抛物化Navier-Stokes方程在求解高超声速流动稳定性分析的基本流中的应用

Application of parabolized Navier-Stokes equations into basic flows for stability analysis of hypersonic flows

通过在边界层内部使用边界层上缘的流向压力梯度代替该处的流向压力梯度,对传统抛物化Navier-Stokes(PNS)方程求解中的流向压力梯度的处理方法进行改进,从而使它可以求解用于稳定性分析的高超声速流动的基本流,并分别计算了平板、零攻角钝锥和小攻角钝锥三种典型算例.对于流向没有分离,且横向流动不强的流动,使用PNS方程计算高超声速流动稳定性分析用的基本流是可靠的.特别是改进后的方法求得的基本流的稳定性分析结果与直接求解Navier-Stokes(N-S)方程的结果非常吻合,但计算的时间消耗和空间占用都减少了一个数量级.

By using streamwise pressure gradient on the edge of the boundary layer instead of that in the boundary layer,traditional solution for streamwise pressure gradient in parabolized Navier-Stokes（PNS） equations was improved and applied to PNS equations as basic flows for stability analysis of hypersonic flows.Three typical examples with flat,blunt cone at zero and small angle of attack,were calculated.For the blunt three-dimension flows or two-dimension flows,PNS equations are reliable to get the hypersonic basic flows for stability analysis,and the results of the stability analysis are in good agreement with those obtained by solving Navier-Stokes（N-S） equations directly,but expense of time and space is an order of magnitude lower than N-S equations.