scholarly journals Stabilization of absolute instability in spanwise wavy two-dimensional wakes

2013 ◽  
Vol 727 ◽  
pp. 346-378 ◽  
Author(s):  
Yongyun Hwang ◽  
Jinsung Kim ◽  
Haecheon Choi
Keyword(s):  
Vortex Shedding ◽  
Bluff Body ◽  
High Efficiency ◽  
Three Dimensional ◽  
Base Flow ◽  
Absolute Instability ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Flow Modification ◽  
Wake Instability

AbstractControlling vortex shedding using spanwise-varying passive or active actuation (namely three-dimensional control) has recently been reported as a very efficient method for regulating two-dimensional bluff-body wakes. However, the mechanism of how the designed controller regulates vortex shedding is not clearly understood. To understand this mechanism, we perform a linear stability analysis of two-dimensional wakes, the base flow of which is modified with a given spanwise waviness. Absolute and convective instabilities of the spanwise wavy base flows are investigated using Floquet theory. Two types of base-flow modification are considered: varicose and sinuous. Both of these modifications attenuate absolute instability of two-dimensional wakes. In particular, the varicose modification is found to be much more effective in the attenuation than the sinuous one, and its spanwise lengths resulting in maximum attenuation show good agreement with those in three-dimensional controls. The physical mechanism of the stabilization is found to be associated with the formation of streamwise vortices from tilting of two-dimensional Kármán vortices and the subsequent tilting of these streamwise vortices by the spanwise shear in the base flow. Finally, the sensitivity of absolute instability to spanwise wavy base-flow modification is investigated. It is shown that absolute instability of two-dimensional wakes is much less sensitive to spanwise wavy base-flow modification than to two-dimensional modification. This suggests that the high efficiency observed in several three-dimensional controls is not due to the sensitive response of the wake instability to the spanwise waviness in the base flow.

Three-dimensional transition in the wake of a transversely oscillating cylinder

2007 ◽  
Vol 577 ◽  
pp. 79-104 ◽  
Author(s):  
JUSTIN S. LEONTINI ◽  
M. C. THOMPSON ◽  
K. HOURIGAN
Keyword(s):  
Bluff Body ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Cylinder Wake ◽  
Oscillating Cylinder ◽  
Single Vortex ◽  
Spatio Temporal ◽  
Mode A

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.

Aerodynamics of a two-dimensional bluff body with the cross-section of a train

2020 ◽  
Vol 23 (12) ◽  
pp. 2679-2693 ◽  
Author(s):  
Huan Li ◽  
Xuhui He ◽  
Hanfeng Wang ◽  
Si Peng ◽  
Shuwei Zhou ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Large Amplitude ◽  
High Speed ◽  
Bluff Body ◽  
Mean Amplitude ◽  
Two Dimensional ◽  
Aerodynamic Forces ◽  
Moderate Reynolds Number ◽  
Amplitude Mode

Experiments on the aerodynamics of a two-dimensional bluff body simplified from a China high-speed train in crosswinds were carried out in a wind tunnel. Effects of wind angle of attack α varying in [−20°, 20°] were investigated at a moderate Reynolds number Re = 9.35 × 104 (based on the height of the model). Four typical behaviors of aerodynamics were identified. These behaviors are attributed to the flow structure around the upper and lower halves of the model changing from full to intermittent reattachment, and to full separation with a variation in α. An alternate transition phenomenon, characterized by an alteration between large- and small-amplitude aerodynamic fluctuations, was detected. The frequency of this alteration is about 1/10 of the predominant vortex shedding. In the intervals of the large-amplitude behavior, aerodynamic forces fluctuate periodically with a strong span-wise coherence, which are caused by the anti-symmetric vortex shedding along the stream-wise direction. On the contrary, the aerodynamic forces fluctuating at small amplitudes correspond to a weak span-wise coherence, which are ascribed to the symmetric vortex shedding from the upper and lower halves of the model. Generally, the mean amplitude of the large-amplitude mode is 3 times larger than that of the small one. Finally, the effects of Reynolds number were examined within Re = [9.35 × 104, 2.49 × 105]. Strong Reynolds number dependence was observed on the model with two rounded upper corners.

