ABSTRACT

This paper addresses the influence of the scheme used in the convective terms of turbulence and transition transport equations on the numerical accuracy of transitional flow simulations. Three transition models are combined with the $k-\omega$ Shear Stress Transport turbulence model: the $\gamma -R{e}_{\theta }$ model, the γ model and the Amplification Factor Transport model. Two airfoils and a 6:1 prolate spheroid are used as test cases. Using first-order upwind in the convective terms of the k and ω transport equations has a weak effect on the numerical accuracy of the simulations when there is no transition model. However, when combined with the transition models, there is a significant improvement if second-order schemes are used. The iterative convergence obtained for the first-order approach was similar to that observed with the second-order schemes. Therefore, common ‘rules of thumb’ from RANS simulations at high Reynolds numbers may fail when transition models are included.

摘要

本文讨论了湍流和过渡输运方程的对流项中使用的方案对过渡流模拟的数值精度的影响。三种过渡模型结合$克-\omega$ 剪切应力传输湍流模型： $\gamma -\mathrm{电阻}{\mathrm{电子}}_{\theta }$模型、γ模型和放大因子传输模型。两个翼型和一个 6:1 长球体用作测试案例。当没有过渡模型时，在k和ω输运方程的对流项中使用一阶迎风对模拟的数值精度有微弱的影响。但是，当与过渡模型结合使用时，如果使用二阶方案，则会有显着的改进。一阶方法获得的迭代收敛与二阶方案观察到的相似。因此，当包含转换模型时，高雷诺数下 RANS 模拟的常见“经验法则”可能会失败。