Flow between two concentric cylinders, with either or both of them rotating, has potential advantages over the conventional process equipment. This flow, which is also termed Taylor - Couette flow and exhibits a variety of flow regimes, has been studied using computational fluid dynamics (CFD) simulations. The onset of centrifugal instability, the various cell patterns, and the velocity profiles have been predicted and compared with the available experimental data. To extend the base of experimental information, new measurements have been made using laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). For the entire range of experimental data, the Reynolds stress model (RSM) was determined to exhibit good predictive ability for the mean components of velocity and the turbulent kinetic energy. The wavelengths of the vortices in various regimes have also been determined using CFD and were observed to be in good conformity with all the available experimental results. Furthermore, very good agreement between the predicted energy dissipation rate with the energy input rate was observed over a wide range of speeds and annular gaps.