A Study Of The Stability, Transition And Turbulence In Supersonic Sharp/Blunt Cone Boundary Layers

With the development of the aeronautics and aerospace technology in recent years, the problems of transition and turbulence in supersonic and hypersonic boundary layers attract more and more attention. In order to be closer to real situation in the engineering problems, boundary layers on supersonic and hypersonic cones are selected as prototypes for our research. Direct numerical simulation (DNS) method is used to study the stability, transition and turbulence of the boundary layers, and the BL turbulence model has also been used to compute the turbulent boundary layers. The main conclusions obtained are as follows:1. The laminar basic flow of the boundary layer of a sharp cone with small angle of attack is calculated by a simplified perturbation method. Through the comparison of the evolution of disturbances obtained by DNS with that obtained by linear stability theory (LST), the reliability of the method is confirmed.2. Through the numerical study and the subsequent analysis of the transition process in the boundary layer of a hypersonic sharp cone with zero angle of attack and oncoming Mach number 6, similar conclusions, in regard with the mechanism of transition, has been found as for the transition in boundary layers on flat plates, i.e., the rapid change of the stability characteristics of the mean flow profile is the inherent mechanism for the breakdown in the transition, and in which the first mode unstable waves play the key role.3. Through the DNS of supersonic turbulent boundary layers on a blunt cone, it is found that, the near-wall law of the mean velocity, under Van Driest transformation, and the similarity of the mean profiles are not influenced by the cone effect, while the mean temperature of the turbulent boundary layers is higher and the compressibility effect is weaker than those for flat plates. The distribution of the Reynolds stresses, the correlation of the fluctuations of turbulent quantities and the budget of turbulent kinetic energy in the turbulent boundary layers of a blunt cone are similar, in tendency, with those for boundary layers on flat plates, and the influence of cone effect is only of quantitative nature.4. Through the comparison between the results obtained by BL turbulence model and the DNS, it is found that the wall friction coefficient obtained by both methods agree well with each other, while the thermodynamic variables do not. The near wall Van Driest transformed velocity profile agrees well with the near-wall law in incompressible turbulent boundary layers, while for other places, there are certain differences between the mean flow profiles obtained by DNS and BL model. In addition, the method proposed in the BL model for predicting the transition is found to be inapplicable for vehicles flying at high altitude, because its parameters seem to be determined by conventional wind tunnel experiments, for which the background disturbances is relatively high.5. By analyzing the result of DNS, it is found that the assumption of a constant turbulent Prandl number in the BL model is the main cause for its incorrect prediction of the thermodynamic variables. Modification is accordingly proposed, and the result is satisfactory.