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Vortex-induced vibration of a sphere close to or piercing a free surface
- Methma M. Rajamuni, Kerry Hourigan, Mark C. Thompson
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- Journal:
- Journal of Fluid Mechanics / Volume 929 / 25 December 2021
- Published online by Cambridge University Press:
- 04 November 2021, A41
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Vortex-induced vibration (VIV) of an elastically mounted sphere placed close to or piercing a free surface (FS) was investigated numerically. The submergence depth ($h$) was systematically varied between $1$ and $-$0.75 sphere diameters ($D$) and the response simulated over the reduced velocity range $U^*\in [3.5,14]$. The incompressible flow was coupled with the sphere motion modelled by a spring–mass–damper system, treating the free-surface boundary as a slip wall. In line with the previous experimental findings, as the submergence depth was decreased from $h^* = h/D =1$, the maximum response amplitude of the fully submerged sphere decreased; however, as the sphere pierced the FS, the amplitude increased until $h^* = -0.375$, and then decreased beyond that point. The fluctuating components of the lift and drag coefficients also followed the same pattern. The variation of the near-wake vortex dynamics over this submergence range was examined in detail to understand the effects of $h^*$ on the VIV response. It was found that $h^* = 1$ is a critical submergence depth, beyond which, as $h^*$ is decreased, the vortical structures in the wake vary significantly. For a fully submerged sphere, the influence of the stress-free condition on the VIV response was dominant over the kinematic constraint preventing flow through the surface. For piercing sphere cases, two previously unseen vortical recirculations were formed behind the sphere near times of maximal displacement, enhancing the VIV response. These were strongest at $h^* = -0.375$, and much weaker for small submergence depths, explaining the observed response-amplitude variation.
Vortex dynamics and vibration modes of a tethered sphere
- Methma M. Rajamuni, Mark C. Thompson, Kerry Hourigan
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- Journal:
- Journal of Fluid Mechanics / Volume 885 / 25 February 2020
- Published online by Cambridge University Press:
- 18 December 2019, A10
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The flow-induced vibration of a tethered sphere was investigated through numerical simulations. A determination of the different modes of sphere vibration was made with simulations conducted at fixed Reynolds numbers (500, 1200 and 2000) with a sphere of mass ratio 0.8 over the reduced velocity range $U^{\ast }\in [3,32]$. The flow was governed by the incompressible Navier–Stokes equations, while the dynamic motion of the sphere was governed by coupled Newtonian mechanics. A new fluid–structure interaction (FSI) solver was implemented to efficiently solve the coupled FSI system. The effect of Reynolds number was found to be significant in the mode I and II regimes. A progressive increase in the response amplitude was observed as the Reynolds number was increased, especially in the mode II regime. The overall sphere response at the highest Reynolds number was relatively close to the observed behaviour of previous higher-$Re$ experimental studies. An aperiodic mode IV response was observed at higher reduced velocities beyond the mode II range in each case, without the intervening mode III regime. However, as the mass ratio increased from 0.8 to 80, the random response of the sphere (mode IV) gradually became more regular, showing a mode III response (characterized by a near-periodic sphere oscillation) at $U^{\ast }=30$. Thus, if the inertia of the system is low, mode IV appears at lower $U^{\ast }$ values, while for high-inertia systems, mode IV appears at high $U^{\ast }$ values beyond a mode III response.
Vortex-induced vibration of a transversely rotating sphere
- Methma M. Rajamuni, Mark C. Thompson, Kerry Hourigan
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- Journal:
- Journal of Fluid Mechanics / Volume 847 / 25 July 2018
- Published online by Cambridge University Press:
- 29 May 2018, pp. 786-820
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The effects of transverse rotation on the vortex-induced vibration (VIV) of a sphere in a uniform flow are investigated numerically. The one degree-of-freedom sphere motion is constrained to the cross-stream direction, with the rotation axis orthogonal to flow and vibration directions. For the current simulations, the Reynolds number of the flow, $Re=UD/\unicode[STIX]{x1D708}$, and the mass ratio of the sphere, $m^{\ast }=\unicode[STIX]{x1D70C}_{s}/\unicode[STIX]{x1D70C}_{f}$, were fixed at 300 and 2.865, respectively, while the reduced velocity of the flow was varied over the range $3.5\leqslant U^{\ast }~(\equiv U/(f_{n}D))\leqslant 11$, where, $U$ is the upstream velocity of the flow, $D$ is the sphere diameter, $\unicode[STIX]{x1D708}$ is the fluid viscosity, $f_{n}$ is the system natural frequency and $\unicode[STIX]{x1D70C}_{s}$ and $\unicode[STIX]{x1D70C}_{f}$ are solid and fluid densities, respectively. The effect of sphere rotation on VIV was studied over a wide range of non-dimensional rotation rates: $0\leqslant \unicode[STIX]{x1D6FC}~(\equiv \unicode[STIX]{x1D714}D/(2U))\leqslant 2.5$, with $\unicode[STIX]{x1D714}$ the angular velocity. The flow satisfied the incompressible Navier–Stokes equations while the coupled sphere motion was modelled by a spring–mass–damper system, under zero damping. For zero rotation, the sphere oscillated symmetrically through its initial position with a maximum amplitude of approximately 0.4 diameters. Under forced rotation, it oscillated about a new time-mean position. Rotation also resulted in a decreased oscillation amplitude and a narrowed synchronisation range. VIV was suppressed completely for $\unicode[STIX]{x1D6FC}>1.3$. Within the $U^{\ast }$ synchronisation range for each rotation rate, the drag force coefficient increased while the lift force coefficient decreased from their respective pre-oscillatory values. The increment of the drag force coefficient and the decrement of the lift force coefficient reduced with increasing reduced velocity as well as with increasing rotation rate. In terms of wake dynamics, in the synchronisation range at zero rotation, two equal-strength trails of interlaced hairpin-type vortex loops were formed behind the sphere. Under rotation, the streamwise vorticity trail on the advancing side of the sphere became stronger than the trail in the retreating side, consistent with wake deflection due to the Magnus effect. This symmetry breaking appears to be associated with the reduction in the observed amplitude response and the narrowing of the synchronisation range. In terms of variation with Reynolds number, the sphere oscillation amplitude was found to increase over the range $Re\in [300,1200]$ at $U^{\ast }=6$ for each of $\unicode[STIX]{x1D6FC}=0.15$, 0.75 and 1.5. The VIV response depends strongly on Reynolds number, with predictions indicating that VIV will persist for higher rotation rates at higher Reynolds numbers.
