Reducing Friction Drag on Flat Plates

Abstract

There are in existence several methods of boundary layer control which have been developed for the purpose of reducing friction drag of streamlined bodies. These include such elements as acceleration of the boundary layer (blowing), injection of a different gas, cooling of the wall, etc. All of them are described in some detail in scientific literature. In this paper, a new method for the reduction of friction drag, which has been insufficiently studied. The proposed method is based on the use of a liquid film on the surface of the streamlined body. One solution to the problem of the flow over a flat semi-infinite plate set at an angle of deflection to the horizon, and having a thin liquid film on its surface by external airflow is presented. The film is formed at the plate in the form of raindrops. Liquid moves by gravity and friction on the outer surface of the film. Influence on the boundary layer raindrops and thermal effects are ignored. In general, the problem is conjugate, including the problem of a film flow (internal problem) and the problem of the boundary layer of incoming air (external problem). For the solution of the dual problem, a method of successive approximations was used. This method assumes the fact that the external and internal problems can be solved separately, either logically or iteratively. At each new approximation, the inner problem is solved with regard to the friction resulting from the external problem; the solution of which, in turn, takes into account the speed at the boundary surface, obtained from the previous approximation of the interior problem. Thus, the iterative process continues until the speed and, consequently, the friction at the phase interface change little from iteration to iteration. For the interior problem, the method of asymptotic expansion in a small parameter was used. This paper gives null and first approximation. The external problem was solved using the numerical method of finite differences. In this paper we present some results showing the reduction of friction drag on the flat plate.