The Effect of In-Line Oscillation on the Forces of a Cylinder Vibrating in a Steady Flow

2010 ◽  
Author(s):  
Sofia Peppa ◽  
Lambros Kaiktsis ◽  
George Triantafyllou
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Time Dependence ◽  
Vibration Frequency ◽  
Oscillation Frequency ◽  
Lift Force ◽  
Computational Study ◽  
Oscillation Amplitude ◽  
Fluid Forces ◽  
Uniform Stream

In this paper we present a computational study of the forces acting on a circular cylinder vibrating both transversely and in-line to a uniform stream. The in-line vibration frequency is equal to twice the transverse frequency. The cylinder thus follows a figure-eight trajectory, emulating the trajectory of a free vortex-induced vibration. We consider three values of transverse oscillation frequency, in the regime of the natural frequency of the Ka´rma´n street, for a Reynolds number of 400. We find that the fluid forces are greatly influenced by the direction in which the figure-eight is traversed. We also find that the spectrum of the lift force is characterized by the strong presence of odd-numbered higher harmonics. Moreover, depending on the combination of oscillation amplitude and frequency, the lift force exhibits aperiodic time dependence.

scholarly journals Vortex-induced vibration of a transversely rotating sphere

2018 ◽  
Vol 847 ◽  
pp. 786-820 ◽  
Author(s):  
Methma M. Rajamuni ◽  
Mark C. Thompson ◽  
Kerry Hourigan
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Rotation Rate ◽  
Lift Force ◽  
Oscillation Amplitude ◽  
Fluid Viscosity ◽  
Sphere Diameter ◽  
Force Coefficient ◽  
Vortex Induced Vibration ◽  
Rotation Rates

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.

Computational Study of Flow Resonances and Forces on a Cylinder Vibrating In-Line to a Steady Flow

2010 ◽  
Author(s):  
Lambros Kaiktsis ◽  
George S. Triantafyllou
Keyword(s):  
Oscillation Frequency ◽  
Computational Study ◽  
Oscillation Amplitude ◽  
Excitation Frequency ◽  
Spectral Element ◽  
Flow Dynamics ◽  
Chaotic Flow ◽  
Cylinder Diameter ◽  
Wide Range ◽  
Two Dimensional Flow

We present computational results of the flow dynamics and forces on a circular cylinder oscillating in-line with respect to a steady uniform stream. A wide range of oscillation frequencies is considered, from 0.5fs to 3fs, where fs is the natural Strouhal frequency of the Karman street. The oscillation amplitude is varied up to half the cylinder diameter. The Reynolds number value is 180, corresponding to two-dimensional flow. Simulations utilize a spectral element method. The computed flow states are characterized based on processed lift signals, and flow visualization. We find that the response of the flow is very sensitive to variations of the cylinder oscillation frequency. At low oscillation frequency, the lift signal and vortex patterns remain regular for low oscillation amplitudes, i.e. correspond to a 2S type of vortex street, and become complex at high oscillation amplitudes. Cylinder oscillation at the Strouhal frequency gives a window of chaotic flow at intermediate amplitudes, while at higher amplitudes 2S wakes are generated, with the sub-harmonic fs/2 and the higher harmonic 3fs/2 dominating the lift spectrum. Oscillation at twice the Strouhal frequency results in symmetric shedding, for oscillation amplitudes close to 30% of the cylinder diameter, and higher. Finally, at an oscillation frequency equal to three times the Strouhal frequency, the flow dynamics is very rich, characterized by “islands” of symmetric and asymmetric shedding at increasing oscillation amplitude. Chaotic flow is obtained only when the excitation frequency is equal to fs or to 3fs.

