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

The onset of fluid-elastic instability in tube arrays is thought to depend primarily on the mean flow velocity, the Scruton number and the natural frequencies of the tubes. However, evidence from experiments suggests that the Reynolds number is also an important parameter, although the available data are insufficient to understand or quantify this effect. We use high resolution direct numerical simulations to solve the penalized two-dimensional Navier–Stokes equations in order to accurately model turbulent flow through tube arrays with a pitch to diameter ratio P∕D=1.5. To investigate the Reynolds number effect we perform simulations that independently vary the mean flow velocity and the Reynolds number at fixed Scruton number. Parameters are chosen so that the simulations are well outside the lock-in regime of resonant vortex excitation. Increasing Reynolds number and mean flow velocity both have strong de-stabilizing effects for rotated arrays. For in-line arrays the effect is weaker and not monotonic with increasing Reynolds number and mean flow velocity. This study clarifies how the onset of fluid-elastic instability depends on Reynolds number (and hence turbulence intensity) and reduces uncertainties arising from the experimental data, which usually do not account for the effect of Reynolds number. It also demonstrates the usefulness of two-dimensional direct numerical simulations to investigate fluid-elastic instability at turbulent Reynolds numbers.