A semi-implicit slip algorithm for mesh deformation in complex geometries, implemented in OpenFOAM

Many engineering applications of computational fluid dynamics (CFD) comprise extensive movement of objects that necessitate complex dynamic mesh treatments. In particular, the mesh motion process frequently requires a proper slipping of mesh points on highly curved surfaces. The currently available implementation of explicit slip boundary conditions in OpenFOAM fails to allow large deformations of the mesh without severely degrading the mesh quality and inverting some of the cells. Thus, a robust semi-implicit slip algorithm, based on the Laplacian smoothing methodology, is developed in the present work to tackle this issue. The algorithm is in fact performed in two steps, one explicit and one implicit. The OpenFOAM implementation of the algorithm includes different mesh motion solvers and boundary conditions, based on the displacement or velocity of points. The method is first verified using simple, yet relevant, test cases, and it is shown that the developed algorithm significantly outperforms some of the well-known proprietary CFD codes. Then, it is applied to a complex practical CFD case study. An engineering application that requires the features of the developed mesh motion algorithm is the transient operation of Kaplan turbines. These double-regulated machines simultaneously adjust the guide vane and runner blade angles while changing the operating condition. CFD simulations of such transient operations are highly complex, as they involve mesh deformation of the guide vane passage and simultaneous mesh deformation and rigid-body rotation of the runner blade passage. The mesh deformation requires points to slip on the curved hub and shroud surfaces while preserving the cell quality in tiny blade clearances. Therefore, the feasibility of the developed algorithm is evaluated for a load rejection sequence of a Kaplan turbine model.

众多计算流体动力学（CFD）的工程应用涉及大量物体的广泛移动，这要求进行复杂的动态网格处理。特别是，网格运动过程通常需要网格点在高度曲率的表面上实现适当的滑动。目前OpenFOAM中显式滑动边界条件的实现，未能允许网格在大变形的情况下使用，而不会严重降低网格质量并使部分单元格发生反转。因此，本研究开发了一种基于拉普拉斯平滑方法的鲁棒半隐式滑动算法，以解决这一问题。实际上，该算法分为两个步骤，一个是显式步骤，另一个是隐式步骤。OpenFOAM对该算法的实现包括基于点位移或速度的不同网格运动求解器和边界条件。该方法首先通过简单而相关的测试案例进行验证，结果表明所开发的算法在性能上显著优于一些知名的专有CFD代码。随后，将其应用于一个复杂的实际CFD案例研究。需要所开发网格运动算法特征的一种工程应用是卡普兰涡轮机的瞬态运行。这些双调节机器在改变运行条件的同时，同时调整导叶和叶轮叶片的角度。此类瞬态运行的CFD模拟非常复杂，因为它们涉及到导叶通道的网格变形以及叶轮通道的网格变形和刚体旋转。网格变形要求点在弯曲的轮毂和叶片外壳表面上滑动，同时保持微小叶片间隙中的单元格质量。因此，对该算法在卡普兰涡轮机模型负载拒绝序列中的可行性进行了评估。