The cavitation separation with the impact on the plate, located in a layer of fluid parallel to its free boundary

Abstract

The paper considers a 2D-problem of the central vertical impact of a horizontal plate placed in the middle plane of the layer of an incompressible fluid. At the moment of the impact the vertical component of the velocity vector of fluid particles at the point of the contact between the fluid and the plate is assumed to be known. In the region of separation of the fluid from the plate and on the surface of the fluid layer the impulsive pressure is equal to zero. The region of separation is unknown and must be determined along with other characteristics of the problem. The problem is reduced to a system of two integral equations by the method of integral transforms. The kernels of these equations are found in the form containing known functions. An approximate form of the solution of the system of equations is sought in the form of an expansion in orthogonal polynomials with explicit characteristic singularities of the unknown functions. The collocation method reduces the system of integral equations to the system of linear algebraic equations regarding the coefficients of these expansions. To determine the boundary points of separation of the fluid from the plate, there is used a new efficient iterative method. It is based on the condition of continuity of the vertical component of the velocity of fluid particles in the separation region. On the basis of direct calculations there are shown the diagrams for the vertical component of the velocity at separation points of the fluid from the plate and points of the layer’s free surface. The distribution of impulsive pressure in the contact area on the back surface of the plate and dependence of the value of the boundary points of the separation region on the relative distance of the plate to the surface of the fluid layer is also demonstrated. A comparison of the obtained results with the known results calculated not taking into account the contact area on the back surface of the plate shows that this contact area significantly changes the velocity field and the impulsive pressures in the region occupied by the fluid.