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Coupling of turbulence wall models and immersed boundaries on Cartesian grids
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2020-11-12 , DOI: 10.1016/j.jcp.2020.109995
Shang-Gui Cai , Johan Degrigny , Jean-François Boussuge , Pierre Sagaut

An improved immersed boundary method coupled to turbulence wall models on Cartesian grids is proposed, for producing smooth wall surface pressure and skin friction at high Reynolds numbers. Spurious oscillations are frequently observed on these quantities with most immersed boundary wall modeling methods, especially for the skin friction which is found to be very sensitive to the solid surface's position and orientation against the Cartesian grids. The problem originates from the irregularity of the wall distance on the stair-step grid boundaries where the immersed boundary conditions are applied. To reduce this directional error, several modifications are presented to enhance the near wall solution. First the commonly used interpolation for the flow velocity is replaced by one for the friction velocity, which has much less variation near wall. The concept of using a fictitious point to retrieve flow fields in wall normal direction is abandoned and the interpolation is performed in the wall parallel plane with existing fluid points. Secondly, the velocity gradients at the approximated boundary are computed with advanced schemes and the normal gradient of the tangential velocity is reconstructed from the wall laws. To further protect the near wall solution, the normal velocity gradient and the working viscosity from the Spalart-Allmaras turbulence model are enforced by their theoretical solutions in the interior fluid close to the wall. Additionally, various post-processing algorithms for reconstructing wall surface quantities and force integrations are investigated. Other related factors are also discussed for their effects on the results. The validity of present method has been demonstrated through numerical benchmark tests on a flat plate at zero pressure gradient, both aligned and inclined with respect to the grid, and the NACA 23012 airfoil flow.



中文翻译:

湍流壁模型与直角网格上的沉浸边界的耦合

提出了一种与笛卡尔网格上的湍流壁模型耦合的改进的浸入边界方法,用于在高雷诺数下产生光滑的壁表面压力和蒙皮摩擦。在大多数浸入式边界墙建模方法中,经常会在这些数量上观察到虚假振荡,尤其是对于皮肤摩擦而言,该摩擦对于实体表面相对于笛卡尔网格的位置和方向非常敏感。问题源于阶梯网格边界处的壁距的不规则性,其中应用了浸入边界条件。为了减少该方向误差,提出了几种改进方案以增强近壁解决方案。首先,将常用的流速插值替换为摩擦速度的插值,该值在壁附近的变化要小得多。放弃了使用虚拟点在壁法线方向上获取流场的概念,并且在壁平行平面中使用现有流体点进行插值。其次,采用先进的方案计算近似边界处的速度梯度,并根据壁定律重建切向速度的法线梯度。为了进一步保护近壁溶液,Spalart-Allmaras湍流模型的法向速度梯度和工作粘度是通过它们在靠近壁的内部流体中的理论解来实施的。另外,研究了用于重建壁表面数量和力积分的各种后处理算法。还讨论了其他相关因素对结果的影响。

更新日期:2020-11-12
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