Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies

1997 ◽  
Vol 351 ◽  
pp. 167-199 ◽  
Author(s):  
S. BALACHANDAR ◽  
R. MITTAL ◽  
F. M. NAJJAR
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Vortex Shedding ◽  
Reynolds Numbers ◽  
Recirculation Region ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Stress Components ◽  
The Mean

The properties of the time- and span-averaged mean wake recirculation region are investigated in separated flows over several different two-dimensional bluff bodies. Ten different cases are considered and they divide into two groups: cylindrical geometries of circular, elliptic and square cross-sections and the normal plate. A wide Reynolds number range from 250 to 140000 is considered, but in all the cases the attached portion of the boundary layer remains laminar until separation. The lower Reynolds number data are from direct numerical simulations, while the data at the higher Reynolds number are obtained from large-eddy simulation and the experimental work of Cantwell & Coles (1983), Krothapalli (1996, personal communication), Leder (1991) and Lyn et al. (1995). Unlike supersonic and subsonic separations with a splitter plate in the wake, in all the cases considered here there is strong interaction between the shear layers resulting in Kármán vortex shedding. The impact of this fundamental difference on the distribution of Reynolds stress components and pressure in relation to the mean wake recirculation region (wake bubble) is considered. It is observed that in all cases the contribution from Reynolds normal stress to the force balance of the wake bubble is significant. In fact, in the cylinder geometries this contribution can outweigh the net force from the shear stress, so that the net pressure force tends to push the bubble away from the body. In contrast, in the case of normal plate, owing to the longer wake, the net contribution from shear stress outweighs that from the normal stress. At higher Reynolds numbers, separation of the Reynolds stress components into incoherent contributions provides more insight. The behaviour of the coherent contribution, arising from the dominant vortex shedding, is similar to that at lower Reynolds numbers. The incoherent contribution to Reynolds stress, arising from small-scale activity, is compared with that of a canonical free shear layer. Based on these observations a simple extension of the wake model (Sychev 1982; Roshko 1993a, b) is proposed.

Vortex Shedding From a Bluff Body Adjacent to a Plane Sliding Wall

1991 ◽  
Vol 113 (3) ◽  
pp. 384-398 ◽  
Author(s):  
M. P. Arnal ◽  
D. J. Goering ◽  
J. A. C. Humphrey
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Solid Wall ◽  
Reynolds Numbers ◽  
Careful Examination ◽  
Recirculation Region ◽  
Stream Velocity ◽  
Flow Past ◽  
Lower Reynolds Number

The characteristics of the flow around a bluff body of square cross-section in contact with a solid-wall boundary are investigated numerically using a finite difference procedure. Previous studies (Taneda, 1965; Kamemoto et al., 1984) have shown qualitatively the strong influence of solid-wall boundaries on the vortex-shedding process and the formation of the vortex street downstream. In the present study three cases are investigated which correspond to flow past a square rib in a freestream, flow past a rib on a fixed wall and flow past a rib on a sliding wall. Values of the Reynolds number studied ranged from 100 to 2000, where the Reynolds number is based on the rib height, H, and bulk stream velocity, Ub. Comparisons between the sliding-wall and fixed-wall cases show that the sliding wall has a significant destabilizing effect on the recirculation region behind the rib. Results show the onset of unsteadiness at a lower Reynolds number for the sliding-wall case (50 ≤ Recrit ≤100) than for the fixed-wall case (Recrit≥100). A careful examination of the vortex-shedding process reveals similarities between the sliding-wall case and both the freestream and fixed-wall cases. At moderate Reynolds numbers (Re≥250) the sliding-wall results show that the rib periodically sheds vortices of alternating circulation in much the same manner as the rib in a freestream; as in, for example, Davis and Moore [1982]. The vortices are distributed asymmetrically downstream of the rib and are not of equal strength as in the freestream case. However, the sliding-wall case shows no tendency to develop cycle-to-cycle variations at higher Reynolds numbers, as observed in the freestream and fixed-wall cases. Thus, while the moving wall causes the flow past the rib to become unsteady at a lower Reynolds number than in the fixed-wall case, it also acts to stabilize or “lock-in” the vortex-shedding frequency. This is attributed to the additional source of positive vorticity immediately downstream of the rib on the sliding wall.

