Lock-On Vortex Shedding Patterns and Bifurcation Analysis of the Forced Streamwise Oscillation of the Cylinder Wake

2015 ◽  
Vol 25 (09) ◽  
pp. 1530022
Author(s):  
N. Nabatian ◽  
N. W. Mureithi

The two-dimensional numerical simulation of the flow over a cylinder forced to oscillate in the streamwise direction for Re = 200 is performed in CFX ANSYS. The controlled-vibration comprises of prescribed inline vibration from displacement amplitude-to-cylinder diameter A/D = 0.05 up to 0.5 with the excitation frequency ratios of 1, 1.5 and 2 including the harmonic and superharmonic excitation regions. The immersed boundary method is used to model the cylinder oscillation. Modal decomposition of the transverse velocity field via the proper orthogonal decomposition (POD) method is applied to uncover the interaction of symmetric and antisymmetric modes of the near wake. A model using the first two POD modes is developed based on symmetry group equivariance. The model predicts the mode interactions and bifurcated solution branches for all cases, and is shown to be in good agreement with numerical as well as previous experimental results. Lock-on is determined for a range of values of the oscillation amplitudes and frequency ratios. It is shown that the lock-on range widens with increasing nondimensional oscillation amplitude. The asymmetric 2S, P + S and symmetric pattern S with symbol S for a single vortex and P for a vortex pair shed per cycle, as well as a regime in which vortex formation is not synchronized with cylinder motion are observed in the cylinder wake depending on the combination of oscillation amplitude and frequency ratio. The frequency ratio variation from 1 to 2 leads to the switching from asymmetric to symmetric modes. The symmetric flow pattern corresponds to a near zero lift coefficient on the cylinder.

2015 ◽  
Vol 39 (4) ◽  
pp. 789-803 ◽  
Author(s):  
Negar Nabatian ◽  
Xiaofei Xu ◽  
Njuki Mureithi

A 3D numerical simulation of a circular cylinder wake is presented in this paper. The cylinder is harmonically forced in the stream-wise direction. The objective of the present work is to investigate the effect of the oscillation amplitude on the secondary transition of the wake. The frequency of the lift force is then linked to the form of the vortex shedding mode. The relation between these vortex shedding modes using POD analysis of the transverse velocity and the unsteady lift coefficient of 3D simulation is in good agreement with the 2D model. Results show that the 3D spanwise effect, which can change the wake structure, is suppressed at Re = 200 by streamwise oscillation of the cylinder. Thus the 2D analysis can effectively model the temporal instability of the wake flow.


2000 ◽  
Vol 123 (6) ◽  
pp. 1139-1148 ◽  
Author(s):  
C. Gau ◽  
S. X. Wu ◽  
H. S. Su

Experiments are performed to study the flow structure and heat transfer over a heated cylinder oscillating radially with small amplitude in streamwise direction. Both flow visualization using a smoke wire in the upstream and the local heat transfer measurements based on wall temperatures around the cylinder were made. The excitation frequencies of the cylinder are selected at Fe/Fn=0, 0.5, 1, 1.5, 2, 2.5, and 3. The oscillation amplitude selected is less than a threshold value of A/D=0.06 where synchronization of vortex shedding with the cylinder excitation was not expected. However, experiments indicate that synchronization still occurs which stimulates a great interest to study its enhancement in the heat transfer. Synchronization occurred at Fe/Fn=2 is antisymmetric vortex formation while synchronization at Fe/Fn=2.5 and 3 is symmetric type. The forward motion (advancing into the cross flow) of the cylinder during one cycle of oscillation has an effect to suppress the instability and the vortex formation. This leads to the occurrence of a smaller and symmetric vortex formation and a less enhancement of heat transfer than the case of antisymmetric type Fe/Fn=2. For excitations at lower frequencies Fe/Fn⩽1.5, all the vortex formations occurred are mostly antisymmetric. The dominant mode of the instability in the shear layer is actually the natural shedding frequency Fn of the vortex. A closer excitation frequency to 2Fn causes a greater enhancement in the heat transfer. During the experiments, the Reynolds numbers varies from 1600 to 3200, the dimensionless amplitude A/D from 0.048 to 0.016.


