Shock Interactions In Hypersonic Internal Conical Flow

Hypersonic inlets are usually accompanied with complex shock interactions,which leads to severe aerothermal/pressure loads on the air-breathing vehicles.Therefore,it is important to understand the shock interactions for performance optimization and innovative design of the vehicles.The inward-turning inlet based on the axisymmetric internal conical flow has shown many advantages,but its intrinsic convergence effects on the shock interaction behaviors are fundamentally different from the planar case.Moreover,when the flow deviates from axisymmetric state,more complicated threedimensional shock interactions occur owing to the flight attitude adjustment of the vehicles.As a result,knowledges of the planar shock are not sufficient to comprehend the shock interactions in inward-turning inlets,which is unfavourable for the innovation development of inlets.In this paper,both the axisymmetric internal conical flow and the internal conical flow deviating from axial symmetry are proposed to investigate the shock convergence and shock reflection using a combination of theoretical analysis,numerical simulation and experiment.The shock convergence generated by an axisymmetric internal cone at an axial incoming flow is theoretically analyzed.According to the equivalence between the steady axisymmetric shock and the two-dimensional cylindrical moving shock described by the hypersonic equivalence principle,a theoretical expression for the shape of axisymmetric shock is derived from the geometrical shock dynamics solution of the cylindrical shock.A quantitative relationship for strength growth rate of the axisymmetric shock is obtained,which reveals that the increased strength and transverse curvature accelerate the shock convergence.The mechanism that the shock convergence is always terminated by a Mach disk is revealed by examining the process of convergence,which provides a basic thought of solving the position of the Mach disk.The expression of the shock shape based on geometrical shock dynamics illustrates that the convergence promotes the shock to meet the von Neumann condition and thus restricts the allowable location of the Mach disk.It is found that the formation of the sonic throat downstream of the Mach disk may depend on or not depend on the expansion waves generated from the trailing edge of the cone.Consequently,the influence of the expansion waves on the position of the Mach disk is clarified.A circular internal cone with a non-axial incoming flow is proposed for the case deviating from the axial symmetry,the angle of attack is applied to examine the deviation,and two stages of shock convergence are found.At a small angle of attack,Mach reflection terminates the shock convergence in the first stage where the shock front maintains continuous and smooth throughout.Theoretical analysis based on the curved shock theory indicates that the earlier behaviors of the shock convergence in the first stage are dominated by the non-uniform shock strength,whereas the effects of non-uniform shock transverse curvature on the shock convergence manifest later.At a relatively large angle of attack,the second stage of the shock convergence appears after the first stage,in which the shock front becomes discontinuous and tends to be planarized.Consequencely,the shock convergence slows down.As the angle of attack further increases,the originally inevitable Mach reflection is replaced by a regular reflection on the symmetry plane.It is revealed that the discontinuity of the shock front and the slowing down of shock enhancement are responsible for the regular reflection.A method based on the hypersonic equivalence principle is proposed to theoretically analyze the three dimensional shock convergence generated by the internal cone at a non-axial incoming flow.This method transforms the three-dimensional steady shock into a two-dimensional near-cylindrical moving shock with initially non-uniform strength.To analyze the evolution of the shock front after the appearance of discontinuity on it,the front-disturbance tracing method based on geometrical shock dynamics is improved by taking the disturbance interactions into account.The improved frontdisturbance tracing method not only predicts the complete evolution of the shock front,but also reveals the formation mechanisms of the two pairs of kinks on the shock front,which deeppens the understanding of the planarization of the shock front after discontinuity.Moreover,the improved front-disturbance tracing method is used to establish a procedure for predicting the shock reflection type on the symmetry plane of the original three-dimensional steady shock,which yields reasonable predictions in a wide range of flow parameters.