Model And Influence Of Secondary Wave Structures For Two Kinds Of Wave Interaction Problem In Supersonic Flow

The phenomenon of wave interference is common and important in supersonic flow.Shock wave intersection and shock wave reflection are common wave interference phenomena.Wave interference will produce new wave structures,change the downstream flow state and have important influence on the local and overall aerodynamic force and aerodynamic heating.Thus,wave interference is an important problem of compressible flow for both academic research and engineering application of high speed vehicle.In the past,people mainly paid attention to the primary interference structure caused by wave system interference,and had not paid enough attention to the influence of the secondary wave structure produced by the primary interference structure.There are two typical problems with secondary wave structures.The first is the Mach reflection problem,which has secondary wave structure on the slip line from the triple point.The second is the supersonic starting flow problem.When the wing suddenly gets a small angle of attack,both stationary Mach wave and unsteady Mach wave are produced on both sides,and secondary waves are generated by the interference of each other.The secondary wave structure is not easily observable and its effect is easy to be ignored.The first problem needs analytical model while the second one needs extension to high angle of attack,both of which will be considered in this work.For the Mach reflection problem,we derive analytical expressions for the shape of slipline and reflected shock wave,accounting for influence of secondary waves.These theoretical relations are further used to obtain analytical theory to determine the Mach stem height and the overall flow structure.The shape of the slip line is predicted by the analytic method,including the slope of the slip line.Using the analytical method we find that,the slip line has a slope discontinuity at the point intersecting the leading transmitted expansion wave,resulting in an oblique shock wave,called here the turning point shock wave.We validate this finding with numerical simulations.For supersonic starting flow problem,we extend the linear theory of Heaslet-Lomax to high angle of attack,by building analytical solutions for uniform flow regions and approximate similarity solution for secondary wave region.This solution is used to obtain normal force coefficient.Numerical computations show that the nonlinear theory thus obtained can predict the pressure coefficient distribution and the time evolution of aerodynamic force accurately at high angles of attack.Furthermore,for the starting flow problem,we find that the adjacent uniform flow regions define a discontinuity at the initial time.The analysis of the Riemann solution shows that the boundary of the secondary wave region may be a shock wave on the Leeward side.By comparing the Riemann solution,pure similarity solution and numerical solution,we find that the boundary of the secondary wave is closer to the results given by the Riemann solution,especially in the leeward side there is a left-going shock wave and inside the secondary waves we have similarity solution.Thus,the solution of the secondary waves is a hybrid Riemann-similarity solution.This paper enriches the theory of shock wave reflection and shock wave interference.