|
Article information
2015 , Volume 20, ¹ 2, p.3-19
Bedarev I.A., Fedorov A.V.
Structure and stability of shock waves in a gas-particle mixture with two pressure
The propagation of shock waves in a mixture of gas and fine solid particles that accounts for the differences of phase velocities and the presence of particles pressure is investigated in the frame of Anderson-type model. A mathematical model describing the movement is reduced to the model of the two interpenetrating interacting gases flow where parameters such as speed, density and pressure, are volume-averaged. Existing types of strong discontinuities (frozen, dispersion, frozen-dispersion et al. of two front configurations) in the dispersion medium and the conditions, where they are implemented, are studied. A mathematical model describing the propagation is a model of two interacting gases interpenetrating continuous flow, with parameters such as velocity, density and pressure are averaged over the volume. The fifth-order Runge - Kutta scheme for the time approximation and third order TVD-type scheme for space approximation are used for the numerical modelling of the initial boundary value problems of the heterogeneous media mechanics equations. The solutions in the class of traveling waves are found. A map of shock waves flow regimes is constructed to determine finite mixture velocity depending on the initial velocity and the gas component mass fraction. The existence of stationary solutions for different types of shock waves is shown numerically. The solutions stability is investigated by solving the Cauchy problem for equations of mechanics of a nonstationary one-dimensional heterogeneous media. It is shown that the “soft” boundary conditions, when the gradient of the boundary parameters is zero, give the stationary wave velocity configurations for both phases. In the case of “wall” conditions the effect of the rarefaction wave leads to a weakening and gradual attenuation of the shock wave.
[full text]
Keywords: mixture of gas and solid particles, particle phase pressure, shock wave structure, frozen and dispersion shock waves
Author(s):
Bedarev Igor Alexandrovich
PhD.
Position: Senior Research Scientist
Office: Khristianovich Institute of Theoretical and Applied Mechanics SB RAS
Address: 630090, Russia, Novosibirsk
Phone Office: (383) 330-85-38
E-mail: bedarev@itam.nsc.ru
Fedorov Alexander Vladimirovich
Dr. , Professor
Position: Head of Laboratory
Office: ITAM SB RAS
Address: 630090, Russia, Novosibirsk, Institutskaja street 4/1
Phone Office: (383) 330-85-38
E-mail: fedorov@itam.nsc.ru
References:
[1] Zenit, R., Hunt, M.L., Brennen, C.E. Collisional particle pressure measurement in solidliquid flows. Journal of Fluid Mechanics. 1997; (353):216–283.
[2] Glasser, B.J., Kevrekids, I.G., Sundars, S. One- and two-dimensional traveling wave solutions in fluidized beds. Journal of Fluid Mechanics. 1996; (306):183–221.
[3] Carlson, D.J., Hoglund, R.F. Particle drag and heat transfer in rocket nozzle. The American Institute of Aeronautics and Astronautics. 1964; 2(11):1980–1984.
[4] Gol’dshtik, M.A., Kozlov, B.N. Elementary theory of concentrated dispersed systems. Journal of Applied Mechanics and Technical Physics. 1973; 14(4):491–499.
[5] Fedorov, A.V. The structure of a shock wave in a mixture of solids (the hydrodynamic approximation). Modelirovanie. v mechanike. 1991; 5(22), 4:135–158. (In Russ.)
[6] Fedorov, A.V. Types of traveling waves in a gas suspension with chaotic pressure. Dynamics of Multiphase Media: Proc. of XIII All-Russ. Sem. (Novosibirsk, 8–10 Oct. 2013). Ed. V.M. Fomin, A.V. Fedorov. Novosibirsk: OOO “Parallel”, 2013. Ń. 157–160. (In Russ.)
[7] Fedorov, A.V., Fedorova, N.N. Structure, propagation, and reflection of shock waves in a mixture of solids (the hydrodynamic approximation). Journal of Applied Mechanics and Technical Physics. 1992; 33(4):487–494.
[8] Zhilin, A.A., Fedorov, A.V. Propagation of shock waves in a two-phase mixture with different pressures of the componentsž. Journal of Applied Mechanics and Technical Physics. 1999. 40(1):46–53.
[9] Hairer, E., Wanner, G. Solving Ordinary Differential Equations. II: Stiff and DifferentialAlgebraic Problems, 2nd revised ed. Berlin: Springer; 1996: 614.
[10] Chakravathy, S.R., Osher, S. New class of high accuracy tvd schemes hyperbolic conservation laws. AAIA Paper. 1983; 85(0363): 11.
[11] Kovenya, V.M., Yanenko, N.N. Metod rasshchepleniya v zadachakh gazovoy dinamiki [The splitting method in problems of gas dynamics].Novosibirsk: Nauka; 1981: 384. (In Russ.)
Bibliography link:
Bedarev I.A., Fedorov A.V. Structure and stability of shock waves in a gas-particle mixture with two pressure // Computational technologies. 2015. V. 20. ¹ 2. P. 3-19
|
