Dual resonance in vortex-induced vibrations at subcritical and supercritical Reynolds numbers

2010 ◽  
Vol 643 ◽  
pp. 395-424 ◽  
Author(s):  
J. M. DAHL ◽  
F. S. HOVER ◽  
M. S. TRIANTAFYLLOU ◽  
O. H. OAKLEY
Keyword(s):  
Reynolds Number ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Reynolds Numbers ◽  
Large Reynolds Number ◽  
Resonant Response ◽  
Third Harmonic ◽  
Vortex Induced Vibrations ◽  
Dual Resonance ◽  
Harmonic Components

An experimental study is performed on the vortex induced vibrations of a rigid flexibly mounted circular cylinder placed in a crossflow. The cylinder is allowed to oscillate in combined crossflow and in-line motions, and the ratio of the nominal in-line and transverse natural frequencies is varied systematically. Experiments were conducted on a smooth cylinder at subcritical Reynolds numbers between 15 000 and 60 000 and on a roughened cylinder at supercritical Reynolds numbers between 320 000 and 710 000, with a surface roughness equal to 0.23 % of the cylinder diameter. Strong qualitative and quantitative similarities between the subcritical and supercritical experiments are found, especially when the in-line natural frequency is close to twice the value of the crossflow natural frequency. In both Reynolds number regimes, the test cylinder may exhibit a ‘dual-resonant’ response, resulting in resonant crossflow motion at a frequency fv, near the Strouhal frequency, and resonant in-line motion at 2 fv. This dual resonance is shown to occur over a relatively wide frequency region around the Strouhal frequency, accompanied by stable, highly repeatable figure-eight cylinder orbits, as well as large third-harmonic components of the lift force. Under dual-resonance conditions, both the subcritical and the supercritical response is shown to collapse into a narrow parametric region in which the effective natural-frequency ratio is near the value 2, regardless of the nominal natural-frequency ratio. Some differences are noted in the magnitudes of forces and the cylinder response between the two different Reynolds number regimes, but the dual-resonant response and the resulting force trends are preserved despite the large Reynolds number difference.

Numerical Simulations of Resonant Heat Transfer Augmentation at Low Reynolds Numbers

2001 ◽  
Author(s):  
Miles Greiner ◽  
Paul F. Fischer ◽  
Henry Tufo
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Natural Frequency ◽  
Flow Rate ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Pumping Power ◽  
Number Systems ◽  
Low Reynolds

Abstract The effect of flow rate modulation on low Reynolds number heat transfer enhancement in a transversely grooved passage was numerically simulated using a two-dimensional spectral element technique. Simulations were performed at subcritical Reynolds numbers of Rem = 133 and 267, with 20% and 40% flow rate oscillations. The net pumping power required to modulate the flow was minimized as the forcing frequency approached the predicted natural frequency. However, mixing and heat transfer levels both increased as the natural frequency was approached. Oscillatory forcing in a grooved passage requires two orders of magnitude less pumping power than flat passage systems for the same heat transfer level. Hydrodynamic resonance appears to be an effective method of increasing heat transfer in low Reynolds number systems where pumping power is at a premium, such as micro heat transfer applications.

Reynolds Number Effects on Hydrodynamic Coefficients for Pure In-Line and Pure Cross-Flow Forced Vortex Induced Vibrations

2009 ◽  
Author(s):  
Jamison L. Szwalek ◽  
Carl M. Larsen
Keyword(s):  
Reynolds Number ◽  
Prediction Models ◽  
Current Knowledge ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Hydrodynamic Coefficients ◽  
Vortex Induced Vibrations ◽  
Reynolds Number Effects ◽  
Sinusoidal Oscillations

In-line vibrations have been noted to have an important contribution to the fatigue of free spanning pipelines. Still, in-line contributions are not usually accounted for in current VIV prediction models. The present study seeks to broaden the current knowledge regarding in-line vibrations by expanding the work of Aronsen (2007) to include possible Reynolds number effects on pure in-line forced, sinusoidal oscillations for four Reynolds numbers ranging from 9,000 to 36,200. Similar tests were performed for pure cross-flow forced motion as well, mostly to confirm findings from previous research. When experimental uncertainties are accounted for, there appears to be little dependence on Reynolds number for all three hydrodynamic coefficients considered: the force in phase with velocity, the force in phase with acceleration, and the mean drag coefficient. However, trends can still be observed for the in-line added mass in the first instability region and for the transition between the two instability regions for in-line oscillations, and also between the low and high cross-flow added mass regimes. For Re = 9,000, the hydrodynamic coefficients do not appear to be stable and can be regarded as highly Reynolds number dependent.

