Flow separation model for the water entry of smoothly curved bodies

During the water impact of a body, owing to the geometrical properties of the body contour or to the variation of the entry velocity, the flow can detach from the body surface. For a correct prediction of the free-surface dynamics and of the hydrodynamic loads, an accurate modelling of the flow separation phenomena is necessary. Generally, the flow separation is modelled by applying a Kutta condition at the separation point, implying that the free-surface leaves the body tangentially. For bodies with hard chines, such as a wedge, impacting the water with either constant or increasing impact velocity, the separation point can be located a priori at the sharp corner. Conversely, in the case of bodies with smoothly curved contours, such as a circular cylinder, or in the case of bodies undergoing large deceleration, the flow separation point is unknown and has to be derived as a part of the numerical solution. Often, it is assumed that the flow detaches from the body contour at the point where the pressure drops below the atmospheric value at least on a reasonably large portion of the wetted area. However, such a criterion seems too strong as there is evidence that negative pressure can occur without flow separation. In this paper, a new flow separation model, based on a kinematic criterion, is presented. The aim is to further extend the capabilities of the 2D fully non-linear potential flow model to deal with the water impact of bodies with smoothly curved contours. After a discussion of the theory lying behind the model, an application to the water entry of a 2D circular cylinder impacting at constant entry velocity is presented.