Vortex-induced vibrations of a cylinder in planar shear flow

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18137 The system composed of a circular cylinder, either fixed or elastically mounted, and immersed in a current linearly sheared in the cross-flow direction, is investigated via numerical simulations. The impact of the shear and associated symmetry breaking are explored over wide ranges of values of the shear parameter (non-dimensional inflow velocity gradient, β ∈ [0, 0.4]) and reduced velocity (inverse of the non-dimensional natural frequency of the oscillator, U * ∈ [2, 14]), at Reynolds number Re = 100; β, U * and Re are based on the inflow velocity at the centre of the body and on its diameter. In the absence of large-amplitude vibrations and in the fixed body case, three successive regimes are identified. Two unsteady flow regimes develop for β ∈ [0, 0.2] (regime L) and β ∈ [0.2, 0.3] (regime H). They differ by the relative influence of the shear, which is found to be limited in regime L. In contrast, the shear leads to a major reconfiguration of the wake (e.g. asymmetric pattern, lower vortex shedding frequency, synchronized oscillation of the saddle point) and a substantial alteration of the fluid forcing in regime H. A steady flow regime (S), characterized by a triangular wake pattern, is uncovered for β > 0.3. Free vibrations of large amplitudes arise in a region of the parameter space that encompasses the entire range of β and a range of U * that widens as β increases; therefore vibrations appear beyond the limit of steady flow in the fixed body case (β = 0.3). Three distinct regimes of the flow-structure system are encountered in this region. In all regimes, body motion and flow unsteadiness are synchronized (lock-in condition). For β ∈ [0, 0.2], in regime VL, the system behaviour remains close to that observed in uniform current. The main impact of the shear concerns the amplification of the in-line response and the transition from figure-eight to ellipsoidal orbits. For β ∈ [0.2, 0.4], the system exhibits two well-defined regimes: VH1 and VH2 in the lower and higher ranges of U * , respectively. Even if the wake patterns, close to the asymmetric pattern observed in regime H, are comparable in both regimes, the properties of the vibrations and fluid forces clearly depart. The responses differ by their spectral contents, i.e. sinusoidal versus multi-harmonic, and their amplitudes are much larger in regime VH1, where the in-line responses reach 2 diameters (0.03 diameters in uniform flow) and the cross-flow responses 1.3 diameters. Aperiodic, intermittent oscillations are found to occur in the transition region between regimes VH1 and VH2; it appears that wake-body synchronization persists in this case.

Aerodynamic performances and wake topology past a square cylinder in the interface of two different-velocity streams

“…Upstream shear has been shown in experiments to delay the onset of periodic vortex shedding, the Reynolds number at which the Hopf bifurcation occurs Re H increasing with K to the point that shedding can be completely suppressed all the way up to Re < 220 1 . This effect has also been observed in numerical simulation 2,50 . Other computational studies, however, did not detect the phenomenon despite exploring similar values of the parameters 36,40 .…”

“…There is some controversy as to the dependence of C d of the circular cylinder on the shear parameter. Several experimental 3,37,39,47 and numerical 36,38,[48][49][50] studies have shown a decreasing trend, in some cases marginal, with K. Others 2,43,45 show the exact reverse trend. Free-stream turbulence levels, which are often dependent on the prescribed shear parameter, might be playing an important role in experimental results 39,43 .…”

“…The transitions among the various flow regimes past bluff bodies are often characterised through irregularities in the trends that some aerodynamic performance indicators follow upon varying the governing parameters. The recirculation bubble length (l r ) in the square cylinder wake increases fast with Re 50 while the flow remains steady, reaches a maximum at the onset of vortexshedding and then quickly recedes (on average) in the interval Re ∈ [50,160] until three-dimensionality kicks in 15,16 . The decrease of l r briefly stagnates for a while across the wake-transition regime for Re ∈ [160, 220] and it is finally resumed at a slowing pace that asymptotically approaches a terminal value for Re > 1000 17,18 .…”

“…Root mean square of lift fluctuations (C l ) have been reported to slowly increase with K in some cases 36,38,50 , decrease in others 33 , or even sharply increase to finally decay and disappear altogether at very low Re following the suppression of vortex shedding 2 . Meanwhile, drag fluctuations (C d ) have been shown to either increase 38,50 or to be nearly imperceptible throughout 2 . Base pressure coefficient fluctuations (C p b ) apparently decrease with K 39 .…”

Fluid–structure–surface interaction of a flexibly mounted pitching and plunging flat plate in proximity to the free surface

“…2014; Zhang et al. 2014; Gsell, Bourguet & Braza 2017). These studies have revealed significant effects on the dynamic behaviour and the resultant fluid and structural forces in the presence of shear flow.…”