OpenFOAM中的湍流模型

李东岳

kEpsilon模型 (7.0)

\begin{equation}
\frac{\p\alpha \rho \varepsilon}{\p t} +\nabla\cdot \left( \alpha \rho \bfU \varepsilon \right)- \nabla\cdot\left(\alpha \rho D_\varepsilon\nabla \varepsilon \right) = C_1 \alpha \rho G \frac{\varepsilon}{k} - \left( \left( \frac{2}{3} C_1 - C_{3,RDT} \right) \alpha \rho \nabla\cdot \bfU \varepsilon \right) - \left( C_2 \alpha \rho \frac{\varepsilon}{k} \varepsilon \right) + S_\varepsilon + S_{\text{fvOptions}}
\end{equation}

\begin{equation}
\frac{\p \alpha \rho k}{\p t} + \nabla\cdot \left( \alpha \rho \bfU k \right) - \nabla\cdot \left( \alpha \rho D_k \nabla k \right) = \alpha \rho G - \left( \frac{2}{3} \alpha \rho \nabla\cdot\bfU k \right) - \left( \alpha \rho \frac{\epsilon}{k} k \right) + S_k + S_{\text{fvOptions}}
\end{equation}

\begin{equation}
G=\nu_t\left(\nabla\bfU+\nabla\bfU^{T}-\frac{1}{3}(\nabla\cdot\bfU)\bfI\right) : \nabla\bfU
\end{equation}

\begin{equation}
\nu_t = C_{\mu} \frac{k^2}{\epsilon}
\end{equation}

\begin{equation}
C_\mu=0.09,C_1=1.44,C_2=1.92,C_{3,RDT}=0,\sigma_k=1,\sigma_\varepsilon=1.3,D_k=\frac{\nu_t}{\sigma_k}+\nu,D_\varepsilon=\frac{\nu_t}{\sigma_\varepsilon}+\nu
\end{equation}

Launder, B. E., & Spalding, D. B. (1972). Lectures in mathematical models of turbulence. Launder, B. E., & Spalding, D. B. (1974). The numerical computation of turbulent flows. Computer methods in applied mechanics and engineering, 3(2), 269-289. El Tahry, S. H. (1983). k-epsilon equation for compressible reciprocating engine flows. Journal of Energy, 7(4), 345-353.

kOmega模型 (7.0)

\begin{equation}
\frac{\p \alpha \rho k}{\p t} + \nabla\cdot \left( \alpha \rho \bfU k \right) - \nabla\cdot \left( \alpha \rho D_k \nabla k \right) = \alpha \rho G - \frac{2}{3} \alpha \rho \nabla\cdot\bfU k - C_\mu\alpha \rho\omega k + S_k + S_{\text{fvOptions}}
\end{equation}

\begin{equation}
\frac{\p\alpha \rho \omega}{\p t} +\nabla\cdot \left( \alpha \rho \bfU \omega \right)- \nabla\cdot\left(\alpha \rho D_\omega\nabla \omega \right) = \gamma \alpha \rho G \frac{\omega}{k} - \frac{2}{3} \gamma \alpha \rho \nabla\cdot \bfU \omega - \beta \alpha \rho \omega^2+ S_\omega + S_{\text{fvOptions}}
\end{equation}

\begin{equation}
G=\nu_t\left(\nabla\bfU+\nabla\bfU^{T}-\frac{1}{3}(\nabla\cdot\bfU)\bfI\right) : \nabla\bfU
\end{equation}

\begin{equation}
\nu_t = \frac{k}{\omega}
\end{equation}

\begin{equation}
C_\mu=0.09,\beta=0.072,\alpha_k=0.5,\alpha_\omega=0.5,\gamma=0.52,D_k=\alpha_k \nu_t+\nu,D_\varepsilon=\alpha_\omega \nu_t+\nu
\end{equation}

符号标识：

$\alpha$:相分数
$\rho$:表示密度
$\bfU$:速度
$k$:湍流动能
$\varepsilon$:湍流动能耗散率
$S_k$:湍流动能源项
$S_\varepsilon$:湍流动能耗散率源项

wjzhang

东岳前辈，东岳流体“CFD中的LES大涡模拟”这项文档中 http://www.dyfluid.com/docs/LES.html ，亚格子偏应力是否应该是: T-1/3(tr T)I？

李东岳

多谢，已更新。
这个文章有点过时了，我要找时间重写一下

ShaneHEEE

李老师，我想请教一下您，为什么在kEpsilon等模型.C文件中计算湍流粘性系数的函数correctNut()给出的形式是这样的：
使用了k的平方根而不是二次方

 template<class BasicTurbulenceModel>
 void kEpsilon<BasicTurbulenceModel>::correctNut()
 {
     this->nut_ = Cmu_*sqr(k_)/epsilon_;
     this->nut_.correctBoundaryConditions();
     fv::options::New(this->mesh_).correct(this->nut_);
  
     BasicTurbulenceModel::correctNut();
 }

Tens

@shaneheee sqr是平方，sqrt才是开根号

ShaneHEEE

@tens 啊这，谢谢前辈

CFD中文网

OpenFOAM中的湍流模型

kEpsilon模型 (7.0)

kOmega模型 (7.0)