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Local and global sensitivity analysis of a coupled heat and moisture transfers model: effect of the variability of cob material properties

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Abstract

Among earthen construction techniques, cob might be an interesting solution to mitigate greenhouse gases emissions and energy consumption of the building industry. One main issue encountered is that the cob material shows large variability of hygrothermal properties, which could consequently have an impact on the reliability of the estimation of the energy consumption of cob buildings. At the wall scale, the hygrothermal properties significantly influence the kinetics of moisture and heat transfers through the building shell, both being coupled. In order to measure the relative contribution of the variation of the hygrothermal properties, a sensitivity analysis of a coupled heat and moisture transfer model has been carried out on a cob wall. More specifically, a local sensitivity analysis has been performed (one model input wobbles around a reference value) and compared with a global sensitivity analysis, which may provide the potential interaction between model inputs. For the latter approach, the Morris method was used and allows to find the influence level of material properties and the relationships with model outputs. Two study cases have been performed: a static loading case, to find temperature and water vapour pressure profiles across the cob wall until the steady state and a dynamic loading case under a 2.5 years external dynamic loading (St-Nazaire meteorological data, France). As main results, the global approach showed in general a higher variability of properties, the sorption isotherms and the water vapour permeability were the most influential input parameters on humidity profiles while on temperature ones, the variability of both properties led up to 0.25 °C variation range. The influence of thermal properties was very sensitive to the daily-loading variation while that of the hygric properties was very sensitive to the seasonal-loading variation.

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Data availability

All data related to this paper are available under request.

Abbreviations

BCs:

Boundary conditions

SI :

Sorption Isotherm

SL:

Static loading

SA:

Sensitivity Analysis

LA:

Local Analysis

DL:

Dynamic loading

\(C_{m}\) [kg/kg.Pa]:

Moisture storage capacity

\(C_p\) [J/kg.K]:

Specific heat capacity

\(j_m\) [\({kg/m^2.s}\)]:

Moisture flux density

\(j_v\) [\({kg/m^2.s}\)]:

Vapour flux density

\(k_m\) [kg/m.s.Pa]:

Moisture permeability

\(k_l\) [kg/m.s.Pa]:

Liquid water permeability

\(k_0\) [\(m^2\)]:

Intrinsic permeability

\(k_T\) [kg/m.s.K]:

Thermogradient coefficient

\(L_v\) [J/kg]:

Evaporation latent heat

\(\lambda\) [W/m.K]:

Thermal conductivity

\(M_w\) [kg/mol]:

Water molecule molar mass

T [K or \(^{\circ }C\)]:

Temperature

\(\mu _w\) [Pa.s]:

Dynamic viscosity of water

\(P_v\) [Pa]:

Water vapour pressure

\(P_{vsat}\) [Pa]:

Water vapour pressure at saturation

R [J/mol.K]:

Ideal gas constant (8.314)

RH [%]:

Relative humidity

\(\rho _w\) [\(kg/m^3\)]:

Water density

\(\rho _s\) [\(kg/m^3\)]:

Material apparent density

\(\sigma _0\) [−]:

Phase change coefficient

w[kg/kg]:

Water content

\(T_{int}\) [K or \(^{\circ }C\)], \(RH_{int}\) [%]:

Interior Temperature and RH

\(T_{init}\) [K or \(^{\circ }C\)], \(RH_{init}\) [%]:

Set point temperature and RH

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Funding

The authors thank the Ecologic Transistion Agency (ADEME, France), the Pays de la Loire Region (France) and Palladio Foundation for supporting this work.

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Authors and Affiliations

  1. Nantes université, GeM UMR 6183, F-44600, Saint-Nazaire, France

    Junior Tchiotsop, Stéphanie Bonnet, Nabil Issaadi  & Philippe Poullain

  2. IRSTV, CNRS FR2488, Ecole Centrale de Nantes, 44300, Nantes, France

    Junior Tchiotsop, Stéphanie Bonnet, Tristan Senga Kiessé, Nabil Issaadi  & Philippe Poullain

  3. Agence de l’environnement et de la Maîtrise de l’Energie 20, avenue du Grésillé- BP 90406, 49004 Cedex 01, Angers, France

    Junior Tchiotsop

  4. INRAE, Institut Agro, SAS, Rennes, France

    Tristan Senga Kiessé

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Appendices

Appendix 1 Effect of the variability of properties on profiles

See Figs. 13, 14 and 15.

Fig. 13
figure 13

Variability of \(P_v\) profiles

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Fig. 14
figure 14

CV of T profiles at wall mid-depth, for various seasons

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Fig. 15
figure 15

CV of \(P_v\) profiles at wall mid-depth, for various seasons

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Appendix 2 \(\mu\)-indexes

See Figs. 16.

Fig. 16
figure 16

\(\mu\)-indices of \(P_v\) profiles

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Appendix 3 \(\sigma/\mu\)-indices

See Fig. 17.

Fig. 17
figure 17

\(\sigma /\mu ^*\)-indices of \(P_v\) profiles

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Tchiotsop, J., Bonnet, S., Kiessé, T.S. et al. Local and global sensitivity analysis of a coupled heat and moisture transfers model: effect of the variability of cob material properties. Heat Mass Transfer 60, 67–87 (2024). https://doi.org/10.1007/s00231-023-03409-0

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