laws:wavat
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laws:wavat [2019/09/20 14:35] helene |
laws:wavat [2023/12/12 16:47] (current) gilles [WAVAT/WAVAT2/WAVAT3] |
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| === Ecoulement du liquide et de la vapeur === | === Ecoulement du liquide et de la vapeur === | ||
| - | En partant de l’équation de Darcy, la vitesse du liquide ( Volume de fluide par unité de surface de sol ) est donnée par : | + | En partant de l’équation de Darcy, la vitesse du liquide (Volume de fluide par unité de surface de sol) est donnée par : |
| \[ | \[ | ||
| \vec{q_l} = - \frac{k_w}{\mu_w}\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\ \text{où}\ k_w = K_w \frac{\mu_w}{\rho_w g}\left[ m^2\right] | \vec{q_l} = - \frac{k_w}{\mu_w}\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\ \text{où}\ k_w = K_w \frac{\mu_w}{\rho_w g}\left[ m^2\right] | ||
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| Following empirical formulations for describing the evolution of the relative permeability, the thermal conductivity and saturation with the suction are possible: see [[appendices:a8|Appendix 8]]. | Following empirical formulations for describing the evolution of the relative permeability, the thermal conductivity and saturation with the suction are possible: see [[appendices:a8|Appendix 8]]. | ||
| For any suction lower than air entry value (AIREV), the saturation is equal to SRFIELD value. \\ | For any suction lower than air entry value (AIREV), the saturation is equal to SRFIELD value. \\ | ||
| - | __Kozeny Karman formulation :__ | + | __Kozeny Karman formulation:__ |
| \[K = C_0 \frac{n^{EXPN}}{(1-n)^{EXPM}}\] | \[K = C_0 \frac{n^{EXPN}}{(1-n)^{EXPM}}\] | ||
| $C_0$ is computed automatically from $C_0 = K_0 \frac{(1-n_0)^{EXPM}}{(n_0)^{EXPn}}$ \\ | $C_0$ is computed automatically from $C_0 = K_0 \frac{(1-n_0)^{EXPM}}{(n_0)^{EXPn}}$ \\ | ||
| - | __GDR Momas formulation :__ | + | __GDR Momas formulation:__ |
| \[ | \[ | ||
| \frac{k}{k_0} = 1+EXPM\left[ \phi - \phi_0\right]^{EXPN}\ \text{où}\ EXPM = 2.10^{12}\ \text{et}\ EXPN = 3 | \frac{k}{k_0} = 1+EXPM\left[ \phi - \phi_0\right]^{EXPN}\ \text{où}\ EXPM = 2.10^{12}\ \text{et}\ EXPN = 3 | ||
| \] | \] | ||
| - | __Coupling permeability-deformation formulation :__ (only in 2D) | + | __Coupling permeability-deformation formulation:__ (only in 2D) |
| \[ | \[ | ||
| K_{ij} = \sum_n K_n^0 (1+A\varepsilon_n^T)^3\beta_{ij} (\alpha_n) | K_{ij} = \sum_n K_n^0 (1+A\varepsilon_n^T)^3\beta_{ij} (\alpha_n) | ||
laws/wavat.1568982900.txt.gz · Last modified: 2020/08/25 15:35 (external edit)
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