Abstract
The flow of a viscous compressible gas from the apex of a flat wedge is considered. It is shown that an asymmetric self-similar flow is possible and is realized when special boundary conditions for the temperature of the channel walls are specified. For the case of low subsonic gas-flow velocities at constant but different temperatures of the wedge walls, an asymptotic solution is found. In the general case, the resulting system of ordinary differential equations is solved numerically.
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REFERENCES
Jeffery, G.B.L., The two-dimensional steady motion of a viscous fluid, London, Edinburgh Dublin Phil. Mag. J. Sci., Ser. 6, 1915, vol. 29, issue 172, pp. 455–465.
Hamel, G., Spiralförmige Bewegungen zäher Flüssigkeiten, Jahresber. Dtsch. Math.-Ver., 1917, vol. 25, pp. 34–60.
Landau, L.D. and Lifshitz, E.M., Gidrodinamika (Fluid Mechanics), Moscow: Nauka, 1986.
Aristov, S.N., Knyazev, D.V., and Polyanin, A.D., Exact solutions of the Navier–Stokes equations with the linear dependence of velocity components on two space variables, Theor. Found. Chem. Eng., 2009, vol. 43, no. 5, pp. 547–566.
Williams, J.C., III, Conical nozzle flow with velocity slip and temperature jump, AIAA J., 1967, vol. 5, no. 12, pp. 2128–2134.
Williams, J.C., III, Diabatic internal source flow, Appl. Sci. Res., 1967, vol. 17, pp. 407–421.
Williams, J.C., III, Conical nozzle flow of a viscous compressible gas with energy extraction, Appl. Sci. Res., 1968, vol. 19, pp. 285–301.
Brutyan, M.A. and Ibragimov, U.G., Self-similar flow of a viscous gas from source in an apex of cone, Uch. Zap. TsAGI, 2018, vol. 49, no. 3, pp. 26–35.
Brutyan, M.A. and Ibragimov, U.G., Self-similarity parameter effect on critical characteristics of Hamel type compressible flow, Tr. Mosk. Aviats. Inst., 2018, issue 100. http://trudymai.ru/published.php?ID=93319.
Byrkin, A.P., Concerning one exact solution of the Navier–Stokes equations for compressible gas, Prikl. Mat. Mekh., 1969, vol. 33, no. 1, pp. 152–157.
Brutyan, M.A., Self-similar solutions of Jeffrey–Gamel type for compressible viscous gas flow, Uch. Zap. TsAGI, 2017, vol. 48, no. 6, pp. 13–22.
Brutyan, M.A. and Krapivskii, P.L., Exact solutions of the stationary Navier-Stokes equations of a viscous heat-conducting gas for a flat jet from a linear source, Prikl. Mat. Mekh., 2018, vol. 82, no. 5, pp. 644–656.
Golubkin, V.N. and Sizykh, G.B., Concerning compressible Couette flow, Uch. Zap. TsAGI, 2018, no. 1, pp. 27–38.
Khorin, A.N. and Konyukhova, A.A., Couette flow of hot viscous gas, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki, 2020, issue 24, no. 2, pp. 365–378.
Brutyan, M.A. and Ibragimov, U.G., Two-dimensional self-similar flow in a channel of viscous gas with transfer coefficients arbitrarily depending on temperature, Prikl. Mat. Mekh., 2021, vol. 85, no. 6, pp. 755–764.
Probstein, R.F. and Kemp, N.H., Viscous aerodynamic characteristics in hypersonic rarefied gas flow, J. Aerosp. Sci., 1960, vol. 27, no. 3, pp. 174–192.
Ferziger, J.H. and Kaper, H.G., Mathematical Theory of Transport Processes in Gases, North-Holland, 1972.
Ernst, M.N., Nonlinear model-Boltzmann equations and exact solutions, Phys. Rev., 1981, vol. 78, no. 1, pp. 1–171.
Ernst, M.N., Exact solutions of nonlinear Boltzmann equation, J. Stat. Phys., 1984, vol. 34, no. 516, pp. 1001–1017.
Bobylev, A.V., Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas, Teor. Mat. Fiz., 1984, vol. 60, no. 2, pp. 280–310.
Lifshitz, E.M. and Pitaevskii, L.P., Fizicheskaya kinetika (Physical Kinetics), Moscow: Nauka, Gl. red. fiz-mat. lit., 1979, vol. 10.
Barenblatt, G.I., Podobie, avtomodel’nost’, promezhutochnaya asimptotika (Self-Similarity, and Intermediate Asymptotics), Leningrad: Gidrometeoizdat, 1982.
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Brutyan, M.A., Ibragimov, U.G. Asymmetric Self-Similar Viscous Gas Flows in a Wedge. Fluid Dyn 57, 923–931 (2022). https://doi.org/10.1134/S0015462822070047
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DOI: https://doi.org/10.1134/S0015462822070047