Two- and Three-Dimensional Simulations of the Flow Around a Cylinder Fitted With Strakes

2012 ◽  
Author(s):  
Bruno S. Carmo ◽  
Rafael S. Gioria ◽  
Ivan Korkischko ◽  
Cesar M. Freire ◽  
Julio R. Meneghini
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
The Body ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Flow Around A Cylinder ◽  
Three Dimensional Simulations ◽  
Angle Of Rotation

Two- and three-dimensional simulations of the flow around straked cylinders are presented. For the two-dimensional simulations we used the Spectral/hp Element Method, and carried out simulations for five different angles of rotation of the cylinder with respect to the free stream. Fixed and elastically-mounted cylinders were tested, and the Reynolds number was kept constant and equal to 150. The results were compared to those obtained from the simulation of the flow around a bare cylinder under the same conditions. We observed that the two-dimensional strakes are not effective in suppressing the vibration of the cylinders, but also noticed that the responses were completely different even with a slight change in the angle of rotation of the body. The three-dimensional results showed that there are two mechanisms of suppression: the main one is the decrease in the vortex shedding correlation along the span, whilst a secondary one is the vortex wake formation farther downstream.

Flow past a rotationally oscillating cylinder

2013 ◽  
Vol 735 ◽  
pp. 307-346 ◽  
Author(s):  
S. Kumar ◽  
C. Lopez ◽  
O. Probst ◽  
G. Francisco ◽  
D. Askari ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Past ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Flow Visualizations ◽  
Hydrogen Bubble Technique

AbstractFlow past a circular cylinder executing sinusoidal rotary oscillations about its own axis is studied experimentally. The experiments are carried out at a Reynolds number of 185, oscillation amplitudes varying from $\mathrm{\pi} / 8$ to $\mathrm{\pi} $, and at non-dimensional forcing frequencies (ratio of the cylinder oscillation frequency to the vortex-shedding frequency from a stationary cylinder) varying from 0 to 5. The diagnostic is performed by extensive flow visualization using the hydrogen bubble technique, hot-wire anemometry and particle-image velocimetry. The wake structures are related to the velocity spectra at various forcing parameters and downstream distances. It is found that the phenomenon of lock-on occurs in a forcing frequency range which depends not only on the amplitude of oscillation but also the downstream location from the cylinder. The experimentally measured lock-on diagram in the forcing amplitude and frequency plane at various downstream locations ranging from 2 to 23 diameters is presented. The far-field wake decouples, after the lock-on at higher forcing frequencies and behaves more like a regular Bénard–von Kármán vortex street from a stationary cylinder with vortex-shedding frequency mostly lower than that from a stationary cylinder. The dependence of circulation values of the shed vortices on the forcing frequency reveals a decay character independent of forcing amplitude beyond forcing frequency of ${\sim }1. 0$ and a scaling behaviour with forcing amplitude at forcing frequencies ${\leq }1. 0$. The flow visualizations reveal that the far-field wake becomes two-dimensional (planar) near the forcing frequencies where the circulation of the shed vortices becomes maximum and strong three-dimensional flow is generated as mode shape changes in certain forcing parameter conditions. It is also found from flow visualizations that even at higher Reynolds number of 400, forcing the cylinder at forcing amplitudes of $\mathrm{\pi} / 4$ and $\mathrm{\pi} / 2$ can make the flow field two-dimensional at forcing frequencies greater than ${\sim }2. 5$.

