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

We perform laminar, weakly compressible, numerical simulations of water impacting cylinders with radius $R$, entry velocity $V$, and spin $\omega$ about their axis. We consider two Froude numbers $F$r=$V/\sqrt{g2R}$=0.5, 1.5 and moderate spin ratios $\Omega$=$\omega R/V \le$3. Our numerical predictions are in agreement with experiments and identify the effects of $F$r and $\Omega$ on the separation points, flow dynamics, and body trajectory. We find that the separation points depend primarily on $F$r and observe two distinct regimes: for $F$r=0.5 quasi-static cavities are obtained, while for $F$r=1.5 the separation points approach a limiting angle of 70$^o\- - $80$^o$ with respect to the negative vertical axis. For times $tV/R>$0.1 the total pressure force on the cylinder decreases with $F$r, obtaining significantly larger values for $F$r=0.5. The corresponding drag reduces with $\Omega$, while lift is towards the windward side and increases with both $\Omega$ and time. As a consequence, free-falling spinning cylinders drop slightly faster, while at a given depth their lateral displacement increases with $\Omega$.