Analytic Characterization of the Wake Behind In-Stream Hydrokinetic Turbines

Abstract

Analytical algorithms developed and optimized for quantifying the wake behind in-stream hydrokinetic turbines are presented. These algorithms are based on wake expressions originally developed for wind turbines. Unlike previous related studies, the optimization of empirical coefficients contained in these algorithms is conducted using centerline velocity data from multiple published experimental studies of the wake velocities behind in-stream hydrokinetic turbine models or porous disks and not using computational fluid dynamics. Empirical coefficients are first individually optimized based on each set of experimental data, and then empirically based coefficient expressions are created using all of the data sets collectively, such that they are functions of ambient turbulence intensity. This expands the applicability of the created algorithms to cover the expected range of operating conditions for in-stream hydrokinetic turbines. Wind turbine wake model expressions are also modified to characterize the dependence of wake velocities on radial location from the centerline of in-stream hydrokinetic turbines. Thus, expressions with empirically optimized coefficients for calculating wake velocities behind in-stream hydrokinetic turbines are described in terms of both centerline and radial positions. Wake predictions made using the Larsen model for radial dependence are shown to diverge from experimental measurements near the wake radius defined by the Jensen model, suggesting that this is a good indication of the cutoff point beyond which numerical estimations no longer apply. Results suggest that using a combined Larsen/Ainslie approach or combined Jensen/Ainslie approach for characterizing wake have similar mean errors to using only a Larsen approach.