Pulsating Flow Past a Square Cylinder: Analysis of Force Coefficient Spectra and Vortex Structure Development

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Thomas S. Fowler ◽  
Freddie D. Witherden ◽  
Sharath S. Girimaji
Keyword(s):  
Vortex Structure ◽  
Lift Coefficient ◽  
Excitation Frequency ◽  
Wake Flow ◽  
Square Cylinder ◽  
Spectral Character ◽  
Force Coefficient ◽  
Force Coefficients ◽  
Shedding Frequency ◽  
Lock In

Abstract This study examines the changes in force coefficients and wake flow structures of a square cylinder subject to pulsating in-flow at different frequencies. The Reynolds number is 200, according to previous literature. Over a range of forcing frequencies, a regime is observed where the shedding frequency scales with the forcing frequency rather than the natural shedding frequency, known as the lock-in phenomenon in literature. The change in spectral character across three frequency regimes—pre-lock-in, lock-in, and post-lock-in—are examined and characterized. During pre-lock-in, the shedding frequency remains equal to the natural shedding frequency. However, the corresponding peak in lift coefficient (CL) power spectral density (PSD) is a single decade larger than that of neighboring minima. This contrasts greatly with subsequent regimes where the amplitudes of the peaks are observed to be substantially larger than the amplitudes of neighboring minima. The onset of lock-in is sharp, and the corresponding excitation frequency is identified. The shedding frequency becomes a function of the forcing frequency within this regime, and the corresponding CL PSD peak is four decades larger than that of neighboring minima. The transition beyond the lock-in regime is gradual with peaks of the spectra broadening until separating into multiple discrete peaks. To comprehend the changes in the force coefficients, the vortex structure in the wake is characterized at different frequencies. The connection between the vortex development sequence and force profile is investigated, and z-vorticity probes are utilized to correlate these qualitative observations with prior quantitative analysis. Three-dimensional flow effects are also examined.

Interactions of Vortices of a Square Cylinder and a Rectangular Vortex Generator Under Couette–Poiseuille Flow

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Dilip K. Maiti ◽  
Rajesh Bhatt
Keyword(s):  
Poiseuille Flow ◽  
Lift Coefficient ◽  
Sudden Change ◽  
Vortex Generator ◽  
Wake Flow ◽  
Square Cylinder ◽  
Operational Parameters ◽  
Critical Spacing ◽  
Spacing Distance ◽  
Nonlinear Velocity

This study focuses on interactions of vortices generated by a family of eddy-promoting upstream rectangular cylinders (of different heights a* and widths b*) with the shear layers of a downstream square cylinder (of height A*) placed near a plane in an in-line tandem arrangement under the incidence of Couette–Poiseuille flow based nonuniform linear/nonlinear velocity profile. The dimensionless operational parameters are cylinders spacing distance S, ratio of heights r2=a*/A* (≤1), aspect ratio r1=b*/a* (≤1), Reynolds number Re (based on the velocity at height A* for Couette flow), ReU2 (based on the velocity at height 10A* for Couette–Poiseuille flow), and nondimensional pressure gradient P at the inlet. The governing equations are solved numerically through a pressure-correction-based iterative algorithm (SIMPLE) with the quadratic upwind interpolation for convective kinematics (QUICK) scheme for convective terms. The major issue of appearing multiple peaks in the spectrum of the fluctuating lift coefficient of the downstream cylinder is addressed and justified exhibiting the flow patterns. While considering the rectangular shape (for the upstream cylinder) and nonlinear velocity (at the inlet), the possibility of generating the unsteadiness in the steady wake flow of the downstream cylinder at a Re (based on height a*) less than the critical Re for the downstream cylinder is documented here. The dependence of flow characteristics of the downstream cylinder on the angle of incident linear velocity at specific S and r1 is also demonstrated here. It is observed that the discontinuous jump in the aerodynamic characteristics (due to a sudden change from one distinct flow pattern to the other in the critical spacing distance regime) is directly proportional to the height of the vortex generator. Increasing P under the same characteristic velocity causes the steady flow of cylinder(s) to convert to a periodic flow and reduces the critical spacing distance for the vortex generator.

