Cavitation streamline flow of lamina in transverse gravitational field
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The problem of cavitation streamline flow located on the linear base of a lamina in a gravity solution current is solved by the systems of Ryabushinskii and Zhukovskii-Roshko. The method of fragment-continuum approximation of the boundary condition at the free boundary was used, in which this condition is exactly satisfied at a finite number of points. In this way the original problem comes down to a solution of a system of nonlinear equations whose solvability can be shown by the method of V. N. Monakhov . The main consideration in the present work was given to a numerical solution of this system of equations on a computer. The problem is similar to the type for large Froude numbers, when the effect of weight on the flow is small, studied in [2-5]. In [6, 7] the flow problems were solved by the method of finite differences. The approximations of the boundary condition at the free boundary used earlier are based on the use of the smallness of these or other characteristics of flow. Thus, for example, the linearization of Levi-Chivit  is rightly used in the assumption of smallness of the change in the modulus and angle of inclination of the velocity at the free flow line; a stronger linearization is based on the requirement of smallness of additional velocities caused by an obstacle in comparison with the velocity of the undisturbed current . In the given work the problems studied lead to a range of cavitation and Froude numbers when the gravitational force exerts a considerable effect on the main characteristics of the flow. As an example of one of the possible applications of the calculation, the solution of the problem of choice of the form of a body of zero buoyancy with a zone of constant pressure is given.
KeywordsCavitation Streamline Flow Free Boundary Original Problem Gravitational Field
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