TY - JOUR

T1 - Plane sound waves of small amplitude in a gas-dust mixture with polydisperse particles

AU - Markelova, T. V.

AU - Arendarenko, M. S.

AU - Isaenko, E. A.

AU - Stoyanovskaya, O. P.

N1 - Funding Information: The work was funded by the Russian Science Foundation (Grant No. 19-71-10026). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/7

Y1 - 2021/7

N2 - The propagation of plane sound waves of small amplitude in a mixture of an isothermal carrier gas and solid particles of different sizes is considered based on a multi-fluid macroscopic model of the medium. In the model, the dispersed phase is represented as a set of N fractions of monodisperse particles, and the dynamics of each fraction is described using the equations of a continuous medium without intrinisc pressure. The fractions exchange momenta with the carrier gas, but not with each other. The whole mixture is acted upon by the total pressure determined by the motion of gas molecules, and the dust particles are considered buoyant. An analytical solution of the problem is obtained using the Fourier method and dispersion analysis. In the general case for an arbitrary value of the relaxation time, the solution is found numerically using the developed and published code. In special cases (infinitely small time of velocity relaxation or relaxation equilibrium and infinitely long time of velocity relaxation or frozen equilibrium), the effective speed of sound in the gas-dust mixture is determined and used to obtain simple analytical representations of the solution of the problem.

AB - The propagation of plane sound waves of small amplitude in a mixture of an isothermal carrier gas and solid particles of different sizes is considered based on a multi-fluid macroscopic model of the medium. In the model, the dispersed phase is represented as a set of N fractions of monodisperse particles, and the dynamics of each fraction is described using the equations of a continuous medium without intrinisc pressure. The fractions exchange momenta with the carrier gas, but not with each other. The whole mixture is acted upon by the total pressure determined by the motion of gas molecules, and the dust particles are considered buoyant. An analytical solution of the problem is obtained using the Fourier method and dispersion analysis. In the general case for an arbitrary value of the relaxation time, the solution is found numerically using the developed and published code. In special cases (infinitely small time of velocity relaxation or relaxation equilibrium and infinitely long time of velocity relaxation or frozen equilibrium), the effective speed of sound in the gas-dust mixture is determined and used to obtain simple analytical representations of the solution of the problem.

KW - CFD test

KW - dispersion relation

KW - hyperbolic sound waves

KW - two-phase polydisperse medium

UR - http://www.scopus.com/inward/record.url?scp=85119987370&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/71a6c051-c242-3a9f-b560-e41d2c74b967/

U2 - 10.1134/S0021894421040167

DO - 10.1134/S0021894421040167

M3 - Article

AN - SCOPUS:85119987370

VL - 62

SP - 663

EP - 672

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 4

M1 - 16

ER -