Abstract:
The propagation of shock waves in a mixture of gas and fine solid particles is considered in the frame of the mathematical model Anderson taking into account the differences between phases velocities and pressures. An approximate mathematical model of the flow is offered, which ignores the dependence of the first phase pressure on the particles volume concentration, but takes into account the terms, representing the particle volume concentration multiplied on a gas phase pressure gradient. The mathematical model has a hyperbolic type in this case. Classification of the shock waves types is done that are realized in the mixture for these heterogeneous media mechanics equations. The propositions about shock waves types are illustrated by numerical calculations in the stationary and non-stationary statements. For this purpose the original numerical TVD-type method is developed.
Keywords:
mixture of gas and solid particles, particle phase pressure, shock wave structure, frozen and dispersion shock waves, numerical methods.
Citation:
A. V. Fedorov, I. A. Bedarev, “The shock waves structure in the gas-particles mixture with chaotic pressure”, Mat. Model., 29:6 (2017), 3–20; Math. Models Comput. Simul., 10:1 (2018), 1–14
This publication is cited in the following 9 articles:
D. A. Gubaidullin, D. A. Tukmakov, “Numerical Investigation of the Mass Transfer of Dispersed Particles during the Passage of a Shockwave in a Mono and Polydisperse Gas Suspension”, Prikladnaya matematika i mekhanika, 87:3 (2023), 461
D. A. Gubaidullin, D. A. Tukmakov, “Numerical Study of the Effect of Polydispersity on the Mass Transfer of the Dispersed Phase during the Passage of a Shock Wave through a Gas Suspension”, Fluid Dyn, 58:7 (2023), 1373
Olga P. Stoyanovskaya, Vitaliy V. Grigoryev, Tatiana A. Savvateeva, Maksim S. Arendarenko, Elizaveta A. Isaenko, Tamara V. Markelova, “Multi-fluid dynamical model of isothermal gas and buoyant dispersed particles: Monodisperse mixture, reference solution of DustyWave problem as test for CFD-solvers, effective sound speed for high and low mutual drag”, International Journal of Multiphase Flow, 149 (2022), 103935
O. Stoyanovskaya, M. Davydov, M. Arendarenko, E. Isaenko, T. Markelova, V. Snytnikov, “Fast method to simulate dynamics of two-phase medium with intense interaction between phases by smoothed particle hydrodynamics: gas-dust mixture with polydisperse particles, linear drag, one-dimensional tests”, J. Comput. Phys., 430 (2021), 110035
T Markelova, O Stoyanovskaya, M Arendarenko, E Isaenko, V Snytnikov, “Acoustic waves in monodisperse and polydisperse gas-dust mixtures with intense momentum transfer between phases”, J. Phys.: Conf. Ser., 1666:1 (2020), 012050
A. V. Fedorov, T. A. Khmel, “About qualitative properties of the collisional model for description of shock-wave dynamics of gas particle suspensions”, Math. Models Comput. Simul., 11:5 (2019), 818–830
A. V. Panov, “Invariant solutions and submodels in two-phase fluid mechanics generated by 3-dimensional subalgebras: barochronous flows”, Int. J. Non-Linear Mech., 116 (2019), 140–146
S M Voronin, A V Panov, M M Turov, “Spherically symmetric stationary flows of a gas suspension”, J. Phys.: Conf. Ser., 1404:1 (2019), 012051
Khmel T., Fedorov A., “Qualitative Properties of a Model of Two-Phase Media For Description of Dynamics of Collisional Gas Particle Mixtures”, AIP Conference Proceedings, 2027, ed. Fomin V., Amer Inst Physics, 2018, 030159-1
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