions.23

Bibliography .24

2

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prEN 15026:2004 (E)

Foreword

This document (prEN 15026:2004) has been prepared by Technical Committee CEN/TC 89 “Thermal

performance of buildings and building components”, the secretariat of which is held by SIS.

This document is currently submitted to the CEN Enquiry.

3

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prEN 15026:2004 (E)

Introduction

This standard defines the practical application of hygrothermal simulation software used to predict one-

dimensional transient heat, air and moisture transfer in multi-layer building envelope components subjected to

non steady climate conditions on either side. In contrast to the steady-state assessment of interstitial

condensation by the Glaser method (as described in EN ISO 13788), transient hygrothermal simulation

provides more detailed and accurate information on the risk of moisture problems within building components

and on the design of remedial treatment. While the Glaser method considers only steady-state conduction of

heat and vapour diffusion, the transient models covered in this standard take account of heat and moisture

storage, latent heat effects, and liquid and convective transport under realistic boundary and initial conditions.

The application of such models has become widely used in building practice in recent years, resulting in a

significant improvement in the accuracy and reproducibility of hygrothermal simulation.

The following examples of transient, one-dimensional heat and moisture phenomena in building components

can be simulated by the models covered by this standard:

� drying of initial construction moisture;

� moisture accumulation by interstitial condensation due to diffusion and convection in winter;

� moisture penetration due to driving rain exposure;

� summer condensation due to migration of moisture from outside to inside;

� exterior surface condensation due to cooling by long wave radiation exchange;

� moisture-related heat losses by transmission and moisture evaporation.

Figure 1 shows the factors relevant to hygrothermal building component simulation. The standard starts with

the description of the physical model on which hygrothermal simulation tools are based. Then the necessary

input parameters and their procurement are dealt with. A benchmark case with an analytical solution is given

for the assessment of numerical simulation tools. The evaluation, interpretation and documentation of the

output form the last part. The post processing tools in Figure 1 are not part of this standard. As far as possible

references to publications dealing with these tools are given.

4

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prEN 15026:2004 (E)

Figure 1 – Flow chart for hygrothermal simulations

5

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prEN 15026:2004 (E)

1 Scope

This standard specifies a method for calculating the non steady transfer of heat and moisture through building

structures. The necessary equations are defined and a benchmark example given.

The hygrothermal simulation models covered by this standard take account of the following storage and one-

dimensional transport phenomena:

� heat storage in dry building materials and absorbed water;

� heat transport by moisture-dependent thermal conduction;

� heat transfer by vapour diffusion and air convection, including phase changes;

� moisture storage by vapour absorption and capillary forces;

� moisture transport by vapour diffusion and air convection;

� moisture transport by liquid transport (surface diffusion and capillary flow);

The models described in this standard account for the following climatic variables:

� internal and external temperature;

� internal and external humidity;

� solar and long wave radiation;

� precipitation (normal and driving rain);

� wind speed and direction;

� air pressure differences.

The hygrothermal models described in this standard shall not be applied in cases where:

• convection takes place in a three-dimensional manner through holes and cracks;

• two-dimensional effects play an important part (e.g. rising damp, conditions around thermal bridges, effect

of gravitational forces);

• hydraulic, osmotic, electrophoretic forces are present;

• daily mean temperatures exceed 50 °C or in cases of fire;

• the effects of ice formation have to be assessed.

6

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prEN 15026:2004 (E)

2 Normative references

The following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.

EN 12524 Building materials and products – Hygrothermal properties –Tabulated design values

EN ISO 7345 Thermal insulation – Physical quantities and definitions

EN ISO 9346 Thermal insulation – Mass transfer – Physical quantities and definitions

EN ISO 10456 Building materials and products – Procedures for determining declared and design thermal

values

EN ISO 12572 Hygrothermal performance of building materials and products – Determination of water

vapour transmission properties

1

EN ISO 15927-3 Hygrothermal performance of buildings – Calculation and presentation of climatic data

– Part 3: Calculation of a driving rain index for vertical surfaces from hourly wind and

rain data

ISO 9053 Acoustics – Materials for acoustical applications – Determination of airflow resistance

ISO 10051 Thermal insulation – Moisture effects on heat transfer – Determination of thermal

transmissivity of a moist material

3 Definitions, symbols and units

3.1 Definitions

For the purposes of this standard, the terms and definitions given in EN ISO 9346 and EN ISO 7345 apply.

Other terms used are defined in the relevant clause of this standard

3.2 Symbols and units

Symbol Quantity Unit

n

C

flow coefficient per unit area m³/(m² s Pa )

D

liquid diffusivity m²/s

l

2

I

total flux of incident solar radiation W/m

sol

P

pressure of the surrounding air Pa

a

∆P total air pressure difference Pa

a

P water pressure inside pores Pa

l

R gas constant of water vapour J/(kg K)

H2O

R

liquid moisture flow resistance of interface, m/s

l

T

thermodynamic temperature K

1) To be published.

