On the Courant-Friedrichs-Lewy criterion of rotating grids in 2D vertical-axis wind turbine analysis

摘要

The Courant-Friedrichs-Lewy (CFL) criterion for the stability of numerical schemes is herein investigated at the conservative interface that divides rotating grids embedded within fixed grids. This issue is of specific interest to correctly assess the power coefficient and the energy production of vertical-axis wind turbines (VAWTs). The CFL number is here manipulated in a convenient form to tackle rotating grids; this manipulation discloses the dependence of the CFL number from the angular location of rotating grid elements and also from the tip speed ratio of the rotating grid. An upper bound of the CFL number that does not depend on the angular location of the rotating grid element is derived. The angular marching step has dramatic effects on the accuracy of results and strongly affects the calculation of the most important integral property (the power coefficient); however, local quantities are affected to a lesser extent and this fact is misleading. Large errors are generated if the angular marching step is too coarse or, in other words, if the CFL criterion is violated. Angular marching steps as small as only 1° do not warrant accurate results, particularly for very small tip speed ratios and fine spatial discretizations. It is found in this study that rotating grids call for a more restrictive (lower) bound (e.g., CFL number less than 0.15) as compared with the literature criterion. This restriction prompts severe limitations to obtain trustable results from numerical simulations of VAWTs.