Numerical Investigation Of Unsteady Viscous Incompressible Liquid Flow In A Partially Filled Rotating Cylinder PDF Download

The liquid flowfield in a full or partially-filled right circular cylinder in rapid axial rotation is investigated numerically. The governing equations ar the axisymmetric, unsteady, viscous, incompressible Navier-Stokes equations. These equations are written in stream function-vorticity form for a cylindrical coordinate system in a nonrotating reference frame. The governing equations are discretized using second-order finite-differences for time and space on a nonuniform grid employing logarithmic stretching in regions where high flow gradients are anticipated. Time dependent solutions for Reynolds numbers between 1,000 and 100,000 have been obtained using a Gauss-Seidel relaxation procedure. For partially filled cases the free surface is assumed to be cylindrical and located at a constant radius from the axis of spin. Numerical solutions for full cylinders are consistent with previous solutions and experimental data. Numerical solutions for a partially-filled cylinder are consistent with experimental data for a liquid centrifuge except at the free surface. Computations of the roll moment exerted on the cylinder by the contained liquid shows a smaller moment for the partially-filled compared with the full cylinder results. Keywords: Finite difference, Incompressible flow, Liquid filled projectile, Liquid moment, Unsteady flow, Rotating liquids. (MJM).