On the influence of linear blowing and constant temperature factor on the values of functionals of hypersonic aerodynamics

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. Dependences of hypersonic aerodynamics functionals (the total heat flow, the total Newton friction force and total blowing system power) on controls (the linear blowing into boundary layer, the constant temperature factor, the constant magnetic field) are investigated. The domains of allowed values of functionals of hypersonic aerodynamics are obtained. The results of the computational experiments are presented: the dependences of total heat flow on controls; the dependences of total Newton friction force on controls; the dependences of blowing system power on controls; the mutual dependences of functionals (as the domains of allowed values “Heat and Friction”).