Time evolution of laminar flow over a three-dimensional backward-facing step

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.

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Mixed Convection Adjacent to 3-D Backward-Facing Step

10.1115/imece2000-1408 ◽

2000 ◽

Author(s):

A. Li ◽

B. F. Armaly

Keyword(s):

Heat Flux ◽

Nusselt Number ◽

Mixed Convection ◽

Buoyancy Force ◽

Three Dimensional ◽

The Other ◽

Convection Flow ◽

Backward Facing Step ◽

Grashof Number ◽

Recirculating Flow

Abstract Results from three-dimensional numerical simulation of laminar, buoyancy assisting, mixed convection airflow adjacent to a backward-facing step in a vertical rectangular duct are presented. The Reynolds number, and duct geometry were kept constant at Re = 200, AR = 8, ER = 2, and S = 1 cm. Heat flux at the wall downstream from the step was kept uniform, but its magnitude was varied to cover a Grashof number (Gr) range between 0.0 to 4000. All the other walls in the duct were kept at adiabatic condition. The flow, upstream of the step, is treated as fully developed and isothermal. The relatively small aspect ratio of the channel is selected specifically to focus on the developments of the three-dimensional mixed convection flow in the separated and reattached flow regions downstream from the step. The presented results focus on the effects of increasing the buoyancy force, by increasing the uniform wall heat flux, on the three-dimensional flow and heat transfer characteristics. The flow and thermal fields are symmetric about the duct’s centerline. Vortex generated near the sidewall, is the major contributor to the three dimensional behavior in the flow domain, and that feature increases as the Grashof number increases. Increasing the Grashof number results in an increase in the Nusselt number, the size of the secondary recirculating flow region, the size of the sidewall vortex, and the spanwise flow from the sidewall toward the center of the channel. On the other hand, the size of the primary reattachment region decreases with increasing the Grashof number. That region lifts away and partially detaches from the downstream wall at high Grashof number flow. The maximum Nusselt number occurs near the sidewalls and not at the center of the channel. The effects of the buoyancy force on the distributions of the three-velocity components, temperature, reattachment region, friction coefficient, and Nusselt number are presented, and compared with 2-D results.

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Recurrence relations and time evolution in the three-dimensional Sawada model

Physical Review B ◽

10.1103/physrevb.30.6756 ◽

1984 ◽

Vol 30 (11) ◽

pp. 6756-6758 ◽

Cited By ~ 14

Author(s):

M. Howard Lee ◽

J. Hong

Keyword(s):

Time Evolution ◽

Recurrence Relations ◽

Three Dimensional

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Study of a temperature gradient metamorphism of snow from 3-D images: time evolution of microstructures, physical properties and their associated anisotropy

The Cryosphere ◽

10.5194/tc-8-2255-2014 ◽

2014 ◽

Vol 8 (6) ◽

pp. 2255-2274 ◽

Cited By ~ 27

Author(s):

N. Calonne ◽

F. Flin ◽

C. Geindreau ◽

B. Lesaffre ◽

S. Rolland du Roscoat

Keyword(s):

Temperature Gradient ◽

Physical Properties ◽

Time Evolution ◽

Three Dimensional ◽

Vertical Direction ◽

Large Set ◽

Correlation Lengths ◽

Snow Properties ◽

Cold Room ◽

Anisotropy Coefficients

Abstract. We carried out a study to monitor the time evolution of microstructural and physical properties of snow during temperature gradient metamorphism: a snow slab was subjected to a constant temperature gradient in the vertical direction for 3 weeks in a cold room, and regularly sampled in order to obtain a series of three-dimensional (3-D) images using X-ray microtomography. A large set of properties was then computed from this series of 3-D images: density, specific surface area, correlation lengths, mean and Gaussian curvature distributions, air and ice tortuosities, effective thermal conductivity, and intrinsic permeability. Whenever possible, specific attention was paid to assess these properties along the vertical and horizontal directions, and an anisotropy coefficient defined as the ratio of the vertical over the horizontal values was deduced. The time evolution of these properties, as well as their anisotropy coefficients, was investigated, showing the development of a strong anisotropic behavior during the experiment. Most of the computed physical properties of snow were then compared with two analytical estimates (self-consistent estimates and dilute beds of spheroids) based on the snow density, and the size and anisotropy of the microstructure through the correlation lengths. These models, which require only basic microstructural information, offer rather good estimates of the properties and anisotropy coefficients for our experiment without any fitting parameters. Our results highlight the interplay between the microstructure and physical properties, showing that the physical properties of snow subjected to a temperature gradient cannot be described accurately using only isotropic parameters such as the density and require more refined information. Furthermore, this study constitutes a detailed database on the evolution of snow properties under a temperature gradient, which can be used as a guideline and a validation tool for snow metamorphism models at the micro- or macroscale.

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Heat Transfer for Laminar Flow in Spiral Ducts of Rectangular Cross Section

Journal of Heat Transfer ◽

10.1115/1.1857950 ◽

2005 ◽

Vol 127 (3) ◽

pp. 352-356 ◽

Cited By ~ 20

Author(s):

Michael W. Egner ◽

Louis C. Burmeister

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Laminar Flow ◽

Cross Section ◽

Rectangular Cross Section ◽

Three Dimensional ◽

Radius Of Curvature ◽

Dean Number ◽

Aspect Ratios ◽

Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

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