On the development of a mathematical model of a two-phase flow in an axisymmetric de Laval nozzle

When modeling the flow of two-phase media, a number of authors use the kinetic approach. In the 1980s, I.M. Vasenin et al. obtained equations describing the flow of gas and liquid particles based on the equation for a drop distribution function in terms of masses, velocities, temperatures, and intrinsic angular momentum. They differ from the known equations by an additional equation for the mean square of the rotation moment. A numerical solution to the equations shows that due to numerous collisions and coagulation, the rotation moments of some drops exceed the critical value, and the drops are destroyed by centrifugal forces. In this paper, the kinetic approach is extended to the model of a two-phase flow in an axisymmetric de Laval nozzle with account for the radial diffusion of drops under the action of the Magnus force acting on a rotating drop. The system of equations is derived from the kinetic equation up to second-order moments using the method of moments. Only second-order moments, which affect diffusion to the wall, are taken into account. Diffusion leads to an earlier occurrence of drops on the wall and therefore must be considered when profiling the contour of the nozzle.