The role of Reynolds number in the fluid-elastic instability of cylinder arrays

Abstract

The onset of fluid-elastic instability in cylinder arrays is usually thought to depend primarily on the mean flow velocity, the Scruton number and the natural frequency of the cylinders. Currently, there is considerable evidence from experimental measurements and computational fluid dynamic (CFD) simulations that the Reynolds number is also an important parameter. However, the available data are not sufficient to understand or quantify this effect. In this study we use a high resolution pseudo-spectral scheme to solve 2-D penalized Navier-Stokes equations in order to accurately model turbulent flow past cylinder array. To uncover the Reynolds number effect we perform simulations that vary Reynolds number independent of flow velocity at a fixed Scruton number, and then analyze the cylinder responses. The computational complexity of our algorithm is a function of Reynolds number. Therefore, we developed a high performance parallel code which allows us to simulate high Reynolds numbers at a reasonable computational cost. The simulations reveal that increasing Reynolds number has a strong de-stabilizing effect for staggered arrays. On the other hand, for the in-line array case Reynolds number still affects the instability threshold, but the effect is not monotonic with increasing Reynolds number. In addition, our findings suggest that geometry is also an important factor since at low Reynolds numbers critical flow velocity in the staggered array is considerably higher than the in-line case. This study helps to better predict how the onset of fluid-elastic instability depends on Reynolds number and reduces uncertainties in the experimental data which usually do not consider the effect of Reynolds number.