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Investigation of nonequilibrium two-phase flows in axisymmetric laval nozzles

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Abstract

The singularities of two-phase flows in Laval nozzles were investigated within the framework of the model of a two-fluid continuous medium [1, 2] mainly in a quasi-one-dimensional approximation ([3] and the bibliography therein). Two-dimensional computations of such flows were performed only recently by using the method of buildup [4–7]. However, systematic computations to clarify the influence of the second phase on such fundamental nozzle characteristics as the magnitude of the specific impulse, its losses, and discharge coefficient were performed only in the quasi-one-dimensional approximation [8, 9] and only for the supersonic parts of the nozzle in the two-dimensional approximation under the assumption of uniform flow in the throat [10, 3]. Such an investigation is performed in this paper in the two-dimensional case for the nozzle as a whole, including the sub-, trans-, and supersonic flow domains, and a comparative analysis is given of the magnitudes of the loss of a unit pulse obtained in the quasi-one-dimensional approximation [8].

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Literature cited

  1. J. R. Kliegel and G. R. Nickerson, “Flow of gas-particle mixtures in axially symmetric nozzles,” in: Progress in Astronautics and Aeronautics: Detonation and Two-Phase Flow, Vol. 6, Academic Press (1962).

  2. A. N. Kraiko and L. E. Sternin, “On the theory of the flows of a two-speed continuous medium with solid and liquid particles,” Prikl. Mat. Mekh.,29, No. 3 (1965).

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  5. V. I. Kopchenov, “Solution of the direct problem of the flow of a two-phase mixture of a gas and foreign solid or liquid particles in a Laval nozzle,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6 (1975).

  6. V. I. Kopchenov, “Numerical solution of the problem of a flow of a mixture of a gas and foreign particles in a Laval nozzle with a large relative particle discharge,” in: Questions of Gas Thermodynamics of Power Plants [in Russian], No. 2, Khar'kov (1975).

  7. I. M. Vasenin and A. D. Rychkov, “Numerical solution of the problem of the flow of a mixture of gas and particles in an axisymmetric Laval nozzle,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5 (1973).

  8. A. P. Tishin and R. I. Khairutdinov, “Generalized dependences to determine the loss in specific impulse in nonequilibrium two-phase flow in a nozzle,” Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., No. 1 (1972).

  9. V. E. Alemasov, A. F. Dregalin, A. P. Tishin, and V. A. Khudyakov, Thermodynamic and Thermophysical Properties of Combustion Products [in Russian], Vol. 1, Moscow (1971).

  10. L. P. Vereshchaka, A. N. Kraiko, and L. E. Sternin, “Method of characteristics tocompute supersonic gas flows with foreign particles in plane and axisymmetric nozzles,” Soobshch. Prikl. Mat., No. 1 (1969).

  11. R. W. MacCormack, “The effect of viscosity in hypervelocity impact cratering” AIAA Pap 69-354 (1969).

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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 86–91, November–December, 1977.

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Glazunov, A.A., Rychkov, A.D. Investigation of nonequilibrium two-phase flows in axisymmetric laval nozzles. Fluid Dyn 12, 887–892 (1977). https://doi.org/10.1007/BF01090324

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  • DOI: https://doi.org/10.1007/BF01090324

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