Wake vortex evolution of square cylinder with a slot synthetic jet positioned at the rear surface

2017 ◽  
Vol 812 ◽  
pp. 940-965 ◽  
Author(s):  
Yuan Qu ◽  
Jinjun Wang ◽  
Mao Sun ◽  
Lihao Feng ◽  
Chong Pan ◽  
...  
Keyword(s):  
Rear Surface ◽  
Excitation Frequency ◽  
Streamwise Velocity ◽  
Synthetic Jet ◽  
Wake Vortex ◽  
Square Cylinder ◽  
Natural Case ◽  
Control Frequency ◽  
The Mean ◽  
Shedding Frequency

Wake vortex evolution of a square cylinder with a slot synthetic jet issuing from the cylinder’s rear surface has been experimentally investigated using the time-resolved particle image velocimetry technique. The Reynolds number based on the side length of the square cylinder is $Re=836$. The excitation frequency normalized by the natural shedding frequency $f_{e}/f_{0}$ varies from 0 to 6 at the dimensionless stroke length $L_{0}/w=72.6$. The distributions of the time-averaged Reynolds stresses present significant differences as the excitation frequency increases. With control, the mean streamwise velocity deficit of the wake recovers more quickly in comparison with the natural case, and the vertical velocity fluctuation intensity becomes weaker. Moreover, a drag reduction can be achieved for the control cases, especially, for $f_{e}/f_{0}=4$ and $f_{e}/f_{0}=6$, a thrust instead of drag reduction can be obtained. The profiles of the mean streamwise velocity tend to have jet-like distributions. The wake vortex dynamics and its evolution with the excitation frequency are revealed. (i) For the low excitation frequency cases ($f_{e}/f_{0}=0.5$, 1, 2), no significant changes in the dominant frequency and the spanwise vortex structures are observed in comparison with the natural case. (ii) For the moderate excitation frequency case ($f_{e}/f_{0}=3$), the wake vortex shedding frequency is locked on half of the control frequency. In this case, the shear layer is divided into two parts by the synthetic jet vortex, and the wake vortices with smaller scales still shed asymmetrically and appear closer to the square cylinder. (iii) For the high excitation frequency case ($f_{e}/f_{0}=6$), the flow is governed by the synthetic jet. As a result of strong perturbations of the synthetic jet, the wake vortex shedding becomes symmetric with the shedding frequency consistent with the control frequency. And the separation is suppressed effectively. The different control effects of the slot synthetic jet on a square cylinder and a circular cylinder are also compared in detail. Generally speaking, the circular cylinder is easier to be controlled due to its non-fixed separation points.

Vortex-Induced Vibration of Horizontal Circular Cylinder in Uniform Flow

2004 ◽  
Author(s):  
Kentaroh Kokubun ◽  
Yasuhiro Wada
Keyword(s):  
Natural Frequency ◽  
Lift Coefficient ◽  
Vertical Displacement ◽  
Peak Frequency ◽  
Uniform Flow ◽  
Vortex Induced Vibration ◽  
Vortex Shedding Frequency ◽  
Nonlinear Form ◽  
Shedding Frequency ◽  
Lock In

This paper treats Vortex-Induced Vibration (VIV) of a cylinder in uniform flow. The cylinder is aluminum, rigid, circular, and 0.490 m in length, 0.025 m in diameter, and its weight is counterbalanced by buoyancy. The cylinder is horizontally mounted in a two-dimensional tank and allowed to move vertically by hanging through a spring during towing. The equation of motion of the structure is described in the nonlinear form and an approximate solution of the equation is obtained by using a vibrational theory. Lock-in phenomena appear when the vortex shedding frequency approaches to the natural frequency of the structure. Experimental results show that the oscillation of structure has remarkable two frequencies corresponding to the shedding frequency and the natural frequency of the structure. By using amplitude of vertical displacement at the top peak frequency, this paper proposes a way of estimating the transverse force, i.e., lift coefficient during VIV. The estimated lift coefficients are similar to the measured lift coefficients with the vertical displacement restricted to be zero. The estimated lift coefficients seem to be feasible.

