Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

1992 ◽  
Vol 238 ◽  
pp. 1-30 ◽  
Author(s):  
George Em Karniadakis ◽  
George S. Triantafyllou
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Period Doubling ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Near Wake ◽  
Vortex Filaments ◽  
Average Flow ◽  
Time Average

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

Three-Dimensional Vortex Structure in a Leading-Edge Separation Bubble at Moderate Reynolds Numbers

1991 ◽  
Vol 113 (3) ◽  
pp. 405-410 ◽  
Author(s):  
Kyuro Sasaki ◽  
Masaru Kiya
Keyword(s):  
Reynolds Number ◽  
Separation Bubble ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Vortex Filaments ◽  
Separated Shear Layer ◽  
Hydrogen Bubbles ◽  
Edge Separation

This paper describes the results of a flow visualization study which concerns three-dimensional vortex structures in a leading-edge separation bubble formed along the sides of a blunt flat plate. Dye and hydrogen bubbles were used as tracers. Reynolds number (Re), based on the plate thickness, was varied from 80 to 800. For 80 < Re < 320, the separated shear layer remains laminar up to the reattachment line without significant spanwise distortion of vortex filaments. For 320 < Re < 380, a Λ-shaped deformation of vortex filaments appears shortly downstream of the reattachment and is arranged in-phase in the downstream direction. For Re > 380, hairpin-like structures are formed and arranged in a staggered manner. The longitudinal and spanwise distances of the vortex arrangement are presented as functions of the Reynolds number.

scholarly journals Localised turbulence in a circular pipe flow with gradual expansion

2015 ◽  
Vol 771 ◽  
Author(s):  
Kamal Selvam ◽  
Jorge Peixinho ◽  
Ashley P. Willis
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Circular Pipe ◽  
Recirculation Region ◽  
Circular Pipe Flow ◽  
Gradual Expansion

We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a gradual expansion. At the inlet, a parabolic velocity profile is applied together with a constant finite-amplitude perturbation to represent experimental imperfections. Initially, at low Reynolds number, the solution is steady. As the Reynolds number is increased, the length of the recirculation region near the wall grows linearly. Then, at a critical Reynolds number, a symmetry-breaking bifurcation occurs, where linear growth of asymmetry is observed. Near the point of transition to turbulence, the flow experiences oscillations due to a shear layer instability for a narrow range of Reynolds numbers. At higher Reynolds numbers, the recirculation region breaks into a turbulent state which remains spatially localised and unchanged when the perturbation is removed from the flow. Spatial correlation analysis suggests that the localised turbulence in the gradual expansion possesses a different flow structure from the turbulent puff of uniform pipe flow.

scholarly journals Transition to turbulence in an elliptic vortex

1996 ◽  
Vol 307 ◽  
pp. 43-62 ◽  
Author(s):  
T. S. Lundgren ◽  
N. N. Mansour
Keyword(s):  
Swirling Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Periodic Wave ◽  
Transition To Turbulence ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Secondary Instabilities ◽  
Vortex Tubes

Stability and transition to turbulence are studied in a simple incompressible two-dimensional bounded swirling flow with a rectangular planform – a vortex in a box. This flow is unstable to three-dimensional disturbances. The instability takes the form of counter-rotating swirls perpendicular to the axis which bend the vortex into a periodic wave. As these swirls grow in amplitude the primary vorticity is compressed into thin vortex layers. These develop secondary instabilities which roll up into vortex tubes. In this way the flow attains a turbulent state which is populated by intense elongated vortex tubes and weaker vortex layers which spiral around them. The flow was computed at two Reynolds numbers by spectral methods with up to 2563 resolution. At the higher Reynolds number broad three-dimensional shell-averaged energy spectra are found with nearly a decade of Kolmogorov k−5/3 law and small-scale isotropy.

