Bifurcation of low Reynolds number flows in symmetric channels

Battaglia, Francine; Tavener, Simon; Kulkarni, A. K.; Merkle, Charles L.

doi:10.2514/3.13469

Cited by 36 publications

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“…14 Moreover, the vertical middle cut plane for the pressure part is similar to the 2D case. 51 It is observed that the left bifurcation mode drives the inlet flow. This behavior is in agreement with the work of Battaglia et al 51 4 Critical Reynolds numbers and bifurcation type of second and third primary bifurcation for several geometric ratios.…”

Section: Bifurcation Vectors Descriptionmentioning

confidence: 99%

Numerical bifurcation analysis for 3‐dimensional sudden expansion fluid dynamic problem

Guevel

Allain

Girault

et al. 2017

Numerical Methods in Fluids

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Summary This paper deals with bifurcation analysis methods based on the asymptotic‐numerical method. It is used to investigate 3‐dimensional (3D) instabilities in a sudden expansion. To do so, high‐performance computing is implemented in ELMER, ie, an open‐source multiphysical software. In this work, velocity‐pressure mixed vectors are used with asymptotic‐numerical method–based methods, remarks are made for the branch‐switching method in the case of symmetry‐breaking bifurcation, and new 3D instability results are presented for the sudden expansion ratio, ie, E=3. Critical Reynolds numbers for primary bifurcations are studied with the evolution of a geometric parameter. New values are computed, which reveal new trends that complete a previous work. Several kinds of bifurcation are depicted and tracked with the evolution of the spanwise aspect ratio. One of these relies on a fully 3D effect as it breaks both spanwise and top‐bottom symmetries. This bifurcation is found for smaller aspect ratios than expected. Furthermore, a critical Reynolds number is found for the aspect ratio, ie, Ai=1, which was not previously reported. Finally, primary and secondary bifurcations are efficiently detected and all post‐bifurcated branches are followed. This makes it possible to plot a complete bifurcation diagram for this 3D case.

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Section: Bifurcation Vectors Descriptionmentioning

confidence: 99%

Numerical bifurcation analysis for 3‐dimensional sudden expansion fluid dynamic problem

Guevel

Allain

Girault

et al. 2017

Numerical Methods in Fluids

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“…Earlier studies, as summarized in Table I, show that Re c for the breaking of flow symmetry (or changing from symmetric to asymmetric flow) was affected by the expansion geometry, as well as the utilized calculation methods. For instance, the numerical simulation carried out by Battaglia et al (1997) showed that Re c was close to 57-58 with E = 3. Durst et al (1974) demonstrated that the symmetry breaking occurred when Re c equalled to 56-114 with the same E value.…”

Section: Resultsmentioning

confidence: 99%

“…The flow with different Re is simulated by FVM and compared with earlier experimental and numerical results of Fearn et al (1990), Alleborn et al (1997) and Battaglia et al (1997). Firstly, one can find the value of the critical Reynolds number (Re c ) for flow in SF-ACA, where Re c specifically means that flow in the expansion zone changes from symmetrical to asymmetrical states.…”

Section: Resultsmentioning

confidence: 99%

“…In this study, Re c is 125 when E = 3 and d = 1 mm. The values of Re c acquired by The Re c -E relationship Symmetry breaking of flow has been investigated extensively in the past several decades (Fearn et al, 1990;Alleborn et al, 1997;Battaglia et al, 1997). However, as far as we know, no experimental or numerical investigations have been reported for flow with different inlet apertures in SF-ACA.…”

Section: Resultsmentioning

confidence: 99%

“…Investigation of flow through a sudden shrinking channel can be found in Denham and Patrick (1974) and Armaly et al (1983). Numerical study of flow bifurcation with low values of Re in symmetrically sudden expansion channels can be found in Battaglia et al (1997), which demonstrated that the Re c value decreased with E (E of 1.5 and 5 corresponded to Re c of 446 and 43, respectively). Macagno and Hung (1967) and Iribarne et al (1972) experimentally studied axisymmetric flow in a sudden expansion SF.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Qian

Zhan

et al. 2015

Hydrol. Process.

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Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Rec) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Rec for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Rec decreases with the increasing E, and the relationship between the logarithm of Rec and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Rec and d for a given E value is vague, and Rec becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (Ji) of J increases monotonically with Re, whereas the viscous component (Jv) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Rec, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.

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Side‐wall effects on the bifurcation of the flow through a sudden expansion

Tsui

Wang

2007

Numerical Methods in Fluids

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SUMMARYThree-dimensional computations have been performed to study the flow through a symmetric sudden expansion with an expansion ratio of 3 at low Reynolds numbers. The aspect ratio of the flow channel is allowed to vary within a wide range to examine its influence on the flow which bifurcates from a symmetric state to an asymmetric state. The results reveal that the critical Reynolds number of the symmetry-breaking bifurcation increases while the aspect ratio is reduced. The flow behaviour near the side walls is illustrated by using limiting streamlines. The origin of the singular points identifiable on the side wall can be traced back to the recirculating flows and the relevant reattachment/separation points in the core of the channel. It is seen that the determination of the exact critical Reynolds number is not trivial because it depends on how to define asymmetric flow. Computations have also been conducted to show that a slight asymmetry in the channel geometry causes a smooth transition from symmetric to non-symmetric states.

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Bifurcation of low Reynolds number flows in symmetric channels

Cited by 36 publications

References 0 publications

Numerical bifurcation analysis for 3‐dimensional sudden expansion fluid dynamic problem

Numerical bifurcation analysis for 3‐dimensional sudden expansion fluid dynamic problem

The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Side‐wall effects on the bifurcation of the flow through a sudden expansion

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