Backwater Assessment for the Energy Conversion through Hydrokinetic Turbines in Subcritical Prismatic Canals

Hydrokinetic turbines exploit partially the total head variation created in natural and artificial waterways. In subcritical flows, the sum of the energy harvested mechanically and the energy dissipated by fluid dynamic losses and viscous friction is balanced through a backwater extending far upstream. The latter depends on the turbine operating condition and, thus, on the thrust force generated. Only the downstream momentum is known, whilst upstream momentum and turbine thrust force are undetermined. To solve this problem, a method is developed to update the inflow factor for a single turbine, thus achieving a single physical solution. Froude number and blockage ratio are updated at each iteration and are used as independent variables for solving the turbine model. According to the actual canal geometry, a specific continuity equation allows to infer the backwater depth from the inflow factor. Hence, this method can be integrated with confined BEM and DMS models to extend the capability of the simulation tool. Experimental data of inflow depth are used to validate this model for single rotors in a subcritical environment, whilst its extension allows the assessment of turbine arrays in artificial canals exploited for hydropower purposes.