Lock-in regions of laminar flows over a streamwise oscillating circular cylinder

2018 ◽  
Vol 858 ◽  
pp. 315-351 ◽  
Author(s):  
Ki-Ha Kim ◽  
Jung-Il Choi
Keyword(s):  
Circular Cylinder ◽  
Aerodynamic Force ◽  
Lift Coefficient ◽  
Lower Boundary ◽  
Laminar Flows ◽  
Velocity Range ◽  
Frequency Range ◽  
Vortex Pattern ◽  
Moving Cylinder ◽  
Lock In

In this paper, flow over a streamwise oscillating circular cylinder is numerically simulated to examine the effects of the driving amplitude and frequency on the distribution of the lock-in regions in laminar flows. At $Re=100$, lock-in is categorized according to the spectral features of the lift coefficient as two different lock-in phenomena: harmonic and subharmonic lock-in. These lock-in phenomena are represented as maps on the driving amplitude–frequency plane, which have subharmonic lock-in regions and two harmonic lock-in regions. The frequency range of the subharmonic region is shifted to lower frequencies with increasing amplitude, and the lower boundary of this subharmonic region is successfully predicted. A symmetric harmonic region with a symmetric vortex pattern is observed in a certain velocity range for a moving cylinder. Aerodynamic features induced by different flow patterns in each region are presented on the driving amplitude–frequency plane. The lock-in region and aerodynamic features at $Re=200$ and $40$ are compared with the results for $Re=100$. A subharmonic region and two harmonic regions are observed at $Re=200$, and these show the same features as for $Re=100$ at a low driving amplitude. Lock-in at $Re=40$ also shows one subharmonic region and two harmonic regions. However, compared with the $Re=100$ case, the symmetric harmonic lock-in is dominant. The features of aerodynamic force at $Re=200$ and $40$ are represented on a force map, which shows similar characteristics in corresponding regions for the $Re=100$ case.

Effect of Corner-Arc on the Flow Structures Around a Square Cylinder

2018 ◽  
Author(s):  
Hariprasad Chakkalaparambil Many ◽  
Vishnu Chandar Srinivasan ◽  
Ajith Kumar Raghavan
Keyword(s):  
Drag Reduction ◽  
Oscillation Amplitude ◽  
Water Channel ◽  
Excitation Frequency ◽  
Flow Structures ◽  
Square Cylinder ◽  
Near Wake ◽  
Vortex Size ◽  
Vortex Shedding Frequency ◽  
Visualization Experiments

In this paper, flow structures around a corner modified square cylinder (side dimension, Bo) are presented and discussed. Cylinders with various corner arcs (circular) were considered (arc radius ‘r’). For various Corner Ratios (CR = r/Bo), values ranging from 0 to 0.5, flow visualization experiments were conducted in a water channel and the results are reported at Re = 2100 (based on Bo). Results presented are for two cases (a) stationary cylinders reporting the values of CD (coefficient of drag), St (Strouhal no.), and D (vortex size) and (b) oscillating cylinders at fe/fs = 1 (fe is the cylinder excitation frequency and fs is the vortex shedding frequency) and a/Bo = 0.8 (a is the cylinder oscillation amplitude). The work is aimed to explore the most effective configuration for drag reduction. Cylinder with corner ratio of 0.2 is proved to be the most effective one among the cases considered in this study with 19.3% drag reduction. As a major highlight, in contrast to the results of the previous studies, current study do not reveal a monotonous decrease of drag with increasing corner modification. Instead, it is shown here that, there is a specific value of CR ratio where the drag is the minimum most. A peculiar type of vortex structure was observed in the cases of stationary cylinders with CR > 0.2, contributing to the increase in drag. In the case of oscillating cylinders, description of one complete cycle for all CR ratios at various time instances are presented. The near-wake structures were observed to be dependent on the CR ratio. Counter intuitively, cylinder oscillation does not bring major difference in vortex size compared to the stationary case.