Analytical and numerical studies of the structure of steady separated flows

1966 ◽  
Vol 24 (1) ◽  
pp. 113-151 ◽  
Author(s):  
Odus R. Burggraf
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Total Power ◽  
Large Reynolds Number ◽  
Boundary Velocity ◽  
Displacement Thickness ◽  
Low Reynolds

The viscous structure of a separated eddy is investigated for two cases of simplified geometry. In § 1, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline. This solution reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor. Quantitatively, the solution shows that a significant inviscid core exists for a Reynolds number greater than 100. At low Reynolds number the vortex centre shifts in the direction of the boundary velocity until the inviscid core develops; at large Reynolds number, the inviscid vortex core is symmetric about the centre of the circle, except for the effect of the boundary-layer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier–Stokes equations for an eddy in a square cavity driven by a moving boundary at the top. These solutions were carried out by a relaxation procedure on a high-speed digital computer, and are described in § 2. Results are presented for Reynolds numbers from 0 to 400 in the form of contour plots of stream function, vorticity, and total pressure. At the higher values of Reynolds number, an inviscid core develops, but secondary eddies are present in the bottom corners of the square at all Reynolds numbers. Solutions of the energy equation were obtained also, and isotherms and wall heat-flux distributions are presented graphically.

Numerical Simulation of the Wind Load on the Mast at Different Wind Angles

2014 ◽  
Vol 580-583 ◽  
pp. 3089-3092
Author(s):  
Rong Sheng Cao ◽  
Yuan Yuan Fang ◽  
Ling Wang
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Wind Load ◽  
Large Reynolds Number ◽  
Vertical Force ◽  
Important Impact

The wind load acted on ship mast at different wind angles of large Reynolds number is numerically simulated in this paper. CFX software was used to analyze the trend of constant and fluctuating forces that the mast surface suffered at different Reynolds numbers.The vortex shedding strength of the wind load around the mast was also analyzed according to the trend of Strouhal number varing with the simulated Reynolds numbers. The results show that the wind angle has an important impact on the lift, drag, and vertical force of the mast. The vertical force of the inclined side wall on the mast can not be ignored,and the angle of direction wind has great impact on the Strouhal number at different Reynolds numbers.

Linear instability of lid- and pressure-driven flows in channels textured with longitudinal superhydrophobic grooves

2021 ◽  
Vol 932 ◽  
Author(s):  
Samuel D. Tomlinson ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Reynolds Number ◽  
Unstable Mode ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Large Reynolds Number ◽  
Spanwise Direction ◽  
Channel Height ◽  
Critical Reynolds Numbers ◽  
Upper Lid ◽  
Pressure Driven

It is known that an increased flow rate can be achieved in channel flows when smooth walls are replaced by superhydrophobic surfaces. This reduces friction and increases the flux for a given driving force. Applications include thermal management in microelectronics, where a competition between convective and conductive resistance must be accounted for in order to evaluate any advantages of these surfaces. Of particular interest is the hydrodynamic stability of the underlying basic flows, something that has been largely overlooked in the literature, but is of key relevance to applications that typically base design on steady states or apparent-slip models that approximate them. We consider the global stability problem in the case where the longitudinal grooves are periodic in the spanwise direction. The flow is driven along the grooves by either the motion of a smooth upper lid or a constant pressure gradient. In the case of smooth walls, the former problem (plane Couette flow) is linearly stable at all Reynolds numbers whereas the latter (plane Poiseuille flow) becomes unstable above a relatively large Reynolds number. When grooves are present our work shows that additional instabilities arise in both cases, with critical Reynolds numbers small enough to be achievable in applications. Generally, for lid-driven flows one unstable mode is found that becomes neutral as the Reynolds number increases, indicating that the flows are inviscidly stable. For pressure-driven flows, two modes can coexist and exchange stability depending on the channel height and slip fraction. The first mode remains unstable as the Reynolds number increases and corresponds to an unstable mode of the two-dimensional Rayleigh equation, while the second mode becomes neutrally stable at infinite Reynolds numbers. Comparisons of critical Reynolds numbers with the experimental observations for pressure-driven flows of Daniello et al. (Phys. Fluids, vol. 21, issue 8, 2009, p. 085103) are encouraging.

