基于混合笛卡尔网格方法的扑动翼型数值模拟

Numerical Simulation of Airfoil Flapping Based on Hybrid Cartesian Grid Method

针对单体扑动翼型与前扑动/后静止串联布置的双翼型发展了适用于运动边界问题的非定常混合笛卡尔网格方法,并进行了数值模拟研究。在物面附近使用贴体结构网格,外部使用自适应笛卡尔网格来填充,使用最近"贡献单元"方法来实现两套网格之间的信息传递。发展了一套非定常可压缩求解器,使用格心格式2阶精度的有限体积方法实现空间离散,使用隐式LU-SGS双时间步方法实现时间离散。物面边界运动过程中,在贴体网格外边界进行笛卡尔网格的动态几何自适应,使用逆距离插值方法进行新鲜网格单元参数的确定。对扑动翼型的研究重点关注了推力系数与推进效率:除却很小的扑动幅值与减缩频率的工况,在单体扑动翼型后部一倍弦长处放置一个静止翼型能够增大推力系数;但推进效率的改变较为复杂,与扑动的幅值以及减缩频率相关。

An unsteady hybrid Cartesian grid method is proposed for moving boundary problems and simu- lation on a single flapping airfoil and a flapping/stationary airfoil combination in tandem is studied. The near body region is discretized by using body- fitted structured grids, while the remaining computational domain is tessellated with generated Cartesian grids. The data communication between the two grid sets is achieved by finding the nearest donor cell. In order to apply this hybrid grid method, a compressible solver for unsteady flow problems is developed with a cell-centered,2 -order accurate finite volume method for spatial discretization and an implicit dual- time stepping LU- SGS approach for temporal discretization. Geometry- based adaptation is employed as the boundary moves during unsteady simulation, in which the flow solution on the new adapted grids is interpolated from the old Cartesian grids by inverse distance weighting interpolation. In the present study, the primary attention is focused on thrust generation and pro- pulsive efficiency. It is concluded that the thrust generated on a flapping/stationary airfoil combination in tandem will significantly increase compared with that on a single flapping airfoil except when the ampli- tude of the flapping motion and the reduced frequency are large enough. The change of propulsive effi- ciency is rather complicated and is found to be a strong function of the amplitude of the flapping motion and the reduced frequency.