Analysis of the influence of linearly decreasing blowing and linearly decreasing temperature factor on the parameters of the mathematical model and local characteristics of heat and mass transfer and friction on the permeable surfaces of hypersonic aircra

Abstract

The article studies the properties of a mathematical model designed to control heat and mass transfer and friction in the laminar boundary layer on permeable cylindrical and spherical surfaces of hypersonic aircraft. The mathematical model is based on the systems of ordinary differential equations obtained by A. A. Dorodnitsyn’s generalized method of integral relations which was used to approximate the systems of partial differential equations describing laminar boundary layers on the permeable cylindrical and spherical surfaces of hypersonic aircraft. The parameters of the mathematical model at the stagnation point were determined using the systems of nonlinear algebraic equations. Blowing on the boundary layer, the temperature factor, and the magnetic field were used as control mechanisms. The article considers the combination of linearly decreasing blowing, linearly decreasing temperature factor, and a constant magnetic field being applied to the entire control segment. The study of this combination of controls included the following stages: formulating a direct problem; studying the influence of heat and mass transfer and friction on the parameters of the mathematical model; making corresponding conclusions regarding the existing dependencies. The dependencies for the linearly decreasing blowing and linearly decreasing temperature factor were compared with the dependencies obtained previously for the other three combinations of controls. The dependencies of the parameters of the mathematical model, as well as local heat and mass transfer and friction characteristics on controls were obtained. The results of the computational experiments are presented. The article also provides recommendations on the application of the results of the computational experiments as initial data in relation to the problem of effective control synthesis, both for the entire segment of control and for its fragments.