Numerical solutions are obtained for fluid spin up from rest in a partially filled cylinder started suddenly so as to spin about it's axis. Flow fields are obtained by integrating the full, time dependent Navier-Stokes equations for incompressible fluid.
Marker & Cell technique is employed to treat the free surface boundary condition and to acquire the transient free surface shape. Surface pressure boundary condition is modified to remove numerical instability at high Reynolds number.
Results on the transient free surface shapes and flow fields are presented for various parameters and compared with the Homicz & Gerber's results obtained by simplified equations.
In inviscid region, the magnitude of radial and axial velocities is order of $Re^{\frac{-1}{2}}$ v like fully filled spin-up.
As Reynolds number decreases, the region where properties are independent of z becomes narrow, so that the columnar flow approximation becomes incorrect.
The spin-up time for a large fill ratio case is longer than that for small when other parameters are being held identical. For the case of a large fill ratio, momentum transfer is slow because of radial velocities at inner region; meridional flow flux which is induced by the Ekman layer suction must spread out over a wider region in the core.
