直角网格壁函数的二维高雷诺数机翼绕流计算

Numerical simulation of 2D airfoil flow in high Reynolds number based on Cartesian grid wall function method

针对传统直角网格方法无法准确计算高雷诺数下近壁面区域的流场及剪切应力问题,本文基于自主开发的二维直角网格CFD求解器,采用添加壁面函数的方式模拟了高雷诺数下的机翼绕流。数值模型基于直角网格有限差分方法对N-S方程进行离散,整体求解器的精度在空间和时间上分别达到二阶。通过对低雷诺数下圆柱绕流及机翼绕流的模拟计算,验证了此求解器的精度和可靠性。在高雷诺数下利用壁面函数修正近壁面的速度剖面,使近壁面区域的速度分布更符合实际流动。研究结果表明:本文方法能够有效求解二维高雷诺数机翼绕流问题。同时利用商业计算流体力学软件Star-CCM+采用贴体网格对同样问题进行模拟,数值模拟结果表明本文方法的网格需求要大于贴体网格。

The traditional Cartesian grid method cannot accurately calculate the flow field and shear stress in the near wall region under a high Reynolds number.Hence,a wall function method is adopted to simulate the high Reynolds number airfoil flow using the two-dimensional Cartesian grid independent development CFD solver.N-S equations are discretized on a Cartesian grid based on the finite difference method,and the accuracy of the present flow solver reaches the second order in space and time dispersion.The accuracy and reliability of the present solver are verified by simulation of the flow around the cylinder and the airfoil under a low Reynolds number.The velocity profile near the wall is modified using the wall function at a high Reynolds number,and the velocity distribution near the wall is found to be consistent with the actual flow field.The results show that the present method can accurately solve the 2D airfoil flow under a high Reynolds number.The commercial CFD software Star-CCM+is also used to simulate the same problem with a body-fitted grid,and the findings show that the grid requirement of the present method is larger than that of the body-fitted grid.