Optimization of a Shock-Wave System

The problem of a system consisting of n + m shock waves which realizes the maximum dynamic pressure is solved for given Mach numbers ahead of the first and the closing shocks provided that the sum of the flow turning angles in the last in waves is equal to the sum of the turning angles in the initial n waves minus the angle of attack. The corresponding necessary conditions of optimality of this shock-wave system, which constitutes a system of nonlinear algebraic equations, are obtained. An efficient iteration method of solving this system of equations, which makes it possible to solve the problem with high accuracy, is developed. The results of solving the problem make it possible to select the optimum supersonic air intake configuration in the preliminary design stage and in the case of a large number of shocks to estimate the limiting air intake parameters and the processes taking place in the air intake.