3-DIMENSIONAL VISCOUS FLOWS BETWEEN CONCENTRIC CYLINDERS EXECUTING AXIALLY VARIABLE OSCILLATIONS - A HYBRID SPECTRAL FINITE DIFFERENCE SOLUTION/

A hybrid spectral/finite difference method is developed in this paper for the analysis of three-dimensional unsteady viscous flows between c oncentric cylinders subjected to fully developed laminar pow and execu ting transverse oscillations. This method uses a partial spectral coll ocation approach, based on spectral expansions of the pow parameters i n the transverse coordinates and time, in conjunction with a finite di fference discretization of the axial derivatives. The finite differenc e discretization uses central differencing for the diffusion derivativ es and a mixed central-upwind differencing for the convective derivati ves, in terms of the local mesh Reynolds number. This mixed scheme can be used with coarser as well as finer axial mesh spacings, enhancing the computational efficiency. The hybrid spectral/finite difference me thod efficiently reduces the problem to a block-tridiagonal matrix inv ersion, avoiding the numerical difficulties otherwise encountered in a complete three-dimensional spectral-collocation approach. This method is used to compute the unsteady fluid-dynamic forces, the real and im aginary parts of which are related, respectively, to the added-mass an d viscous-damping coefficients. A parametric investigation is conducte d to determine the influence of the Reynolds and oscillatory Reynolds (or Stokes) numbers on the axial variation of the real and imaginary c omponents of the unsteady forces. A semi-analytical method is also dev eloped for the validation of the hybrid spectral method, in the absenc e of previous accurate solutions or experimental results for this prob lem. Good agreement is found between these very different methods, wit hin the applicability domain of the semi-analytical method.