Numerical modeling of polydisperse two-phase flows in an ax-isymmetric de Laval nozzle with account for the Magnus force acting on rotating droplets

V. P. Bushlanov   ; V. G. Butov   ; A. A. Glazunov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 66-78

Résumé

The available papers on two-phase flows in de Laval nozzles are focused on the effect of various initial conditions, models of coagulation, fragmentation, and rotation of droplets on their local and integral characteristics. Some papers note that due to the difference in the velocities of the gas and droplets along the nozzle axis, the Magnus force acts on the rotating droplets perpendicular to the specified difference and deflects the trajectories of the droplets toward the nozzle wall. In an earlier paper, the authors proposed a mathematical model of a two-phase flow in an axisymmetric de Laval nozzle that accounts for the Magnus force on the basis of the kinetic equation. The present article is devoted to a numerical study of a polydisperse two-phase flow in a de Laval nozzle with account for the coagulation, fragmentation, and rotation of droplets and the Magnus force. This study is based on the “monodisperse” model of fragments developed by I.M. Vasenin and A.A. Shreiber, the method of labeled drops (the Lagrange method), and the finite-difference schemes of second order accuracy. The calculations are carried out for a test nozzle configuration with condensate formation on the nozzle wall both with and without the Magnus force accounted. The calculated results show that the Magnus force has different impacts on the trajectories of droplets of various sizes. It should be noted that the limiting trajectories of the droplets approach the nozzle wall due to the Magnus force, resulting in the earlier dropout on the wall. Therefore, when designing the divergent section of the nozzle, it is necessary to consider the revealed approach of the location of the dropout, which is associated with the Magnus force, to the nozzle throat.

Détail

Keywords: two-phase flow, and fragmentation of droplets, the Magnus force, mathematical model.
Mots-clés : coagulation, rotation

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