The turbulent flow and macro-mixing processes in gas liquid liquid stirred vessels agitated by a Rushton turbine have been numerically simulated, based on the Eulerian multifluid approach. Both the isotropic k-epsilon model and anisotropic Reynolds stress model are used for turbulence modeling. The numerical models are validated by comparing simulated flow field of agitated immiscible liquid liquid dispersions to the corresponding experimental data from the literature. The predicted time traces of normalized concentration of inertial tracer and mixing time in gas liquid liquid stirred tanks are compared to the experimentally measured ones as well. Both turbulence models correspond reasonably well to the experimental data in liquid-liquid and gas-liquid-liquid stirred tanks, and the Reynolds stress model produces better results, in terms of flow field, homogenization curve, and mixing time, than the k-epsilon model. The information reported in this work is useful for chemical/process engineers when undertaking relevant engineering process designs.