Riabouchinsky Flow with Partially Penetrable Obstacle

The investigation of hydrodynamic models with partially penetrable obstacles has been initiated by the recent progress in the development of free flow turbines [l] for the purpose of estimating their efficiency limit [2]. In the previous paper [3], an explicitly solvable analog of the Kirchhoff cavitation flow was obtained. As in the classical situation, the main deficiency of the Kirchhoff model is the infinite size of the stagnation domain that resulted from the assumption that the pressure in the stagnation domain is equal to the pressure at infinity. In the Riabouchinsky model (Figure lb), a virtual obstacle past the actual one is introduced to make the stagnation domain finite. In this model, the separating streamlines y and y’ join the edges of both obstacles. The velocity V, on y and y’ is greater than the velocity at infinity V, and the pressure in the stagnation domain is less than the pressure at infinity. The number 0, s.t.