Waves on the surface of a thin liquid film entrained by a turbulent gas flow in a narrow channel

Abstract

The paper considers the problem of a joint flow in a narrow vertical channel of a turbulent gas flow and a wave film of liquid flowing down its walls. The calculation of tangential stresses on the interface is performed. The components of the Reynolds stress tensor were determined within the framework of the Boussinesq hypothesis. The turbulent viscosity coefficient was taken into account both when calculating the average velocity profile and when considering disturbances caused by wavy interface. The main difference this case and the semi-infinite channel case is observed in the longwave region. Nonlinear waves on a liquid film flowing down under the action of gravity are studied in a known stress field at the interface. For the case of low Reynolds numbers of the liquid (Re ∼1), the problem is reduced to a nonlinear integro-differential equation for the deviation of the layer thickness from the unperturbed level. For this equation, the character of branching from the unperturbed solution of weakly nonlinear steady-state traveling solutions, whose wave numbers lie in the neighborhood of neutral points, is studied. A numerical study of the evolution of periodic perturbations, whose wave numbers noticeably differ from neutral wave numbers, has been carried out. Several characteristic scenarios for the development of such disturbances are presented.