A method for the treatment of the evolution of the wake of aerodynamic bodies has been implemented. A vortex particle method 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 release vortex particles are allowed to freely convect under the action of the blade, the freestream and other particles. Induced velocities are calculated with a regularized form of the Biot-Savart kernel, adapted for vortex particles. Vortex trajectories are integrated in a Lagrangian sense. Provision is made in the model for the rate of 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 the numerical simulation to the experimental measurements of the Mexico rotor. A range of tip speed ratios are investigated and the blade loading and induced wake velocities are compared to experiment and finite-volume numerical models.
The computational expense of this method scales quadratically with the number of released wake particles N. This results in 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 by the polynomial order of the interpolation. It is demonstrated that by 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 emphasizes the opportunity for industry to move from low fidelity, less accurate blade-element-momentum methods towards higher fidelity free vortex wake models while keeping the advantage of short problem turnaround times.
