Abstract
The shock wave structure in a diatomic gas is investigated using the direct statistical simulation (Monte-Carlo) method. The energy exchange between translational and rotational degrees of freedom (TR-exchange) is calculated by solving the dynamic problem of the interaction between rigid-rotator molecules within the framework of classical mechanics. The density profiles calculated are compared with the experimental data and on this basis the nitrogen rotational relaxation time is estimated. The possibility of using simplified intermolecular interaction models, namely, the variable-diameter sphere model employed together with a phenomenological consideration of the TR-exchange, is studied. Gasdynamic parameter profiles in the shock wave are analyzed. Simple approximations of the velocity gradient and translational and rotational temperature profiles are obtained on the basis of a parametric calculation of the shock wave structure. This makes it possible approximately to describe the gasdynamic parameter profiles in terms of elementary functions.
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REFERENCES
A. N. Kraiko, N. I. Tillyayeva, and S.A. Shcherbakov, “Comparison of integrated characteristics and shapes of profiled contours of Laval nozzles with “smooth” and abrupt contractions,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 129 (1986).
A.N. Kraiko and V. E. Sokolov, “Specific momentum of a flow in the minimal cross section of a Laval nozzle and in the outlet cross section of a contracting nozzle,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 186 (1976).
A. N. Kraiko, Variational Problems of Gas Dynamics [in Russian], Nauka, Moscow (1979).
Yu.D. Shmyglevskii, Analytical Studies in Gas and Fluid Dynamics [in Russian], Editorial URSS, Moscow (1999).
P. R. Spalart and S. R. Allmaras, “A one-equation turbulencemodel for aerodynamic flows,” Rech. A´erosp., No. 1, 5 (1994).
G. M. Bam-Zelikovich, “Calculation of boundary layer separation,” Izv. Akad. Nauk SSSR, OTN, No. 12, 68 (1954).
V.Ya. Neiland and V.V. Sychev, “Asymptotic solutions for the Navier-Stokes equations in regions with large local perturbations,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 43 (1966).
V.Ya. Neiland, “Asymptotic theory for calculating heat fluxes near the corner of a body,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 53 (1969).
V.Ya. Neiland, “The asymptotic theory of the interaction of a supersonic flow with a boundary layer,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 41 (1971).
V.Ya. Neiland, “Asymptotic problems of the theory of viscous supersonic flows,” Tr. TsAGI, No. 1529 (1974).
V.Ya. Neiland, “Asymptotic theory of separation and supersonic gas flow/boundary layer interaction,” Usp. Mekh., 4, No. 2, 3 (1981).
V. I. Kopchenov and A.N. Kraiko, “A monotonic second-order difference scheme for hypersonic systems in two independent variables,” Zh. Vych. Mat. Mat. Fiz., 23, 848 (1983).
E.V. Myshenkov and E.V. Myshenkova, “Calculations of base and lateral separation flows using a grid adapted to the solution,” in: Abstracts of XI Int. Conf. on Comput. Mech. and Modern Software, Istra, 2000 [in Russian], Moscow Aviation Institute (2001), p. 265.
E.A. Ashratov and L. I. Sorkin, “Viscous supersonic flow past an external corner,” Izv. Akad. Nauk SSSR, Mekhanika, No. 4, 165 (1965).
A. N. Kraiko and K. S. P'yankov, “Constructing airfoils and engine nacelles supercritical in transonic inviscid flow,” Zh. Vych. Mat. Mat. Fiz., 40, 1890 (2000).
A. N. Kraiko, K. S. P'yankov, and N. I. Tillyayeva, “Profiling the supersonic part of a plug nozzle with a nonuniform transonic flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4 (2002).
A. N. Kraiko and N. I. Tillyayeva, “Optimal profiling of the supersonic part of a plug nozzle contour,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 172 (2000).
R.K. Tagirov, “Effect of the boundary layer on the flow rate and specific thrust of a convergent nozzle,” Izv. Vuzov, Avia. Tekhn., No. 1, 77 (1988).
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Erofeev, A.I. Investigation of the Nitrogen Shock Wave Structure on the Basis of Trajectory Calculations of the Molecular Interaction. Fluid Dynamics 37, 970–982 (2002). https://doi.org/10.1023/A:1022364700228
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DOI: https://doi.org/10.1023/A:1022364700228