Transverse flow-induced vibrations of a sphere
- Methma M. Rajamuni, Mark C. Thompson, Kerry Hourigan
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- Journal:
- Journal of Fluid Mechanics / Volume 837 / 25 February 2018
- Published online by Cambridge University Press:
- 05 January 2018, pp. 931-966
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Flow-induced vibration of an elastically mounted sphere was investigated computationally for the classic case where the sphere motion was constrained to move in a direction transverse to the free stream. This study, therefore, provides additional insight into, and comparison with, corresponding experimental studies of transverse motion, and distinction from numerical and experimental studies with specific constraints such as tethering (Williamson & Govardhan, J. Fluids Struct., vol. 11, 1997, pp. 293–305) or motion in all three directions (Behara et al., J. Fluid Mech., vol. 686, 2011, pp. 426–450). Two sets of simulations were conducted by fixing the Reynolds number at $Re=300$ or 800 over the reduced velocity ranges $3.5\leqslant U^{\ast }\leqslant 100$ and $3\leqslant U^{\ast }\leqslant 50$ respectively. The reduced mass of the sphere was kept constant at $m_{r}=1.5$ for both sets. The flow satisfied the incompressible Navier–Stokes equations, while the coupled sphere motion was modelled by a spring–mass–damper system, with damping set to zero. The sphere showed a highly periodic large-amplitude vortex-induced vibration response over a lower reduced velocity range at both Reynolds numbers considered. This response was designated as branch A, rather than the initial/upper or mode I/II branch, in order to allow it to be discussed independently from the observed experimental response at higher Reynolds numbers which shows both similarities and differences. At $Re=300$, it occurred over the range $5.5\leqslant U^{\ast }\leqslant 10$, with a maximum oscillation amplitude of ${\approx}0.4D$. On increasing the Reynolds number to 800, this branch widened to cover the range $4.5\leqslant U^{\ast }\leqslant 13$ and the oscillation amplitude increased (maximum amplitude ${\approx}0.6D$). In terms of wake dynamics, within this response branch, two streets of interlaced hairpin-type vortex loops were formed behind the sphere. The upper and lower sets of vortex loops were disconnected, as were their accompanying tails. The wake maintained symmetry relative to the plane defined by the streamwise and sphere motion directions. The topology of this wake structure was analogous to that seen experimentally at higher Reynolds numbers by Govardhan & Williamson (J. Fluid Mech., vol. 531, 2005, pp. 11–47). At even higher reduced velocities, the sphere showed distinct oscillatory behaviour at both Reynolds numbers examined. At $Re=300$, small but non-negligible oscillations were found to occur (amplitude of ${\approx}0.05D$) within the reduced velocity ranges $13\leqslant U^{\ast }\leqslant 16$ and $26\leqslant U^{\ast }\leqslant 100$, named branch B and branch C respectively. Moreover, within these reduced velocity ranges, the centre of motion of the sphere shifted from its static position. In contrast, at $Re=800$, the sphere showed an aperiodic intermittent mode IV vibration state immediately beyond branch A, for $U^{\ast }\geqslant 14$. This vibration state was designated as the intermittent branch. Interestingly, the dominant frequency of the sphere vibration was close to the natural frequency of the system, as observed by Jauvtis et al. (J. Fluids Struct., vol. 15(3), 2001, pp. 555–563) in higher-mass-ratio higher-Reynolds-number experiments. The oscillation amplitude increased as the reduced velocity increased and reached a value of ${\approx}0.9D$ at $U^{\ast }=50$. The wake was irregular, with multiple vortex shedding cycles during each cycle of sphere oscillation.