Gravity effects in two-dimensional and axisymmetric water impact models

The effect of gravity during the water entry of two-dimensional and axisymmetric bodiesis investigated analytically and numerically. An extension to the Wagner model of waterimpact is proposed in order to take into account the effect of gravity. For this purpose,the free-surface condition is modified. The pressure is computed using the modifiedLogvinovich model of Korobkin (Eur. J. Appl. Maths, vol. 6, 2004, pp. 821-838). Themodel has been implemented and validated through comparisons with fully nonlinearpotential flow simulations of different two-dimensional and axisymmetric water entryproblems. Our investigation shows that it is equally important to account for gravity whencomputing the pressure distribution and to account for gravity when computing the sizeof the wetted surface in order to obtain accurate force results with the Wagner model.Simulations of wedges and cones with different values of deadrise angle (?) enteringwater at constant speed (V) demonstrate the accuracy of the semi-analytical model andshow that the effect of gravity in such? water impacts is governed by the effective Froudenumber defined as Fr^* = V/( ?gh ?tan ?), with g the acceleration due to gravity and hthe penetration depth. The accuracy of the semi-analytical model for decelerated waterentries is also demonstrated by investigating the water entry of a wedge and a cone witha 15^° deadrise angle with deceleration until full stop. The semi-analytical model is ableto accurately predict the effect of gravity during both two-dimensional and axisymmetricwater entry problems with deceleration.