Model reduction and mechanism for the vortex-induced vibrations of bluff bodies

2017 ◽  
Vol 827 ◽  
pp. 357-393 ◽  
Author(s):  
W. Yao ◽  
R. K. Jaiman
Keyword(s):  
Reynolds Number ◽  
Bluff Body ◽  
Low Reynolds Number ◽  
Smooth Curve ◽  
Bluff Bodies ◽  
Sharp Corner ◽  
Mass Ratio ◽  
Square Cylinder ◽  
Low Reynolds ◽  
Lock In

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.

scholarly journals A Study of Drag Reduction on Cylinders with Different V-Groove Depths on the Surface

Water ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 36
Author(s):  
Jiyang Qi ◽  
Yue Qi ◽  
Qunyan Chen ◽  
Fei Yan
Keyword(s):  
Drag Reduction ◽  
Drag Coefficient ◽  
Vortex Structure ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Groove Surface ◽  
Smooth Cylinder ◽  
Groove Structure ◽  
Reduction Effect

In this study, the drag reduction effect is studied for a cylinder with different V-groove depths on its surface using a k-ω/SST (Shear Stress Transport) turbulence model of computational fluid dynamics (CFD), while a particle image velocimetry (PIV) system is employed to analyze the wake characteristics for a smooth cylinder and a cylinder with different V-groove depths on its surface at different Reynolds numbers. The study focuses on the characteristics of the different V-groove depths on lift coefficient, drag coefficient, the velocity distribution of flow field, pressure coefficient, vortex shedding, and vortex structure. In comparison with a smooth cylinder, the lift coefficient and drag coefficient can be reduced for a cylinder with different V-groove depths on its surface, and the maximum reduction rates of lift coefficient and drag coefficient are about 34.4% and 16%, respectively. Otherwise, the vortex structure presents a complete symmetry for the smooth cylinder, however, the symmetry of the vortex structure becomes insignificant for the V-shaped groove structure with different depths. This is also an important reason for the drag reduction effect of a cylinder with a V-groove surface.

Experimental Identification of Dynamic Force Coefficients for a 110 mm Compliantly Damped Hybrid Gas Bearing

2014 ◽  
Author(s):  
Adolfo Delgado
Keyword(s):  
Load Capacity ◽  
Excitation Frequency ◽  
Dynamic Test ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Test Parameters ◽  
Gas Bearing

Compliant hybrid gas bearings combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate that the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

scholarly journals Dynamical effect of the total strain induced by the coherent motion on local isotropy in a wake

2013 ◽  
Vol 720 ◽  
pp. 393-423 ◽  
Author(s):  
F. Thiesset ◽  
L. Danaila ◽  
R. A. Antonia
Keyword(s):  
Circular Cylinder ◽  
Large Scale ◽  
Bluff Body ◽  
Initial Conditions ◽  
Scale Up ◽  
Wake Flow ◽  
Total Strain ◽  
Coherent Motion ◽  
Square Cylinder ◽  
Local Isotropy

AbstractWe assess the extent to which local isotropy (LI) holds in a wake flow for different initial conditions, which may be geometrical (the shape of the bluff body which creates the wake) and hydrodynamical (the Reynolds number), as a function of the dynamical effects of the large-scale forcing (the mean strain, $ \overline{S} $, combined with the strain induced by the coherent motion, $\tilde {S} $). LI is appraised through either classical kinematic tests or phenomenological approaches. In this respect, we reanalyse existing LI criteria and formulate a new isotropy criterion based on the ratio between the turbulence strain intensity and the total strain ($ \overline{S} + \tilde {S} $). These criteria involve either time-averaged or phase-averaged quantities, thus providing a deeper insight into the dynamical aspect of these flows. They are tested using hot wire data in the intermediate wake of five types of obstacles (a circular cylinder, a square cylinder, a screen cylinder, a normal plate and a screen strip). We show that in the presence of an organized motion, isotropy is not an adequate assumption for the large scales but may be satisfied over a range of scales extending from the smallest dissipative scale up to a scale which depends on the total strain rate that characterizes the flow. The local value of this scale depends on the particular nature of the wake and the phase of the coherent motion. The square cylinder wake is the closest to isotropy whereas the least locally isotropic flow is the screen strip wake. For locations away from the axis, the study is restricted to the circular cylinder only and reveals that LI holds at scales smaller than those that apply at the wake centreline. Arguments based on self-similarity show that in the far wake, the strength of the coherent motion decays at the same rate as that of the turbulent motion. This implies the persistence of the same degree of anisotropy far downstream, independently of the scale at which anisotropy is tested.

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