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.

Turbulence characteristics of the boundary layer on a rotating disk

1994 ◽  
Vol 266 ◽  
pp. 175-207 ◽  
Author(s):  
Howard S. Littell ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Structural Model ◽  
Rotating Disk ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Dimensional Boundary ◽  
The Mean

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.

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.

The Unsteady Lift on Bluff Cylindrical Bodies in Unsteady Flow

1982 ◽  
Vol 33 (3) ◽  
pp. 219-236 ◽  
Author(s):  
H. Stapountzis ◽  
J.M.R. Graham
Keyword(s):  
Vortex Shedding ◽  
Elliptic Cylinder ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Mean Flow ◽  
Vortex Shedding Frequency ◽  
The Mean ◽  
Shedding Frequency ◽  
Naca 0015 ◽  
Unsteady Lift

SummaryThe unsteady lift generated on a NACA 0015 aerofoil, a D cylinder (with the flat face down-stream) and an elliptic cylinder was measured when these bodies were exposed to a flow with a two-dimensional sinusoidal upwash at reduced frequencies 0.05 to 0.8. The mean flow Reynolds numbers were in the range 1.2 × 105 to 3 × 105. Unsteady thin aerofoil theory was used in an attempt to predict the unsteady lift on the bluff bodies, as well as the aerofoil section for fequencies in the low range below the vortex shedding frequency. The results were quite accurate for the aerofoil and the D cylinder, but the aerodynamic admittance predicted by this theory for the elliptic cylinder was significantly above that measured experimentally. The movement of the two free separation points was found to play an important role in the characteristic lift behaviour of the elliptic cylinder.

scholarly journals CFD study of mass transfer in spacer filled membrane module

2012 ◽  
Vol 31 ◽  
pp. 33-41 ◽  
Author(s):  
Sharmina Hussain
Keyword(s):  
Mass Transfer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Cfd Simulations ◽  
Size And Shape ◽  
Mass Transfer Enhancement

The present paper is devoted to investigate the mass transfer in two dimensional spacer filled channels. Three different configurations of the cylindrical spacers are considered with different channel Reynolds number and mesh length. Different size and shape of formation of recirculation region, upstream and downstream of the spacers are closely observed. This recirculation regions have an important role in enhancing the mass transfer in the reattachment region. CFD simulations show that the submerged spacers have the highest efficiency with highest wall shear stress and mass transfer enhancement whilst the cavity spacer have the least performance.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10306GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 33-41

An experimental study of reverse transition in two-dimensional channel flow

1968 ◽  
Vol 31 (3) ◽  
pp. 609-623 ◽  
Author(s):  
M. A. Badri Narayanan
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Wave Number ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Lateral Direction ◽  
Reverse Transition ◽  
Lissajous Figures ◽  
The Mean ◽  
Prime 2

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$and$\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but$\overline{u^{\prime}v^{\prime}} $tends to become zero at a reasonably well-defined point. During reverse transition$\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$also decreases as the flow moves downstream and Lissajous figures taken withu’ andv’ signals confirm this trend. There is approximate similarly between$\overline{u^{\prime 2}} $profiles if the value of$\overline{u^{\prime 2}_{\max}} $and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of$\overline{u^{\prime 2}} $is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

Experimental and Computational Investigation of the Two-Dimensional Channel Flow Over Two Fences in Tandem

1988 ◽  
Vol 110 (1) ◽  
pp. 48-54 ◽  
Author(s):  
F. Durst ◽  
M. Founti ◽  
S. Obi
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Channel Flow ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Blockage Ratio ◽  
Two Dimensional ◽  
Computational Investigation ◽  
Recirculation Zones ◽  
The Mean

