Laminar Flow of a Nonlinear Viscoplastic Fluid Through an Axisymmetric Sudden Expansion

1999 ◽  
Vol 121 (2) ◽  
pp. 488-495 ◽  
Author(s):  
Khaled J. Hammad ◽  
M. Volkan O¨tu¨gen ◽  
George C. Vradis ◽  
Engin B. Arik
Keyword(s):  
Laminar Flow ◽  
Numerical Solutions ◽  
Computational Study ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
Viscoplastic Fluid ◽  
Sudden Expansion ◽  
Test Fluid ◽  
Flow Zone ◽  
Recirculating Flow

A combined experimental and computational study was carried out to investigate the laminar flow of a nonlinear viscoplastic fluid through an axisymmetric sudden expansion. The yield-stress, power-law index, and the consistency index of the yield shear-thinning test fluid were 0.733 Pa, 0.68, and 0.33 Pa · s0.68, respectively, resulting in a Hedstrom number of 1.65. The Reynolds number ranged between 1.8 and 58.7. In addition, the flow of a Newtonian fluid through the same expansion was also studied to form a baseline for comparison. Velocity vectors were obtained on the vertical center plane using a digital particle image velocimeter (PIV). From these measurements. two-dimensional distributions of axial and radial velocity as well as the stream function were calculated covering the separated, reattached and redeveloping flow regions. These results were compared to finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations. The calculations were found to be in good agreement with the experimental results. Both computational and experimental results indicate the existence of two distinct flow regimes. For low Reynolds numbers, a region of nonmoving fluid is observed immediately downstream of the step and no separated flow zone exists. For the higher Reynolds numbers, a recirculating flow zone forms downstream of the expansion step, which is followed by a zone of stagnant fluid adjacent to pipe wall characterizing reattachment.

Laminar Flow of a Herschel-Bulkley Fluid Over an Axisymmetric Sudden Expansion

2001 ◽  
Vol 123 (3) ◽  
pp. 588-594 ◽  
Author(s):  
Khaled J. Hammad ◽  
George C. Vradis ◽  
M. Volkan O¨tu¨gen
Keyword(s):  
Laminar Flow ◽  
Flow Regime ◽  
Power Law ◽  
Numerical Solutions ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Sudden Expansion ◽  
High Yield ◽  
Recirculating Flow ◽  
Power Law Index

The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically. Finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations were obtained within the laminar flow regime for a range of Reynolds numbers, yield numbers, and power-law index values. The Reynolds number, based on the upstream pipe diameter and bulk velocity, was varied between 50 and 200, while the yield number was varied between 0 and 2. The power-law index values mapped the 0.6–1.2 range, allowing for the investigation of both shear-thinning and shear-thickening effects. Two distinct flow regimes are identified. One is associated with a combination of low yield numbers, high Reynolds numbers, and high power-law indexes, and exhibits a recirculating flow region at the step corner which is similar to that seen in Newtonian flows. The other flow regime, however, is characterized by a dead-zone behind the step corner, and is obtained for a combination of high yield numbers, low Reynolds numbers, and low power-law indexes. The yield number appears to be the dominant parameter affecting the shape and extent of the corner flow region as well as flow redevelopment further downstream. In general, the influence of the power-law index on the flow structure is stronger when the yield number is small. A flow character that is an exception to this general trend is the recirculating corner vortex intensity which decreases substantially with decreasing power-law index values for all investigated yield numbers.

The Axisymmetric Sudden Expansion Flow of a Non-Newtonian Viscoplastic Fluid

1997 ◽  
Vol 119 (1) ◽  
pp. 193-200 ◽  
Author(s):  
G. C. Vradis ◽  
M. V. O¨tu¨gen
Keyword(s):  
Reynolds Numbers ◽  
Bingham Fluid ◽  
Viscoplastic Fluid ◽  
Sudden Expansion ◽  
Reattachment Length ◽  
Internal Flows ◽  
Recirculating Flow ◽  
Finite Difference Technique ◽  
Wide Range ◽  
Fluid Properties

The flow of a non-Newtonian viscoplastic Bingham fluid over an axisymmetric sudden expansion is studied by numerically solving the governing fully-elliptic continuity and momentum equations. Solutions are obtained for a wide range of Reynolds and yield numbers in the laminar flow regime with constant fluid properties. The present work demonstrates that the finite-difference technique can successfully be employed to obtain solutions to separating/reattaching internal flows of Bingham plastics. The results demonstrate the strong effects of the yield and Reynolds numbers on both the integral and the local structure of the separating and reattaching flow. Higher yield numbers result in larger overall effective viscosities and thus faster flow recovery downstream of the sudden expansion. The reattachment length decreases with increasing yield numbers, eventually reaching an asymptotic nonzero value which, in turn, is dependent on the Reynolds number. The strength of the recirculating flow also decreases with increasing yield 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.