Author(s):  
N. Nabatian ◽  
N. W. Mureithi

Vortex shedding over a cylinder is strongly affected by the cylinder oscillation. The dynamics of the cylinder wake subjected to harmonic forced excitation in the inline direction at Re = 200 is investigated in this work. Two dominant modes of the transverse velocity field are considered to model and predict the nonlinear interaction of 2D vortex shedding. The normal form symmetries have the main role in the pattern formation. The interaction of two steady modes in the presence of O(2) × S1 symmetry is described by equivariant theory. Considering the symmetries, the amplitude equations are developed with the frequency saturation information included by the addition of complex coefficients. The reduced model is expanded up to 7th order, in order to include the spatio-temporal effects. The coefficients of the model are obtained from 2D simulations of the cylinder wake flow. The physical significance of the inline amplitude oscillation on the wake dynamics is captured by the variation of the two linear coefficients of the low order model. Similarly to the numerical results, as the amplitude of oscillation increases, two limit cycles undergo the symmetry-breaking bifurcation leading to a quasi-periodic state. The existence of the second frequency in addition to the natural shedding frequency is manifested as the small amplitude oscillation in the quasi-periodic state. For a forcing amplitude A/D = 0.5, the quasi-periodic state undergoes a torus doubling bifurcation. The dominant frequency of the bifurcated S mode matches the lift coefficient shedding frequency at A/D = 0.5 obtained from the numerical computation. The lift coefficient signal is not absolutely periodic due to the presence of the other peaks in addition to the dominant one at St = 0.1 representing the quasi-periodic flow pattern. The modulated travelling waves bifurcated from the low order model have mode S as the basic v-velocity mode which verifies the symmetric torus-doubled transverse velocity pattern observed in CFD simulation. Thus the proposed low order model can predict, with reasonable accuracy, the bifurcation sequence of the forced cylinder wake dynamic transitions observed in the numerical computation results.


2007 ◽  
Vol 577 ◽  
pp. 79-104 ◽  
Author(s):  
JUSTIN S. LEONTINI ◽  
M. C. THOMPSON ◽  
K. HOURIGAN

A Floquet stability analysis of the transition to three-dimensionality in the wake of a cylinder forced to oscillate transversely to the free stream has been undertaken. The effect of varying the oscillation amplitude is determined for a frequency of oscillation close to the natural shedding frequency. The three-dimensional modes that arise are identified, and the effect of the oscillation amplitude on their structure and growth rate quantified.It is shown that when the two-dimensional wake is in the 2S configuration (which is similar to the Kármán vortex street), the three-dimensional modes that arise are similar in nature and symmetry structure to the modes in the wake of a fixed cylinder. These modes are known as modes A, B and QP and occur in this order with increasing Re. However, increasing the amplitude of oscillation causes the critical Reynolds number for mode A to increase significantly, to the point where mode B becomes critical before mode A. The critical wavelength for mode A is also affected by the oscillation, becoming smaller with increasing amplitude. Elliptic instability theory is shown also to predict this trend, providing further support that mode A primarily arises as a result of an elliptic instability.At higher oscillation amplitudes, the spatio-temporal symmetry of the two-dimensional wake changes and it takes on the P + S configuration, with a pair of vortices on one side of the wake and a single vortex on the other side, for each oscillation cycle. With the onset of this configuration, modes A, B and QP cease to exist. It is shown that two new three-dimensional modes arise from this base flow, which we call modes SL and SS. Both of these modes are subharmonic, repeating over two base-flow periods. Also, either mode can be the first to become critical, depending on the amplitude of oscillation of the cylinder.The emergence of these two new modes, as well as the reversal of the order of inception of the three-dimensional modes A and B, leads to the observation that for an oscillating cylinder wake there are four different modes that can lead the transition to three-dimensionality, depending on the amplitude of oscillation. Therefore this type of flow provides a good example for studying the effect of mode-order inception on the path taken to turbulence in bluff-body wakes.For the range of amplitudes studied, the maximum Re value for which the flow remains two-dimensional is 280.


2001 ◽  
Vol 442 ◽  
pp. 67-88 ◽  
Author(s):  
SEUNG-JIN BAEK ◽  
SANG BONG LEE ◽  
HYUNG JIN SUNG

A systematic numerical analysis is performed for superharmonic excitations in a wake where a circular cylinder is rotationally oscillated in time. Emphasis is placed on identifying the secondary and tertiary lock-on in the forced wakes. The frequency responses are scrutinized by measuring the lift coefficient (CL). A direct numerical simulation has been conducted to portray the unsteady dynamics of wake flows behind a circular cylinder. The Reynolds number based on the diameter is Re = 106, and the forcing magnitude is 0.10 [les ] Ωmax [les ] 0.40. The tertiary lock-on is observed, where the shedding frequency (St0) is one third of the forcing frequency (Sf), i.e. the 1/3 subharmonic lock-on. The phase shift of CL with respect to the forcing frequency is observed. It is similar to that of the primary lock-on. However, in the secondary superharmonic excitation, modulated oscillations are observed, i.e. the lock-on does not exist. As Ωmax increases, St0 is gradually shifted from the natural shedding frequency (St*0) to lower values. The magnitudes and phases of Sf and St0 are analysed by the phase diagram. The vorticity contours are employed to examine the vortex formation mode against the forcing conditions.


