## SemiParabollicFOAM

The model derives from a previous elliptic model and it is inspired on the parabolic technique of other models such as UPMPARK and Windfarmer but using the actuator disk technique to represent the wind turbine instead of wind speed deficit.

The wind turbine is represented as an actuator disk uniformly loaded. This means that the wind turbine acts as a sink of momentum, associated to the drag force exerted over the incoming flow. The reference wind speed for each disk is initially calculated from the wind speed at the position of the disk and corrected through the method proposed by Calaf et.al.

The solution algorithm consists of a decomposition of the domain into a finite number of adjacent subdomains that are solved sequentially in the axial direction, using the output of each subdomain as input for the next one. This is done until the end of the domain is reached. This way the computational time becomes significantly lower in comparison to the solution of a single domain by means of a purely elliptic approach.

The main advantage of this technique is that the near wake is calculated instead of modeled, alternative anisotropic turbulence models can be tested and since it is based on an open source code, it can be solved for an unlimited number of nodes, getting an approximate decrease in computational time of the order of 10 has been estimated in comparison to purely elliptic models.

[1] OpenCFD, “OpenFOAM: The Open Source CFD Toolbox – Programmer’s Guide v1.7”, 2010

[2] Cabezon D., Migoya E., Crespo A., “Comparison of turbulence models for the computational fluid dynamics simulation of wind turbine wakes in the atmospheric boundary layer”, Journal of Wind Energy, DOI: 10.1002/we.516

[3] Barthelmie RJ, Frandsen ST, Rathmann O, Hansen K, Politis ES, Prospathopoulos J, Cabezón D, Rados K, van der Pijl SP, Schepers JG, Schlez W, Phillips J, Neubert A. Flow and wakes in large wind farms in complex terrain and offshore. In European Wind Energy Conference and Exhibition, Brussels, 2008.

[4] Barthelmie, R.J., Frandsen, S.T., Hansen, K., Politis, E., Cabezón, D., Schepers, J.G., Rados, K.and Schlez, W. 2010: Power losses due to wind turbine wakes in large wind farms offshore and in complex terrain. World Renewable Energy Congress, Abu Dhabi, September 2010.

[5] Cabezón D., Sumner J., Crespo A., “Prediction of wake effects on wind farm power production using a RANS approach. Part II: Offshore. Case studies from the UPWIND project”, Wake Conference, Gotland (Sweeden), 2011

[6] Cabezón D, Hansen K, Barthelmie RJ. Analysis and validation of CFD wind farm models in complex terrain Wakes induced by topography and wind turbines. In European Wind Energy Conference and Exhibition, Warsaw, 2010.

[7] Prospathopoulos, J., Cabezon D., Politis E., Chaviaropoulos P.K., Rados K., Schepers J.G., Hansen K.S., Barthelmie R.J., “Simulation of wind farms in flat and complex terrain using CFD”, Conference on the science of making torque from wind, Heraklion, Crete (Greece), June 2010

[8] Prospathopoulos, J., Cabezón, D., Politis, E.P., Chaviaropoulos, P.K., Rados, K.G., Schepers, G.S., Hansen, K.S. and Barthelmie, R.J. 2010: Simulation of wind farms in flat and complex terrain using CFD, The Science of Making Torque from Wind, Crete, June 2010. 12 pp

[9] Politis, E., Prospathopoulos, J., Cabezon D., Hansen, K.S., Chaviaropoulos P.K., Barthelmie, R.J., 2011, “Modelling wake effects in large wind farms in complex terrain: the problem, the methods and the issues”, Journal of Wind Energy, DOI 10.1002/we.481

[10] Calaf M, Meneveau C, Meyers J. Large eddy simulation study of fully developped wind-turbine array boundary layers. Physics of Fluids 2010; 22: 015110.

[11] Cabezón D.,Migoya E., Crespo A., “A semi-parabolized wake model for big offshore wind farms based on the open source CFD solver OpenFOAM”, Journal of Informatics and Mathematics, accepted for publication

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