scholarly journals Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160092 ◽  
Author(s):  
J. C. Klewicki ◽  
G. P. Chini ◽  
J. F. Gibson
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
High Fidelity ◽  
Dynamical Structure ◽  
Mathematical Methods ◽  
High Reynolds ◽  
Turbulent Wall

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Numerical Simulations of Resonant Heat Transfer Augmentation at Low Reynolds Numbers

2002 ◽  
Vol 124 (6) ◽  
pp. 1169-1175 ◽  
Author(s):  
Miles Greiner ◽  
Paul F. Fischer ◽  
Henry Tufo
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Natural Frequency ◽  
Flow Rate ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Pumping Power ◽  
Number Systems ◽  
Low Reynolds

The effect of flow rate modulation on low Reynolds number heat transfer enhancement in a transversely grooved passage was numerically simulated using a two-dimensional spectral element technique. Simulations were performed at subcritical Reynolds numbers of Rem=133 and 267, with 20 percent and 40 percent flow rate oscillations. The net pumping power required to modulate the flow was minimized as the forcing frequency approached the predicted natural frequency. However, mixing and heat transfer levels both increased as the natural frequency was approached. Oscillatory forcing in a grooved passage requires two orders of magnitude less pumping power than flat passage systems for the same heat transfer level. Hydrodynamic resonance appears to be an effective method of increasing heat transfer in low Reynolds number systems, especially when pumping power is at a premium.

Mode Shape Variation for a Low-Mode Number Flexible Cylinder Subject to Vortex-Induced Vibrations

2014 ◽  
Author(s):  
Ersegun D. Gedikli ◽  
Jason M. Dahl
Keyword(s):  
Natural Frequency ◽  
Mode Shape ◽  
Frequency Ratio ◽  
Cross Flow ◽  
Mode Number ◽  
Rigid Cylinder ◽  
Vortex Induced Vibrations ◽  
The Cross ◽  
The Impact ◽  
Structural Mode

The excitation of two low-mode number, flexible cylinders in uniform-flow is investigated to determine effects of structural mode shape on vortex-induced vibrations. Experiments are performed in a re-circulating flow channel and in a small flow visualization tank using object tracking and digital particle image velocimetry (DPIV) to measure the excitation of the cylinder, to estimate forces acting on the structure, and to observe the wake of the structure under the observed body motions. Previous research has focused on understanding the effect of in-line to cross-flow natural frequency ratio on the excitation of the structure in an attempt to model the excitation of multiple structural modes on long, flexible bodies. The current research investigates the impact of structural mode shape on this relationship by holding the in-line to cross-flow natural frequency constant and attempting to excite a specific structural mode shape. It is found that the combination of an odd mode shape excited in the cross-flow direction with an even mode shape in the in-line direction results in an incompatible synchronization condition, where the dominant forcing frequency in-line may experience a frequency equal to the cross-flow forcing frequency, a condition only observed in rigid cylinder experiments when the natural frequency ratio is less than one. This is consistent with the first mode being excited in both in-line and cross-flow directions, however this leads to an asymmetric wake. The wake is observed using DPIV on a rigid cylinder with forced motions equivalent to the flexible body. A case of mode switching is also observed where the even in-line mode exhibits an excitation at twice the cross-flow frequency; however the spatial mode shape in-line appears similar to the first structural mode shape. It is hypothesized that this situation is possible due to variation in the effective added mass along the length of the cylinder.

Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers

2015 ◽  
Vol 783 ◽  
pp. 72-102 ◽  
Author(s):  
Weiwei Zhang ◽  
Xintao Li ◽  
Zhengyin Ye ◽  
Yuewen Jiang
Keyword(s):  
Linear Model ◽  
Natural Frequency ◽  
Coupled System ◽  
Reynolds Numbers ◽  
High Mass ◽  
Low Reynolds Numbers ◽  
Reduced Order ◽  
Vortex Induced Vibrations ◽  
Low Reynolds ◽  
Lock In

In this study, a CFD-based linear dynamics model combined with the direct Computational Fluid Dynamics/Computational Structural Dynamics (CFD/CSD) simulation method is utilized to study the physical mechanisms underlying frequency lock-in in vortex-induced vibrations (VIVs). An identification method is employed to construct the reduced-order models (ROMs) of unsteady aerodynamics for the incompressible flow past a vibrating cylinder at low Reynolds numbers ($Re$). Reduced-order-model-based fluid–structure interaction models for VIV are also constructed by coupling ROMs and structural motion equations. The effects of the natural frequency of the cylinder, mass ratio and structural damping coefficient on the dynamics of the coupled system at $Re=60$ are investigated. The results show that the frequency lock-in phenomenon at low Reynolds numbers can be divided into two patterns according to different induced mechanisms. The two patterns are ‘resonance-induced lock-in’ and ‘flutter-induced lock-in’. When the natural frequency of the cylinder is in the vicinity of the eigenfrequency of the uncoupled wake mode (WM), only the WM is unstable. The dynamics of the coupled system is dominated by resonance. Meanwhile, for relatively high natural frequencies (i.e. greater than the eigenfrequency of the uncoupled WM), the structure mode becomes unstable, and the coupling between the two unstable modes eventually leads to flutter. Flutter is the root cause of frequency lock-in and the higher vibration amplitude of the cylinder than that of the resonance region. This result provides evidence for the finding of De Langre (J. Fluids Struct., vol. 22, 2006, pp. 783–791) that frequency lock-in is caused by coupled-mode flutter. The linear model exactly predicts the onset reduced velocity of frequency lock-in compared with that of direct numerical simulations. In addition, the transition frequency predicted by the linear model is in close coincidence with the amplitude of the lift coefficient of a fixed cylinder for high mass ratios. Therefore, it confirms that linear models can capture a significant part of the inherent physics of the frequency lock-in phenomenon.

Dynamic Behavior of a Streamwise Oscillating Heated Cylinder

2021 ◽  
Author(s):  
Ussama Ali ◽  
MD Islam ◽  
Isam Janajreh
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Natural Frequency ◽  
Strouhal Number ◽  
Frequency Ratio ◽  
Lift Coefficient ◽  
Cylinder Wall ◽  
Forcing Function ◽  
Lower Amplitude

Abstract The influence of oscillation and heat transfer on the lift and drag coefficients over a circular cylinder is numerically studied in this work. Temperature difference of 300, 600 and 900 K is used between the cylinder wall and the incoming fluid flow for Reynolds number of 100. Air is used as the fluid and the temperature dependent properties of air are used for the analysis as a significant change in the properties of air incurred. Numerical simulation is done on Ansys/fluent with O-type mesh and the vibration in the circular cylinder is induced using user defined function. The vibration of the cylinder in streamwise direction is induced at a frequency ratio of 0.5, 1, and 2, with the natural frequency of the cylinder being 2.5 Hz marking its Strouhal number. It is observed that for all the induced frequencies, the forcing function interacts with the natural frequency of the system, and the beating phenomenon spectrum is observed, where two distinct frequencies appear which correspond to the sum and difference between the natural and the forcing frequency. At the frequency ratio of 0.5 (1.25 Hz), the spectrum of lift coefficient is characterized with three peaks centered at 2.5 Hz (natural frequency), 3.75 Hz (sum) and 1.25 Hz (difference). Oscillating the isothermal cylinder at a frequency ratio of 0.5 caused a negligible increase in the rms value of the lift coefficient by 2.13%, drag coefficient by 0.17%, and had no effect on the natural frequency of the system, however at a frequency ratio of 2, a drastic increase in the rms value of lift coefficient by 137.4% and drag coefficient by 13.9% occurred, indicating the lock-on regime. As compared to the stationary isothermal cylinder, heating the cylinder 300K above the incoming flow, decreased the rms value of the lift coefficient by 62.7% and the natural frequency by 16%, while increased the drag coefficient by 7.3%. The results show that heating of cylinder in cross-flow is equivalent to running the flow at a reduced Reynolds number and in the laminar region, this is associated with lower Strouhal number and lower amplitude of lift but a higher drag.

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