A new fully Lagrangian approach to numerical simulation of 2D transient flows of viscous gas with inertial microparticles is proposed. The method is applicable to simulation of unsteady viscous flows with a dilute admixture of non-colliding particles which do not affect the carrier phase. The novel approach is based on a modification and combination of the full Lagrangian method for the dispersed phase, proposed by Osiptsov , and a Lagrangian mesh-free vortex-blob method for Navier-Stokes equations describing the carrier phase in the format suggested by Dynnikova . In the combined numerical algorithm, both these approaches have been implemented and used at each time step. In the first stage, the vortex-blob approach is used to calculate the fields of velocity and spatial derivatives of the carrier-phase flow. In the second stage, using Osiptsov’s approach, particle velocities and number density are calculated along chosen particle trajectories. In this case, the problem of calculation of all parameters of both phases (including particle concentration) is reduced to the solution of a high-order system of ordinary differential equations, describing transient processes in both carrier and dispersed phases.
The combined method is applied to simulate the development of vortex ring-like structures in an impulse two-phase microjet. This flow involves the formation of local zones of particle accumulation, regions of multiple intersections of particle trajectories, and multi-valued particle velocity and concentration fields. The proposed mesh-free approach enables one to reproduce with controlled accuracy these flow features without excessive computational costs.