2015 ◽  
Vol 783 ◽  
pp. 567-604 ◽  
Author(s):  
Trushar B. Gohil ◽  
Arun K. Saha ◽  
K. Muralidhar

The bifurcation and the blooming of jets have been numerically investigated at moderate Reynolds numbers. The study is motivated by a review article of Reynolds et al. (Annu. Rev. Fluid Mech., vol. 35, 2003, pp. 295–315) in which flow visualization images of jet blooming have been discussed, when the flow is subjected to inflow perturbations. Dual-mode perturbation, a combination of axisymmetric and helical excitations, has been used at the inflow plane to control the jet structures. In addition to the excitation frequency ratio, the effects of small-scale perturbation, excitation amplitude and initial momentum thickness have been examined. Results obtained at a Reynolds number of 2000 show that the number of branches formed in the blooming jet is strongly dependent on the excitation frequency ratio. For frequency ratios of 2, 2.5, 2.25, 2.4 and 2.22, the number of branches seen is 2, 5, 9, 12 and 20 respectively. In a blooming jet, the offset angle lies in the range 140°–180°. An equal number of branches is seen in the time-averaged flow field as well. The range of excitation frequency of the axisymmetric mode of perturbation is found to be $0.45<\mathit{St}_{D}<0.525$, with an excitation frequency ratio range of $2<R_{f}<2.6$, for which blooming jets are formed. The role of inlet shear layer thickness is less important as far as the blooming jet is concerned, while increasing excitation amplitude increases entrainment. Time-averaged data show that the blooming patterns persist in time, showing a substantial increase in spreading and entrainment.


2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Sang Bong Lee

Two-dimensional (2D) numerical simulations of multiphase flows past a circular cylinder close to free surface waves were performed to investigate an interaction of vortex formation around a cylinder with periodic waves by utilizing waves2Foam. The lock-on responses of lift coefficient at low frequencies were lower than those of the natural response due to the existence of “out-of-phase” between the fluctuations of lift coefficient by vortex formation and the vertical force fluctuations by wave motions. The resonant effect of an external excitation by the periodic waves on the lift coefficient fluctuations was not significant despite the occurrence of lock-on.


2019 ◽  
Vol 15 (S356) ◽  
pp. 348-350
Author(s):  
Eva Šrámková ◽  
K. Goluchová ◽  
G. Török ◽  
Marek A. Abramowicz ◽  
Z. Stuchlík ◽  
...  

AbstractA strong quasi-periodic modulation has recently been revealed in the X-ray flux of the X-ray source XMMUJ134736.6+173403. The two observed twin-peak quasiperiodic oscillations (QPOs) exhibit a 3:1 frequency ratio and strongly support the evidence for the presence of an active galactic nucleus black hole (AGN BH). It has been suggested that detections of twin-peak QPOs with commensurable frequency ratios and scaling of their periods with BH mass could provide the basis for a method intended to determine the mass of BH sources, such as AGNs. Assuming the orbital origin of QPOs, we calculate the upper and lower limit on the AGN BH mass M, reaching M ≍ 107–109M⊙. Compared to mass estimates of other sources, XMMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on the AGN BH mass obtained from the QPO observations.


2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Farzam Mortazavi ◽  
Alan Palazzolo

Circumferentially grooved, annular liquid seals typically exhibit good whirl frequency ratios (WFRs) and leakage reduction, yet their low effective damping can lead to instability. The current study investigates the rotordynamic behavior of a 15-step groove-on-rotor annular liquid seal by means of computational fluid dynamics (CFD), in contrast to the previous studies which focused on a groove-on-stator geometry. The seal dimensions and working conditions have been selected based on experiments of Moreland and Childs (2016, “Influence of Pre-Swirl and Eccentricity in Smooth Stator/Grooved Rotor Liquid Annular Seals, Measured Static and Rotordynamic Characteristics,” M.Sc. thesis, Texas A&M University, College Station, TX). The frequency ratios as high as four have been studied. Implementation of pressure-pressure inlet and outlet conditions make the need for loss coefficients at the entrance and exit of the seal redundant. A computationally efficient quasi-steady approach is used to obtain impedance curves as functions of the excitation frequency. The effectiveness of steady-state CFD approach is validated by comparison with the experimental results of Moreland and Childs. Results show good agreement in terms of leakage, preswirl ratio (PSR), and rotordynamic coefficients. It was found that PSR will be about 0.3–0.4 at the entrance of the seal in the case of radial injection, and outlet swirl ratio (OSR) always converges to values near 0.5 for current seal and operational conditions. The negative value of direct stiffness coefficients, large cross-coupled stiffness coefficients, and small direct damping coefficients explains the destabilizing nature of these seals. Finally, the influence of surface roughness on leakage, PSR, OSR, and stiffness coefficients is discussed.


Author(s):  
Hariprasad Chakkalaparambil Many ◽  
Vishnu Chandar Srinivasan ◽  
Ajith Kumar Raghavan

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.


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