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.

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.

Magnetic Field Effects On Backward-facing Step Flow of Ferrofluids

2021 ◽  
Author(s):  
Wenming Yang ◽  
Boshi Fang ◽  
Beiying Liu
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Magnetic Field Effects ◽  
Backward Facing Step ◽  
Number Range ◽  
Concave Corner ◽  
Small Reynolds Numbers ◽  
Recirculation Length

Abstract Backward-facing step (BFS) flow is a benchmark case study in fluid mechanics. Its control by means of electromagnetic actuation has attracted great interest in recent years. This paper focuses on the effects of a uniform stationary magnetic field on the laminar ferrofluid BFS flows for the Reynolds number range 0.1=Re=400 and different expansion ratios. The coupled ferrohydrodynamic equations, including the microscopically derived magnetization equation, for a two-dimensional domain are solved numerically by an Open FOAM solver after validation and a test of accuracy. The application of a magnetic field causes the corner vortices in the concave corner behind the step to be retracted compared with their positions in the absence of a magnetic field. The maximum percentage of the normalized decrease in length of these eddies reaches 41.23% in our simulations. For small Reynolds numbers (<10), the flow separation points on the convex corner are lowered in the presence of a magnetic field. Furthermore, the dimensionless total pressure drop between the channel inlet and outlet decreases almost linearly with Reynolds number Re, but the drop is greater when a magnetic field is applied. On the whole, the normalized recirculation length of the corner vortex increases nonlinearly with increasing magnetic Reynolds number Rem and Brownian Péclet number Pe, but it tends to constant values in the limits Re ≪ 1 and Re ≫ 1.

scholarly journals Three-dimensional instability in flow over a backward-facing step

2002 ◽  
Vol 473 ◽  
pp. 167-190 ◽  
Author(s):  
DWIGHT BARKLEY ◽  
M. GABRIELA M. GOMES ◽  
RONALD D. HENDERSON
Keyword(s):  
Reynolds Number ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Linear Instability ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Computational Stability ◽  
Two Dimensional Flow

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

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.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

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.

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