Dimensionless numbers for the assessment of mesh and timestep requirements in CFD simulations of Darrieus wind turbines

Computational Fluid Dynamics is thought to provide in the near future an essential contribution to the development of Vertical-Axis Wind Turbines. The unsteady flow past rotating blades is, however, a challenging application for a numerical simulation and some critical issues have not been settled yet. In particular, if some studies in the literature report detailed analyses on the assessment of the computational model, there is still no adequate convergence on the requirements in terms of spatial and temporal discretizations. In the present study, a multivariate sensitivity analysis was first carried out on a specific case study at different tip-speed ratios in order to define the optimal mesh and timestep sizes needed for an accurate simulation. Once full insensitivity had been reached, the spatial and temporal requirements needed to properly describe the flow phenomena were related to two dimensionless numbers, one for each domain, which can be used to assess the suitability of the selected settings for each specific simulation. The simulations revealed that the spatial requirements must be selected in order to ensure an accurate description of velocity gradients in the near-blade region. To this purpose, a Grid-Reduced form of vorticity is proposed as the best indicator for the quality of the mesh refinement. It is also shown that the temporal requirements are made stricter at low tip-speed ratios by the need of correctly describing the vortices detaching from the blades in the upwind region. To do so, proper thresholds for the Courant Number are highlighted in the study.