Energy extraction in the dynamic modes of flow for airfoil's laminar separation flutter

Abstract

This paper aims to gain new insight into the physical mechanism of laminar separation flutter (LSF) from the perspective of energy transfer and dynamic mode decomposition (DMD) modes of flow. An online DMD method accounting for the airfoil's pitch motion is developed, and the relationship between the topology of energy map and DMD modes is established. Simulation results indicate that there are two limit cycle branches in energy map, but only one branch is stable. The LSF time response state can be predicted accurately by the stable limit cycle branch. The topology of an energy map is dominated by the DMD mode corresponding to the airfoil's pitch frequency. The developed DMD method can extract the variation of flow structures effectively. The pressure distribution of DMD mode corresponding to the pitch frequency is dominated by the leading-edge suction and bubble's suction. The bubble's suction is induced by the trailing-edge laminar separation bubble or laminar separation bubble (LSB). When the pitch amplitude is larger than 4°, the trailing-edge laminar separation bubble transforms to LSB. The inherent mechanism is that increasing the trailing-edge separation bubble's intensity promotes the energy extraction while the occurrence of LSB mitigates it.