Abstract
A flow of a thin layer of liquid is simulated on a flat surface of a body located in a stream of air. Liquid film on the surface of the body reduces frictional resistance and can be used as a boundary layer control element. The paper presents a mathematical model of the film flow on a half-plane, located at an angle to the horizon. The fluid flow is determined by the force of gravity and friction from the external air current. A model of an incompressible viscous fluid is used in the boundary-layer approximation. The terms of the motion equation are averaged over the film thickness according to the Leibniz rule. In the cross section of the film, a quadratic law is adopted for the distribution of the longitudinal velocity, taking into account friction on the film surface. An analytical solution of the problem is obtained in the form of series in powers of the small parameter for determining the film thickness and the average longitudinal velocity along the length of the plate. It is shown that the friction decreases with flow around a half-plane with a film of liquid on the surface.
Highlights
Problems of liquid film flow are quite often encountered in technical applications and are discussed by many authors
Paper [1] presents the results of investigation of films for a gas-liquid two-phase flow in short horizontal pipes
An analytical solution of the problem is obtained for the average velocity and film thickness in the form of series in powers of the small parameter with allowance for the zero and first approximations
Summary
Problems of liquid film flow are quite often encountered in technical applications and are discussed by many authors. In paper [4], the solution of the conjugate problem for the air flow over a flat plate with a thin liquid film on the surface is presented. The results of theoretical and numerical studies of liquid films are presented in papers [6,7], and experimental studies have been performed in [8,9,10]. The problem of condensate film stability on a vertical surface is analytically studied in paper [14]. An analytical model for the laminar flow of a condensate film on the outer surface of an isothermal vertical pipe is presented in [15]. An analytical model for the laminar flow of a condensate surface of an isothermal vertical pipe is presented in [15]. Surface of the body in the airflow is simulated for its ability to reduce frictional resistance
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