7

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prEN 15026:2004 (E)

T air temperature of the surrounding environment K

a

T equivalent temperature of the surrounding environment K

eq

T

mean radiation temperature of the surrounding K

r

environment

T arbitrary reference temperature K

ref

T surface temperature K

s

c specific heat capacity at constant pressure of air J/(kg K)

p,a

c specific heat capacity at constant pressure of liquid J/(kg K)

p,l

water

c

specific heat capacity at constant pressure of solid J/(kg K)

p,s

matrix

d thickness of the layer I m

I

g density of moisture flow rate kg/(m² s)

g density of air mass flow rate kg/(m² s)

r

g density of liquid moisture flow rate kg/(m² s)

l

g available water due from to precipitation kg/(m² s)

p

g density of vapour flow rate kg/(m² s)

v

2

h convective heat transfer coefficient

W/(m ⋅K)

c

h specific enthalpy of liquid-vapour phase change J/kg

e

2

h effective heat transfer coefficient

W/(m ⋅K)

eff

2

h radiative heat transfer coefficient

r W/(m ⋅K)

n

flow exponent -

p

partial vapour pressure, Pa

v

p

saturated vapour pressure Pa

v,sat

2

q

density of heat flow rate W/m

2

q density of conduction heat flow rate W/m

cond

2

q density of convection heat flow rate W/m

conv

s suction Pa

∆s suction difference across interface Pa

s

mean suction at interface Pa

s equivalent vapour diffusion thickness m

d

v wind speed m/s

3

w moisture content kg/m

3

w water content kg/m

l

solar absorptance -

α

sol

permeability of vapour in air kg/m s Pa

δ

0

ε long-wave emissivity of the external surface -

thermal conductivity

λ W/(m⋅K)

8

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prEN 15026:2004 (E)

moisture conductivity for capillary water transport s

λ

m,l

relative humidity -

ϕ

diffusion resistance factor -

µ

liquid water density kg/m³

ρ

l

density of air kg/m³

ρ

a

density of solid matrix kg/m³

ρ

s

2 4

Stefan-Boltzmann constant

σ W/(m ⋅K )

s

4 Model components and material properties

4.1 Assumptions

The components of the hygrothermal model discussed in the following clauses were developed under the

following additional assumptions:

• constant geometry, no swelling and shrinkage;

• no chemical reaction, heat of sorption is neglected;

• no change in material properties by damage or ageing;

• local equilibrium between liquid and vapour without hysteresis;

• the temperature dependence of the moisture storage function is neglected;

• only the partial vapour pressure is used for the calculation of the vapour diffusion; the additional

influence of temperature and barometric pressure gradients are neglected;

• the formation of ice is not considered.

The development of the equations is based on the conservation of energy and mass (air and moisture). The

mathematical expression of the conservation laws are the balance equations. The conserved quantity

changes in time, only if there is a source or sink inside a small representative volume (control volume) or if it is

transported between neighbouring control volumes. Considering the restrictions of nearly constant pressure,

the heat storage of a control volume can be expressed by the specific heat at constant pressure from the solid

matrix and the liquid water inside the pore structure. Phase change between liquid and vapour, i.e. the release

of latent heat, is considered as part of the convective heat flow through the structure.

∂T ∂q

()c ⋅ ρ + c ⋅ w ⋅ = − (1)

p,s s p,l l

∂t ∂x

q = q + q (2)

cd cv

Conservation of mass can be used to determine the air flow rate. If buoyancy can be neglected the air flow

rate is calculated from the total pressure difference over the construction.

n

g = ρ C∆ P (3)

a a a

NOTE For a whole construction, the coefficients C and n can be measured according to EN 12114. The air flow

coefficient per area has to be calculated by division of the flow coefficient by the overall area of the building component.

The increase of the moisture content of a control volume is determined by the net inflow of moisture. The

moisture flow rate equals the sum of the vapour flow rate and the flow rate of liquid water.

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prEN 15026:2004 (E)

∂w ∂g

= − (4)

∂t ∂x

g = g + g (5)

v l

In an unsaturated porous building material the moisture flow is always a mixture of flow in the vapour and the

liquid state. An additional flow of moisture can also take place in the surface absorbed moisture. The term

liquid is used in the following clauses if there is a continuous path of liquid moisture in the volume under

consideration. The following equations are based on the assumption of a local equilibrium between the solid

matrix, the flowing phases and the absorbed moisture. This means that the temperature of each part inside a

control volume is equal and the moisture distribution between the absorbed moisture and the flowing phases

equals the equilibrium distribution. To describe the amount of vapour, different state variables can be used

which are related by a number of equations.

