Obtaining the efficiency limits of axial hydrokinetic turbines

For a hydrokinetic turbine in an open field setting, in the absence of flow restrictions, Betz’s limit represents the maximum power coefficient possible. The efficiency of turbines is evaluated against this value, under the assumption that they are connected to the grid, and therefore continuously operating at their maximum power. However, in island model operation (disconnected to the mains) the turbines operate at points between the no load and the maximum power coefficient, being the efficiency limits different from the Betz’s limit. In the present study, a function has been found defining the power efficiency limits depending on the tip speed ratio, for axial turbines in an open channel without blockage. Mathematical deduction uses the actuator disk theory within an open channel, complemented by the Euler equation for turbomachinery. The approach assumes flow simplifications, including steady, one-dimensional, incompressible, and turbulent-free conditions. Furthermore, two dimensionless parameters have been proposed relating the real coefficient curve with the limit one. These parameters enable a better definition -in the whole range of tip speed ratios- of the difference between the actual efficiency and the limits, as well as the potential for improvement. Function and parameters have been calculated for a numerically simulated turbine and three different turbines from a literature benchmark.