The Ratio of the Wall Shear Stresses in Concentric Annuli

1968 ◽  
Vol 72 (688) ◽  
pp. 345-346 ◽  
Author(s):  
Alan Quarmby
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
Experimental Results ◽  
Bulk Velocity ◽  
Shear Stresses ◽  
Wall Shear

Summary Experimental results are presented of the measurement of the ratio of the wall shear stresses at the inner and outer surfaces of concentric annuli. Five radius ratios were investigated with Reynolds numbers in the range 2000-89 000 with air. The Reynolds number is defined as where ū is the bulk velocity. It is concluded that the ratio of the shear stresses is very different from the corresponding laminar flow value and is a function of both radius ratio and Reynolds number.

Numerical Modeling of Unsteady, Separated Viscous Flow

1977 ◽  
Vol 99 (4) ◽  
pp. 657-665 ◽  
Author(s):  
A. R. Giaquinta
Keyword(s):  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Main Flow ◽  
Sudden Expansion ◽  
Spatial Diffusion ◽  
Transient Phase ◽  
Transient Solution ◽  
Steady State Condition

Numerical solutions of the equations governing the laminar flow of an incompressible fluid through a two-dimensional sudden expansion are discussed. The fluid motion is started impulsively from rest and is examined in detail during the transient phase to the steady-state condition. Solutions are obtained by two independent finite-difference methods which are discussed. The development of the flow in the zone of separation is investigated, and, during the earliest phases of motion, the generation of vorticity at the solid boundaries and its spatial diffusion is studied in the region of uniform flow. The numerical treatment of the boundary conditions is discussed. Characteristics of the transient solution for two different Reynolds numbers in the laminar range are presented. Included with the results is the temporal development of the streamline dividing the zone of separation from the main flow.

Flow in a Curved Pipe With a Sudden Expansion

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Michael Shusser ◽  
Artyom Ramus ◽  
Oleg Gendelman
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Vortex Pair ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Straight Pipe ◽  
Curved Pipe ◽  
Recirculation Flow ◽  
Recirculating Flow ◽  
Steady Laminar

This study considers a combination of two well studied flows: the flow in a curved pipe and the flow in a straight pipe with a sudden expansion. Steady laminar flow of an incompressible fluid through an axisymmetric sudden expansion followed by a curved pipe was investigated numerically. The influence of the expansion ratio and the Reynolds number on the vortex pair in the bend and on the recirculating flow caused by the sudden expansion was studied. A correlation for the length of the recirculation flow was obtained.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Vol 128 (4) ◽  
pp. 671-679 ◽  
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 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 failed to capture completely the total expansion effect on the flow, which is influenced by 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 two-dimensional simulations were performed using 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 were compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, thus sustaining laminar flow symmetry to higher Reynolds numbers. Last, and most important, when the logarithm of the critical Reynolds number 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.

Heat transfer enhancement using second mode self-oscillating structures

2019 ◽  
Vol 30 (7) ◽  
pp. 3827-3842
Author(s):  
Samer Ali ◽  
Zein Alabidin Shami ◽  
Ali Badran ◽  
Charbel Habchi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Flow Regime ◽  
Vortex Generator ◽  
Reynolds Numbers ◽  
Content Type ◽  
Laminar Flow Regime ◽  
Second Mode

Purpose In this paper, self-sustained second mode oscillations of flexible vortex generator (FVG) are produced to enhance the heat transfer in two-dimensional laminar flow regime. The purpose of this study is to determine the critical Reynolds number at which FVG becomes more efficient than rigid vortex generators (RVGs). Design/methodology/approach Ten cases were studied with different Reynolds numbers varying from 200 to 2,000. The Nusselt number and friction coefficients of the FVG cases are compared to those of RVG and empty channel at the same Reynolds numbers. Findings For Reynolds numbers higher than 800, the FVG oscillates in the second mode causing a significant increase in the velocity gradients generating unsteady coherent flow structures. The highest performance was obtained at the maximum Reynolds number for which the global Nusselt number is improved by 35.3 and 41.4 per cent with respect to empty channel and rigid configuration, respectively. Moreover, the thermal enhancement factor corresponding to FVG is 72 per cent higher than that of RVG. Practical implications The results obtained here can help in the design of novel multifunctional heat exchangers/reactors by using flexible tabs and inserts instead of rigid ones. Originality/value The originality of this paper is the use of second mode oscillations of FVG to enhance heat transfer in laminar flow regime.

Heat Transfer in a Surfactant Drag-Reducing Solution—A Comparison With Predictions for Laminar Flow

2005 ◽  
Vol 128 (6) ◽  
pp. 557-563 ◽  
Author(s):  
Paul L. Sears ◽  
Libing Yang
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Reynolds Numbers ◽  
High Heat ◽  
High Heat Flux ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Drag Reducing Additive ◽  
Good Agreement

Heat transfer coefficients were measured for a solution of surfactant drag-reducing additive in the entrance region of a uniformly heated horizontal cylindrical pipe with Reynolds numbers from 25,000 to 140,000 and temperatures from 30to70°C. In the absence of circumferential buoyancy effects, the measured Nusselt numbers were found to be in good agreement with theoretical results for laminar flow. Buoyancy effects, manifested as substantially higher Nusselt numbers, were seen in experiments carried out at high heat flux.

A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Expansion

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.

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