A combined viscous-vortex, thermal-blob and Lagrangian method for non-isothermal, two-phase flow modelling

•A meshless method for modelling two-phase flows with phase transition is developed.•Carrier phase parameters are calculated using the vortex and thermal blob methods.•Droplet parameters are calculated using the Lagrangian approach.•The method is verified against the analytical solution for the Lamb vortex.•The method is used to model an impulse two-phase cold jet injected into hot gas. A meshless method for modelling of 2D transient, non-isothermal, gas-droplet flows with phase transitions, based on a combination of the viscous-vortex and thermal-blob methods for the carrier phase with the Lagrangian approach for the dispersed phase, is developed. The one-way coupled, two-fluid approach is used in the analysis. The method makes it possible to avoid the ‘remeshing’ procedure (recalculation of flow parameters from Eulerian to Lagrangian grids) and reduces the problem to the solution of three systems of ordinary differential equations, describing the motion of viscous-vortex blobs, thermal blobs, and evaporating droplets. The gas velocity field is restored using the Biot–Savart integral. The numerical algorithm is verified against the analytical solution for a non-isothermal Lamb vortex and some asymptotic results known in the literature. The method is applied to modelling of an impulse two-phase cold jet injected into a quiescent hot gas, taking into account droplet evaporation. Various flow patterns are obtained in the calculations, depending on the initial droplet size: (i) low-inertia droplets, evaporating at a higher rate, form ring-like structures and are accumulated only behind the vortex pair; (ii) large droplets move closer to the jet axis, with their sizes remaining almost unchanged; and (iii) intermediate-size droplets are accumulated in a curved band whose ends trail in the periphery behind the head of the cloud, with larger droplets being collected at the front of the two-phase region.