6 results
Stability analysis of passive suppression for vortex-induced vibration
- S. R. Bukka, A. R. Magee, R. K. Jaiman
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- Journal:
- Journal of Fluid Mechanics / Volume 886 / 10 March 2020
- Published online by Cambridge University Press:
- 14 January 2020, A12
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In this paper, we present a stability analysis of passive suppression devices for the vortex-induced vibration (VIV) in the laminar flow condition. A data-driven model reduction approach based on the eigensystem realization algorithm is used to construct a reduced-order model in a state-space format. From the stability analysis of the coupled system, two modes are found to be dominant in the phenomenon of self-sustained VIV: namely, the wake mode, with frequency close to that of the wake flow behind a stationary cylinder; and the structure mode, with frequency close to the natural frequency of the elastically mounted cylinder. The present study illustrates that VIV can be suppressed by altering the structure mode via shifting of the eigenvalues from the unstable to the stable region. This finding is realized through the simulations of passive control devices, such as fairings and connected-C devices, wherein the presence of appendages breaks the self-sustenance of the wake–body interaction cycle. A detailed proper orthogonal decomposition analysis is employed to quantify the effect of a fairing on the complex interaction between the wake features. From the assessment of the stability characteristics of appendages, the behaviour of a connected-C device is found to be similar to that of a fairing, and the trajectories of the eigenspectrum are nearly identical, while the eigenspectrum of the cylinder–splitter arrangement indicates a galloping behaviour at higher reduced velocities. Finally, we introduce a stability function to characterize the influence of geometric parameters on VIV suppression.
Decomposition of wake dynamics in fluid–structure interaction via low-dimensional models
- T. P. Miyanawala, R. K. Jaiman
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- Journal:
- Journal of Fluid Mechanics / Volume 867 / 25 May 2019
- Published online by Cambridge University Press:
- 28 March 2019, pp. 723-764
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We present a dynamic decomposition analysis of the wake flow in fluid–structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational FSI solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Reynolds number ($Re$). The snapshot data from high-dimensional FSI simulations are projected to a low-dimensional subspace using the proper orthogonal decomposition (POD). We utilize each corresponding POD mode to detect features of the organized motions, namely, the vortex street, the shear layer and the near-wake bubble. We find that the vortex shedding modes contribute solely to the lift force, while the near-wake and shear layer modes play a dominant role in the drag force. We further examine the fundamental mechanism of this dynamical behaviour and propose a force decomposition technique via low-dimensional approximation. To elucidate the frequency lock-in, we systematically analyse the decomposed modes and their dynamical contributions to the force fluctuations for a range of reduced velocity at low Reynolds number laminar flow. These quantitative mode energy contributions demonstrate that the shear layer feeds the vorticity flux to the wake vortices and the near-wake bubble during the wake–body synchronization. Based on the decomposition of wake dynamics, we suggest an interaction cycle for the frequency lock-in during the wake–body interaction, which provides the interrelationship between the high-amplitude motion and the dominating wake features. Through our investigation of wake–body synchronization below critical $Re$ range, we discover that the bluff body can undergo a synchronized high-amplitude vibration due to flexibility-induced unsteadiness. Owing to the wake turbulence at a moderate Reynolds number of $Re=22\,000$, a distorted set of POD modes and the broadband energy distribution are observed, while the interaction cycle for the wake synchronization is found to be valid for the turbulent wake flow.