The wake behind a cylinder rolling on a wall at varying rotation rates

2010 ◽  
Vol 648 ◽  
pp. 225-256 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Number Range ◽  
Rotation Rates ◽  
Transition Mechanism ◽  
Three Dimensional Simulations

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

Global frequency selection in the observed time-mean wakes of circular cylinders

2008 ◽  
Vol 601 ◽  
pp. 425-441 ◽  
Author(s):  
MOSES KHOR ◽  
JOHN SHERIDAN ◽  
MARK C. THOMPSON ◽  
KERRY HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Circular Cylinders ◽  
Near Wake ◽  
Mean Velocity ◽  
Number Range ◽  
Wake Instability ◽  
Karman Vortex

Observations have been made of the time-mean velocity profile at midspan in the near-wake of circular cylinders at moderate Reynolds numbers between 600 and 4600, well beyond the Reynolds number of approximately 200 at which the wake becomes three-dimensional. The measured profiles are found to be represented quite accurately by a family of function profiles with known linear instability characteristics. The complex instability frequency is then determined as a function of wake position, using the function profiles. In general, the near wake undergoes a transition from convective to absolute instability; the distance downstream to the point of transition is found to increase over the Reynolds number range investigated. The emergence of a significant region of convective instability is consistent with the known appearance of Bloor–Gerrard vortices. The selected frequency of the wake instability is determined by the saddle-point criterion; the Strouhal numbers for Bénard–von Kármán vortex shedding are found to compare well with the values in the literature.

A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop

2000 ◽  
Vol 411 ◽  
pp. 325-350 ◽  
Author(s):  
SAEED MORTAZAVI ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Poiseuille Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Lateral Position ◽  
Physical Parameters ◽  
Computational Domain ◽  
Two Dimensional ◽  
Lateral Migration

The cross-stream migration of a deformable drop in two-dimensional Hagen–Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (< 1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For viscosity ratio 0.125 a drop moves toward the centre of the channel, while for ratio 1.0 it moves away from the centre until halted by wall repulsion. The rate of migration increases with the deformability of the drop. At higher Reynolds numbers (5–50), the drop either moves to an equilibrium lateral position about halfway between the centreline and the wall – according to the so-called Segre–Silberberg effect or it undergoes oscillatory motion. The steady-state position depends only weakly on the various physical parameters of the flow, but the length of the transient oscillations increases as the Reynolds number is raised, or the density of the drop is increased, or the viscosity of the drop is decreased. Once the Reynolds number is high enough, the oscillations appear to persist forever and no steady state is observed. The numerical results are in good agreement with experimental observations, especially for drops that reach a steady-state lateral position. Most of the simulations assume that the flow is two-dimensional. A few simulations of three-dimensional flows for a modest Reynolds number (Re = 10), and a small computational domain, confirm the behaviour seen in two dimensions. The equilibrium position of the three-dimensional drop is close to that predicted in the simulations of two-dimensional flow.

Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers

2004 ◽  
Vol 126 (3) ◽  
pp. 362-374 ◽  
Author(s):  
G. Biswas ◽  
M. Breuer ◽  
F. Durst
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Wall Jets ◽  
Number Range ◽  
Reynolds Number Range ◽  
Concave Corner

This paper is concerned with the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0. A literature survey was carried out and it was found that the flow shows a strong two-dimensional behavior, on the plane of symmetry, for Reynolds numbers ReD=ρUbD/μ below approximately 400 (Ub=bulk velocity and D=hydraulic diameter). In this Reynolds number range, two-dimensional predictions were carried out to provide information on the general integral properties of backward-facing step flows, on mean velocity distributions and streamlines. Information on characteristic flow patterns is provided for a wide Reynolds number range, 10−4⩽ReD⩽800. In the limiting case of ReD→0, a sequence of Moffatt eddies of decreasing size and intensity is verified to exist in the concave corner also at ReD=1. The irreversible pressure losses are determined for various Reynolds numbers as a function of the expansion ratio. The two-dimensional simulations are known to underpredict the primary reattachment length for Reynolds numbers beyond which the actual flow is observed to be three-dimensional. The spatial evolution of jet-like flows in both the streamwise and the spanwise direction and transition to three-dimensionality were studied at a Reynolds number ReD=648. This three-dimensional analysis with the same geometry and flow conditions as reported by Armaly et al. (1983) reveals the formation of wall jets at the side wall within the separating shear layer. The wall jets formed by the spanwise component of the velocity move towards the symmetry plane of the channel. A self-similar wall-jet profile emerges at different spanwise locations starting with the vicinity of the side wall. These results complement information on backward-facing step flows that is available in the literature.

Three-dimensional flow over two spheres placed side by side

1993 ◽  
Vol 246 ◽  
pp. 465-488 ◽  
Author(s):  
Inchul Kim ◽  
Said Elghobashi ◽  
William A. Sirignano
Keyword(s):  
Reynolds Number ◽  
Vortical Structure ◽  
Three Dimensional ◽  
Numerical Data ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Confined Flow ◽  
Small Spacing

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.

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