Pressure inverse problem of three-dimensional supersonic flow

In order to explore valid methods for three-dimensional supersonic flow design, a technology was proposed to solve the pressure inverse problem by finding inviscid contour on the basis of a preassigned pressure distribution along the wall. A bicharacteristic algorithm is used to solve the inverse problem. Three-dimensional wall coordinates can be calculated directly according to the flow condition and predetermined boundary pressure. The designed three-dimensional contour can be compatible with preassigned pressure distribution by moving forward the solution plane along the x coordinate. The accuracy order of the solver was tested by comparing numerical solutions with analytical results of Prandtl-Meyer expansion wave. Three-dimensional supersonic nozzles with round or oval inlet were designed in this paper on the basis of one-dimensional pressure distributions. The reliability of the solver was validated by corresponding CFD numerical simulations. It can be found that the numerical solutions of the present solver are in good agreement with those of CFD simulations. The solver has the ability for three-dimensional supersonic aerodynamic design by solving the inverse problem based on the bicharacteristics method. Moreover, this solver has advantages of high accuracy, pure three-dimensional solutions, and controllable wall pressure distribution. The method has promising potential of playing a supporting role in the applications of further hypersonic aerodynamic design.