On the problems of analysis and synthesis of control of boundary layer on permeable surfaces of hypersonic aircraft

Abstract

The problems of mathematical modeling of effective control of heat and mass transfer and friction on permeable cylindrical and spherical surfaces of hypersonic aircraft are considered. The systems of ordinary differential equations are obtained by A.A.Dorodnicyn generalized integral relations method to approximate the systems of partial differential equations describing laminar boundary layers on permeable cylindrical and spherical surfaces of hypersonic aircraft. The joint systems are applied in the mathematical model. The parameters of the mathematical model at the flow stagnation point are determined from the joint systems of nonlinear algebraic equations. The blowing into boundary layer, temperature factor and magnetic field are used as controls. Integration, observation and control meshes are introduced throughout the entire control segment. The local and integral characteristics of heat transfer and friction computed according to the parameters of the mathematical model corresponding to the given controls are analyzed in direct problems. The controls corresponding to the given characteristics of heat transfer and friction are synthesized in inverse problems. The direct and inverse problems in ordinary and extreme statements are considered throughout the entire control segment. The statements of the hybrid direct extreme problem are given. A hybrid objective function is introduced. The statements of two-dimensional inverse problems that have, in contrast to one-dimensional ones that admit only interpolation and approximation statements, additionally two mixed statements are considered in details. Additional restrictions for inverse problems in the approximation statement are described. Classification of the listed problems is carried out on the entire control segment. The results of the classification are presented in the form of tables.