A multi-fidelity reduced-order model to quantify aerodynamic forces on a vertical-axis wind turbine with uncertain rotational speed

Wind turbines experience various uncertainties that can impact both design and control. In particular, rotational velocity is a crucial parameter, often controlled to ensure a stable and optimal power output or to avoid turbine overspeeding. This work investigates uncertainty quantification (UQ) for a vertical-axis wind turbine (VAWT), with a focus on the Darrieus VAWT type, using a multi-fidelity (MF) non-intrusive reduced order model (ROM), parameterized on the tip-speed ratio (TSR). A 2D computational fluid dynamic (CFD) model gives the high-fidelity (HF) representation of a three-bladed Darrieus VAWT with NACA0015 airfoils. A similar model with a coarser computational mesh represents the low-fidelity (LF) one. Both allow us to study the aerodynamic forces acting on the blades at different azimuthal angles for a wide range of TSRs. However, multiple evaluations of the HF model can become excessively expensive due to high computational costs, making demanding operations such as UQ not always a feasible choice. ROMs, on the other hand, can compute HF approximations in almost real-time. However, ROMs can be burdensome due to their high off-line computational costs relative to the training phase. Multi-fidelity methods extended to ROMs aim to reduce the amount of HF data required, leveraging inexpensive LF information. The present study compares the effectiveness of a MF ROM to more classical UQ approaches, such as Polynomial Chaos Expansion (PCE) on the HF solutions, and whether it is advantageous to equivalent single-fidelity ROMs. In particular, the focus is on the effect of rotational speed uncertainty on the aerodynamic forces acting on the blades, which are pivotal for turbine performances. Moreover, evaluating a ROM multiple times enables slow-convergence methods, such as Monte Carlo, with minimal effort. The MF ROM showed good UQ performance when compared to an equivalent single-fidelity ROM, especially for the mean estimates, closing the gap with a 4th degree PCE in the proposed use-case.