Evaluation of a semi-analytical bimodal Gaussian model for the estimation of the lateral velocity distribution behind a tidal stream turbine

The wake of a tidal stream turbine is influential for maximizing the global output of tidal farms but as well is problematic to predict, in specific just behind the rotor. In this paper, the framework of a bimodal Gaussian model is presented using Momentum Theory, although with important modifications for considering the channel blockage. Equations for the momentum deficit, central velocity, wake radius are obtained from the flume tests on a scaled turbine operating at peak power coefficient $(C_P=0.33)$ and tip speed ratio of $\lambda \approx 3.9$, within a turbulent flow. A comparison of the lateral wake distribution for downstream distances up to $x/D=14$ diameter rotors is made against two popular models: Gaussian and Lam–Chen. The experimental lateral wake velocities exhibit the bimodal Gaussian nature near the wake but transition to the well-known bell curve, thereafter. A slight bypass acceleration ensues due to the channel blockage. Compared to the standard Gaussian distribution, the relative error of the bimodal Gaussian distribution is about $0.7\%$ higher in the far-wake $(x/D\ge 8)$ and 0.6–9.7 % lower in near-wake region $(x/D\le 3)$. The overall error of the bimodal Gaussian model is less than $6.5\%$, successfully portraying the effect of the shear flow generated by the rotor tips.