Dynamics of the fluid in a spinning coning cylinder

The fluid motion inside a cylinder that simultaneously spins and cones is determined according to linear theory for small coning angles. The Navier-Stokes equations are solved by expansions in spatial eigenfunctions. This form of spectral method gives an efficient solver over a range of Reynolds numbers; cases of Re ≤ 2500 have been computed. The results are validated by comparing computed pressure and moment coefficients with experimental observations and numerical calculations. In particular, comparisons are made with results from a finite difference method applied to the nonlinear Navier-Stokes equations for which the CPU time is about 400 times that of the present method. The CPU time for the spatial eigenvalue method varies from 10 s at Re = 10 to 25 min at Re = 1000 on a VAX 8600. The restriction of linear theory is not severe.