The relative humidity is defined by using the saturated vapour pressure or the humidity by volume

at saturation

p

v

ϕ = (6)

p (T )

v,sat

The liquid phase of water inside a building material can be described by the moisture content mass by volume.

Due to the capillary forces the pressure inside the water is different from the pressure of the surrounding air.

The difference is called suction.

s = P − P (7)

a l

The suction of the pore water is related to the relative humidity of the surrounding air by the Kelvin equation:

s = −ρ R T lnϕ (8)

l H2O

The relation between the state variables φ, p , s, T and the moisture content of a building material is defined by

v

the moisture storage function. The moisture storage function of a building material can be expressed as the

moisture content as a function of suction (suction curve), w(s), or as the moisture content as a function of the

relative humidity (sorption curve), w(φ). As a simplification, a constant reference temperature is used in

Equation (8) so that the temperature dependence can be neglected.

4.2 Transport of heat, air and moisture

4.2.1 Heat transport

4.2.1.1 Heat transport inside materials

The transport equation for heat can be split into heat conduction and convective heat transport:

q = q + q (9)

cd cv

The heat transport through heat conduction is calculated with Fourier’s law and includes all processes where

the transport of heat is closely correlated to the temperature gradient. The second heat flow term accounts for

the effects of both air flow and moisture flow, including sensible and latent heat:

∂T

q = −λ(w,T ) ⋅ (10)

cd

∂x

q = c ⋅()T − T ⋅ g + c ⋅()T − T ⋅ g + h ⋅ g (11)

cv p,a ref a p,l ref l e v

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prEN 15026:2004 (E)

4.2.1.2 Heat transport across boundaries

The heat flow from the surrounding environment into the construction consists of convection, shortwave

radiation from the sun and longwave radiation exchange with sky and surrounding surfaces. Additionally heat

can be transported to or from the construction by air or liquid water transport across the boundary.

Air (and liquid moisture) flow into the construction:

q = h ⋅ (T − T )+ g ⋅ c ⋅()T − T + g ⋅ c ⋅()T − T + h ⋅ g (12)

eff eq surf air p,air air ref l p,l air ref e v

Air flow (and no liquid moisture flow) out of the construction:

( ) ()

q = h ⋅ T −T + g ⋅c ⋅ T −T + h ⋅ g (13)

eq s a p,a s ref e v

The effective heat transfer coefficient and the equivalent temperature are

h = h + h (14)

c r

1

T = T +()I α +()T − T h (15)

eq a sol sol r a r

h

NOTE The radiative and convective heat exchange has been lumped into an equivalent temperature. Other means of

accounting for these effects may be used.

4.2.2 Moisture transport

4.2.2.1 Moisture transport inside materials

Moisture is transported by capillary forces, air transport and diffusion. The transport equations can be

formulated using the partial vapour pressure and the suction as the driving potentials.

g = g + g (16)

v l

∂p g p

1

v a v

g = − δ (T ) + (17)

v 0

µ(ϕ) ∂x ρ R T

a H O

2

∂s

g = λ (s) (18)

l m,l

∂x

The temperature dependence of the liquid moisture conductivity may be neglected.

NOTE For the liquid transport alternative potentials such as relative humidity, moisture content and temperature may

be used, if the transport coefficients are transformed and the interfaces between two materials are handled in such a way

that the suction and the partial vapour pressure are still a continuous function across the interface.

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4.2.2.2 Moisture transport across material interfaces

The details of the contact between two layers of building materials can have a large influence on the liquid

moisture transport. Additional coatings, such as adhesives, can also modify the diffusive moisture transport.

Small air gaps between materials and the modification of pore structure at material interfaces, because of

chemical reactions products, reduce the capillary water transport across the interface. The influence of the

interface on the liquid moisture flow can be described by a resistance.

∆ s

g = (19)

l

R (s)

l

External interfaces

Coatings and paints can cause additional resistance for water uptake and drying. The impact on diffusion can

be described by an additional moisture resistance. For air flowing into the structure:

g p

δ

a v,a

0

()

g = ± p − p + (20)

v v,a v,s

s ρ R T

d,s a H O a

2

and for air flowing out of the structure:

g p

δ

a v,s

0

g = ±()p − p + (21)

v v,a v,s

s ρ R T

d,s a H O s

2

where s is the equivalent vapour diffusion thickness of the interface, in m.

d,s

The positive sign in equations (20) and (21) is used for the surface where the normal surface vector out of the

construction points into the direction of the negative x-coordinate and the minus sign for the other surface.

The uptake of driving rain is limited by the amount of water which can be absorbed by the material:

∂s

g =λ (22)

m,l

l,max

∂x

s

so that:

g = min(g , g ) (23)

l p l,max

where g is the water available for absorption from precipitation.

p

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prEN 15026:2004 (E)

4.3 Material properties

4.3.1 Necessary material data set and measurement methods

Table 1 provides a list of relevant material pro

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