Effects of wall temperature on boundary layer stability over a blunt cone at Mach 7.99

Abstract

Effects of wall temperature on stabilities of hypersonic boundary layer over a 7° half-cone-angle blunt cone are studied by using both direct numerical simulation (DNS) and linear stability theory (LST) analysis. Four isothermal wall cases with T w / T 0 = 0.5 , 0.7 , 0.8 and 0.9 , as well as an adiabatic wall case are considered. Results of both DNS and LST indicate that wall temperature has significant effects on the growth of disturbance waves. Cooling the surface accelerates unstable Mack II mode waves and decelerates the first mode (Tollmien–Schlichting mode) waves. LST results show that growth rate of the most unstable Mack II mode waves for the cases of cold wall T w / T 0 = 0.5 and 0.7 are about 45% and 25% larger than that for the adiabatic wall, respectively. Numerical results show that surface cooling modifies the profiles of ρ du t dy n and temperature in the boundary layers, and thus changes the stability characteristic of the boundary layers, and then effects on the growth of unstable waves. The results of DNS indicate that the disturbances with the frequency range from about 119.4 to 179.1 kHz, including the most unstable Mack modes, produce strong mode competition in the downstream region from about 11 to 100 nose radii. And adiabatic wall enhances the amplitudes of disturbance according to the results of DNS, although the LST indicates that the growth rate of the disturbance of cold wall is larger. That because the growth of the disturbance does not only depend on the development of the second unstable mode.