跨声速开槽壁超临界翼型洞壁干扰的N－S方程模拟

Simulation of Transonic Slot Wall Interference on Supercritical Airfoil Using N-S Equation

本文采用二维可压缩非定常Ｎ－Ｓ方程模拟了带有上下开槽壁的跨声速二维管风洞中超临界翼型绕流的流场。网格生成中内层采用解双曲型偏微分方程，外层采用代数生成法。开槽壁采用只有压力梯度没有顶板运动的Ｃｏｕｅｔｔｅ流动的解析解近似。推导出槽间流动与开闭比的三次方关系。上下壁边界层可由无滑移条件直接模拟，也可用平板边界层近似。本文对驻室压力作了几种近似处理，结果表明，所给Ｎ－Ｓ方程的边界条件与风洞实验多接近一步，其结果就符合得更好，这为下一步用Ｎ－Ｓ方程进行洞壁干扰修正打下了基础。

Transonic tube wind tunnel flows over supercritical airfoils with slots on both upper and lower walls have been simulated by using compressible unsteady two dimensional Navier-Stokes equations. Hyperbolic partial differential equations have been used in grid generation of the inner layer. Grid generation of the outer layer is completed by algebraic methods. Flows in the slot are approximated by the analytical solution of couette flows without upper wall movement and the only impetus of the flows is pressure gradient. The third-order relationship between the flow in the slot and the ratio of slot area to wall area is obtained in the paper. Wall boundary conditions can be nonslip velocity condition or approximated by flat plate boundary layer. The chamber pressure has been dealt with by using several approximations. The results show that the more consistent between the boundary condition of the N-S equation and the condition of the wind tunnel experiment, the closer the results between the experiment and the computation.