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"Heating of a homogeneous volume" +date = 2023-02-10T16:12:48+01:00 +weight = 100 +image = "domain.png" ++++ + +{{< data-link >}} +This example is one of the mini-benchmarks of FE-Modelling Task Force +(by Andrés Alcolea et. al.). The example is aimed to simulate the coupled THM + processes in a fully water saturated unit cubic porous medium ($[0, 1]^3\,\text{m}^3$) + with a linear homogeneous temperature increment from + 20$^{\circ}$C to 30$^{\circ}$C in 100 days. + +The gravity is not considered in all balance equations. + Since the temperature is homogeneous, the specific heat capacity is set to zero + and thermal conductivity can be any non-zero number. The liquid density is + given as + $$\rho_L = \rho_0 \exp (\beta_L (p_L-p_0)+\alpha_L^T(T-T_{ref})) $$ + with + +- $\rho_0=1002.6$ kg/m$^3$ the initial liquid density, +- $\beta_L=4.5\cdot10^{-10}$ Pa the liquid compressibility, +- $\alpha_L^T=-2.0\cdot 10^{-4} \text{ K}^{-1}$ the liquid thermal expansivity, +- $T_{ref} = 273.15 \text{ K}$ the reference temperature. + + While the liquid viscosity is defined as + $$\mu_L = \text{A}\exp(\text{B}/T)$$ +with A=$2.1\cdot 10^{-6} \text{ Pa}\cdot\text{s}$, and B=1808.5 K. + + The other material parameters are given below: + +| Property | Value | Unit | +|------------------------|-------|-------------| +| Young's modulus | 1 | GPa | +| Poisson ratio | 0.35 | - | +| Solid thermal expansion | $3 \cdot 10^{-6}$ |$\text{K}^{-1}$ | +| Biot's coefficient | 0.96111 | - | +| Porosity | 0.1 | - | +| Intrinsic permeability |$3.0 \cdot 10^{-20}$ | m$^2$| + +Initially, the temperature is $20 ^{\circ}$C, the pore pressure is + $2\cdot 10^6$ Pa, and all effective stress components are zero. + +At the boundary surfaces, there is no heat or flow flux, and the normal + displacement is fixed to zero. + +As a CTest, only 5 time steps with a fixed time step size $1.728\cdot 10^4$ s + are computed. If the example is run up to 50 time steps, corresponding to 100 + days of simulation time, the variations of pressure and effective + stress can be obtained as that are shown in the two figures below: + +<figure> +<img src="p.png" alt="drawing" width="400"/> +<img src="Szz.png" alt="drawing" width="415"/> +</figure> diff --git a/web/content/docs/benchmarks/thermo-hydro-mechanics/heating-homogeneous-domain/p.png b/web/content/docs/benchmarks/thermo-hydro-mechanics/heating-homogeneous-domain/p.png new file mode 100644 index 0000000000000000000000000000000000000000..e7ea7be191def3a0713e39f3dda2c50dbe539475 GIT binary patch literal 21029 zcmbWf1yq%5v^BgD#UeyWDJ7-5%b+9`kPd03Lpm*_5$QGv0Vx4tOG~#12uOE#_rG4w zx%ZxP@BO~<jo&dCp5xxU@x)ql%{kZO|3Fb1=hF2{C=?3kzKn!23U!7bg~G_YfCc~Z z$WcNC{t|p9sqsw3#`Kx9fxQVz!Qh##rOh+Tr-nD2Oza(=+E{b5@v(8S+<5ZrnXQ8m zJG<3?eu2%#-i-a$EQujp<f5&NrUMFvXMp@*d=^iCib6encVFU;s!PJskgG<d<M_$R zjDhr70^>&#ZT9@V*u;4}%x%x=l}zIQ@EK`pVlkO#px@sOo-pn=j1^3aW#!9OJ7d0F 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