Effect Of Local Hump And Its Combination On Stability Of Boundary Layer On Flat Plate

Local hump and its combination cannot avoid to existing on the surface of supersonic aircraft,which will affect the instability of the flow.The effect of local cosine hump and its combination on a compressible boundary layer on a flat plate was studied by using numerical simulation and linear stability theory.The basic flow on a flat plate with Mach number 4.5 was numerically simulated at first,on which stability analysis was carried out by linear stability theory,then the amplitude evolution of unstable disturbances was calculated by solving the perturbation equation,at last the effects of the width,location and distance of local humps on the disturbances with difference frequency were studied quantitatively with the concept of transmission coefficient.The result shows:i.The effect of local hump increases or decreases monotonously as the increase of the width of local hump,and the transmission coefficient tends to be a constant,indicating that the effect of local hump on the amplitude of disturbance is limited.The transmission coefficient reaches 95% of the limitation when the width of local hump is 12,while the wavelength of the most unstable wave at the center of local hump x=40 is about 3,implying that the optimal width of local hump to control the flow is about 4 times of the wavelength of the most unstable wave at the center of local hump.ii.The transmission coefficient decreases linearly as the increase of the location of local hump in the stream-wise direction,suggesting that the location of the local hump should be selected with a careful consideration both with the frequency of most unstable disturbance and which frequency of the disturbance to control,otherwise it may get the opposite effect.iii.A combination hump has the same influence on the disturbance as two individual local humps,and the transmission coefficient decreases linearly with the increase of the distance of the two local humps.Serials of local humps at different appropriate locations can be designed to promote or inhibit the growth of disturbances.