The Method Of Characteristics For The Inverse Problem Of Three-Dimensional Hypersonic Aerodynamics

With the development of hypersonic ramjet technology,the intergrated design technology of airframe and propulsion of the airbreathing hypersonic vehicle has become one of the most important key technologies to restrict its overall aerodynamic performance.However,the existing design methods can not achieve the uniform transition of the space complex curved surface from the perspective of flow.Therefore,the study of three-dimensional supersonic aerodynamic inverse problem is always an urgent and difficult subject.In order to explore valid methods for the inverse problem of three-dimensional hypersonic aerodynamics,the method of characteristic for three-dimensional supersonic flow was analyzed,and the bicharacteristic method for streamline pressure inverse problem and the reference plane method for curved face shock wave inverse problem were proposed.Based on the proposed methods,three-dimensional supersonic nozzles,variable cross-section flow and curved shock wave were designed,and the progress of pressure wave transmission and wave cancelling was discussed.In the Cartesian coordinate system,the general characteristic equations and compatible equations of supersonic flow were deduced from three-dimensional,steady,inviscid and compressible control equations.Based on the concept of Bicharacteristics and Butler algorithm,an abbreviated iMOC-3D solver for three-dimensional pressure inverse problem was established.The three-dimensional coordinates of inviscid contour would be calculated directly according to the flow condition and predetermined boundary pressure.The accuracy order of expansion and compression progress of the scheme was tested by comparing iMOC-3D solutions with analytical results of Prandtl-Meyer expansion wave and Busemann flow.The reliability of iMOC-3D solution was proved to some extent by the order of relative error was 1×10^-4.In the cylindrical coordinate system,the characteristic equations and compatible equations for the reference plane method were deduced from three-dimensional,steady,inviscid and compressible control equations.Combined with two-dimensional step by step form along streamline in vortex flow field,a reference plane method for the inverse problem of three-dimensional shock wave was proposed.The characteristic equations and the compatibility equations were solved in the reference plane which had a same form of two-dimensional MOC.The integral iteration method was applied in the direction of perpendicular to the reference plane in order to determine the cross derivations of solution points,which could insure the second-order accuracy.In order to evaluate the accuracy of reference plane method,conical shock wave and plane shock wave were designed,which was compared with analytical results of Taylor-Maccoll flow and oblique shock relation.By contrast,it could be found that the pressure maximum relative error is 1.3e-3 and 6.1e-5 respectively.Applying iMOC-3D solver,three-dimensional supersonic nozzles with different inlet shapes such as circle,ellipse,rectangle and triangle were designed by presetting one-dimensional wall pressure distribution.The solver’s reliability was verified by comparing simulations between CFD and this solver.Based on the mathematical properties of the hyperbolic partial differential equation,a three-dimensional design method for supersonic variable cross-section flow was proposed.The three-dimensional shape transitions of round to ellipse,round to quadrilateral petals and round to six side petals were designed on the preassigned two-dimensional pressure distribution,which verified the easy control of local wall pressure.A study of wave incomplete propagation caused by local deformation of supersonic circle section flow was discussed.The study involved three-dimensional intersection,reflection,focusing and dissipation of Mach wave.Applying a proposed method of pressure inverse problem,three-dimensional curved face was designed,on which steady local high/low pressure zones were formed.In the process of wave cancelling,the three-dimensional propagation,intersection,focusing and dissipation of pressure wave were explored.The geometrical deformation characteristics of wall were discussed.The coupling effect of pressure wave and wall deformation was studied.And intersecting processes of the pressure waves generated by the multi-disturbance sources were studied.Applying reference plane method,the inverse problem of curved shock wave was proposed.A three-dimensional surface generating a conical shock wave at 3 degrees of attack angle was design.The shock wave curves on their own reference plane were design using MOC,and trustworthiness of three-dimensional flow field was assured by considering the gradient of the plane normal direction.The reliability of reference plane method was verified by comparing CFD simulations.