Inverted Flag Flapping

Simulation of the fluid/structure interaction that dominates the dynamics of these flows poses a formidable challenge to even the most advanced numerical techniques, and is currently at the forefront of ongoing work in computational fluid dynamics. A major challenge in the implementation of any non-boundary conforming methodology is the establishment of the relation between the Lagrangian coordinates of the body and the underlying Eulerian grid and the imposition of boundary conditions.

We present a new numerical methodology for simulating fluid–structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet–Neumann partitioning technique. The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid–fluid interfaces where the structural nodal positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems.

Understanding the self-excited oscillations of an inverted flag in fluid flow for potential energy harvesting applications.

The presented validation test case is a stringent and challenging case as it involves the flapping oscillations of an inverted flag at high Reynolds number and corresponds to a recently published laboratory experiment of Kim et al. (2013) . The problem is referred to as the inverted flag because the flag, a thin flexible sheet of length L, is mounted on its trailing edge with its leading edge free to move in response to a uniform incoming flow u_∞. Kim et al. (2013) carried out a series of experiments by varying u_∞ and/or the structural properties of the flag and identified a dynamically rich phase space of flag responses.

Oue computed results are in excellent agreement with the experimental measurements. The simulations not only capture the amplitude and period of oscillations with good accuracy but also resolve the two local deflection maxima (minima) that occur in the vicinity of maximum (minimum) flag deflection. A more quantitative comparison with the measurements reveals that the maximum discrepancy between experiments and simulations, which occurs around maximum and minimum tip deflection, does not exceed 7% of the measured values.

The simulation reveals the highly unsteady and massively separated wake dynamics.

To our knowledge the results we have reported herein elucidate for the first time the three-dimensional structure of the wake of a flapping inverted flag and clearly illustrate the ability of our CURVIB-FE-FSI method to solve a very complex, high Reynolds number problem involving complex large amplitude vibrations of a thin structure. Even though not shown herein, we have carried out simulations for values of βin all three experimentally identified flag response regions and our results are in very good agreement with the experiments of Kim et al. (2013) .