Study on effects of thickness on airfoil-stall at low Reynolds numbers by cusp-catastrophic model based on GA(W)-1 airfoil

The phenomena of an airfoil stall present the behaviors of catastrophe and hysteresis at low Reynolds numbers.Numerical simulation results of two-dimensional airfoil GA(W)-1 show that the width of the hysteresis loop of airfoil stall will gradually decrease and even disappear with the decrease of thickness ratio.These nonlinear characteristics are in accordance with the topological features of the cusp catastrophic model.According to the topological invariant principle,a novel topological mapping method is developed to establish the mapping relationship between cusp catastrophic model and stall characteristics of the airfoil,then the effect of thickness ratio on airfoil stall is successfully described quantitatively by cusp catastrophic model.Further,based on the established topological mapping relationship,combined with the mean flow field of the airfoil stall,potential function approach of cusp catastrophic model is first introduced to interpret the catastrophe and hysteresis of the airfoil stall,and it is found that as the thickness ratio decreases,the system’s maximal potential energy gradually disappears,and the short separation bubble at the leading edge of the airfoil changes to long separation bubble,so the airfoil stall changes from a bistable system to a monostable system.