Dispersed multiphase flows are common in nature and industry and are governed by complex physical phenomena. The complex features of the turbulence continuity carrier phase and the dispersed phase make the problem of a dispersed multiphase flow much more complex than a single phase flow. This research work focuses on modelling and analysing one type of dispersed multiphase flows: solid particles suspended in a turbulent channel flow. The aim of this thesis is to numerically investigate the effects of Stokes number, particle shape and particle volume fraction on the behaviour of gas-solid turbulent channel flows with non-spherical particles. This study not only considers spherical particles but also studies non-spherical fibre-like ellipsoids suspended in the channel flow. To fully describe the complex dynamics of non- spherical particles, the rotational motion and orientation is efficiently and accurately re- solved by applying unit Quaternions. To address inevitable numerical errors caused by the Quaternion integration algorithms in previous studies, a novel Quaternion integration method is derived, validated and applied for more accurately updating the unit Quaternions. This work also derives a new Quaternion equation to relate second order tensor variables between different frameworks. This research work applies four-way coupling to accurately model the complex gas-solid turbulent channel flows, and the fluid-particle, particle-particle and particle-wall interactions are all taken into account. Important conclusions from this work are summarized as follows. In four-way coupled simulations, the average viscosity of the fluid flow is not affected by the particles, whereas the turbulence intensity is reduced by adding small heavy particles. The average direct dissipation by the particles is negligible, and the primary mechanism by which the particles affect the flow is by altering the turbulence structure near and around the turbulence kinetic energy peak. For non-spherical particles, the distributions of the orientation angles clearly demonstrate that ellipsoids tend to align within the plane that lies perpendicular to the span-wise direction in the very near wall region, follow the stream-wise direction in the buffer layer, and almost randomly distribute in the central region of the channel.