Formation and evolution of secondary streamwise vortices in the compressible transitional boundary layers over a flat plate are studied using a direct numerical simulation method with high-order accuracy and highly effective non-reflecting characteristic boundary conditions.Generation and development processes of the secondary streamwise vortices in the complicated transitional boundary flow are clearly analyzed based on the of numerical results,and the effects on the formation of the ring-like vortex that is vital to the boundary layer transition are explored.A new mechanism forming the ring-like vortex through the mutual effect of the primary and secondary streamwise vortices is expressed.
At the late stage of transitional boundary layers, the nonlinear evolution of the ring-like vortices and spike structures and their effects on the surrounding flow were studied by means of direct numerical simulation with high order accuracy. A spatial transition of the flat-plate boundary layers in the compressible flow was conducted. Detailed numerical results with high resolution clearly represented the typical vortex structures, such as ring-like vortices and so on, and induced ejection and sweep events. It was verified that the formation of spike structures in transitional boundary layers had close relationship with ring-like vortices. Especially, compared to the newly observed positive spike structure in the experiments, the same structure was found in the present numerical simulations, and the mechanism was also studied and analyzed.
通过研究一种基于函数值的(3,2)1阶二元有理插值样条函数中诸如边界插值、极限、解析和正则等性质,指出极限曲面是双曲抛物面,揭示了参数对这种插值曲面的影响.首先引入双8次矩阵表示的凸性判别函数,推导了判定插值曲面凸性的充要条件;然后根据该条件给出数值实例,展示如何适当选取参数实现有理插值样条曲面的局部保凸性.特别发现了这种插值曲面凸性在某些点处即使型值是凸的数据也是相对刚性的,并提出了插值曲面局部保凸的必要条件.最后还讨论了文献(Zhang Y,Duan Q,Twizell E H.Convexity control of a bivariate rational interpolating spline surfaces.Computers&Graphics,2007,31(5):679-687)中存在的部分计算问题.
