Implementation of the multi-level multi-integration cluster method to the treatment of vortex particle interactions for fast wind turbine wake simulations

A method for the treatment of the evolution of the wake ofaerodynamic bodies has been implemented. A vortex particlemethod approach has been used whereby the flow field is discretized into numerical volumes which possess a given circulation. A lifting line formulation is used to determine the circulation of the trailing and shed vortex elements. Upon their releasevortex particles are allowed to freely convect under the action ofthe blade, the freestream and other particles. Induced velocitiesare calculated with a regularized form of the Biot-Savart kernel,adapted for vortex particles. Vortex trajectories are integrated ina Lagrangian sense. Provision is made in the model for the rateof change of the circulation vector and for viscous particle interaction; however these features are not exploited in this work.The validity of the model is tested by comparing results of thenumerical simulation to the experimental measurements of theMexico rotor. A range of tip speed ratios are investigated andthe blade loading and induced wake velocities are compared toexperiment and finite-volume numerical models.The computational expense of this method scales quadratically with the number of released wake particles N. This resultsin an unacceptable computational expense after a limited simulation time. A recently developed multilevel algorithm has been implemented to overcome this computational expense. This method approximates the Biot-Savart kernel in the far field by using polynomial interpolation onto a structured grid node system. The error of this approximation is seen to be arbitrarily controlled bythe polynomial order of the interpolation. It is demonstrated thatby using this method the computational expense scales linearly.The model's ability to quickly produce results of comparable accuracy to finite volume simulations is illustrated and emphasizesthe opportunity for industry to move from low fidelity, less accurate blade-element-momentum methods towards higher fidelityfree vortex wake models while keeping the advantage of shortproblem turnaround times.