Several Modifications to Improve Numerical Stability of Leishmen-Beddoes Dynamic Stall Model

Abstract

Dynamic stall is dominant to aerodynamic performance of vertical axis wind turbines where angles of attack (AoAs) of blades vary periodically during operation. Therefore, dynamic stall models are necessarily employed in the simulation of wind turbines. Among them the Leishmen-Beddoes (LB) dynamic stall model are widely accepted nowadays. In the LB model, aerodynamic forces of blades are determined by AoAs and their rates of change. However, in consideration of the inevitable existence of numerical errors of AoAs, calculations of the rates of change may cause unexpected numerical problems. This paper focused on presence of fluctuations of blade forces due to minor numerical errors of AoAs in the LB model. Then three modifications, namely the implementation of filters of AoAs, alternative calculation of change of variables and scaling of time constants, were employed and their effect on numerical stability of the LB model was evaluated. It is found that the implementation of filters of AoAs can eliminate fluctuations of outcome forces but the phase delay is the side effect. In addition, alternative calculation of change of variables and scaling of time constants can reduce the maximum nominal fluctuations of results from 16.4% to 5.8% and 5.1%, respectively.