The role of wake stiffness on the wake-induced vibration of the downstream cylinder of a tandem pair

Abstract

When a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. Assi, Bearman & Meneghini (J. Fluid Mech., vol. 661, 2010, pp. 365-401) concluded that the WIV excitation mechanism has its origin in the unsteady vortex-structure interaction encountered by the cylinder as it oscillates across the wake. In the present paper we investigate how the cylinder responds to that excitation, characterising the amplitude and frequency of response and its dependency on other parameters of the system. We introduce the concept of wake stiffness, a fluid dynamic effect that can be associated, to a first approximation, with a linear spring with stiffness proportional to Re and to the steady lift force occurring for staggered cylinders. By a series of experiments with a cylinder mounted on a base without springs we verify that such wake stiffness is not only strong enough to sustain oscillatory motion, but can also dominate over the structural stiffness of the system. We conclude that while unsteady vortex-structure interactions provide the energy input to sustain the vibrations, it is the wake stiffness phenomenon that defines the character of the WIV response.

Wake-induced ‘slaloming’ response explains exquisite sensitivity of seal whisker-like sensors

“…At the two closest distances, all three shapes show signs of wake induced response similar to trends reported in the literature for cylinders in tandem at similar distances: d x /d = 2 to 5.6 (Hover & Triantafyllou 2001;Assi et al 2006Assi et al , 2010Assi et al , 2013. The circular cylinder vibrates at roughly similar amplitudes in the wake as it does in open water (except at the closest distance).…”

“…The upstream cylinder continues to have significant effect on the downstream cylinder's response when the two are of unequal diameter and at relatively small distances apart (Sayers & Saban 1994;Lam & To 2003;Assi 2014b;Gao et al 2014). It was also found that a 'wake stiffness' exists -that is, the vortical wake of the upstream cylinder causes a restoring force on the downstream cylinder, which is equivalent to a linear spring, hence affecting its natural frequency (Assi et al 2013). No studies for large distances are available.…”

Passive wake detection using seal whisker-inspired sensing

“…At the two closest distances, all three shapes the cylinder, the elliptical cylinder, and the whisker show signs of wake induced response, which is similar to trends reported in the literature for cylinders in tandem at similar distances d x /d = 2 to 5.6 [65,5,4,3].…”

“…This is a new result, which is different from the case of two interacting cylinders of comparable diameter, wherein the downstream flexibly mounted cylinder oscillates at a frequency determined by its mass and spring properties, the value of the added mass, and the wake spring constant of the wake defined in [3]. In the case of a stationary upstream cylinder with significantly larger diameter than the downstream body (2.5x, 4x, and 11x in our experiments), the flexibly mounted downstream body vibrates freely at the Strouhal frequency of the upstream cylinder, following a path that slaloms among the vortices of the oncoming wake.…”

“…Most research has been conducted in studying two interacting circular cylinders of equal or comparable diameter [65,102,5,4] and it is shown that the upstream cylinder has significant effect on the amplitude and frequency of motion of the downstream cylinder even when it is placed at 25 diameters apart. It was also found that the vortical wake of the upstream cylinder causes a restoring force on the downstream cylinder, which is equivalent to a linear spring, hence affecting its natural frequency [3]. In the few studies conducted with interfering cylinders of unequal diameter [115,82,40,41,39], it was found that the upstream cylinder also affects the response of the downstream cylinder, reducing its amplitude relative to the single cylinder case, while the frequency of oscillation of the downstream cylinder was found to be either equal to, or twice the value of the frequency of the upstream cylinder.…”