Abstract
A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.
Highlights
Liquid film flow problems are quite frequent for technical appendixes and works by many authors
The purpose of this research is the development of a mathematical model of a liquid film flow over a flat surface, forced by gravitation and the external airflow for the further simulation of a variable thickness film wave flow
The results can be used for calculation of frictional resistance, which is a component of an aircraft resistance
Summary
Liquid film flow problems are quite frequent for technical appendixes and works by many authors. Work [1] presents film research findings for a two-phase gas-liquid flow in short horizontal pipes. Work [2] contains film flow dynamic properties under a counter current airflow. Work [3] examines a three-dimensional dynamic model of film flow over a cylindrical surface. The film is exposed to gravity, and surface-tension, as well as a drag of a countercurrent gas flow. Work [4] presents solution for related problem for airflow over a flat plate with a thin liquid film at the surface. Works [6] - [7] contain findings of theoretical and numerical research of liquid films, works [8] – [10] present experimental research
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