Simulation of Low-Reynolds Number Flow Around a Circular Cylinder Following a Slender Elliptical Path

2013 ◽  
Author(s):  
László Baranyi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Amplitude Ratio ◽  
Oscillation Amplitude ◽  
Base Pressure ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Lock In

Two-dimensional flow around a circular cylinder forced to follow an elliptical path at low Reynolds numbers is investigated numerically using a thoroughly tested in-house code based on the finite difference method. Time-mean (TM) and rms values of lift, drag and base pressure coefficients are investigated within the lock-in region against the transverse oscillation amplitude for Reynolds number Re = 150 at frequency ratios of 0.8, 0.9 and 1.0 while the ratio of in-line and transverse cylinder oscillation amplitudes is kept at six different values yielding slender elliptical cylinder paths. The objective of the paper is to investigate the effect of the shape of the path, or amplitude ratio, on force coefficients. Findings show that for the cases investigated the rms of lift and TM of drag and base pressure are hardly affected by the amplitude ratio, while its effects are pronounced on the TM of lift and rms of drag and base pressure.

On a Circular Cylinder in a Uniform Planar Shear Flow at Subcritical Reynolds Number

2002 ◽  
Author(s):  
D. Sumner ◽  
O. O. Akosile
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Lift Force ◽  
Experimental Studies ◽  
Reynolds Numbers ◽  
Low Velocity ◽  
Static Pressure Distribution ◽  
Planar Shear ◽  
The Mean

An experimental investigation was conducted of a circular cylinder immersed in a uniform planar shear flow, where the approach velocity varies across the diameter of the cylinder. The study was motivated by some apparent discrepancies between numerical and experimental studies of the flow, and the general lack of experimental data, particularly in the subcritical Reynolds number regime. Of interest was the direction and origin of the steady mean lift force experienced by the cylinder, which has been the subject of contradictory results in the literature, and for which measurements have rarely been reported. The circular cylinder was tested at Reynolds numbers from Re = 4.0×104 − 9.0×104, and the dimensionless shear parameter ranged from K = 0.02 − 0.07, which corresponded to a flow with low to moderate shear. The results showed that low to moderate shear has no appreciable influence on the Strouhal number, but has the effect of lowering the mean drag coefficient. The circular cylinder develops a small steady mean lift force directed towards the low-velocity side, which is attributed to an asymmetric mean static pressure distribution on its surface. The reduction in the mean drag force, however, cannot be attributed solely to this asymmetry.

Lift on a steady 2-D symmetric airfoil in viscous uniform shear flow

2017 ◽  
Vol 837 ◽  
Author(s):  
Patrick R. Hammer ◽  
Miguel R. Visbal ◽  
Ahmed M. Naguib ◽  
Manoochehr M. Koochesfahani
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Rate ◽  
Lift Force ◽  
Computational Study ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Boundary Layer Development

We present an investigation into the influence of upstream shear on the viscous flow around a steady two-dimensional (2-D) symmetric airfoil at zero angle of attack, and the corresponding loads. In this computational study, we consider the NACA 0012 airfoil at a chord Reynolds number $1.2\times 10^{4}$ in an approach flow with uniform positive shear with non-dimensional shear rate varying in the range 0.0–1.0. Results show that the lift force is negative, in the opposite direction to the prediction from Tsien’s inviscid theory for lift generation in the presence of positive shear. A hypothesis is presented to explain the observed sign of the lift force on the basis of the asymmetry in boundary layer development on the upper and lower surfaces of the airfoil, which creates an effective airfoil shape with negative camber. The resulting scaling of the viscous effect with shear rate and Reynolds number is provided. The location of the leading edge stagnation point moves increasingly farther back along the airfoil’s upper surface with increased shear rate, a behaviour consistent with a negatively cambered airfoil. Furthermore, the symmetry in the location of the boundary layer separation point on the airfoil’s upper and lower surfaces in uniform flow is broken under the imposed shear, and the wake vortical structures exhibit more asymmetry with increasing shear rate.

