Abstract
The problem of plane, nonstationary gas motion under the effect of a piston in the shape of a dihedral angle moving at constant velocity in the gas is considered. In contrast to one-dimensional motion under the effect of a flat piston, a curvilinear shockwave originates here, and the flow becomes nonisentropic and vortical. This problem is examined herein in a linear formulation when the angle of the piston breakpoint is assumed small. The linear problem reduces to an inhomogeneous Riemann—Hilbert problem whose solution is found explicitly. The problem under consideration adjoins a circle of problems associated with shockwave diffraction and reflection studied by Lighthill [1], Smyrl [2], Ter-Minassiants [3], etc.
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M. J. Lighthill, “Diffraction of blast,” Proc. Roy. Soc., Ser.A200, 554–565 (1970).
J. L. Smyrl, “The impact of a shockwave on a thin two-dimensional aerofoil moving at supersonic speed,” J. Fluid Mech.,15, Pt. 2 (1963).
S. M. Ter-Minassiants, “The diffraction accompanying the regular reflection of a plane obliquely impinging shock wave from the walls of an obtuse wedge,” J. Fluid Mech.,35, Pt. 2 (1969).
L. V. Ovsyannikov, Group Properties of Differential Equations [in Russian], Novosibirsk, Akad. Nauk Sibirsk. Otdel. SSSR Press (1962).
E. T. Whittaker and G. N. Watson, Modern Analysis, Cambridge University Press (1927).
F. D. Gakhov, Boundary Value Problems [in Russian], Moscow, Fizmatgiz (1963).
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 45–50, May–June, 1971.
The author is grateful to L. V. Ovsyannikov for interest in the research and useful comments.
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Teshukov, V.M. Plane nonstationary gas flow with a strong discontinuity. J Appl Mech Tech Phys 12, 381–386 (1971). https://doi.org/10.1007/BF00851619
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DOI: https://doi.org/10.1007/BF00851619