Defining the Characteristic Velocity for the Reynolds Number in Turbine Experiments

The Reynolds number can significantly affect the performance of lift-based wind and water turbines, particularly at laboratory-scale. It is, therefore, important to use a consistent and physically-meaningful definition for the length and velocity scales. In these applications, the most meaningful length scale is the blade chord. For simplicity, common definitions of the Reynolds number take the characteristic velocity as either the tangential speed of the blade or the free-stream velocity. However, the flow over the blade can vary with rotational position and depends on the flow induction, free-stream velocity, and tangential blade speed. To explore the most meaningful choice of the characteristic velocity, this study tests a cross-flow current turbine over a range of Reynolds numbers. The Reynolds number is varied first by changing the temperature of the water, which alters the viscosity. The turbine is tested again at constant temperature and varying free-stream velocity. The implications of the choice of characteristic velocity scale are explored by determining the conditions under which performance is invariant between the two experiments.