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Optimal shock-wave systems under constraints on the total flow turning angle


A “shock and subsequent rarefaction wave” shock-wave system in a plane supersonic inviscid non-heat-conducting gas flow is considered. An exact analytic solution of the problem of determining the intensities of the waves leading to extreme values of the gasdynamic variables (static pressure, temperature, etc.) behind the wave is found using Lagrangian multipliers. These systems are related to the optimal ones [1, 2]. The parameters of the problem are the free-stream Mach number, the specific heat ratio, and the total flow turning angle in the wave system. Analytic solutions determining the boundaries of monotonic and nonmonotonic behavior of the gasdynamic variables behind the system are presented. The effect of the specific heat ratio on the dimensions of the domains of existence of the optimal waves is investigated.

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Additional information

St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–150, July–August, 1996.

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Omel'chenko, A.V., Uskov, V.N. Optimal shock-wave systems under constraints on the total flow turning angle. Fluid Dyn 31, 597–603 (1996).

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  • Fluid Dynamics
  • Mach Number
  • Lagrangian Multiplier
  • Static Pressure
  • Total Flow