Effects of Froude number and geometry on water entry of a 2-D ellipse

By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics (CFD) results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4πa/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.