The Effect Of Single Roughness Element On The Stability In A Compressible Boundary Layer On A Flat Plate

To get the effect of the roughness elements to the instability of the boundary layer, the method which combined direct numerical simulation and stability analysis was adopted to investigate the influence of the roughness elements of various heights on the Tollmien-Schlichting (T-S) disturbance waves of different frequencies. At first, mean flow at Mach number of4.5was obtained by solving the Navier-Stokes (N-S) equations, of which was performed on the two-dimensional compressible boundary layer of a flat plate with a roughness element of different heights. Stability analysis was employed to investigating the mean flow according to linear stability theory (LST). Then the perturbation equations was used to analyzing the interaction of disturbance waves of different frequencies and roughness elements of various heights. Finally, a transmission coefficient was settled to characterize the effect of roughness elements on the instability.Investigating of the results of42kinds of working conditions, conclusions can be drawn as follow:1、The roughness elements affects the mean flow locally, a mach wave was appeared near the roughness element, the mean flow gets back to the original state of parallel flow away from the roughness element. The higher the roughness element is, the impact on the mean flow is greater.2、The influence of different heights roughness elements of work on the disturbance waves is different at various frequencies. When the disturbance waves are at the same frequencies, the higher the roughness element is, the affect it impacts on the disturbance waves is more obvious. When the heights of the roughness elements are the same, the roughness element destabilizes the low-frequency disturbances and stabilizes the high-frequency disturbances.3、Transmission coefficient AN(ω,h) describes the impact of roughness element on the flow instability quantitatively. With transmission coefficient, we can quickly know the influence of the roughness element of height h on the disturbance wave of frequency ω:when transmission coefficient AN(ω, h) is positive, the roughness element destabilizes the disturbance wave; transmission coefficient AN (ω,h) is negative, the roughness element stabilizes the disturbance wave. The absolute value of the transmission coefficient quantifies the correction of N the roughness element works on the disturbance wave. Transmission coefficient can be used to predict the transition location on the flow with roughness element effectively and efficiently.