Numerical simulation of flow-induced vibration of two cylinders elastically mounted in tandem by immersed moving boundary method

Abstract

A numerical study is performed on flow-induced vibrations of two cylinders of diameter D, in tandem configuration relative to the free-stream uniform flow U at low Reynolds numbers Re=UD/ν. In order to solve numerically the incompressible momentum and continuity equations, the in-house code Incompact3D is used. Compact sixth-order finite differences for spatial differentiation and second-order Adams–Bashforth scheme for time advancement are employed. The cylinders movement is modeled as a mass-damper-spring system which is solved by a fourth-order Runge–Kutta scheme. To represent the multiple moving cylinders in an immersed boundary method framework, a modification in the Poisson equation is proposed. The modified algorithm was evaluated and applied for scenarios with zero, one and two translational degrees of freedom to oscillate. The validation is carried out against several numerical and experimental previous works. The results are analyzed in terms of the forces on cylinders, Strouhal number of the wake, streamwise velocity profiles and cylinders oscillation amplitudes and frequencies. The algorithm could satisfactorily represent the resonance and wake-flutter phenomena. In the most cases, the rear cylinder has greater oscillations than the front cylinder. However, a state was identified where the cross-stream oscillation amplitudes of the front cylinder are lower than those of the rear cylinder. In this state, the lift force acts as negative spring on the front cylinder (amplifying its oscillations) and as a damper on the rear cylinder (controlling its oscillations). The scenarios with two degrees of freedom (2dof) have higher oscillation amplitudes than the equivalent scenarios with one degree of freedom. Moreover, the streamwise oscillation amplitudes are not negligible in relation to the cross-stream oscillation amplitudes. On the other hand, for 2dof, when the Reynolds number increases the clashing risk also increases, since the cylinders proximity is narrowed.