Computational Fluid Dynamics Method for Low Reynolds Number Flow in a Precessing/Spinning, Liquid Filled Cylinder with Rounded Endcaps

The flight stability of liquid-filled, spin-stabilized projectiles has been considered for a wide variety of conditions. The three-dimensional, steady, laminar, Navier-Stokes equations are solved using an implicit finite- difference scheme based on successive-over-relaxation. These numerical simulations are used to predict the behavior of incompressible liquids undergoing steady spin and steady precession at a fixed precession angle. The liquid is contained in a fully-filled cylinder with flat or rounded endcaps. These numerical simulations can predict steady viscous and pressure moments due to the liquid fill at low Reynolds number. These moments tend to increase the precession angle and reduce the spin rate of the container. Liquid-induced roll and side yaw moments are computed as functions of endcap height to cylinder radius, cylinder half-height to radius, Reynolds number, ratio of precession to spin rate, and precession angle. For a given cylinder, rounded endcaps can decrease the resonant liquid-induced moment by about 25 and shift the resonance to a smaller Reynolds number.