A semi-parabolic wake model for large offshore wind farms based on the open source CFD solver OpenFOAM

Abstract

Wake effect represents one of the main sources of energy loss and uncertainty when designing offshore wind farms. Traditionally analytical models have been used to optimize and estimate power deficits. However these models have shown to underestimate wake effect and consequently overestimate output power (1, 2). This means that analytical models can be very helpful at optimizing preliminary layouts but not as accurate as needed for an ultimate fine design. Different techniques can be found in the literature to study wind turbine wakes that include simplified kinematic models and more advanced field models, that solve flow equations with different turbulence closure schemes. See the review papers of Crespo et al. (3), Vermeer et al. (4), and Sanderse et al. (5). Purely elliptic Computational Fluid Dynamics (CFD) models based on the actuator disk technique have been developed during the last years (6-8). They consider wind turbine rotor as a disk where a distribution of axial forces act over the incoming air. It is a fair approach but it can still be computationally expensive for big wind farms in an operative mode. With this technique still active, an alternative approach inspired on the parabolic wake models (9, 10) is proposed. Wind turbine rotors continue to be represented as actuator disks but now the domain is split into subdomains containing one or more wind turbines. The output of each subdomain is mapped onto the input boundary of the next one until the end of the domain is reached, getting a considerable decrease on computational time, by a factor of order 10. As the model is based on the open source CFD solver OpenFOAM, it can be parallelized to speed-up convergence. The near wake is calculated so no initial wind speed deficit profiles have to be supposed as in totally parabolic models and alternative turbulence models, such as the anisotropic Reynolds Stress Model (RSM) can be used. Traditional problems of elliptic models related to the estimation of the reference wind speed at each rotor position are mitigated due to the semi-parabolic algorithm. The model has been validated at the ECN test farm and at the offshore Horns Rev wind farm with significant results and also have been compared to other wake models.