The anatomy of the mixing transition in homogeneous and stratified free shear layers

2000 ◽  
Vol 413 ◽  
pp. 1-47 ◽  
Author(s):  
C. P. CAULFIELD ◽  
W. R. PELTIER
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Small Scale ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Free Shear Layers ◽  
Nonlinear Amplification

We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free shear layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable sublayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of shear layer evolution, with the flow Reynolds number (defined on the basis of shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified shear layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified shear layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Evolution of stream wise vortices and generation of small-scale motion in a plane mixing layer

1991 ◽  
Vol 231 ◽  
pp. 257-301 ◽  
Author(s):  
K. J. Nygaard ◽  
A. Glezer
Keyword(s):  
Surface Film ◽  
Mixing Layer ◽  
Excitation Frequency ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Base Flow ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Plane Mixing Layer ◽  
Scale Motion

The evolution of streamwise vortices in a plane mixing layer and their role in the generation of small-scale three-dimensional motion are studied in a closed-return water facility. Spanwise-periodic streamwise vortices are excited by a time-harmonic wavetrain with span wise-periodic amplitude variations synthesized by a mosaic of 32 surface film heaters flush-mounted on the flow partition. For a given excitation frequency, virtually any span wise wavelength synthesizable by the heating mosaic can be excited and can lead to the formation of streamwise vortices before the rollup of the primary vortices is completed. The onset of streamwise vortices is accompanied by significant distortion in the transverse distribution of the streamwise velocity component. The presence of inflexion points, absent in corresponding velocity distributions of the unforced flow, suggests the formation of locally unstable regions of large shear in which broadband perturbations already present in the base flow undergo rapid amplification, followed by breakdown to small-scale motion. Furthermore, as a result of spanwise-non-uniform excitation the cores of the primary vortices are significantly altered. The three-dimensional features of the streamwise vortices and their interaction with the base flow are inferred from surfaces of r.m.s. velocity fluctuations and an approximation to cross-stream vorticity using three-dimensional single component velocity data. The striking enhancement of small-scale motion and the spatial modification of its distribution, both induced by the streamwise vortices, can be related to the onset of the mixing transition.

The stability of the variable-density Kelvin–Helmholtz billow

2008 ◽  
Vol 612 ◽  
pp. 237-260 ◽  
Author(s):  
JÉRÔME FONTANE ◽  
LAURENT JOLY
Keyword(s):  
Stability Analysis ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Variable Density ◽  
Base Flow ◽  
Shear Instability ◽  
Numerical Continuation ◽  
Small Scale ◽  
Two Dimensional ◽  
Two Fluids

We perform a three-dimensional stability analysis of the Kelvin–Helmholtz (KH) billow, developing in a shear layer between two fluids with different density. We begin with two-dimensional simulations of the temporally evolving mixing layer, yielding the unsteady base flow fields. The Reynolds number is 1500 while the Schmidt and Froude numbers are infinite. Then exponentially unstable modes are extracted from a linear stability analysis performed at the saturation of the primary mode kinetic energy. The spectrum of the least stable modes exhibits two main classes. The first class comprises three-dimensional core-centred and braid-centred modes already present in the homogeneous case. The baroclinic vorticity concentration in the braid lying on the light side of the KH billow turns the flow into a sharp vorticity ridge holding high shear levels. The hyperbolic modes benefit from the enhanced level of shear in the braid whereas elliptic modes remain quite insensitive to the modifications of the base flow. In the second class, we found typical two-dimensional modes resulting from a shear instability of the curved vorticity-enhanced braid. For a density contrast of 0.5, the wavelength of the two-dimensional instability is about ten times shorter than that of the primary wave. Its amplification rate competes well against those of the hyperbolic three-dimensional modes. The vorticity-enhanced braid thus becomes the preferred location for the development of secondary instabilities. This stands as the key feature of the transition of the variable-density mixing layer. We carry out a fully resolved numerical continuation of the nonlinear development of the two-dimensional braid-mode. Secondary roll-ups due to a small-scale Kelvin–Helmholtz mechanism are promoted by the underlying strain field and develop rapidly in the compression part of the braid. Originally analysed by Reinoud et al. (Phys. Fluids, vol. 12, 2000, p. 2489) from two-dimensional non-viscous numerical simulations, this instability is shown to substantially increase the mixing.

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