Fast Multilevel Panel Method for Wind Turbine Rotor Flow Simulations

Abstract

A fast multilevel integral transform method has been developed that enables the rapid analysis of unsteady inviscid flows around wind turbines rotors. A low order panel method is used and the new multi-level multi-integration cluster (MLMIC) method reduces the computational complexity for calculating the wake deformation downstream of the wind turbine rotor from O(N 2) for a conventional approach to O(N). The method discretizes the volume surrounding the configuration with cubes. Each cube contains a grid of nodes that are used in the interpolation of the Green's functions underlying the panel method. The formulation of the panel method is described concisely and verified using exact solutions for a tri-axial ellipsoid in uniform flow and for a rotating ellipsoid in air at rest. For these tests the panel method exhibits an error varying quadratically with panel size. The MLMIC fast multilevel method is described and its accuracy and O(N) computational speed are verified for some model problems. Surface pressure distributions obtained with the fast panel method are compared with results from the MEXICO wind tunnel experiment and with results from a state-of-the-art numerical simulation method based on the Reynolds-averaged Navier-Stokes (RaNS) equations. This work repositions panel methods in the computational landscape as valuable intermediate fidelity computational design method for wind turbine engineering.

Wind Turbine Aerodynamics from an Aerospace Perspective

“…The accuracy of the selected pressure transducers is well balanced to the prevailing dynamic pressure at the rotating tip of the turbine, whereas the accuracy of experimental pressure data decreases towards the hub. In addition to the results obtained by the ENSOLV numerical solution method the results obtained by a fast multilevel panel method 20,21 that models inviscid, incompressible flow are also shown. Other cases computed with the ENSOLV numerical solution method and compared with experimental data consist of a turbulent wake state (wind speed of 10 m/s, tip speed ratio of 10), a separated flow case (wind speed of 24.12 m/s, tip speed ratio of 4.2) and a standstill condition (wind speed of 29.92 m/s, tip speed ratio 0), the latter only being instructive for the assessment of aerodynamic loads predictions on the rotor in vane position.…”

“…Recent progress 20,21 in reducing the computational burden of the classical panel method for wind turbine applications makes this approach an attractive proposition. Figure 11 shows an example of achieved reductions in integral evaluation time for the newly developed multilevel panel method.…”

“…However, by that time the vast investments in numerical flow simulation methods based on the Euler equations, their successful application, and the prospect of extending the method to general viscous flows was the reason the project was abandoned for good. For wind turbine designs, where the trend is towards higher subsonic rotor tip speeds (currently ~100 m/s), this approach could be revived while keeping the computational costs limited through the use of the fast multilevel panel method 20,21 .…”

Tidal and wind turbine simulation with the simulation code DOROTHY

“…In the meantime, in order to have access within the Dorothy code to reliable and more immediate results in terms of loads, a lifting line alternative, named here LL-VPM, has been added to represent the turbines. Lifting line details can be found in (Katz & Plotkin 2001, van Garrel 2003, Shaler et al 2020.…”

Towards vortex-based wind turbine design using GPUs and wake accommodation

“…Approaches aiming at reducing computational costs have been introduced in the literature. Multilevel or fast-multipole algorithms can be used, as shown in [22], [6]. Our approach rather relies on reducing the number of wake elements and GPU acceleration to achieve better performances.…”