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中文核心期刊

超声速平板边界层斜波失稳转捩过程研究

The study of flow transition process induced by oblique wave instability in a supersonic flat-plate boundary layer

  • 摘要: 以5阶迎风和6阶对称紧致格式混合差分求解三维可压缩滤波Navier-Stokes方程,对Mach数为4.5, Reynolds数为10000的空间发展平板边界层湍流进行了大涡模拟. 时间推进采用紧致存储3阶Runge-Kutta方法,亚格子尺度模型为修正Smagorinsky涡黏性模型. 通过在入口边界叠加一对线性最不稳定第一模态斜波扰动,数值模拟得到了平板层流边界层失稳转捩直至湍流的演化过程. 对流场转捩过程中瞬时量及统计平均量的分析表明,数值模拟结果与理论吻合,得到的Y型剪切层、交替\Lambda涡结构以及转捩后期的发卡涡结构的发展变化与相关文献结果一致,湍流流谱定性合理.

     

    Abstract: The spatial large eddy simulations of the transition process and thefull turbulence in a supersonic flat-plate boundary layer at a free-streamMach number M_\infty = 4.5 and a Reynolds number Re = 10000 arecarried out by solving the three-dimensionalcompressible Favre-filtered Navier-Stokes equations with a hybrid method of a fifth-order upwind compact difference anda sixth-order symmetric compact difference. The compact storagethird-order explicit Runge-Kutta method is applied for the time-integration. Thesub-grid scales are formulated according to the modified Smagorinskyeddy-viscosity model. Based on the linear stability theory, a pair of themost unstable oblique first mode disturbances is imposed on the inflowboundary and the evolution of flow from laminar, transition to fullturbulence, is simulated successfully. The instant and statistical parametersare obtained, and numerical results show a good agreementwith the relevant flat-plate boundary layer theory. Especially the linearand weakly nonlinear growth of disturbance, the appearance of staggered\Lambda -vortex pattern, and the evolution of \Lambda -vortex intohairpin vortex are consistent with related findings in literature.

     

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