The plane Symmetric sudden-expansion flow at low Reynolds numbers
TL;DR: In this article, velocity measurements and numerical predictions are presented for the flow through a plane nominally two-dimensional duct with a Symmetric sudden expansion of area ratio 1:2.
Abstract: Detailed velocity measurements and numerical predictions are presented for the flow through a plane nominally two-dimensional duct with a Symmetric sudden expansion of area ratio 1:2. Both the experiments and the predictions confirm a symmetry-breaking bifurcation of the flow leading to one long and one short Separation zone for channel Reynolds numbers above 125, based on the upstream channel height and the maximum flow velocity upstream. With increasing Reynolds numbers above this value, the short separated region remains approximately constant in length whereas the long region increases in length.The experimental data were obtained using a one-component laser-Doppler anemometer at many Reynolds number values, with more extensive measurements being performed for the three Reynolds numbers 70, 300 and 610. Predictions were made using a finite volume method and an explicit quadratic Leith type of temporal discretization. In general, good agreement was found between measured and predicted velocity profiles for all Reynolds numbers investigated.
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TL;DR: In this article, the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0 was investigated.
Abstract: 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.
259 citations
TL;DR: In this paper, a numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out, and the results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers.
Abstract: A numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out. Computations were performed for various Reynolds number and expansion ratios. The results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers. The computations indicated that the critical Reynolds number of the symmetry‐breaking bifurcation reduces when increasing the expansion ratio while the flow regains symmetry downstream of an initial channel length. The flow asymmetries were verified by comparing several discretization schemes up to fourth order of accuracy as well as various iterative solvers.
218 citations
TL;DR: In this article, the design and operation of a liquid core liquid-cladding (L2) lens formed by the laminar flow of three streams of liquids in a microchannel whose width expands laterally in the region where the lens forms is described.
Abstract: This paper describes the design and operation of a liquid-core liquid-cladding (L2) lens formed by the laminar flow of three streams of liquids in a microchannel whose width expands laterally in the region where the lens forms. Two streams of liquid with a lower refractive index (the cladding) sandwich a stream of liquid with a higher refractive index (the core). As the core stream enters the expansion chamber, it widens and becomes biconvex in shape, for some rates of flow. This biconvex fluidic element focuses light. Manipulating the relative rates of flow of the streams reconfigures the shape, and therefore the focal distance, of the L2 lens. This paper also describes a technique for beam tracing, and for characterization of a lens in an enclosed micro-scale optical system. The use of a cladding liquid with refractive index matched to that of the material used in the fabrication of the microfluidic system (here, poly(dimethylsiloxane)) improves the quality of the focused beam.
189 citations
TL;DR: In this paper, the flow fields in two-dimensional channels with discontinuous expansions are studied numerically to understand how the channel expansion ratio influences the symmetric and nonsymmetric solutions that are known to occur.
Abstract: The flowfields in two-dimensional channels with discontinuous expansions are studied numerically to understand how the channel expansion ratio influences the symmetric and nonsymmetric solutions that are known to occur. For improved confidence and understanding, two distinct numerical techniques are used. The general flowfield characteristics in both symmetric and asymmetric regimes are ascertained by a time-marching finite difference procedure. The flowfields and the bifurcation structure of the steady solutions of the Navier-Stokes equations are determined independently using the finite element technique. The two procedures are then compared both as to their predicted critical Reynolds numbers and the resulting flowfield characteristics. Following this, both numerical procedures are compared with experiments.
142 citations
Cites background from "The plane Symmetric sudden-expansio..."
...been observed to change from a stable symmetric jet to a stable asymmetric jet with increasing Reynolds number [1]{[6]....
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...In addition, Durst, Pereira & Tropea [6] have reported a combined numerical-experimental study of a 1:2 expansion ratio channel....
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TL;DR: In this article, the authors present a numerical investigation of instability in non-Newtonian flows through a sudden expansion, which is manifested by a symmetry breaking of the flow separation and the onset of the instability depends on the specific parameters involved in each model's constitutive equation.
Abstract: The paper presents a numerical investigation of instabilities occurring in non-Newtonian flows through a sudden expansion. Three non-Newtonian models, used in the literature for simulating the rheological behaviour of blood, are employed, namely the Casson, Power-Law, and Quemada models. The computations reveal that similar to Newtonian flow through a suddenly expanded channel, an instability also occurs in non-Newtonian flows. The instability is manifested by a symmetry breaking of the flow separation. The onset of the instability depends on the specific parameters involved in each model’s constitutive equation. The investigation encompasses a parametric study for each model, specifically the critical values at which transition from stable to unstable flow occurs. Due to the fact that for each of the Casson and Quemada models, two characteristic flow parameters exist, the relation between the critical values for each of these parameters is also examined.
116 citations
References
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Book•
01 Jan 1980
TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.
Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.
21,858 citations
TL;DR: In this paper, a convective modeling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencings.
4,190 citations
01 Jan 1979
2,299 citations
TL;DR: In this paper, the velocity distribution and reattachment length of a single backward-facing step mounted in a two-dimensional channel were measured using laser-Doppler measurements.
Abstract: Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.Although the high aspect ratio of the test section (1:36) ensured that the oncoming flow was fully developed and two-dimensional, the experiments showed that the flow downstream of the step only remained two-dimensional at low and high Reynolds numbers.The present study also included numerical predictions of backward-facing step flow. The two-dimensional steady differential equations for conservation of mass and momentum were solved. Results are reported and are compared with experiments for those Reynolds numbers for which the flow maintained its two-dimensionality in the experiments. Under these circumstances, good agreement between experimental and numerical results is obtained.
1,637 citations
TL;DR: In this paper, the authors investigated the dynamic characteristics of the pressure and velocity fields of the unsteady incompressible laminar wake behind a circular cylinder, and the initiation mechanism for vortex shedding and evaluation of the body forces are presented for Reynolds-number values of 100, 200 and 1000.
Abstract: The dynamic characteristics of the pressure and velocity fields of the unsteady incompressible laminar wake behind a circular cylinder are investigated numerically and analysed physically. The governing equations, written in a velocity—pressure formulation and in conservative form, are solved by a predictor—corrector pressure method, a finite-volume second-order-accurate scheme and an alternating-direction-implicit (ADI) procedure. The initiation mechanism for vortex shedding and the evaluation of the unsteady body forces are presented for Reynolds-number values of 100, 200 and 1000.The vortex shedding is generated by a physical perturbation imposed numerically for a short time. The flow transition becomes periodic after a transient time interval. The frequency of the drag and lift oscillations agree well with the experimental data.The study of the interactions of the unsteady pressure and velocity fields shows the phase relations between the pressure and velocity, and the influence of different factors: the strongly rotational viscous region, the convection of the eddies and the almost inviscid flow.The interactions among the different scales of structures in the near wake are also studied, and in particular the time-dependent evolution of the secondary eddies in relation to the fully developed primary ones is analysed.
779 citations