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未分类

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formula 1：

$$\begin{aligned} -\nabla p & =\frac{\mu}{\kappa} \mathbf{u}+\beta \rho \mathbf{u}|\mathbf{u}| \\ \beta & =\frac{c_{F}}{\sqrt{\kappa}} \end{aligned}$$

CF is Forchheimer parameter
𝜅 is permeability

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fomula 2：

$$\begin{aligned} S=-\left(\frac{\mu \phi}{K}+\frac{\rho \phi^{2} F|\boldsymbol{u}|}{\sqrt{K}}\right) \boldsymbol{u} \end{aligned}$$

𝜙 is void fraction;
F is Forchheimer parameter
K is permeability

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fomula 3(with Ergun equation)：
from this paper,I got the following formula by working backwards from the result of this paper(The detailed calculation formula is not given in this paper)

$$\begin{aligned} -\nabla p & =\frac{\mu\epsilon_{p}}{\kappa} \mathbf{u}+\beta \rho \mathbf{u}|\mathbf{u}| \\ \beta=\frac{1.75}{d_{p}}\frac{1-\epsilon_{p}}{\epsilon_{p}^{3}}\\ \kappa=\frac{d_{p}^{2}}{150}\frac{\epsilon_{p}^{3}}{(1-\epsilon_{p})^{2}} \end{aligned}$$

dp is porous diameter
𝜅 is permeability

$$\begin{aligned}\epsilon_{p}\ is\ void\ fraction\end{aligned}$$