Numerical investigation of the water entry of cylinders without and with spin

We consider the water entry of horizontal cylinders with vertical impact velocity, either kept constant or freely falling, without and with spin, into quiescent water under the effect of gravity. We focus on the flow and cavity forming stages with non-dimensional submergence time$t$, Froude numbers$Fr$, spin ratios$\unicode[STIX]{x1D6FC}$and mass ratios$m$, all of$O(1)$. We develop numerical simulations using a modified smoothed particle hydrodynamics method to obtain predictions for the impact kinematics and dynamics. These are in detailed agreement with available experiments. We elucidate the evolutions of the free surface, contact point positions, flow field, forces and trajectories and their dependence on$Fr$,$\unicode[STIX]{x1D6FC}$and$m$. We define and quantify the contact point location$\unicode[STIX]{x1D703}(t)$as a function of$Fr$, clarifying the qualitative difference between sub- and supercritical$Fr$and the observed absence of air-entrained trailing cavities at low$Fr$. By subtracting the buoyancy associated with$\unicode[STIX]{x1D703}(t)$, we show that, unlike the total drag, the remaining dynamic components are qualitatively similar for all$Fr$. For a freely falling cylinder, we show that the total drag can be predicted from the constant velocity case with the same instantaneous velocity, providing a simple way to predict its trajectory based on the latter. The presence of spin results in lift, even when the asymmetry in$\unicode[STIX]{x1D703}$is small. For fixed$\unicode[STIX]{x1D6FC}$, lift increases with subcritical$Fr$. For a freely falling cylinder, the lateral motion causes an appreciable asymmetry in$\unicode[STIX]{x1D703}$and a reduction in lift.