Cantilever in the Wake of Square Cylinder.

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.

A cantilever mounted at the downstream face of a square cylinder was simulated. Depending on the flow regime (Reynolds number) and the geometric, material and structural properties, the cantilever may develop complex vibration modes close to either the first or second natural modes. Understanding vortex-induced vibration of flexible structures in fluid flow is critical for many engineering applications. The cantilever problem we solve is identical to the problem solved by Hübner et al. (2004), and gives rise to the second natural mode of cantilever vibrations, namely kinematics resembling a travelingwave with a stagnation point. The following values for the various parameters are used for this problem: shell’s density ρs=2 ·10^3 kg/m3, Young’s modulus E=2 ·10^5 Pa, Poisson’s ratio ν=0.35, shell’s thickness h0=6 ·10^−4 m, fluid density ρf=1.18 kg/m3, fluid viscosity μ =1.82 ·10−5 Pa.s, inflow velocity u_∞=0.315 m/s. The square cylinder length is L_0=10−2 m and the resulting Reynolds number is Re=204. The cantilever is discretized with 320 triangular elements and the background fluid grid is discretized with a mesh 161 ×91 ×5, the nondimentional time step is equal to t=0.01. This problem is characterized by high density ratio (ρ_s/ρ_f∼1690), hence the loose coupling FSI iteration scheme is adequate for obtaining robust solutions.

Contours of instantaneous out-of-plane vorticity show the 2nd mode of oscillation with complex wake dynamics.

We have developed a new computational approach for simulating fluid–structure interaction (FSI) problems in complex domains with thin flexible solid structures. Our method is based on integrating our sharp-interface CURVIB solver, previously developed for FSI problems with rigid structures, with an accurate and efficient rotation-free FE formulation for thin shells into a coupled FSI framework that is able to handle thin structures undergoing arbitrarily large oscillation amplitudes.