1. Reference problem#

1.1. Presentation#

In this test case, we study the pure thermal behavior of a porous medium saturated by a single fluid: water in its liquid phase. In Code_Aster, this is a THM model. The associated law of fluid behavior is of type LIQU_SATU.

1.2. Geometry#

_images/Object_7.svg

Coordinates of points \((m)\):

\(A\text{:}\mathrm{-}\mathrm{0,5}\text{}\mathrm{-}\mathrm{0,5}\text{}C\text{:}\mathrm{0,5}\text{}\mathrm{0,5}\)

\(B\mathrm{:}\text{}\mathrm{0,5}\text{}\mathrm{-}\mathrm{0,5}\text{}D\text{:}\mathrm{-}\mathrm{0,5}\text{}\mathrm{0,5}\)

1.3. Material properties#

solid

Density \(({\mathrm{kg.m}}^{-3})\) Drained Young’s module \(E(\mathrm{Pa})\) Poisson’s ratio Coefficient of thermal expansion of solid \(({K}^{-1})\)

\(2\mathrm{\times }{10}^{3}\)

\(225.\mathrm{\times }{10}^{6}\) \(0.\) \(8.\mathrm{\times }{10}^{\mathrm{-}6}\)

Thermal

Homogenized conductivity \(({\mathrm{W.K}}^{-1.}{m}^{-1})\) Derivative of conductivity homogenized with respect to temperature

\(1.7\) \(0.\)

Homogenization coefficients

Biot coefficient

Porosity »

\({10}^{-12}\) \(0.4\)

Homogenized coefficients

Density \(({\mathrm{kg.m}}^{-3})\) Constant stress heat \(({\mathrm{J.K}}^{-1})\)

\(1.6\times {10}^{3}\)

\(2.85\times {10}^{6}\)

1.4. Boundary conditions and loads#

  • Full item:

    • trips \({u}_{x}=0.0m,{u}_{y}=0.0m,{u}_{z}=0.0m\).

    • fluid pressure \(\mathrm{PRE1}=0.0\mathrm{Pa}\)

  • Underside:

    • temperature \(T=273K\)

  • Upper side:

    • heat flow \(\mathrm{FLUN}=0.5{\mathrm{J.s}}^{-1}\mathrm{.}{m}^{-2}\)

1.5. Initial conditions#

The displacement fields, pressure, temperature are initially all zero, but the reference temperature is not zero. It is worth \({T}_{0}=273K\).