用隐式方法和WENO格式计算悬停旋翼跨声速无粘流场

寻找一种能够准确计算以涡为主要特征的复杂流场和克服尾迹耗散问题的数值方法,一直是旋翼空气动力学研究的热点和难点。本文发展了一种基于高阶迎风格式计算悬停旋翼无粘流场的隐式数值方法。无粘通量采用Roe通量差分分裂格式,为提高精度,使用五阶WENO格式进行左右状态插值,并与MUSCL插值进行比较。为提高收敛到定常解的效率,时间推进采用LU-SGS隐式方法。用该方法对一跨声速悬停旋翼无粘流场进行了数值计算,数值结果表明WENO-Roe的激波分辨率高于MUSCL-Roe,体现出了格式精度的提高对计算结果的改善,LU-SGS隐式方法的计算效率比5步Runge-Kutta显式方法的高。

Numerical simulation on the inviscid flowfield of transonic hovering rotor using implicit method and WENO schemes

The most complex flows in aviation are probably those that occur over rotorcraft. To search one numerical method to exactly predict the rotor wake is an unsolved problem. A high-order upwind scheme is developed to compute the inviscid flow field of a helicopter rotor in hover using implicit finite volume method. Roe Riemann solver which is a high-resolution scheme and a flux-difference splitting scheme is adopted to compute inviscid flux. For better accuracy, 5th order weighted essentially non-oscillatory (WENO) schemes are adopted to interpolate higher order left and right states across a cell interface, and compared with MUSCL schemes. To improve the efficiency and convergence to steady state, the LU-SGS implicit algorithm is used. The performance of the schemes is investigated in a transonic inviscid flow around hovering rotor. The results reveal that WENO-Roe has the great capabilities to capture shock with higher resolution than MUSCL-Roe, which shows the advantage of increasing precision, and the implicit LU-SGS scheme is more efficient than 5th order Runge-Kutta method.