A Validation Study of the Aerodynamic Behaviour of a Wind Turbine: Three-Dimensional Rotational Case

Numerical modelling and simulation of a rotating, tapered, and twisted three-dimensional blade with turbulent inflow conditions and separating flows is a challenging case in Computational Fluid Dynamics (CFD). The numerical simulation of the fluid flow behaviour over a wind turbine blade is important for the design of efficient machines. This paper presents a numerical validation study using the experimental data collected by the National Renewable Energy Laboratory (NREL). All the simulations are performed on the sequence S of the extensive experimental sequences conducted at the NASA/Ames wind tunnel with constant RPM and variable wind speeds. The results show close agreement with the NREL UAE experimental data. The CFD model captures closely the totality of the defining quantities. The shaft torque is well-predicted pre-stall but under-predicted in the stall region. The three-dimensional flow and stall are well captured and demonstrated in this paper. Results show attached flow in the pre-stall region. The separation appears at a wind speed of 10 m/s near the blade root. For V>10m/s, the blade appears to experience a deep stall from root to tip.

Mass-conserving diffusion-based dynamics on graphs

An emerging technique in image segmentation, semi-supervised learning and general classification problems concerns the use of phase-separating flows defined on finite graphs. This technique was pioneered in Bertozzi and Flenner (2012, Multiscale Modeling and Simulation10(3), 1090–1118), which used the Allen–Cahn flow on a graph, and was then extended in Merkurjev et al. (2013, SIAM J. Imaging Sci.6(4), 1903–1930) using instead the Merriman–Bence–Osher (MBO) scheme on a graph. In previous work by the authors, Budd and Van Gennip (2020, SIAM J. Math. Anal.52(5), 4101–4139), we gave a theoretical justification for this use of the MBO scheme in place of Allen–Cahn flow, showing that the MBO scheme is a special case of a ‘semi-discrete’ numerical scheme for Allen–Cahn flow. In this paper, we extend this earlier work, showing that this link via the semi-discrete scheme is robust to passing to the mass-conserving case. Inspired by Rubinstein and Sternberg (1992, IMA J. Appl. Math.48, 249–264), we define a mass-conserving Allen–Cahn equation on a graph. Then, with the help of the tools of convex optimisation, we show that our earlier machinery can be applied to derive the mass-conserving MBO scheme on a graph as a special case of a semi-discrete scheme for mass-conserving Allen–Cahn. We give a theoretical analysis of this flow and scheme, proving various desired properties like existence and uniqueness of the flow and convergence of the scheme, and also show that the semi-discrete scheme yields a choice function for solutions to the mass-conserving MBO scheme.

Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.