Extended Momentum Model for Single and Multiple Hydrokinetic Turbines in Subcritical Flows

This thesis proposes equations extending the Free Surface Actuator Disc Theory to yield drag forces and interference factors from a series of two porous discs in open channel flows. The new model includes blockage ratio and Froude number as independent variables, which are inferred in advance to yield a single solution in the prescribed domain. The theoretical extension is integrated with the Blade Element Theory in a Double Multiple Streamtube model (DMS) to predict axial loads and the performance of confined Darrieus turbines. The turbine thrust force influences the flow approaching the rotor. Hence, a momentum method is applied to solve the hydraulic transition in the channel, achieving the unknown inflow factor from the undisturbed flow imposed downstream. The upstream blockage ratio and Froude number are thus updated iteratively to adapt the DMS to subcritical applications. The DMS is corrected further to account for the energy losses due to mechanical struts and turbine shaft, flow curvature, turbine depth, and streamtube expansion. Sub-models from the literature are partly corrected to comply with the extended actuator disc model. The turbine model is validated with experimental data of a high-solidity cross-flow hydrokinetic turbine that was previously tested at increasing rotor speeds. Turbine arrays are investigated by integrating the previous turbine model with wake sub-models to predict the plant layout maximizing the array power. An assessment of multi-row plants shows that the array power improves with closely spaced turbines. In addition, highly spaced arrays allow a partial recovery of the available power to be exploited upstream by a new turbine array. The highest array power is predicted by simulations on different array layouts considering constant array blockage ratio and rotor solidity. Finally, assuming a long ideal channel, the deviation in the inflow depth is speculated to become asymptotic after many arrays, implying almost identical power conversion upstream.