Problem of optimal control of a laminar boundary layer on permeable cylindrical surfaces in supersonic flows

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An approximate method for solving the boundary value problem for the equations of an optimally controlled laminar boundary layer on permeable cylindrical surfaces in high-speed gas flows is considered.

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作者简介

I. Mukhametzyanov

Vostok Branch, Tupolev Kazan National Research Technical University

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Email: m.ilshat@mail.ru
俄罗斯联邦, Chistopol

参考

  1. Sirazetdinov T.K. Optimal problems of gas dynamics // Rus. Aeron., 1963, no. 2, pp. 11–21.
  2. Garaev K.G., Mukhametzyanov I.R. To the theory of an optimally controlled boundary layer on permeable surfaces at various flow modes // Rus. Aeron., 2020, vol. 63, no. 3, pp. 413–424.
  3. Garaev K.G., Mukhametzyanov I.R. Optimally controlled turbulent boundary layers in supersonic gas flows // Math. Models&Comput. Simul., 2023, vol. 15, suppl. 1, pp. S18–S26.
  4. Garaev K.G., Mukhametzyanov I.R. Problem of optimal control of the turbulent boundary layer on a permeable surface in supersonic gas flow // Fluid Dyn., 2018, vol. 53, no. 4, pp. 573–581.
  5. Mukhametzyanov I.R. Optimal control of a turbulent boundary layer on a permeable cylindrical surface in a supersonic gas flow // Rus. Aeron., 2020, vol. 63, no. 1, pp. 67–74.
  6. Garaev K.G. Lie Groups and Noether Theory in the Control Problem with Applications to Optimal Problems of Boundary Layer. Kazan: KSTU Pub., 1994. 240 p. (in Russian)
  7. Garaev K.G., Kuznetsov V.K. An invariant variational problem of the laminar boundary layer // JAMM, 2011, vol. 75, no. 4, pp. 404–409.
  8. Garaev K.G., Kusnetsov V.K. Optimally Controlled Laminar Boundary Layers in Supersonic Gas Flows. Kazan: KSTU Pub., 2013. 164 p. (in Russian)
  9. Dorodnitsin A.A. Laminar Boundary Layer in a Compressible Gas. Moscow: Oborongiz, 1957. pp. 140–173.
  10. Lyu Shen-Tsyuan. Calculation of the laminar boundary layer in a compressible gas in the presence of suction or blowing // Comput. Math.&Mathem. Phys., 1963, vol. 2, no. 5, pp. 1000–1020.
  11. Garaev K.G. Optimal control of heat and mass transfer in a laminar compressible-gas boundary layer on permeable surfaces // Fluid Dyn., 1988, vol. 23, no. 3, pp. 399–406.
  12. Pavlovskii Yu.N. The numerical calculation of the laminar boundary layer in a compressible gas // Comput. Math.&Mathem. Phys., 1963, vol. 2, no. 5, pp. 1021–1042.

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2. Fig. 1. Dependence of the optimal injection speed of the solution of problems 1–3 on the coordinate

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