No abstract

The direct numerical simulation of boundary layer transition over a 5°half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors' previous work ͓Li et al., AIAA J. 46, 2899 ͑2008͔͒, the whole boundary layer flow over the cone is simulated ͑while in the author's previous work, only two 45°regions around the leeward and the windward sections are simulated͒. The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient ͑C f ͒. The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20°Յ Յ 30°͑ = 0°is the leeward section͒. The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory ͑LST͒. It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20°Յ Յ 30°, which leads to the delayed transition location. Very low frequency waves ͑VLFWs͒ are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.

Direct numerical simulation of transition flow over a blunt cone with a freestream Mach number of 6, Reynolds number of 10,000 based on the nose radius, and a 1-deg angle of attack is performed by using a seventh-order weighted essentially nonoscillatory scheme for the convection terms of the Navier-Stokes equations, together with an eighth-order central finite difference scheme for the viscous terms. The wall blow-and-suction perturbations, including random perturbation and multifrequency perturbation, are used to trigger the transition. The maximum amplitude of the wall-normal velocity disturbance is set to 1% of the freestream velocity. The obtained transition locations on the cone surface agree well with each other for both cases. Transition onset is located at about 500 times the nose radius in the leeward section and 750 times the nose radius in the windward section. The frequency spectrum of velocity and pressure fluctuations at different streamwise locations are analyzed and compared with the linear stability theory. The second-mode disturbance wave is deemed to be the dominating disturbance because the growth rate of the second mode is much higher than the first mode. The reason why transition in the leeward section occurs earlier than that in the windward section is analyzed. It is not because of higher local growth rate of disturbance waves in the leeward section, but because the growth start location of the dominating second-mode wave in the leeward section is much earlier than that in the windward section.