Parametrization Effects of the Non-Linear Unsteady Vortex Method with Vortex Particle Method for Small Rotor Aerodynamics

Abstract

The aim of this article is to investigate the parameter sensitivity of the (Non-Linear) Unsteady Vortex Lattice Method-Vortex Particle Method [(NL-)UVLM-VPM] with Particle Strength Exchange-Large Eddy Simulations (PSE-LES) method on a lower Reynolds number rotor. The previous work detailed the method, but introduced parameters whose influence were not investigated. Most importantly, the Vreman model coefficient was chosen arbitrarily and was not suitable to ensure stability for this lower Reynolds number rotor simulation. In addition, the previous work presented a consistency study where geometry and time discretization were refined simultaneously. The present article starts with a comparative literature review of potential methods used to solve the aerodynamics of an isolated hovering rotor. This review highlights the differences in modeling, discretizations, sensitivity analysis, validation cases, and the results chosen by the different studies. Then, a transparent and thorough parametric study of the method is presented alongside discussions of the observed results and their physical interpretation regarding the flow. The sensitivity analysis is performed for the three free parameters of UVLM, namely Vatistas core size, the geometry and the temporal discretizations, and then for the three additional parameters introduced by UVLM-VPM, which are the Vreman model coefficient, the particle spacing, and the conversion time. The effect of different databases in the non-linear coupling is also shown. The method is shown to be consistent with both geometry and temporal refinements. It is also consistent with the expected behavior of the different parameters change, including the numerical stability that depends on the strength of the LES diffusion controlled by the Vreman model coefficient. The effect of discretization refinement presented here not only shows the integrated coefficients where different errors can cancel each other, but also looks at their convergence and where relevant, the distributed loads and tip singularity position. Finally, the aerodynamics results of the method are compared for different databases and with higher fidelity Unsteady Reynolds Averaged Navier–Stokes (URANS) 3D results on a lower Reynolds number rotor.