Numerical Simulation of Small Amplitude Oscillatory Cylinder Under Incompressible Laminar 2D Fluid Flow: ALE, ARF and Transpiration Methods

In this paper, we compare the performances of ALE and Transpiration methods aided by an third method in non-inertial referential: ARF — Accelerated Reference Frame —. The approach ALE (Donea and Hughes finite element approach) is a powerful tool to treat coupled problems. However, the ALE performance for determining fluid-elastic forces to small vibrations amplitudes is still ignored. The Transpiration method is a simplified approach for calculation of fluid-elastic forces to relatively small vibrations amplitudes. Based on a first order development of velocity boundary conditions, this method allows the use of a fluid domain fixed in time during a dynamic computation, by avoiding hence the problems due to the mesh distortions. We aim to provide a numerical fluid-elastic forces estimate of a moving tube under 2D transverse fluid flow. At first, we carried out a numerical validation on vortex wake characteristic behind an isolated rigid cylinder 2D with Re = 200: Strouhal number Sh and lift’s and drag’s coefficients, C_L and C_D respectively. These values were useful for following simulations. Finally, a harmonic movement perpendicular to flow is imposed on the cylinder, having a frequency ratio f_o/f_k and a reduced amplitude S_o/D. We compare ALE and Transpiration methods, with aid of ARF method, considering the temporal lift signals and their power spectra. The test parameters of vibrating cylinder with Re = 200 are the frequency ratios f_o/f_k ∈ [0.85–1.20] and the reduced amplitudes of S_o/D = 0.01 and 0.05. Simulations were compared with Sonneville’s and Gibert’s experimental results. In order to obtain satisfactory converged results, simulations were continued for 100 periods of vibrations. These methods are implemented in Cast3M, a numerical platform of French Nuclear Agency CEA/Saclay.