Actuator line modeling of vertical-axis turbines

To bridge the gap between high and low fidelity numerical modeling tools for vertical-axis (or cross-flow) turbines (VATs or CFTs), an actuator line model (ALM) was developed and validated for both a high and a medium solidity vertical-axis turbine at rotor diameter Reynolds numbers $Re_D \sim 10^6$. The ALM is a combination of classical blade element theory and Navier--Stokes based flow models, and in this study both $k$--$\epsilon$ Reynolds-averaged Navier--Stokes (RANS) and Smagorinsky large eddy simulation (LES) turbulence models were tested using the open-source OpenFOAM computational fluid dynamics framework. The RANS models were able to be run on coarse grids while still providing good convergence behavior in terms of the mean power coefficient, and also approximately four orders of magnitude reduction in computational expense compared with 3-D blade-resolved RANS simulations. Submodels for dynamic stall, end effects, added mass, and flow curvature were implemented, resulting in reasonable performance predictions for the high solidity rotor, more discrepancies for the medium solidity rotor, and overprediction for both cases at high tip speed ratio. The wake results showed that the ALM was able to capture some of the important flow features that contribute to VAT's relatively fast wake recovery---a large improvement over the conventional actuator disk model. The mean flow field was better realized with the LES, which still represented a computational savings of two orders of magnitude compared with 3-D blade-resolved RANS, though vortex breakdown and subsequent turbulence generation appeared to be underpredicted, which necessitates further investigation of optimal subgrid scale modeling.