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TRACE User Guide
TRACE Version 9.6.1
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TRACE User Guide
TRACE Version 9.6.1
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The governing equations for the \(\gamma\)- \(Re_\theta\) transition model [33] [30] [28] read
\begin{eqnarray} \DD{\rhobar \gamma}{t} &=& \parfrac{}{x_j} \left[ \left( \mu + \sigma_\gamma \mu_T \right) \parfrac{\gamma}{x_j} \right] + F_\text{length} c_{a1} \rhobar S (\gamma F_\text{onset})^{c_\alpha} (1 - c_{e1} \gamma) \\ &&+ c_{a2} \rhobar W \gamma F_\text{turb} (1 - c_{e2} \gamma) \\ \DD{\rhobar \tilde{Re}_{\theta t}}{t} &=& \parfrac{}{x_j} \left[ \sigma_{Re_\theta} \left( \mu + \mu_T \right) \parfrac{ \tilde{Re}_{\theta t}}{x_j} \right] + c_{\theta t} \frac{(\rhobar U)^2}{c_t \mu} (Re_{\theta t} - \tilde{Re}_{\theta t})(1 - F_{\theta t}) \end{eqnarray}
with
\begin{eqnarray} S &=& \sqrt{2 S_{ij}^* S_{ij}^*} \\ W &=& \sqrt{2 W_{ij} W_{ij}} \\ U &=& \sqrt{U_1^2 + U_2^2 + U_3^2} \end{eqnarray}
The effective intermittency is computed by
\begin{equation} \gamma_\text{eff} = \max (\gamma, \gamma_\text{sep}) \end{equation}
with
\begin{equation} \gamma_\text{sep} = \min \left[ s_1 \max \left( \frac{Re_v}{3.235 Re_{\theta c}} - 1, 0 \right) F_\text{reattach}, s_2 \right] F_{\theta t} \end{equation}
Implemented as in [28] with the correlation for the transition onset momentum thickness Reynolds number \(Re_{\theta t}\) as in [33] .
Implemented as in [28] .
Malan's correlations [30] read
\begin{eqnarray} Re_{\theta c} &=& \min \left( c_{Re_{\theta c} 1} \tilde{Re}_{\theta t} + c_{Re_{\theta c} 2}, \tilde{Re}_{\theta t} \right) \\ F_\text{length} &=& \min \left[ \exp \left( c_{F_\text{length} 1} - c_{F_\text{length} 2} \tilde{Re}_{\theta t} \right) + c_{F_\text{length} 3}, c_{F_\text{length} 4} \right] \end{eqnarray}
1.9.1