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@wangfei9088 确实如此👍
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@李东岳 哈哈，好。
根据文献和网页，写一下SA湍流模型的公式，方便在OpenFOAM中植入。
$$
\frac{\partial \tilde \nu}{\partial t}+\nabla \cdot (\mathbf{U} \tilde \nu) = c_{b1}(1-f_{t2}) \tilde S \tilde \nu +\frac{1}{\sigma} \left[ \nabla \cdot ((\nu + \tilde \nu)\nabla \tilde \nu) +c_{b2} (\nabla \tilde \nu)^2) \right] - \left[ c_{w1} f_w - \frac{c_{b1}}{\kappa ^2} f_{t2} \right] \left[ \frac{\tilde \nu}{d} \right]^2 + f_{t1} \Delta \mathbf{U} ^2
$$$$
\nu_t = \tilde \nu f_{v1} ,
f_{v1} = \frac{\chi ^3}{\chi ^3 + c_{v1} ^3} ,
\chi = \frac{\nu_t} {\nu}
$$$$
\tilde S = \Omega + \frac {\tilde \nu} {\kappa ^2 d^2} f_{v2} ,
\Omega = \sqrt {2} |\mathbf{W}|,
\mathbf{W} = \frac{1}{2} (\nabla \mathbf{U} - \nabla \mathbf{U} ^T) ,
f_{v2} = 1-\frac{\chi}{1+\chi f_{v1}}
$$
说明：原文用的是$S$表示涡量，这里和网页保持一致，用的$\Omega$。$$
f_w = g \left[\frac {1+c_{w3}^6}{g^6+c_{w3}^6} \right]^{1/6}
$$$$
g = r + c_{w2} (r^6 - r) ,
r = min \left[\frac{\tilde \nu}{\tilde S \kappa ^2 d^2}, 10 \right]
$$$$
f_{t2} = c_{t3} exp(- c_{t4} \chi ^2)
$$$$
f_{t1} = c_{t1} g_t exp \left(- c_{t2} \frac{\omega_t ^2}{\Delta \mathbf{U} ^2}[d^2+g_t ^2 d_t^2] \right) ,
g_t = min \left(0.1, \frac{\Delta \mathbf{U}}{\omega_t \Delta x_t} \right)
$$$$
c_{b1} = 0.1355 ,
\sigma = 2/3 ,
c_{b2} = 0.622 ,
\kappa = 0.41 ,
c_{w1} = \frac{c_{b1}}{\kappa ^2} + \frac{1+c_{b2}}{\sigma}
$$$$
c_{w2} = 0.3 ,
c_{w3} = 2 ,
c_{v1} = 7.1 ,
c_{t1} = 1 ,
c_{t2} = 2 ,
c_{t3} = 1.2 ,
c_{t4} = 0.5
$$壁面边界条件：
$$
\tilde \nu_{wall} = 0 ,
\nu_{t,wall} = 0
$$far field边界条件：
注：方程有无最后一项，far field边界条件是不一样的，如下：
$$
0 \leq \tilde \nu_{farfield} < \frac{1}{10} \nu_{\infty} ,
0 \leq \nu_{t,farfield} < 0.27940 \times 10^{-6} \nu_{\infty}
$$$$
3\nu_{\infty} \leq \tilde \nu_{farfield} \leq 5 \nu_{\infty} ,
0.210438\nu_{\infty} \leq \nu_{t,farfield} \leq 1.294234 \nu_{\infty}
$$ -
$$
\frac{\p\alpha \rho \tilde{\nu}}{\p t} +\nabla\cdot \left( \alpha \rho \bfU \tilde{\nu} \right)- \nabla\cdot\left(\alpha \rho D_{\tilde{\nu}}\nabla \tilde{\nu} \right)
= \alpha\rho \frac{C_{b2}}{\sigma_{\nu_t}} |\nabla \tilde{\nu}|^2
+\alpha\rho C_{b1} \tilde{\nu}\tilde{S}
-\alpha\rho C_{w1} f_w\frac{\tilde{\nu}^2}{{y}^2}+S_{\tilde{\nu}}
$$$$
S_{\tilde{\nu}}=-\alpha\rho f_{t2}\tilde{\nu}\tilde{S}+\alpha\rho f_{t1}(\Delta\bfU)^2+\alpha\rho f_{t2}\frac{C_{b1}}{\kappa^2}\frac{\tilde{\nu}^2}{y^2}
$$我对比了一些，主要是多了个上面这个源项。所以OpenFOAM植入这个应该就是所谓的没有$f_{t2}$项与trip项的SA模型。但是这个$\Delta\bfU$还有后面的$\Delta x$怎么理解？
