局部粗糙边界层流中二维T-S波的非线性演化

采用局部喷、吸、喷与吸组合的结构来模拟局部粗糙壁面,通过数值计算获得了稳定的三维边界层基本流的数值解.在此基础上,研究了最不稳定的和稳定的二维扰动T-S波在时、空间演化过程中非线性问题;探讨了局部粗糙的形式、强度大小及分布结构对二维T-S波的非线性演化的影响及其对增长速率贡献的大小.数值结果表明,三维局部粗糙壁面诱导产生的基本流是扰动波得以增长的关键因素;最不稳定的二维扰动T-S波在非线性演化过程中,由于非线性相互作用的不断增强,逐渐诱导激发出三维扰动波及高次谐波,其三维扰动波的流向波数和频率与二维扰动波的流向波数和频率大致相同.此外,展向速度的大小激励着二维扰动波的快速增长,随后发生初次失稳、流向涡形成、正负相间剪切层逐渐增强、诱导产生三维不稳定扰动波及高阶失稳等机制.上述结论与实验结果相吻合.

NONLINEAR EVOLUTION OF TWO-DIMENSIONAL T-S WAVE IN LOCALIZED ROUGH BOUNDARY LAYER

Numerical simulations are carried out to investigate the mechanism of the nonlinear evolution of two-dimensional (2-D) Tollmien-Schlichting (T-S) wave on a localized rough boundary layer. The three-dimensional (3-D) numerical solution of a base flow on a boundary layer is obtained for the localized rough wall with the localized ejection, the localized suction and the combination of ejection and suction. Based on numerical simulations, the processes of stable and the most instable nonlinear evolution of the 2-D disturbance T-S wave are studied. The effects of the form on the localized roughness, the intensity, and the distribution structure on the nonlinear evolution of 2-D T-S wave and the growth rate are discussed. Results show that the basic flow induced by the localized rough wall is a key factor causing the fast growth of the disturbance wave. Due to the change of the average flow profile and the existence of the spanwise velocity, the localized rough wall enhances the instability of the flow. Consequently, the instable region of the neutral curve is enlargened, and the maximnum growth rate of the 2-D T-S wave is increased. In the process of the nonlinear evolution of 2-D disturbance T-S wave, with the increase of the nonlinear interaction, the most instable 2-D disturbance wave triggers the appearance of the 3-D disturbance wave and the high-frequency harmonic wave. Its streamwise wave number and the frequency are the same as those of 2-D disturbance wave. The spanwise velocity can excite the growth of the 2-D disturbance wave, the instability of 2-D wave, the formation of the streamwise vortex, and the generation of 3-D disturbance wave. Simulation results agree well with experimental results.