Wake transition in the flow around a circular cylinder with a splitter plate

2014 ◽  
Vol 755 ◽  
pp. 582-602 ◽  
Author(s):  
Douglas Serson ◽  
Julio R. Meneghini ◽  
Bruno S. Carmo ◽  
Ernani V. Volpe ◽  
Rafael S. Gioria
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Strouhal Number ◽  
Three Dimensional ◽  
Period Doubling ◽  
Spectral Element ◽  
Splitter Plate ◽  
Neutral Stability ◽  
Number Curve ◽  
Wake Transition

AbstractA simple way to decrease the drag and oscillating lift forces in the flow around a circular cylinder consists of positioning a splitter plate in the wake, parallel to the flow. In this paper, the effect of the splitter plate on the wake dynamics, more specifically on the wake transition, is described in detail. First, two-dimensional and three-dimensional direct numerical simulations (DNS) using the spectral element method were used to observe the behaviour of the wake in the presence of the splitter plate. Then, a linear stability analysis based on the Floquet theory was performed in order to obtain information on how the splitter plate changes the instabilities that lead to wake transition. Simulations were carried out for several gaps between the splitter plate and the cylinder, with the Reynolds number varying in the range between 100 and 350, which corresponds to the wake transition in the flow around a circular cylinder. The results of the simulations showed a discontinuity in the Strouhal number curve that is consistent with the results available in the literature. The stability analysis showed how the splitter plate modifies the transition of the flow to a three-dimensional configuration. The splitter plate has a stabilizing effect on the flow for small gaps, delaying the appearance of three-dimensional structures to higher Reynolds numbers. Mode A and a quasi-periodic (QP) mode are observed for such small gaps. As the gap is increased the discontinuity in the Strouhal number curve also caused a clear change in the characteristics of the neutral stability curve, and the existence of an unstable period-doubling mode was observed. The onset characteristics of the unstable modes are analysed and discussed in depth.

scholarly journals Three-dimensional Floquet stability analysis of the wake of a circular cylinder

1996 ◽  
Vol 322 ◽  
pp. 215-241 ◽  
Author(s):  
Dwight Barkley ◽  
Ronald D. Henderson
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Numerical Stability Analysis ◽  
Mode A

Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 188.5±1.0. The critical spanwise wavelength is 3.96 ± 0.02 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0.822 diameters at onset. Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300.

Organization of Cylinder Wake Using a Splitter-Plate Active Flow Control

2010 ◽  
Author(s):  
Chris Weiland ◽  
Pavlos Vlachos
Keyword(s):  
Circular Cylinder ◽  
Flow Control ◽  
Strouhal Number ◽  
Active Flow Control ◽  
Leading Edge ◽  
Splitter Plate ◽  
Cylinder Wake ◽  
Time Resolved ◽  
Image Velocimetry ◽  
Active Flow

Time Resolved Digital Particle Image Velocimetry (TRDPIV) was used in conjunction with spectral analysis to study the effects of Leading Edge Blowing (LEB) flow control on the near-wake of a circular cylinder. The airfoil was placed 1.9 circular cylinder diameters downstream, effectively acting as a splitter plate. Spectral measurements of the TRDPIV results indicated that the presence of the airfoil decreased the Strouhal number from 0.19 to 0.12 as anticipated. When activated the LEB jet organized the circular cylinder wake, effectively neutralizing the effect of the splitter plate and modifying the wake so as to return the Strouhal number to 0.19. Thus the circular cylinder wake returned to its normal shedding frequency, even in the presence of the airfoil. Evidence presented in this study supports the notion that the LEB jet directly excites the circular cylinder shear layers causing instability, roll up, and subsequent vortex shedding.

Flow instabilities in the wake of a circular cylinder with parallel dual splitter plates attached

2019 ◽  
Vol 874 ◽  
pp. 299-338 ◽  
Author(s):  
Rui Wang ◽  
Yan Bao ◽  
Dai Zhou ◽  
Hongbo Zhu ◽  
Huan Ping ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Rear Surface ◽  
Three Dimensional ◽  
Spectral Element ◽  
Cylinder Wake ◽  
Flow Topology ◽  
Weakly Nonlinear ◽  
Plate Length ◽  
Splitter Plates ◽  
Mode A

