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ABSTRACT
In this work, a macroscopic model of hygrothermal transfers in porous building materials was developed, using periodic homogenization, where the air infiltration was added to the classical mass and energy balance equations written at the microscopic scale. The corresponding infiltration, hygric, and thermal input parameters were carefully identified. Numerical calculations of thermal and diffusion tensors were performed on a representative concrete elementary cell. Further, the diffusion tensor was compared to the equivalent experimental results available in the literature, and its sensitivity to the water content variations and porosity has been evaluated on the concerned elementary cell.
Nomenclature
| C | = | volumetric heat capacity [j/m3 k] |
| Dv | = | self-diffusion coefficient of water vapor in the gaseous phase [m2/s] |
| = | macroscopic (or effective) diffusion tensor [m2/s] | |
| hl | = | specific enthalpy of the liquid [J/Kg] |
| hlv | = | specific enthalpy of vaporization [J/Kg] |
| I | = | identity matrix |
| L | = | characteristic macroscopic length [m] |
| l | = | characteristic microscopic length [m] |
| nij | = | normal unit vector directed from the domain Ωi toward the domain Ωj |
| ni | = | volume fractions of the materials i |
| P | = | total pressure [Pa] |
| Pc | = | capillary pressure [Pa] |
| Pv | = | water vapor pressure [Pa] |
| Pvs | = | saturated vapor pressure [Pa] |
| T | = | temperature [K] |
| t | = | time [s] |
| v | = | velocity [m/s] |
| X | = | dimensional space variable [m] |
| x | = | macroscopic dimensionless space variable |
| y | = | microscopic dimensionless space variable |
| Greek letters | = | |
| Γ | = | interface between two different phases |
| ε | = | scale separation parameter |
| εp | = | porosity [%] |
| λ | = | thermal conductivity [W/m K] |
| λhom | = | macroscopic (or effective) conductivity tensor [W/m K] |
| φ | = | relative humidity [%] |
| ρ | = | density [Kg/m3] |
| ωlg | = | Liquid–gas interface velocity [m/s] |
| Ω | = | period |
| Ωi | = | part of the period occupied by the pores by mediums i [m3] |
| Subscripts | = | |
| s | = | solid |
| l | = | water liquid |
| g | = | gas |
| a | = | dry air |
| v | = | water vapor |
| r | = | reference variable |
| * | = | dimensional variable |
Nomenclature
| C | = | volumetric heat capacity [j/m3 k] |
| Dv | = | self-diffusion coefficient of water vapor in the gaseous phase [m2/s] |
| = | macroscopic (or effective) diffusion tensor [m2/s] | |
| hl | = | specific enthalpy of the liquid [J/Kg] |
| hlv | = | specific enthalpy of vaporization [J/Kg] |
| I | = | identity matrix |
| L | = | characteristic macroscopic length [m] |
| l | = | characteristic microscopic length [m] |
| nij | = | normal unit vector directed from the domain Ωi toward the domain Ωj |
| ni | = | volume fractions of the materials i |
| P | = | total pressure [Pa] |
| Pc | = | capillary pressure [Pa] |
| Pv | = | water vapor pressure [Pa] |
| Pvs | = | saturated vapor pressure [Pa] |
| T | = | temperature [K] |
| t | = | time [s] |
| v | = | velocity [m/s] |
| X | = | dimensional space variable [m] |
| x | = | macroscopic dimensionless space variable |
| y | = | microscopic dimensionless space variable |
| Greek letters | = | |
| Γ | = | interface between two different phases |
| ε | = | scale separation parameter |
| εp | = | porosity [%] |
| λ | = | thermal conductivity [W/m K] |
| λhom | = | macroscopic (or effective) conductivity tensor [W/m K] |
| φ | = | relative humidity [%] |
| ρ | = | density [Kg/m3] |
| ωlg | = | Liquid–gas interface velocity [m/s] |
| Ω | = | period |
| Ωi | = | part of the period occupied by the pores by mediums i [m3] |
| Subscripts | = | |
| s | = | solid |
| l | = | water liquid |
| g | = | gas |
| a | = | dry air |
| v | = | water vapor |
| r | = | reference variable |
| * | = | dimensional variable |
Acknowledgments
This work was supported by the French National Research Agency (ANR) through the Program Solar Buildings (project HYGROBAT N°ANR-10-HABISOL-005).