微型直升机旋翼的不可压Euler方程数值计算

Numerical Simulation of Flowfield around Micro Helicopter Rotors by Solving Incompressible Euler Equations

采用拟压缩方法求解低速不可压流动具有效率高、稳定性好的优点。通过求解拟压缩性修正后的Eu ler方程成功地模拟了悬停时微型直升机旋翼的绕流。计算网格采用O-H拓扑形式的结构网格,空间离散采用中心有限体积法,时间推进为五步Runge-K utta方法。采用了当地时间步长、压强阻尼及隐式残值平均方法来加速收敛。应用此方法对低速条件下旋翼进行了数值模拟,计算结果与实验数据吻合得较好,经气动分析,证明拟压缩性方法运用于微型直升机旋翼完全可行。

Two significant technical barriers, which prevent correctly simulating the flow around micro air vehicles, are： （1） the difficulty in finding proper algorithm to solve the very low speed flow; （2） the difficulty in considering the very low Reynolds number. This paper is aimed at solving the first problem. We use a pseudo compressibility method to simulate the hovering flowfield of micro-rotor. This method has been found to be an efficient method for obtaining the solution to the incompressible Euler equations. An O-H type grid around one blade is generated. Finite volume method with central discretization and Runge-Kutta time stepping is used. The technique of local time stepping, pressure damping and implicit residual smoothing are used to increase the convergence rate. The lift of the micro helicopter of centimeter scale is estimated using our computational code. The results show that, with a blade angle of attack of 15°, the micro helicopter can be lifted from the ground ,which is consistent with the experimental results. We can conclude that the pseudo compressibility method is correct and reliable in simulating flow around the micro-rotors.