Low Reynolds number flow of a variable property gas past a heated circular cylinder

1969 ◽  
Vol 39 (3) ◽  
pp. 465-476 ◽  
Author(s):  
P. F. Hodnett
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Low Reynolds Number ◽  
Low Reynolds Number Flow ◽  
Variable Property ◽  
Reynolds Number Flow ◽  
Stream Condition ◽  
Number Flow ◽  
Uniform Stream

The low Reynolds number flow of a variable property gas past an infinite heated circular cylinder is studied when the temperature difference between the cylinder and the free stream is appreciable. The velocity field (and hence the drag on the cylinder) is calculated by the method of matched asymptotic expansions. It is found that the zero-order velocity field calculated on the Stokes approximation satisfies both the no slip condition at the cylinder and the uniform stream condition at infinity which is in strong contrast with the corresponding velocity field for incompressible slow flow past an unheated cylinder where the uniform stream condition at infinity cannot be satisfied. When the temperature of the cylinder is twice the temperature at infinity it is found that the drag on the cylinder is almost twice the drag on a similar unheated cylinder.

scholarly journals Experimental Studies and Analysis on Mobilization of the Cohesionless Sediments Through Alluvial Channel: A Review

2021 ◽  
Vol 7 (5) ◽  
pp. 915-936
Author(s):  
Akash Anand ◽  
Mubeen Beg ◽  
Neeraj Kumar
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Lift Force ◽  
Experimental Studies ◽  
Friction Angle ◽  
Force Balance ◽  
Complete Analysis ◽  
Rough Boundary ◽  
Fluid Forces ◽  
River Bed

Entrainment of river bed particles by turbulent flow is a core matter of study in river hydrodynamics. It is of great interest to river engineers to evaluate the shear stress for initiating river bed motion. The main objective is to calculate transport rates for bed load, to predict changes in bed level which are scoured or aggraded and to design a stable channel. Forces acting upon the particle especially fluid forces which give a major role in the incipient motion of the particle on the rough boundary. For calculation generally use shield’s diagram but some other modified methods and approaches are discussed. Modeling criteria are discussed for the hydraulically smooth and rough boundary depending on Reynolds number. In the past, experimental studies on tractive shear stress have been done by many researchers but consideration of lift force to analyze the movement of sediment is very limited. For suspended load transport, a detailed analysis of lift force is required. Based on the study it has been observed that shear stress depends on channel slope not only due to gravitational force but also many other factors like drag force, lift force, friction angle, fluctuations, velocity profile, etc. Complete analysis of these factors provides slope dependency over shear stress. To improve past studies, some factors have been discussed, to give a more correct force balance equation. This is very difficult task to analyze more and more variable’s dependency on the slope. Consideration of the possible number of variable holds complete analysis of experimental study. This paper also reviews the effect of particle Reynolds number and relative submergence over critical shield stress. Doi: 10.28991/cej-2021-03091700 Full Text: PDF

Phase jump and energy transfer of forced oscillating circular cylinder in uniform flow

2016 ◽  
Vol 231 (2) ◽  
pp. 496-510
Author(s):  
Guoqiang Tang ◽  
Lin Lu ◽  
Ming Zhao ◽  
Mingming Liu ◽  
Zhi Zong
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Circular Cylinder ◽  
Phase Difference ◽  
Uniform Flow ◽  
Phase Jump ◽  
Fluid Forces ◽  
Special Cases ◽  
Lock In ◽  
Transfer Direction

The phase jump, energy transfer, and the associated vortex shedding modes of a circular cylinder undergoing forced oscillation normal to the incoming uniform flow are investigated numerically at Reynolds number ( Re) of 200. The dependence of the fluid forces on the non-dimensional oscillating amplitude A* =  A/ D ∈ [0.1, 0.6] and frequency f* =  fe/ fs ∈ [0.5, 2.0] is examined, where A is the oscillating amplitude, D is the cylinder diameter, fe is the cylinder oscillating frequency, and fs is the Strouhal frequency of fixed cylinder at the same Reynolds number, respectively. The lock-in region is identified by the combination of Fourier analysis and Lissajous phase diagram. The phase difference between displacement and lift fluctuation and the energy transfer between fluid and structure are discussed. Within the lock-in region, a jump in the phase difference is found to occur in the cases with A* = 0.5 and 0.55 without a wake mode transition. The numerical results reveal that the appearance of the phase jump is consistent with the reversal of the energy transfer direction. For the special cases of A* = 0.5 and 0.55, changes in the sign of energy transfer are observed, while no reversal of energy transfer is observed at other amplitudes. The energy transfer direction is either from fluid to cylinder when A* ∈ [0.1, 0.4] or from cylinder to fluid when A* ≥ 0.6. It is confirmed that the energy transfer between fluid and cylinder is not only dependent on cylinder oscillating frequency but also on cylinder oscillating amplitude.

