Collective dynamics of a stack of inverted flags

Abstract

The dynamics of a stack of inverted flags under a free stream are experimentally investigated, in which multiple flags are initially placed parallel to the free stream with no gaps between them. With increasing free-stream velocity, the stacked inverted flags transition from an initial straight mode to a quasi-static mode where their leading edges are spread out with significant deflection. An irregular flapping mode then occurs, followed by a collective in-phase flapping mode. Within the regime of the irregular flapping mode, an interesting phenomenon appears: the flags clap periodically near a centerline. By varying the number, height, and thickness of the flags, the critical conditions for the mode transitions are identified. While the critical flow velocity is insensitive to the number of flags in the transition to irregular flapping, it increases with the number of flags in the transition to the in-phase flapping mode. The observation that the in-phase flapping mode of the stacked flags is similar to the large-amplitude flapping mode of a single flag leads us to propose a dimensionless flow velocity, which accounts for the effect of the number of flags, to predict the stability thresholds. Using this dimensionless flow velocity, the dynamic characteristics of in-phase flapping, such as the dimensionless amplitude, frequency, and strain energy, are examined, and these parameters are found to be almost independent of the number of flags.