| Abstract: | Three schemes of potential flow around a convex contour are examined: free jet; in the presence of a jet-directing wall extending to the contour (without a gap); and in the presence of a jet-directing wall not extending to the contour (with a gap). It is assumed that the jet, not branching, flows around the contour and on one side. The existence and (with certain limitations) uniqueness of the solution of integral equations corresponding to the first two schemes are proved. Their analytic solutions are given for the case of a flow of a sufficiently thin jet around a circle. The first problem is calculated numerically in the entire region of the parameters. The scheme with a gap is examined for the case of flow around a half-plane. The problem of closure of the given potential models is dicsussed. In the case of the scheme without a gap the situation is typical for potential flow problems: The position of the separation point is a free parameter of the model. At the same time, in the presence of a gap (in particular, for the case of a free jet) the flow is determined completely by a system ofa priori assigned geometric parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–22, July–August, 1978.The author is grateful to M. A. Gol'dshtik for attention to the work and discussion of the results. |
