Experimental evidence of new three-dimensional modes in the wake of a rotating cylinder

Abstract

A recent numerical study by Rao et al. (J. Fluid Mech., vol. 717, 2013, pp. 1–29) predicted the existence of several previously unobserved linearly unstable three-dimensional modes in the wake of a spinning cylinder in cross-flow. While linear stability analysis suggests that some of these modes exist for relatively limited ranges of Reynolds numbers and rotation rates, this may not be true for fully developed nonlinear wakes. In the current paper, we present the results of water channel experiments on a rotating cylinder in cross-flow, for Reynolds numbers $200\leqslant \mathit{Re}\leqslant 275$ and non-dimensional rotation rates $0\leqslant \alpha \leqslant 2. 5$. Using particle image velocimetry and digitally post-processed hydrogen bubble flow visualizations, we confirm the existence of the predicted modes for the first time experimentally. For instance, for $\mathit{Re}= 275$ and a rotation rate of $\alpha = 1. 7$, we observe a subharmonic mode, mode C, with a spanwise wavelength of ${\lambda }_{z} / d\approx 1. 1$. On increasing the rotation rate, two modes with a wavelength of ${\lambda }_{z} / d\approx 2$ become unstable in rapid succession, termed modes D and E. Mode D grows on a shedding wake, whereas mode E consists of streamwise vortices on an otherwise steady wake. For $\alpha \gt 2. 2$, a short-wavelength mode F appears localized close to the cylinder surface with ${\lambda }_{z} / d\approx 0. 5$, which is presumably a manifestation of centrifugal instability. Unlike the other modes, mode F is a travelling wave with a spanwise frequency of ${\mathit{St}}_{3D} \approx 0. 1$. In addition to these new modes, observations on the one-sided shedding process, known as the ‘second shedding’, are reported for $\alpha = 5. 1$. Despite suggestions from the literature, this process seems to be intrinsically three-dimensional. In summary, our experiments confirm the linear predictions by Rao et al., with very good agreement of wavelengths, symmetries and the phase velocity for the travelling mode. Apart from this, these experiments examine the nonlinear saturated state of these modes and explore how the existence of multiple unstable modes can affect the selected final state. Finally, our results establish that several distinct three-dimensional instabilities exist in a relatively confined area on the $\mathit{Re}$–$\alpha $ parameter map, which could account for their non-detection previously.

Experimental investigation of flow-induced vibration of a rotating circular cylinder

“…This has been seen in rotating cylinder wakes previously, e.g. figure 5 from Radi et al (2013). This is consistent with rotation causing the two separation points, which feed the shed vortices, to move together, thereby restricting the vorticity shed into each wake vortex and increasing cross-annihilation.…”

Flow past a rotating cylinder translating at different gap heights along a wall

“…For gap heights G=D≲0:22, mode E is the first three-dimensional mode to become unstable and this occurs for a steady base flow. While this mode was previously observed in the studies of rotating cylinders near a wall (Stewart et al, 2010;Rao et al, 2011Rao et al, , 2013dHourigan et al, 2013), the nomenclature used here is borrowed from studies of an isolated rotating cylinder (Rao et al, 2013a(Rao et al, ,b, 2015aRadi et al, 2013), given the perturbation field of mode E from those studies bears a strong similarity (also see section 3.6, Figs. 6 and 7 of Rao et al, 2013d).…”

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

“…At higher rotation rates, the flow becomes increasingly unstable to perturbations at Re = 200 in the range 3 α 5 (Meena et al 2011). Recent numerical and experimental investigations (Mittal & Kumar 2003;Rao et al 2013b,a;Radi et al 2013) have identified several new three-dimensional transitions for Re < 400. In the Mode I shedding regime, five three-dimensional modes were found to become unstable and, in the steady regime of flow α 2, four three-dimensional modes were observed.…”