Abstract
The results of an investigation of the dynamics of hard particles and liquid drops in the flow behind a transmitted shock wave are presented. From the equation of motion of a particle in the shock wave, relations for the displacement, velocity and acceleration as functions of time and certain velocity-relaxation parameters taking into account the properties of the gas and the aerodynamic drag of the particles are obtained for unsteady flow around the particles at an acceleration of 103–104 m/s2. It is shown that the velocity-relaxation parameters are universal. Approaches to finding the aerodynamic drag of freely-accelerating bodies from the dynamics of their acceleration after being suddenly exposed to the flow are considered. It is established that under these conditions the drop dynamics observed can be well described in terms of the same velocity-relaxation parameters with account for linear growth of the transverse drop size. All the kinematic functions obtained are confirmed experimentally.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.I. Nigmatulin, Dynamics of Multiphase Media, Pt 1 (Nauka, Moscow, 1987) [in Russian].
S.L. Soo, Fluid Dynamics of Multiphase Systems (Blaisdell, Waltham, MA, 1967).
C.B. Henderson, “Drag Coefficients of Spheres in Continuum and Rarefied Flows,” AIAA Journal 14(6), 707–708 (1976).
T. Sarpkaya, “Separated Flow about Lifting Bodies and Impulsive Flow about Cylinders,” AIAA Journal 4(3), 414–420 (1966).
S.R. Keim, “Fluid Resistance to Cylinders in Accelerated Motion,” Proc. Amer. Soc. Civil. Eng. J., Hydraulics Division 82(6), 1113-1–1113-14 (1956).
B.E. Gelfand, “Droplet Breakup Phenomena Inflows with Velocity Lag,” Progr. Energy Combust. Sci. 22(3), 201–265 (1996).
D.D. Joseph, J. Belanger, and G.S. Beavers, “Breakup of a Liquid Drop Suddenly Exposed to a High-Speed Airstream,” Intern. J. Multiphase Flow 25(6/7), 1263–1303 (1999).
O. Igra and K. Takayama, “Shock Tube Study of the Drag Coefficient of a Sphere in a Non-Stationary Flow,” Proc. Roy. Soc., London 442(1915), 231–247 (1993).
A. Britan, T. Elperin, O. Igra, and J. P. Jiang, “Acceleration of a Sphere behind Planar Shock Waves,” in Proc. 20th Intern. Symp. Shock Waves: Pasadena, 1995, Vol. 2, 1285–1290.
T. Suzuki, Y. Sakamura, T. Adachi, et al., “Shock Tube Study of Particles Motion behind Planar Shock Waves,” in Proc. 22nd Intern. Symp. Shock Waves, London, GB, 1999. Vol. 2, 1411–1416.
C. Devals, G. Jourdan, J.-L. Estivalezes, et al., “Shock Tube Spherical Particle Accelerating Study for Drag Coefficient Determination,” Shock Waves 12, 325–331 (2003).
C. Ortiz, D.D. Joseph, and G.S. Beavers, “Acceleration of a Liquid Drop Suddenly Exposed to a High-Speed Airstream,” Intern. J. Multiphase Flow 30(2), 217–224 (2004).
V.M. Boiko, V.P. Kiselev, S.P. Kiselev, et al., “Shock Wave Interaction with a Cloud of Particles,” Shock Waves 7(5), 275–285 (1997).
V.M. Boiko, V.V. Pickalov, N.V. Chugunova, and S.V. Poplavski, “Determination of the Gas Parameters in Nonrelaxing Two-Phase Flow on Dynamics of Admixture Particles,” in Proc. Intern. Conf. Methods Aerophys. Research, Vol. 2 (Publ. House SB RAS, Novosibirsk, 2000), 31–36.
O.D. Neikov and I.N. Logachev, Aspiration and Decontamination of Air in Powder Manufacturing (Metallurgiya, Moscow, 1981) [in Russian].
V.M. Boiko, A.N. Papyrin, and S.V. Poplavski, “Dynamics of Drop Breakup in Shock Waves,” Prikl. Mekh. Tekh. Fiz., No. 2, 108–115 (1987).
Additional information
Original Russian Text © V.M. Boiko, S.V. Poplavskii, 2007, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2007, Vol. 42, No. 3, pp. 110–120.
Rights and permissions
About this article
Cite this article
Boiko, V.M., Poplavskii, S.V. Particle and drop dynamics in the flow behind a shock wave. Fluid Dyn 42, 433–441 (2007). https://doi.org/10.1134/S0015462807030118
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0015462807030118