Boundary Layer Stability Characteristics Of Hypersonic Flow Over A Blunt Cone

This thesis investigates the stability characteristics of boundary layers in hypersonic flows around a blunt cone by using a kind of parabolized stability equations (PSE) in a general orthogonal curvilinear system of coordinates, to-gether with a shock-fitting method. The main contributions in this work are as follows:(1) The parallel algorithm of the original shock-fitting method is consider-ably improved, and hence the efficiency of solving problems in parallel with the method is appreciably raised and its applicability scope enlarged. Additionally, a seventh-order upwind compact finite difference scheme is developed for improving resolution of the present method. The numerical tests indicate that the presented numerical method and code are effective and reliable, and could be employed to simulate the receptivity in the boundary layer of super/hypersonic flows around blunt cones, even to reproduce the time evolution of the small disturbances of order 10-5 - 10-4 in free stream.(2) A new PSE (parabolized stability equation) software system is devel-oped in the general orthogonal curvilinear coordinates, consisting of two solvers respectively for linear and nonlinear PSEs. Compared to DNS, the PSE is not only convenient to analyze the evolution of disturbance in the boundary layer, but also reduce the computing time at least by one order of magnitude. The numerical examples show that the presented PSE solvers could give simulated results agreeing well with the DNS results and LST predictions, providing an efficient and reliable computing tool for analyzing the stability characteristics of super/hypersonic boundary layer.(3)The effects of wall temperature on the boundary layer stability for the case of a spherical nose with the radius of 3.81 x 10-3m and a half cone angle of 7°at the Mach number of 7.99 are meticulously analyzed and the following meaningful results are obtained.i) The DNS results indicate that the wall temperature remakably impact the number and positions of GIPs (general inflection points) along the wall normal direction in the boundary layer of hypersonic flow around the blunt cone. The LST results show that decreasing the wall temperature accelerates the growth of the second-mode disturbance and restrains the growth of the first-mode dis-turbance. The frequency of the most unstable second-mode local disturbance decreases monotonically along the streamwise direction. However, the frequency of the most unstable first-mode local disturbance does not monotonically change, which first increases and then decreases. The growth rates of the first mode and second mode keep increasing along the streamwise direction. But the growth rate of the second mode is much larger than that of the first mode. The neutral curve moves toward downstream with decreasing wall temperature. Therefore, the wall temperature has significant effects on the stability of hypersonic boundary layers.ii) When the free-stream disturbances are of the order 10-4, the DNS re-sults imply that the amplitude of disturbance at about 290 times of nose radius downstream along the surface does not change monotonically with the wall tem-perature. There exists a critical wall temperature Tc∈(280,375K) for cold wall. If the wall temperature is lower than Tc, then the amplitude of disturbance for the cold wall is larger than that for the adiabatic wall, and vice versa. Such a conclusion agrees with that drawn by Stetson [79].iii) The receptivity analysis shows that the receptivity coefficient decreases with decreasing wall temperature. The receptivity of lower frequency disturbance waves falls into the interval (0.1,0.2), and that of higher ones into the interval (0.7,0.8). Hence the strength of the receptivity for the second modes is larger than that of the first ones.iv) The results of linear PSE show that decreasing the wall temperature ap-preciably affects the streamwise wave number, growth rate, and amplitude of 2D and 3D small disturbances. The streamwise wavenumber decreases with decreas-ing wall temperature at the front of a given point on the wall surface, but the situation is in contrast behind this point, which depends on the wall temperature. The amplitude of disturbance increases with decreasing wall temperature.v) The nonlinear PSE simulations indicate that lots of high harmonics are enhanced quickly after sufficiently long time evolution of finite amplitude distur-bances. Moreover, decreasing the surface temperature promotes the growth of the higher harmonics, and the 3D harmonic modes have larger growth rate than the 2D ones.