Flapping dynamics of a flag in a uniform stream

作者：Benjamin S. H. Connell, Dick K. P. Yue · 发表于：Journal of Fluid Mechanics · 年份：2007 · DOI：10.1017/s0022112007005307 · 被引用次数：407 · 研究领域：Biomimetic flight and propulsion mechanisms、Fluid Dynamics and Turbulent Flows、Lattice Boltzmann Simulation Studies

We consider the flapping stability and response of a thin two-dimensional flag of high extensional rigidity and low bending rigidity. The three relevant non-dimensional parameters governing the problem are the structure-to-fluid mass ratio, μ = ρsh/(ρfL); the Reynolds number,Rey=VL/ν; and the non-dimensional bending rigidity,KB=EI/(ρfV2L3). The soft cloth of a flag is represented by very low bending rigidity and the subsequent dominance of flow-induced tension as the main structural restoring force. We first perform linear analysis to help understand the relevant mechanisms of the problem and guide the computational investigation. To study the nonlinear stability and response, we develop a fluid–structure direct simulation (FSDS) capability, coupling a direct numerical simulation of the Navier–Stokes equations to a solver for thin-membrane dynamics of arbitrarily large motion. With the flow grid fitted to the structural boundary, external forcing to the structure is calculated from the boundary fluid dynamics. Using a systematic series of FSDS runs, we pursue a detailed analysis of the response as a function of mass ratio for the case of very low bending rigidity (KB= 10−4) and relatively high Reynolds number (Rey= 103). We discover three distinct regimes of response as a function of mass ratio μ: (I) a small μ regime of fixed-point stability; (II) an intermediate μ regime of period-one limit-cycle flapping with amplitude increasing with increasing μ; and (III) a large μ regi...