In this paper, instabilities in the flow over a circular cylinder of diameter $D$ with dual splitter plates attached to its rear surface are numerically investigated using the spectral element method. The key parameters are the splitter plate length $L$, the attachment angle $\unicode[STIX]{x1D6FC}$ and the Reynolds number $Re$. The presence of the plates was found to significantly modify the flow topology, leading to substantial changes in both the primary and secondary instabilities. The results showed that the three instability modes present in the bare circular cylinder wake still exist in the wake of the present configurations and that, in general, the occurrences of modes A and B are delayed, while the onset of mode QP is earlier in the presence of the splitter plates. Furthermore, two new synchronous modes, referred to as mode A$^{\prime }$ and mode B$^{\prime }$, are found to develop in the wake. Mode A$^{\prime }$ is similar to mode A but with a quite long critical wavelength. Mode B$^{\prime }$ shares the same spatio-temporal symmetries as mode B but has a distinct spatial structure. With the exception of the case of $L/D=0.25$, mode A$^{\prime }$ persists for all configurations investigated here and always precedes the transition through mode A. The onset of mode B$^{\prime }$ occurs for $\unicode[STIX]{x1D6FC}>20^{\circ }$ with $L/D=1.0$ and for $L/D>0.5$ with $\unicode[STIX]{x1D6FC}=60^{\circ }$. The characteristics of all the transition modes are analysed, and their similarities and differences are discussed in detail in comparison with the existing modes. In addition, the physical mechanism responsible for the instability mode B$^{\prime }$ is proposed. The weakly nonlinear feature of mode B$^{\prime }$, as well as that of mode A$^{\prime }$, is assessed by employing the Landau model. Finally, selected three-dimensional simulations are performed to confirm the existence of these two new modes and to investigate the nonlinear evolution of the three-dimensional modes.

Three Dimensional Film Stability and Draw Resonance

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Zahir U. Ahmed ◽  
Roger E. Khayat
Keyword(s):  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Physical Mechanism ◽  
Three Dimensional ◽  
Neutral Stability ◽  
Film Stability ◽  
New Approach ◽  
Draw Resonance

In order to understand the effects of inertia and gravity on draw resonance and on the physical mechanism of draw resonance in three-dimensional Newtonian film casting, a linear stability analysis has been conducted. An eigenvalue problem resulting from the linear stability analysis is formulated and solved as a nonlinear two-point boundary value problem to determine the critical draw ratios. Neutral stability curves are plotted to separate the stable/unstable domain in different appropriate parameter spaces. Both inertia and gravity stabilize the process and the process is more unstable to two- than to three-dimensional disturbances. The effects of inertia and gravity on the physical mechanism of draw resonance have been investigated using the eigenfunctions from the eigenvalue problem. A new approach is introduced in order to evaluate the traveling times of kinematic waves from the perturbed thickness at the take-up, which satisfies the same stability criterion illustrating the general stability of the system.

scholarly journals Spectral Element Numerical Investigation of Flow between Three Cylinders in an Equilateral-Triangular Arrangement with Different Spacing Distances

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Zhenzhong Bao ◽  
Guoliang Qin ◽  
Wenqiang He ◽  
Yazhou Wang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Root Mean Square ◽  
Strouhal Number ◽  
Stokes Equations ◽  
Spectral Element ◽  
Mean Square ◽  
Distance Ratio ◽  
Spacing Distance ◽  
Small Spacing

Two-dimensional incompressible Navier-Stokes equations are numerically solved using the high resolution spectral element method at Reynolds number 200. The flow between three cylinders in an equilateral-triangular arrangement is investigated. The center-to-center spacing distance ratio between two circular cylinders is varied from 1.5 to 12. Present numerical results show that the flow patterns and force characteristics are the result of the combined effects of Reynolds number, spacing distance, configuration arrangement, and incident angle. For the small spacing distance ratio of 1.5, the well-known biased flow phenomenon in the gap of downstream cylinders is found. And the biased flow is bistable in our study but not monostable. A small spacing distance means lower Strouhal number, drag, and root-mean-square lift coefficients. In the medium spacing distance ratio of 4.0, the suppressed effect of vortex shedding for the presence of the side-by-side downstream cylinders disappeared. Mean drag coefficients of downstream cylinders are basically identical to the value of flow past around a single circular cylinder. For the large spacing distance ratio of 8.0, the effects between three cylinders basically disappeared. The mean drag and lift coefficients, root-mean-square lift coefficients, and Strouhal number of three cylinders are essentially equivalent to those values of a single circular cylinder.

Effect of confinement on three-dimensional stability in the wake of a circular cylinder

2009 ◽  
Vol 642 ◽  
pp. 477-487 ◽  
Author(s):  
SIMONE CAMARRI ◽  
FLAVIO GIANNETTI
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Dimensional Stability ◽  
Opposite Sign ◽  
Three Dimensional ◽  
The Body ◽  
Karman Street

This paper investigates the three-dimensional stability of the wake behind a symmetrically confined circular cylinder by a linear stability analysis. Emphasis has been placed on discussing analogies and differences with the unconfined case to highlight the role of the inversion of the von Kármán street in the nature of the three-dimensional transition. Indeed, in this flow, the vortices of opposite sign that are alternately shed from the body into the wake cross the symmetry line further downstream and they assume a final configuration which is inverted with respect to the unconfined case. It is shown that the transition to a three-dimensional state has the same space–time symmetries of the unconfined case, although the shape of the linearly unstable modes is affected by the inversion of the wake vortices. A possible interpretation of this result is given here.

