The numerical investigation of the unsteady flow patterns around a Pelton bucket can be helpful to improve the overall turbine efficiency by optimizing the bucket design based on identified loss mechanisms. Since the flow is highly turbulent, modeling the effect of turbulence can bring about improved predictions. In this paper, two RANS-based eddy viscosity models (namely the standard and realizable k-epsilon) have been implemented as a module in a particle-based in-house solver, GPU-SHPEROS. A scalable wall function based on the log-law has been utilized to model the flow in the near-wall region. The solver has been accelerated on GPUs and is based on the Finite Volume Particle Method (FVPM), which is a locally conservative and consistent particle-based method including many of the attractive features of both particle-based methods (e.g. SPH) and conventional mesh-based methods (e.g. FVM). As a mesh-five method based on the Arbitrary Lagrangian Eulerian (ALE) formulation, FVPM is robust in handling five surface flows and large boundary deformations, such as the ones found in rotating Pelton buckets. The validation of the turbulence models implementation within FVPM is presented for internal and free surface flows. Then, the effectiveness of the turbulence models in the case of rotating Pelton buckets is assessed by comparing the predicted torque time histories to experimental data acquired on a model-scale test rig.