Rotor-stator mixers provide high deformation rates to a limited volume, resulting in intensive mixing, milling, and/or dispersion/emulsification. CFD simulations of mixers provide flow field information that benefit designers and end users. This thesis focuses on transient three-dimensional simulations of the Greerco pipeline mixer, using ANSYS FLUENT. The modeled unit consists of two conical rotor-stator stages aligned for axial discharge flow. Flow and turbulence quantities are studied on a per stator slot and per rotor stage basis. Comparisons are made between the LES and RANS realizable k-ε model predictions at various mesh resolutions. Both simulations predict similar mean velocity, flow rate, and torque profiles. However, prediction of deformation rates and turbulence quantities, such as turbulent kinetic energy and its production and dissipation rates, show strong dependencies on mesh resolution and simulation method. The effect of operating conditions on power draw, throughput, and other quantities of practical utility are also discussed.