$\Delta\bfU$ is the difference between the velocity at the field point and that at the trip (on the wall)
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A "trip" in the context of computational fluid dynamics (CFD) and the Spalart-Allmaras turbulence model refers to a turbulent trip. Specifically:
A turbulent trip is a device used to trigger a transition from laminar to turbulent flow in a fluid dynamics experiment or simulation. Fluids can flow in either a smooth, laminar state or a chaotic, turbulent state depending on conditions like velocity, viscosity, and surface roughness.
In CFD using the Spalart-Allmaras model, adding a "trip term" attempts to model the effects of an actual physical trip device that would be used in an experimental flow setup. This trip modeling triggers the transition to turbulence in the simulation.
So in the sentence you referenced, the "trip term" refers to an addition made to the Spalart-Allmaras equations that mimics the effect of a physical turbulent trip, forcing a transition from laminar to turbulent modeling. This trip modeling can be important to accurately replicating real experimental conditions in the CFD simulation.
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A turbulent trip is a device...
厉害了各位老铁。我知道了。感觉这个trip应该不需要植入，如果没有trip的话。那对于没有trip的SA模型，就是
$$
\frac{\p\alpha \rho \tilde{\nu}}{\p t} +\nabla\cdot \left( \alpha \rho \bfU \tilde{\nu} \right)- \nabla\cdot\left(\alpha \rho D_{\tilde{\nu}}\nabla \tilde{\nu} \right)
= \alpha\rho \frac{C_{b2}}{\sigma_{\nu_t}} |\nabla \tilde{\nu}|^2
+\alpha\rho C_{b1} \tilde{\nu}\tilde{S}
-\alpha\rho C_{w1} f_w\frac{\tilde{\nu}^2}{{y}^2}+S_{\tilde{\nu}}
$$$$
S_{\tilde{\nu}}=-\alpha\rho f_{t2}\tilde{\nu}\tilde{S}
+\alpha\rho f_{t2}\frac{C_{b1}}{\kappa^2}\frac{\tilde{\nu}^2}{y^2}
$$只需要搞ft2就可以。要简单不少。那个ft1太长了。
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没人试试SA么，那我还是把坑填上吧。
@xpqiu 在 Wray-Agarwal湍流模型 中说：
A "trip" in the context of
@李东岳 在 Wray-Agarwal湍流模型 中说：
只需要搞ft2就可以。要简单不少。那个ft1太长了。
对，我也这么理解的。
含$f_{t2}$两项，不含$f_{t1}$的SA模型，of10版本。mySpalartAllmaras里wmake，pitzDaily里simpleFoam。感兴趣的可以试试，已测试，没问题，供参考。mySpalartAllmarasTurbulenceModel.tar.xz
注：11楼和14楼的源项少了一个系数$C_{b1}$，应该是：
$$
S_{\tilde \nu} = -\alpha \rho C_{b1} f_{t2} \tilde \nu \tilde S + \alpha \rho \frac{C_{b1}}{\kappa ^2} f_{t2} \left[ \frac{\tilde \nu}{y} \right]^2
$$ -
李 李东岳 被引用 于这个主题
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W wangfei9088 被引用 于这个主题
