Exact solution of the problem of collision between a nonuniform jet and a plane obstacle

Abstract

The problem of collision between a nonuniform subsonic jet and a plane obstacle has been studied numerically (see, for example, [1, 2]) within the limits of the model of an ideal fluid. This approach is generally accepted for the study of flows in which there is turning of the flow [3]. In this case, the information that the flow is viscous outside the region of turning of the flow is contained only in the boundary conditions. In the present study this same model of the flow is used, but in contrast to [1, 2] the Gaussian profile is taken as the profile of the velocity at a sufficient distance from the obstacle. It gives a good description of the main sector of the jet [4,5]. As a result, a linear partial differential equation can be obtained for the flow function, and it can be solved analytically. The equations obtained in what follows for the components of the velocity field and pressure field on the obstacle are in satisfactory agreement with the experimental results, and can be used in engineering calculations and in debugging programs for numerical modeling of similar flows.