This study is concerned with the modelling of single-phase and two-phase turbulent flows in a square duct over a range of Reynolds numbers with attention focused on the deposition, dispersion and re-suspension of particles. Reynolds averaged Navier Stokes (RANS) modelling is used in conjunction with a Lagrangian particle tracker (LPT). Modelling and simulation of single- and two-phase turbulent flows in circular pipes with the presences of stationary flat beds are also considered using the previously stated methodologies, as well as large eddy simulation (LES). The performance of the RANS modelling technique is evaluated against available experimental, simulation and empirical data. The RANS modelling technique is seen to perform with qualitative accuracy across all of the test cases considered within this thesis, and it can be said that this approach is capable of reproducing many of the key feature' associated with these flows. In almost all cases, qualitative agreement is seen between the RANS modelling results and the available experimental data, simulation results and empirical correlations. A key failing of the RANS modelling technique is the inaccurate representation of the magnitude of the secondary velocities found in square ducts and pipes with variable bed height. The RANS modelling technique with a Reynolds stress model (RSM) for turbulence, coupled with a LPT, can be usefully used in modelling particle-laden duct and pipe flow. across a range of conditions. Important qualitative information can be gained from this technique in terms of particle deposition, dispersion and re-suspension. For more detailed studies on the physics of these flows, the preferred methodologies are the more advanced simulation techniques of LES and direct numerical simulation CDNS), while there is also a clear need for further experimental investigations of such particle- laden flows.