A numerical study of the expansion of a gas-particles mixture with axial symmetry

The article deals with the study of new phenomena that accompany the free or wall-bounded expansion of a nonequilibrium in terms of velocities and temperatures mixture of gas and particles of various sizes with axial symmetry. The dynamics of the gas suspension is considered in the multifluid model of a calorically perfect inviscid gas and incompressible monodisperse spherical particles. The Eulerian approach is used to describe the motion of each phase of the mixture. For numerical simulation, a hybrid large-particle method of the second order of approximation in space and time with nonlinear correction of artificial viscosity, an additive combination of fluxes, and a semi-implicit scheme for calculating interfacial friction and heat transfer are implemented. The efficiency and accuracy of the method for a two-dimensional problem with axial symmetry are confirmed by comparing the solutions obtained in a one-dimensional formulation in a cylindrical coordinate system. In the case of small particles (with a diameter of d = 0.1 μm), the relaxation time of the phases is much less than the characteristic time of the problem and the gas and particles mixture behaves as a homogeneous medium similar to the gas flow. For sufficiently large particles (d = 20 μm), the effects of the difference in the inertia of the phases and nonequilibrium, associated with the mismatch of the velocities and temperatures of the gas and particles, are manifested. These effects cause the splitting of the initial interface of the media into a contact discontinuity in the gaseous phase and the surface between the suspension and the pure gas (a jump in porosity). At subsequent moments, the flow pattern changes to the opposite, which is explained by the deceleration of the gas, the appearance of a reverse flow to the center of expansion due to rarefaction in the vicinity of the axis of symmetry, and the formation of a secondary shock wave. Then there are fluctuations with a change in the relative position of the phase boundaries. In this case, fractures of the gas contact trajectories (the break of the first derivative) are observed, which are associated with the passage of the shock wave reflected from the wall and the plane of symmetry. Over time, due to baroclinic instability (the mismatch of density and pressure gradients), vortex structures begin to appear at the interface boundaries. In addition, in the case of expansion of the gas suspension in a closed volume, a complex shockwave structure is formed, due to multiple reflections of shock waves from the walls and their interaction with the contact surfaces. The practical significance of the results obtained is to identify the fundamental physical effects that should be taken into account when setting and solving problems in chemical technologies, pneumatic transport, and other areas. In addition, the numerical solutions can be useful in testing the resolution of other difference schemes for reproducing the vortex instability of contact boundaries and shock wave structures in the flows of relaxing gas suspensions.