Анализ влияния сочетаний линейных управляющих воздействий на область значений функционалов гиперзвуковой аэродинамики

Григорий Григорьевич Бильченко; Наталья Григорьевна Бильченко

doi:10.17308/sait.2021.2/3501

Authors

Grigorij G. Bilchenko Kazan National Research Technical University named after A. N. Tupolev – KAI https://orcid.org/0000-0001-5020-7403 (unauthenticated)
Natalya G. Bilchenko Kazan National Research Technical University named after A. N. Tupolev – KAI https://orcid.org/0000-0002-4101-6151 (unauthenticated)

DOI:

https://doi.org/10.17308/sait.2021.2/3501

Keywords:

control, heat and mass transfer, laminar boundary layer, hypersonic flows, permeable surfaces, linearly increasing blowing, linearly decreasing blowing, linearly increasing temperature factor, linearly decreasing temperature factor, total heat flow, total Newton friction force

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 flow stagnation point are determined from the joint systems of nonlinear algebraic equations. The blowing into boundary layer, the temperature factor and the magnetic field are used as controls.

The article considers the combinations of linear blowing, linear temperature factor and a constant magnetic field being applied to the entire control segment. The statement of direct problem is given. The hypersonic aerodynamics functionals (the total heat flow and the total Newton friction force) dependences on controls (the blowing into boundary layer and the temperature factor) are obtained. The computational experiments results are presented.

Author Biographies

Grigorij G. Bilchenko, Kazan National Research Technical University named after A. N. Tupolev – KAI

PhD in Physics and Mathematics, Researcher, Laboratory of Modeling of Physical and Technical Processes, Department for Heat and Power Engineering
Natalya G. Bilchenko, Kazan National Research Technical University named after A. N. Tupolev – KAI

PhD in Physics and Mathematics, Researcher, Laboratory of Modeling of Physical and Technical Processes, Department for Heat and Power Engineering, Associate Professor of Department of Theoretical and Applied Mechanics and Mathematics

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