Simulation of flow across a row of transversely oscillating square cylinders

2011 ◽  
Vol 680 ◽  
pp. 361-397 ◽  
Author(s):  
C. M. SEWATKAR ◽  
ATUL SHARMA ◽  
AMIT AGRAWAL
Keyword(s):  
Reynolds Number ◽  
Oscillation Frequency ◽  
Amplitude Ratio ◽  
Numerical Study ◽  
Lift Coefficient ◽  
Oscillation Amplitude ◽  
Flow Regimes ◽  
Flow Parameters ◽  
Square Cylinders ◽  
Wake Interaction

A numerical study of flow across a row of transversely oscillating square cylinders (of diameter d) has been undertaken using the lattice Boltzmann method, for a better understanding of fluid–structure interaction problems. The effects of cylinder oscillation frequency ratio (fe/fo, where fe is the cylinder oscillation frequency and fo is the corresponding vortex shedding frequency for stationary row of cylinders), amplitude ratio (A/d), non-dimensional spacing between the cylinders (s/d) and Reynolds number (Re) on ensuing flow regimes and flow parameters have been studied to understand the flow physics. Six different flow regimes observed in this study are the quasi-periodic non-lock-on-I, synchronous lock-on, quasi-periodic lock-on, quasi-periodic non-lock-on-II, synchronous non-lock-on and chaotic non-lock-on. It is observed that the range of the lock-on regime depends upon the relative dominance of incoming flow and cylinder motion. Although the lock-on regime in the case of Re = 80, s/d = 4 and A/d = 0.2 is substantially larger as compared to that for a single oscillating cylinder, the range of the lock-on regime shrinks with a reduction in the cylinder spacing, increase in the Reynolds number or decrease in the oscillation amplitude. It is also observed that the wake interaction behind the cylinders weakens with an increase in fe/fo, Re, A/d or s/d, leading to the formation of independent wakes and synchronous nature of the flow. For fe/fo ≥ 1.2, independent and intact oscillating wakes are noted and an additional frequency (wake oscillation frequency) is obtained in the time series of the lift coefficient. Although it was expected that the complexity in the wake interaction would increase with cylinder oscillation or amplitude ratio, an opposite effect (that is, formation of independent wakes) is noted from the results.

On the forces acting on a circular cylinder set obliquely in a uniform stream at low values of Reynolds number

1953 ◽  
Vol 219 (1137) ◽  
pp. 233-244 ◽  
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Viscous Fluid ◽  
Tangential Stress ◽  
Longitudinal Force ◽  
Transverse Force ◽  
Total Force ◽  
Expansion Formulae ◽  
Transverse And Longitudinal Components ◽  
Uniform Stream

The forces acting on a circular cylinder set obliquely to a uniform stream of an incompressible viscous fluid are discussed for small values of Reynolds number. The total force on the cylinder is calculated by resolving it into the transverse and longitudinal components, N and L , and the general formulae as well as expansion formulae in powers of the Reynolds number axe given for these two components. Further, a certain relation between the component due to the tangential stress r θ ͡͡ on the surface, of the transverse force N and the longitudinal force L is examined at low values of the Reynolds number; this relation has been obtained recently by Sir Geoffrey Taylor for larger values of the Reynolds number. The present work is intended to make some contribution to a new field in hydrodynamics which has been developed by Sir Geoffrey Taylor in connexion with the mechanics of swimming of long and narrow animals in a viscous fluid.

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