Turbulent pow in concentric and eccentric annuli is numerically simulated as part of an investigation aimed at modeling drilled cuttings transport in wellbores. A numerical code is developed to solve the time-averaged momentum equation wherein the Reynolds stresses are modeled using the eddy viscosity approach. A nonorthogonal curvilinear, boundary-fitted coordinate system is used to facilitate the implementation of boundary conditions. Several turbulence models, including a one-layer mixing length model developed as part of this study, a two-layer mixing-length model, and a low Reynolds number, two-equation (k-tau) model are used to simulate turbulent pow in several concentric and eccentric annuli. Performance of these turbulence models is evaluated by comparing numerical predictions to experimental data obtained from several sources. Results show that the proposed one-layer mixing length model performs as well as the two-layer mixing length model and the two-equation model while avoiding so,nc of the difficulties associated with the implementation of these models.