DIRECT NUMERICAL SIMULATION OF VIBRATIONINDUCED T-S WAVE ON BOUNDARY LAYER WALL

The spatial growth of the disturbance in the boundary layer is directly numerically simulated, and the receptivity of the Blasius basic flow to the local two-dimensional （2-D） sustainable micro-vibration is investigated. Results show that the disturbance velocity presents the sine vibration features with the change of time, and the vibration period is identical to the vibration of the local wall. The disturbance velocity presents the fluctuation feature downstream, and the streamwise wave length approximates to the results from the Orr-Sommerfeld equation （OSE）. The growth rate from direct numerical simulation（DNS） is a little greater than that from OSE, and their trends are almost consistent. Under the condition of Re= 2 800, the disturbance amplitude gradually grows in the given computational region with the period T=30. However, it firstly increases and then decreases with the period T= 20. The disturbance harmonic of the former is obviously larger than that of the latter. The maximum streamwise and vertical disturbance velocities from DNS do not fully coincide with those from OSE at the vicinity of the local vibration wall, but coincide well with the former when they travel downstream. The 2-D disturbance induced by the local micro-vibration represents the form of Tollmien-Schlichting （T-S） wave on the boundary layer.

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 local- ized 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 lo- calized rough wall is a key factor causing the fast growth of the disturbance wave. Due to the change of the aver- age 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 in- crease of the nonlinear interaction, the most instable 2-D disturbance wave triggers the appearance of the 3-D dis- turbance 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.