VAWT Dynamic Stall Model tuning using URANS

Abstract

Vertical-axis wind turbine (VAWT) blades experience large and continuous variations in inflow angle of attack and velocity over a turbine revolution, leading to unsteady aerodynamic effects such as dynamic stall. In aero-elastic tools for VAWT power and load prediction, these effects are often modelled using semi-empirical dynamic stall models, such as the Beddoes-Leishman and {Ris\o} models. These models rely on a set of airfoil-specific tuning parameters, which can influence the predicted power coefficient of a floating MW-scale VAWT by more than $5\%$. Historically, these parameters have been determined using experimental wind tunnel data, which is not readily available for a wide range of airfoils. This thesis investigates whether URANS-based computational fluid dynamics (CFD) can partially or fully replace experimental wind tunnel data for the tuning of semi-empirical dynamic stall models for VAWT applications.

Unsteady Reynolds-averaged Navier-Stokes simulations using an incompressible $k$-$\omega$ SST turbulence model are first assessed for their ability to reproduce unsteady airfoil aerodynamics. It is found that the URANS model can accurately replicate the magnitude, phase, and frequency content of the experimental lift response of a pitching NACA0018 airfoil in attached-flow conditions. As a result, URANS simulations are shown to be suitable for determining the four parameters associated with attached-flow unsteadiness in the semi-empirical {Ris\o} dynamic stall model. However, the two remaining time-lag parameters cannot be identified with sufficient confidence, as the incompressible URANS approach is unable to accurately capture the separated-flow regimes and compressibility effects governing these parameters. Experimental data is therefore required to tune this subset of the model parameters.

Based on these findings, multiple tuning strategies are evaluated. A physics-informed hybrid approach is proposed, in which attached-flow parameters are determined using URANS simulations, while parameters governing separated-flow dynamics and compressibility effects are calibrated using experimental data. In addition, two optimisation-based tuning strategies are considered: one minimising the global error over the full unsteady lift response, and one optimising a set of key aerodynamic metrics, including the maximum lift coefficient, the angle of attack at maximum lift, and the phase error. All tuning strategies are evaluated at both the airfoil and the turbine level, demonstrating that relatively small differences in airfoil-level unsteady response can lead to significant differences in predicted VAWT power output when integrated over a full turbine rotation. The results show that while URANS-based CFD cannot fully replace experimental data for dynamic stall model tuning, a hybrid CFD–experimental approach provides a practical method for reducing experimental dependency in VAWT aero-elastic modelling.