边界层流中当地感受性过程的数值研究

Numerical Study of Local Receptivity in the Boundary Layer

边界层流中当地感受性问题的研究对层流向湍流转捩过程的预测与控制起着非常关键的作用,尤其是对边界层内诱导产生三维Tollmien-Schlichting(T-S)波成因过程的探讨具有更加重要的理论意义.采用高精度、高分辨率变间距的紧致有限差分方法,直接数值模拟了在自由来流湍流与二维壁面局部粗糙相互作用下边界层内的当地感受性问题.数值计算发现,在自由来流湍流与二维壁面局部粗糙作用下,边界层内诱导形成的当地感受性过程是真实存在的;且被激发的一组三维T-S波波包沿流向发展的过程中流向涡结构将逐渐形成,其强度将越演越烈.数值结果还显示,边界层内被诱导产生当地感受性过程的波长转换机制仅使流向波数发生改变,而展向波数保持不变;以及自由来流湍流运动方向的改变将决定三维T-S波波包的传播方向,但其传播速度的大小都近似为无穷远来流速度的1/3.另外,还建立了自由来流湍流的强度和运动方向以及二维壁面局部粗糙的长度和高度与边界层内的当地感受性问题之间的关系等.这一课题的深入研究,将在进一步理解和认识层流向湍流转捩的理论机制,以及湍流的形成机理等方面均起到十分重要的作用.

The research on local receptivity in the boundary layer is very important for the prediction and control of the laminar-turbulent transition, and especially the study on the formation mechanism of 3D Tollmien-Schlichting （T-S） waves is meaningful in theory. The high-order high-resolution non：uniform compact finite difference schemes were utilized to study the local receptivity under the interaction of free-stream turbulence and 2D localized wall roughness. The numerical results verify the exsistance of the local receptivity under the interaction of free- stream turbulence and 2D localized wall roughness, and the streamwise vorticity forms and gets stronger downstream as the excited 3D T-S wave packets evolve in the streamwise direction. The numerical results also show that the propagation direction of the excited 3D T-S wave packets is influenced by the propagation direction of the free-stream turbulence, and the propagation speed is close to 1/3 of the free-stream velocity; the wave-length conversion mechanism only changes streamwise wave number α, whereas spanwise wave number fl keeps unchanged. In addition, the relation between the free-stream amplitude and incident angle, the localized wall roughness height and length, and the local receptivity, is confirmed. The in-depth research on this subject is helpful for further understanding of the laminar-turbulent transition and tubulence formation.