Measurements and computations of the mean streamwise velocity and its fluctuations are reported for an arrangement of two similar fences mounted in tandem in fully developed channel flow. The influence of Reynolds number and blockage ratio, in terms of the size and location of the primary and secondary recirculation zones, were investigated. The flow field around each fence was found to be similar to one another as well as to the corresponding single fence flow, for Reynolds numbers (based on the fence height) of up to 100. For higher Reynolds numbers, the shear layer developing from the first fence was significantly disturbed by the second fence resulting in earlier transition and higher turbulence intensities. This effect was most evident in the measured differences of the recirculation lengths downstream of each fence.

A Study of Active Control of Vortex Shedding and Wake From a Cylinder

2002 ◽  
Author(s):  
Hani H. Nigim ◽  
Kohta Shiino ◽  
Hide S. Koyama ◽  
Hyung Jin Sung
Keyword(s):  
Reynolds Number ◽  
Active Control ◽  
Vortex Shedding ◽  
Control Method ◽  
Sound Field ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Phase Lag ◽  
Field Velocity ◽  
The Mean

The control of vortex shedding and wake from a circular cylinder was studied experimentally at Reynolds numbers, ranging from 160 to 400, using an acoustic active control system. The investigation has been carried by, quantitatively, hot-wire to measure the mean and fluctuating velocities and, qualitatively, by using smoke-wire flow visualization technique to examine the formation of the flow field downstream of the cylinder. The present active control method is able to influence the rate of entrainment from main flow into the wake flow. When the Reynolds number is relatively small, it is the size of the cylinder and the induced sound field velocity rather than Reynolds number which are the significant parameters in determining the controlling reverse and optimum phase lag angels.

scholarly journals Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers

1989 ◽  
Vol 206 ◽  
pp. 579-627 ◽  
Author(s):  
C. H. K. Williamson
Keyword(s):  
Reynolds Number ◽  
Boundary Conditions ◽  
Vortex Shedding ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Cylinder Wake ◽  
Completely Continuous ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Central Flow

Two fundamental characteristics of the low-Reynolds-number cylinder wake, which have involved considerable debate, are first the existence of discontinuities in the Strouhal-Reynolds number relationship, and secondly the phenomenon of oblique vortex shedding. The present paper shows that both of these characteristics of the wake are directly related to each other, and that both are influenced by the boundary conditions at the ends of the cylinder, even for spans of hundreds of diameters in length. It is found that a Strouhal discontinuity exists, which is not due to any of the previously proposed mechanisms, but instead is caused by a transition from one oblique shedding mode to another oblique mode. This transition is explained by a change from one mode where the central flow over the span matches the end boundary conditions to one where the central flow is unable to match the end conditions. In the latter case, quasi-periodic spectra of the velocity fluctuations appear; these are due to the presence of spanwise cells of different frequency. During periods when vortices in neighbouring cells move out of phase with each other, ‘vortex dislocations’ are observed, and are associated with rather complex vortex linking between the cells. However, by manipulating the end boundary conditions, parallel shedding can be induced, which then results in a completely continuous Strouhal curve. It is also universal in the sense that the oblique-shedding Strouhal data (Sθ) can be collapsed onto the parallel-shedding Strouhal curve (S0) by the transformation, S0 = Sθ/cosθ, where θ is the angle of oblique shedding. Close agreement between measurements in two distinctly different facilities confirms the continuous and universal nature of this Strouhal curve. It is believed that the case of parallel shedding represents truly two-dimensional shedding, and a comparison of Strouhal frequency data is made with several two-dimensional numerical simulations, yielding a large disparity which is not clearly understood. The oblique and parallel modes of vortex shedding are both intrinsic to the flow over a cylinder, and are simply solutions to different problems, because the boundary conditions are different in each case.

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