Tidal farm analysis using an analytical model for the flow velocity prediction in the wake of a tidal turbine with small diameter to depth ratio

Abstract

A tidal turbine is a device converting hydrodynamic power into electrical power. Lately, more and more projects have been developed in order to optimize the productivity of this kind of energy. In such research with industrial interest, under the impact of the wake effect on the output power, the analysis of a tidal farm layout is regarded as the first priority. Simple approaches such as those developed for wind farms could be used in tidal turbine arrangement optimization. These methodologies can be improved by taking into account the turbulence in tidal farms and tidal turbines' mechanical characteristics. The goal of this work is to propose a predictive analytical model to estimate the tidal speed in the far wake of tidal turbines with small diameter to depth ratio (20% here). It is a first step prior to integrate the wake model in a tidal farm layout optimization algorithm. The wake model development is achieved reanalyzing the far wake's equations used in wind farm applications. A turbine represented by an Actuator Disc (AD) in conjunction with a Computational Fluid Dynamics (CFD) numerical model is used as a reference for this purpose. The CFD-AD model has been validated with experimental results from literature. The novelty of the present work consists in expressing the far wake's radius expansion as a function of the ambient turbulence and the thrust coefficient. The proposed equation is used in conjunction with the Jensen's model in a manner that the velocities downstream a tidal turbine can be estimated. The velocity distribution in the far wake of a single turbine obtained by the proposed model is in good agreement with the CFD numerical model. As a matter of fact, the model provides satisfactory accuracy in the cases of two parks: one with five aligned turbines and one with ten staggered turbines.