Dynamics and stability of gap-flow interference in a vibrating side-by-side arrangement of two circular cylinders
- B. Liu, R. K. Jaiman
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- Journal:
- Journal of Fluid Mechanics / Volume 855 / 25 November 2018
- Published online by Cambridge University Press:
- 20 September 2018, pp. 804-838
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In this work, the coupled dynamics of the gap flow and the vortex-induced vibration (VIV) of a side-by-side (SBS) arrangement of two circular cylinders is numerically investigated at Reynolds numbers $100\leqslant Re\leqslant 500$. The influence of VIV is incorporated by allowing one of the cylinders to vibrate freely in the transverse direction, which is termed as a vibrating side-by-side (VSBS) arrangement. A comparative three-dimensional study is performed between the stationary side-by-side (SSBS) and the VSBS arrangements to examine the characteristics of the complex coupling between the VIV and the gap flow. The results are also contrasted against the isolated configurations without any proximity and gap-flow interference. Of particular interest is to establish a relationship between the VIV, the gap flow and the near-wake instability behind bluff bodies. We find that the kinematics of the VIV regulates the streamwise vorticity concentration, which accompanies a recovery of the two-dimensional hydrodynamic response at the peak lock-in. Moreover, the near-wake instability may develop around an indeterminant two-dimensional streamline saddle point along the interfaces of a pair of imbalanced counter-signed vorticity clusters. The interaction between the imbalanced vorticity clusters and the gap-flow momentum are closely interlinked with the prominence of streamwise vortical structures. In both SSBS and VSBS arrangements, the flip-flopping frequency is significantly low for the three-dimensional flow, except at the VIV lock-in for the VSBS arrangement. While an early onset of VIV lock-in is observed for the vibrating configuration, a quasi-stable deflected gap-flow regime with stably deflected gap flow is found at the peak lock-in. The increase of the gap-flow proximity interference promotes the energy transfer and stabilizes the VIV lock-in. Finally, we employ the dynamic mode decomposition procedure to characterize the space–time evolution of the vortex wake system behind the cylinders.
Model reduction and mechanism for the vortex-induced vibrations of bluff bodies
- W. Yao, R. K. Jaiman
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- Journal:
- Journal of Fluid Mechanics / Volume 827 / 25 September 2017
- Published online by Cambridge University Press:
- 22 August 2017, pp. 357-393
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We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier–Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency $(F_{s})$, while maintaining fixed values of the Reynolds number ($Re$) and mass ratio ($m^{\ast }$). The effects of the Reynolds number $Re$, the mass ratio $m^{\ast }$ and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance–flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for $30\leqslant Re\leqslant 100$ at $m^{\ast }=10$. In the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with 1:3 synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.
Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm
- W. Yao, R. K. Jaiman
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- Journal:
- Journal of Fluid Mechanics / Volume 827 / 25 September 2017
- Published online by Cambridge University Press:
- 22 August 2017, pp. 394-414
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We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid–structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.
Self-induced flapping dynamics of a flexible inverted foil in a uniform flow
- P. S. Gurugubelli, R. K. Jaiman
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- Journal:
- Journal of Fluid Mechanics / Volume 781 / 25 October 2015
- Published online by Cambridge University Press:
- 28 September 2015, pp. 657-694
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We present a numerical study on the self-induced flapping dynamics of an inverted flexible foil in a uniform flow. A high-order coupled fluid–structure solver based on fully coupled Navier–Stokes and nonlinear structural dynamic equations has been employed. Unlike a conventional flexible foil flapping where the leading edge is clamped, the inverted elastic foil is fixed at the trailing edge and the leading edge is allowed to oscillate freely. We investigate the evolution of flapping instability of an inverted foil as a function of the non-dimensional bending rigidity, $K_{B}$, Reynolds number, $\mathit{Re}$, and structure-to-fluid mass ratio, $m^{\ast }$, and identify three distinct stability regimes, namely (i) fixed-point stable, (ii) deformed steady and (iii) unsteady flapping state. With the aid of a simplified analytical model, we show that the fixed-point stable regime loses its stability by static-divergence instability. The transition from the deformed steady state to the unsteady flapping regime is marked by a flow separation at the leading edge. We also show that an inverted foil is more vulnerable to static divergence than a conventional foil. Three distinct unsteady flapping modes have been observed as a function of decreasing $K_{B}$: (i) inverted limit-cycle oscillations, (ii) deformed flapping and (iii) flipped flapping. We characterize the transition to the deformed-flapping regime through a quasistatic equilibrium analysis between the structural restoring and the fluid forces. We further examine the effects of $m^{\ast }$ on the post-critical flapping dynamics at a fixed $\mathit{Re}=1000$. Finally, we present the net work done by the fluid and the bending strain energy developed in a flexible foil due to the flapping motion. For small $m^{\ast }$, we demonstrate that the flapping of an inverted flexible foil can generate $O(10^{3})$ times more strain energy in comparison to a conventional flexible foil flapping, which has a profound impact on energy harvesting devices.