Effect of Inclination Angle of Splitter Plate on Flow Over a Circular Cylinder

2011 ◽  
Author(s):  
Li Zhang ◽  
Lin Ding
Keyword(s):  
Circular Cylinder ◽  
Strouhal Number ◽  
Inclination Angle ◽  
Vortex Shedding ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Splitter Plate ◽  
Plate Length ◽  
Pressure Distributions ◽  
Vortex Shedding Frequency

Two-dimensional unsteady laminar flow over a circular cylinder with an attached splitter plate was investigated numerically. To see the effect of the splitter plate length and inclination angle on the pressure distributions and vortex shedding, numerical simulations were done for moderate Reynolds numbers ranging from 100 to 500 in two different splitter plate lengths (1 and 2 diameters), and the angles between splitter plate and wake centerline was changed from 0 to 45 deg. Results indicate that the wake structure and length are dependent on the inclination angle of splitter plate. Near wake length is almost unchanged when θ>25 deg. On the other hand, circular cylinder’s drag coefficient is distinctly affected by the position of vortex. And significant local peaks of the RMS lift coefficient are obtained at θ=15 deg and 5 deg for L=1D and 2D respectively. The lift force is in one direction when the inclination angle is over a critical value. In addition, the non-dimensional Strouhal number representing the vortex shedding frequency characteristics varies as a function of the angle and has peak values at θ=20 and 5 deg for L=1D and 2D respectively. And the longer splitter plate causes more decrease in the Strouhal number for θ>15 deg.

Mode C flow transition behind a circular cylinder with a near-wake wire disturbance

2013 ◽  
Vol 727 ◽  
pp. 30-55 ◽  
Author(s):  
I. Yildirim ◽  
C. C. M. Rindt ◽  
A. A. van Steenhoven
Keyword(s):  
Circular Cylinder ◽  
Particle Image ◽  
Three Dimensional ◽  
Period Doubling ◽  
Feedback Mechanism ◽  
Near Wake ◽  
Number Range ◽  
Image Velocimetry ◽  
The Wire ◽  
Secondary Vortices

AbstractThe three-dimensional transition of the flow behind a circular cylinder with a near-wake wire disturbance has been investigated experimentally. The asymmetric placement of a wire in the near-wake region of the cylinder causes an unnatural mode of shedding to occur, namely mode C. We performed flow visualization and particle image velocimetry (PIV) experiments to investigate the influence of the wire on various properties of the flow, such as the dynamics of the streamwise secondary vortices. Experiments were performed at the Reynolds number range of Re = 165–300. From these experiments, it can be concluded that mode C structures are formed as secondary streamwise vortices around the primary von Kármán vortices. The spanwise wavelength of those mode C structures is determined to be approximately two cylinder diameters. The presence of the wire also triggered the occurrence of period doubling in the wake. Each new set of mode C structures is out of phase with the previous set, i.e. doubling the shedding period. This period-doubling phenomenon is due to a feedback mechanism between the consecutively shed upper vortices.

Optimal Disturbances in Three-Dimensional Natural Convection Flows

2012 ◽  
Author(s):  
Elia Merzari ◽  
Paul Fischer ◽  
W. David Pointer
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Natural Circulation ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Spectral Element ◽  
Base Flow ◽  
The Stability ◽  
Optimal Disturbances

Buoyancy-driven systems are subject to several types of flow instabilities. To evaluate the performance of such systems it is becoming increasingly crucial to be able to predict the stability of a given base flow configuration. Traditional Modal Linear stability Analysis requires the solution of very large eigenvalue systems for three-dimensional flows, which make this problem difficult to tackle. An alternative to modal Linear stability Analysis is the use of adjoint solvers [1] in combination with a power iteration [2]. Such methodology allows for the identification of an optimal disturbance or forcing and has been recently used to evaluate the stability of several isothermal flow systems [2]. In this paper we examine the extension of the methodology to non-isothermal flows driven by buoyancy. The contribution of buoyancy in the momentum equation is modeled through the Boussinesq approximation. The method is implemented in the spectral element code Nek5000. The test case is the flow is a two-dimensional cavity with differential heating and conductive walls and the natural circulation flow in a toroidal thermosiphon.

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