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Numerical investigation of nonequilibrium flows of mixtures of fusible metal particles and gases in a laval nozzle


There are numerous papers [1–11] on the determination of the parameters of condensed oxide particles which are formed during combustion of metallized fuels. The ambiguity, and sometimes the contradictoriness, of the test results obtained [3–5, 9–11] indicate the difficulties in conducting correct experimental investigations. In this connection, numerical studies using mixtures of calibrated liquid-metal particles and different gases are of practical interest. Different probes can be calibrated by using “calibrated” two-phase flows, the two-phase flow around models and probes can be studied, as can the interaction between liquid-metal particles and the front of an aerodynamic compression shock, their intrusion in different entraining media, the interaction between fine particles (particle-projectiles) and large size particles (particle-targets), etc. In many cases, the prehistory of the flow and the parameters of the gas mixture with the particles in the area of the nozzle exit section must be known to investigate the above-mentioned phenomena. The parameters of different nonequilibrium flows of mixtures of gallium particles and gases in a Laval nozzle are investigated numerically in this paper; the maximum diameter (upper boundary of the spectrum) of the particles (ds = 30 μ) which are not destroyed in the nozzle under the effect of the aerodynamic forces and are suitable for use in a “calibrated” two-phase stream is determined. The computations were carried out in a one-dimensional approximation according to [12–14].

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Literature cited

  1. 1.

    L. P. Bakhir and G. I. Levashenko, “Investigation of aluminum oxide drop size near a burning fuel surface,” Fiz. Goreniya Vzryva,9, No. 6 (1973).

  2. 2.

    L. D. Buglaeva, I. I. Vernidub, Yu. A. Korsunov, É. M. Timokhin, and A. P. Tishin, “Experimental determination of the aluminum oxide drop crushing conditions in a high-temperature gas stream,” Inzh.- Fiz. Zh.,26, No. 5 (1974).

  3. 3.

    B. Brown, “Rocket motor performance nozzle configuration effects in two-phase flow,” Pyrodynamics,3, 3–4 (1966).

  4. 4.

    G. T. Crowe and P. G. Willoughby, “A mechanism for particle growth in a rocket nozzle,” AIAA J.,4, No. 9 (1966).

  5. 5.

    G. T. Crowe and P. G. Willoughby, “A study of particle growth in a rocket nozzle,” AIAA J.,5, No. 7 (1967).

  6. 6.

    L. E. Dean, R. C. Keith, T. L. Summer, and M. V. Taylor, “Ignition and combustion of aluminum in small-scale liquid rocket engines,” J. Spacecr. Rockets,2, No. 5 (1965).

  7. 7.

    R. A. Dobbins, “Measurement of mean particle size in a gas-particle flow,” AIAA J.,1, No. 8 (1963).

  8. 8.

    R. A. Dobbins, “Remote size measurements of particulate products of heterogeneous combustion” in: The Eleventh International Symposium on Combustion, Pittsburg, (1967).

  9. 9.

    R. A. Dobbins and L. D. Strand, “A comparison of two methods of measuring particle size of A12O3 produced by a small rocket motor,” AIAA J.,8, No. 9 (1970).

  10. 10.

    B. Brown and K. P. McArty, “Particle size of condensed oxide from combustion of metallized solid propellent,” in; Proceedings of the Eighth International Symposium on Combustion, Baltimore (1962).

  11. 11.

    H. S. Cheung and N. Cohen, “Performance of solid propellant containing metal additives,” AIAA J.,3 No. 2 (1965).

  12. 12.

    J. R. Kliegel and G. R. Nickerson, “Flow of gas-particle mixtures in axially symmetric nozzles,” in: Detonation and Two-Phase Flow (edited by S. S. Penner and F. P. Williams), Academic Press, New York (1962).

  13. 13.

    S. D. Grishin, A. P. Tishin, and R. L. Khairutdinov, “Nonequilibrium two-phase flow in a Laval nozzle with coagulation of polydispersed condensate particles,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2 (1969).

  14. 14.

    A. P. Tishin and R. I. Khairutdinov, “On the computation of condensate particle coagulation in Laval nozzles,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5 (1971).

  15. 15.

    I. A. Sheka, I. S. Chaus, and T. T. Mityureva, Gallium [in Russian], Naukova Dumka, Kiev (1963).

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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 86–91, March–April, 1976.

The authors are grateful to V. K. Starkov and U. G. Pirumov for discussing the results of the research and to N. M. Alekseev for aid in constructing the graphs.

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Ivanov, N.N., Ivanova, R.A. Numerical investigation of nonequilibrium flows of mixtures of fusible metal particles and gases in a laval nozzle. J Appl Mech Tech Phys 17, 213–216 (1976).

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  • Gallium
  • Metal Particle
  • Oxide Particle
  • Nozzle Exit
  • Aerodynamic Force