2019. Vol. 14. Issue 2, Pp. 125–131

URL: http://mfs.uimech.org/mfs2019.2.017

DOI: 10.21662/mfs2019.2.017

URL: http://mfs.uimech.org/mfs2019.2.017

DOI: 10.21662/mfs2019.2.017

Numerical study of velocity slip of phases during the passage of a shock wave of low intensity from a pure gas to a dusty medium

Tukmakov D.A.

Institute of Mechanics and Engineering, Kazan Scientific Center of the RAS, Kazan

In this paper, the process of the movement of a direct shock wave from a pure gas into a dusty medium is numerically modeled. The mathematical model took into account the viscosity, compressibility and thermal conductivity of the carrier phase. Also, the modeling technique made it possible to describe the interphase force interaction, which included the Stokes force, the dynamic force of Archimedes, the strength of the attached masses. In addition, interfacial interaction included heat transfer between the carrier and dispersed phases. The numerical solution was carried out using the explicit finite-difference method, with the subsequent application of the nonlinear correction scheme for the grid function. As a result of numerical calculations, it was revealed that with an increase in the linear particle size of the gas suspension, the velocity slip between the carrier and dispersed phases increases. Numerical modeling also showed that the absolute value of the difference between the velocities of the carrier and the dispersed phase reaches the largest value at the leading edge of the compression wave. The revealed regularities can be explained by the fact that the particles of the dispersed phase are assumed to be spherical in shape. Due to this, a multiple increase in particle size leads to a three-fold increase in their mass, a twofold increase in the area of one particle and a three-fold decrease in the number of particles. Thus, an increase in particle size leads to a decrease in the area of interfacial contact and an increase in the inertia of the particles, which in turn affects the interfacial velocity slip.

numerical simulation,

Navier-Stokes equation,

dusty media,

shock waves

**Purpose.** The processes associated with the movement of multiphase media are found both in nature and
in industrial technologies. Therefore, one of the relevant sections of fluid and gas mechanics is the study of the dynamics of inhomogeneous media,
including gas suspensions of droplets and solid particles. Since in many cases the experimental study of such flows is difficult, mathematical modeling
is essential. The article simulated the movement of a direct shock wave from a pure gas into a dusty medium.

**Methodology.** In this work, the dynamics of gas suspension of solid particles - a dusty medium is described on the basis of a two-speed,
two-temperature model taking into account the inter-component heat transfer, as well as the inter-component force interaction, which includes
the Stokes force, the dynamic force of Archimedes and the strength of the attached masses.

**Findings.** Numerical simulation shows that during the movement of a shock wave through a dusty medium, a decrease in the dispersion
of particles of a gas suspension located in a low-pressure chamber leads to an increase in pressure in the compression wave and to a decrease
in the velocity of propagation of the shock wave. From the calculations it follows that in a gas suspension with a larger particle size,
a higher velocity of the gas flow is observed. At the same time, in a dusty medium, an increase in the linear particle size leads to a decrease
in the velocity of the dispersed phase. For finely dispersed gas suspensions, high-speed sliding is insignificant. In this case, for gas suspensions
with both a coarse and finely dispersed solid phase, the largest value of the absolute value of the velocity difference between the carrier and disperse
phase is observed at the leading edge of the compression wave. In a coarse-grained gas suspension, an increase in the absolute value of the velocity
difference between the solid and gaseous phases is observed from the contact area between the dusty medium and pure gas to the leading edge
of the compression wave.

Originality. In the process of the movement of a direct shock wave from pure gas into a dusty medium with an increase in particle size, an increase in the velocity of the disturbance and a decrease in pressure at the leading edge of the compression wave occur. The largest value of the modulus of the velocity difference between the carrier and the dispersed phase is observed at the leading edge of the compression wave in front of the unperturbed medium.

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