Periodic Free Wake Simulation Using a Numerical Optimization Method

A novel method has been developed for the free vortex wake simulation of rotors under the assumption of periodicity. An error measure is introduced which is based on the mismatch between prevailing convection velocities and the assumed wake element positions. The systematic reduction of this defined error results in a numerically robust method for the computation of wake geometries. Two strategies are compared for the error reduction. The first uses the repeated evaluation of the velocity field to update the wake geometry as long as the defined error decreases. In the second strategy, the application of a Levenberg-Marquardt method is added, in which the error is further reduced using an analytically defined Jacobian matrix. Results correlate well with experiments for single rotor and tandem rotor cases. While the Levenberg-Marquardt method achieves an additional error reduction, correlation with experimental data is not generally improved by including this method.