Understanding savonius turbine wake for 2-D and 3-D simulations: proper orthogonal decomposition of velocity components

Abstract

Savonius turbines, known for their low cost and ease of maintenance, are widely used as small-scale wind and hydrokinetic turbines. However, significant discrepancies exist between two-dimensional (2-D) and three-dimensional (3-D) computational fluid dynamics (CFD) simulations, particularly in predicting wake dynamics. This study investigates wake characteristics across varying tip speed ratios (TSRs) using proper orthogonal decomposition (POD) of velocity components from 3-D simulations. POD analysis reveals that for TSR ≤ 1.0, vortex shedding from blade tips dominates, whereas for TSR > 1.0, rotational motion becomes more prominent, followed by vortex shedding. The vertical velocity component shows dominant POD modes at the rotational frequency and its harmonics, while the streamwise and lateral components are primarily influenced by the vortex shedding frequencies. These dynamics are absent in 2-D simulations due to the lack of vortex stretching in the third direction, leading to fundamentally different modal structures. Additionally, results show vertical transport is critical to wake recovery, significantly outweighing lateral transport up to two rotor diameters downstream—an effect not captured in 2-D simulations. Since accurate wake modelling is essential for predicting the performance of Savonius turbine arrays, especially in streamwise configurations, the limitations of 2-D simulations pose a challenge. This study provides physical insights into the origins of those limitations and highlights the necessity of 3-D simulations for reliable prediction of array power coefficients. The findings also serve as a foundation for future development of reduced-order models for low-cost array simulations.