A discrete force allocation algorithm for modelling wind turbines in computational fluid dynamics

This paper describes an algorithm for allocating discrete forces in computational fluid dynamics (CFD). Discrete forces are useful in wind energy CFD. They are used as an approximation of the wind turbine blades’ action on the wind (actuator disc/line), to model forests and to model turbulent inflows. Many CFD codes are designed with collocated variables layout. Although this approach has many attractive features, it can generate a numerical decoupling between the pressure and the velocities. This issue is addressed by the Rhie–Chow control volume momentum interpolation. However, this algorithm does not address the specific cases where discrete forces are present. The velocities and pressure exhibit some significant numerical fluctuations at the position where the body forces are applied. While this issue is limited in space, it is usually critical to accurately estimate the velocity at the position of the wind turbine rotor to estimate correctly the power production and the rotor loading. The method proposed in this paper solves this issue by spreading the force on the direct neighbouring cells and applying an equivalent pressure jump at the cell faces. This can potentially open the possibility of coarsening the mesh where the forces are applied and have a considerable effect in reducing the computational cost of modelling wind turbines, wind farms and forests. This approach gives excellent results with three test cases where an analytical solution is known. This correction is also applicable in other fields of CFD that use discrete body forces. Copyright © 2011 John Wiley & Sons, Ltd.