Pressure moment on a liquid-filled projectile: Solid body rotation

The liquid produced moment on a liquid filled spinning cylinder executing angular motion is determined, where the liquid originally is in solid body rotation. In an approximation to free flight spiraling motion of a projectile, the cylinder is nutating at constant frequency about a point on its axis and is undergoing timewise exponential yaw growth. The assumption of small yaw angle permits the formulation of a linearized viscous flow problem as a perturbation on solid body rotation. The pressure obtained from the resulting linearized flow is used to obtain the moment. Moment due to shear stresses is not considered. This moment is incorporated into the dynamical equations of gyroscopic motion to determine yaw growth rate and mutational frequency. This report provides a presentation of the equations and computational procedures. The approach is to apply a modal analysis in the flow solution which gives rise to ordinary differential equations, and then to make a correction required to compensate for neglect of the no slip conditions at the endwalls in the modal analysis. Results are compared with those of other theoretical work and with experimental data for endwall pressure, pressure moment, and yaw growth rate of projectiles and gyroscopes. In general, results agree well for high Reynolds number. Relative discrepancies are more prominent at low Reynolds numbers, particularly in yaw growth rate data. Qualitative agreement of present results with concurrent theoretical work of Murphy appears to be consistently good.