悬停旋翼无粘流场数值模拟中的多重网格方法

The mutilgrid method in Euler equation computation about a helicopter rotor in hover

发展了一种基于不同空间离散格式的多重网格算法,并应用于悬停旋翼无粘绕流的Euler方程数值模拟。由于悬停旋翼流场中存在不可压区域,同时旋翼尾涡系统的发展需要较长的时间,使得旋翼流场的收敛速度远低于固定翼流场,因此研究旋翼流场的多重网格算法具有重要意义。空间离散采用了Roe s FDS格式和Jameson中心有限体积格式,时间推进应用了五步Runge-Kutta方法。采用多重网格V循环方式,对一跨声速悬停旋翼无粘流场进行了数值计算。计算结果表明:多重网格算法可以显著加速悬停旋翼无粘流场的数值计算收敛速度;无论在激波分辨率还是在计算精度上,Roe s FDS格式都优于JST格式。

An effective multigrid method has been developed to compute the Euler solution for a helicopter rotor in hover using different space discrete schemes. The reasons of using multigrid method are the following. the flow near the hub is incompressible flow, which can slow the convergence; for the most part, the net flow velocity at the plane of the rotor and in the rotor wake itself is comprised of the velocities induced by the wake especially by the tip vortices. So the full development of wake is very important for the convergence of the flow field, but it require a long time in the numerical simulation. Accordingly, the application of acceleration measure is very useful for the rotor computation. In this Euler solver, Roe＇s FDS scheme and Jameson finite volume methods are used in space solution and five-step Runge-Kutta methods are used in time solution. A three-level V cycle multigrid method is implemented in a transonic flow computation. Numerical results show that the present multigrid method can speed up the rotor flow convergence rate remarkably and no matter what is in shock-capturing or computation accuracy Roe＇s FDS scheme is better than JST scheme.