Dynamic response of vortex breakdown flows to a pitching double-delta wing

Abstract

A finite volume-based solver with rigid moving mesh and delayed detached eddy simulation (DDES) techniques is implemented to investigate the unsteady flows around an 80°/65° double-delta wing (DDW) subjected to sinusoidal pitching motions. The focus concentrates on understanding the behaviour of the burst point (BP), helical mode instability, pressure fluctuations, and dynamic pitching stability. The role of the reduced frequency (RF) in the response of the above features is analyzed in detail. It is in consistence with the previous experiments that the movement of the BP is nearly a simple harmonic motion and locked with the frequency of the pitching motion accompanied with a phase lag that is strongly affected by the RF. It is found that the time-averaged flow in the post-breakdown regions is approximately a conical flow, whose cone angle also depends on the RF. The natural frequency of BP oscillation at the stationary state of AOA = 36° is the critical frequency, which determines the sign of dynamic pitching derivative. A pair of critical frequencies is found, by which the features of the BP, cone angle of the helical structures, and dynamic pitching stability are divided into several linear sections. Two simplified 1st and 2nd order differential models are proposed and applied for predicting the dynamic behaviour of the BP, and the 2nd order model can give coincident hysteresis loops with the present computational fluid dynamics (CFD) results in a certain range.