scholarly journals Effect of Asymmetry of Channels on Flows in Parallel Plates with a Sudden Expansion

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1857
Author(s):  
Takuya Masuda ◽  
Toshio Tagawa
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Channel Flow ◽  
Multiple Solutions ◽  
Critical Reynolds Number ◽  
Entrance Region ◽  
Expansion Rate ◽  
Sudden Expansion ◽  
Parallel Plates ◽  
The Third

In order to quantitatively grasp the influence of asymmetry of a channel, flow in an eccentric sudden expansion channel, in which the channel centers are different on the upstream and downstream sides, was calculated to be less than the Reynolds number of 400, where the expansion rate was 2. The asymmetry of a channel is expressed by an eccentricity S, where a symmetric expansion channel is S = 0 and a channel with one side step is S = 1. Both flows firstly reattached on the wall located on the short and long side of a sudden expansion and were observed in the range of S ≤ 0.2, although only the former was seen in the range of S > 0.2. The critical Reynolds number of the multiple solutions increases parabolically to S. At least two separation vortices occur, and the third separation vortex is generated in both solutions above the critical Reynolds number of the third vortex. The length of an entrance region increases linearly to the Reynolds number and slightly with the increase in S. The pressure drop coefficient is proportional to the power of the Reynolds number and increases with S.

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.

Difference in Critical Reynolds Number Between Hagen-Poiseuille and Plane Poiseuille Flows

2001 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Poiseuille Flow ◽  
Average Velocity ◽  
Critical Reynolds Number ◽  
Inlet Section ◽  
Parallel Plates ◽  
Plane Poiseuille Flow ◽  
Contraction Ratio ◽  
Significant Difference

Abstract For plane Poiseuille flow, results of previous investigations were studied, focusing on experimental data on the critical Reynolds number, the entrance length, and the transition length. Consequently, concerning the natural transition, it was confirmed from the experimental data that (i) the transition occurs in the entrance region, (ii) the critical Reynolds number increases as the contraction ratio in the inlet section increases, and (iii) the minimum critical Reynolds number is obtained when the contraction ratio is the smallest or one, and there is no-shaped entrance or straight parallel plates. Its value exists in the neighborhood of 1300, based on the channel height and the average velocity. Although, for Hagen-Poiseuille flow, the minimum critical Reynolds number is approximately 2000, based on the pipe diameter and the average velocity, there seems to be no significant difference in the transition from laminar to turbulent flow between Hagen-Poiseuille flow and plane Poiseuille flow.

Computerized Model of Transition in Circular Pipe Flows: Part 1 — Experimental Definition of the Problem

1999 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Natural Disturbance ◽  
Reynolds Numbers ◽  
Entrance Region ◽  
Circular Pipe ◽  
Experimental Investigations ◽  
Circular Pipes ◽  
Definition Of

Abstract A conceptual model was constructed for the problem of determining in circular pipes the conditions under which the transition from laminar to turbulent flow occurs, so that it becomes possible to calculate the minimum critical Reynolds number. Up until now this problem has been investigated by stability theory with disturbances at the pipe inlet. However, the minimum critical Reynolds number has not yet been obtained theoretically. Hence, the author took up the problem directly from many previous experimental investigations and found that (i) plots of the transition length versus the Reynolds number show that the transition occurs in the entrance region under the condition of a natural disturbance, and (ii) plots of the critical Reynolds number versus the ratio of bellmouth diameter to the pipe diamter show that with larger shapes of bellmouths, laminar flow will persist to higher Reynolds numbers. The problem is thus defined clearly as: Under the condition of an ordinary disturbance, the transition from laminar to turbulent flow occurs in the entrance region of a straight circular pipe, then the Reynolds number takes a minimum value of about 2000.

Computerized Model of Transition in Circular Pipe Flows: Part 2 — Calculation of the Minimum Critical Reynolds Number

1999 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Radial Component ◽  
Entrance Region ◽  
Wall Strength ◽  
Normal Wall ◽  
Acceleration Force ◽  
Profile Changes ◽  
Grid Points ◽  
Pipe Inlet

Abstract From the conclusions of the previous paper, Part 1, it is clear that the transition occurs in the entrance region and the critical Reynolds number takes the minimum value of about 2000 for the case of a straight pipe. In the entrance region, the velocity profile changes from a uniform distribution at the pipe inlet to a parabolic one at the entrance length. Kanda and Oshima (1998b) found that in the entrance region, the radial component of the curl of vorticity multiplied by (2/Re), which we call the normal wall strength, works as an acceleration force together with the continuity equation, and that the normal wall strength decreases inversely as the Reynolds number increases. Hence, the onset of the transition should depend on whether or not the acceleration power provided by the normal wall strength exceeds a required value. In this study the author calculated the acceleration power via finite difference calculations, and thus obtained the minimum critical Reynolds number of 2040 when using J0 = 101 grid points, and 2630 when using J0 = 51.

Analysis of the Fluid Flow in 3D Symmetric Enlarged Channel

2015 ◽  
Vol 813-814 ◽  
pp. 652-657
Author(s):  
Seranthian Ramanathan ◽  
M.R. Thansekhar ◽  
P. Rajesh Kanna ◽  
S. Shankara Narayanan
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Software Package ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
3 Dimensional ◽  
Ansys Workbench

A 3-Dimensional fluid flow over the sudden expansion region of a horizontal duct for various Reynolds numbers have been studied by using the CFD Software package ANSYS Workbench Fluent v 13.0. The expansion ratio and aspect ratio for the sudden expansion are taken as 2.5 and 4 respectively. This work deals with the finding of critical Reynolds number for a fluid and also the length of re-attachments on stepped walls at various Reynolds numbers for the same fluid. The simulation is carried out in sudden expansion for Reynolds number ranging from 200 to 4000. The variations of local Nusselt number along the stepped walls of the sudden expansion are presented with the heat flux of 35 W/m2 on the stepped walls. Also, the plots of pressure coefficient (Cp) along the stepped walls for different Reynolds numbers are presented in this work.

PIV and POD Investigations of Coherent Vortices Downstream Circular or Rectangular Obstacles Located Between Two Parallel Plates

2019 ◽  
Author(s):  
Fethi Aloui ◽  
Amal Elawady ◽  
Khaled J. Hammad
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Chaotic Behavior ◽  
Rectangular Channel ◽  
Experimental Investigations ◽  
Parallel Plates ◽  
Piv Measurements ◽  
Coherent Vortices ◽  
Karman Vortex ◽  
Proper Orthogonal

Abstract The study is an experimental investigations using PIV. The measurements were obtained by PIV for an unsteady laminar flow across a rectangular channel with a cross-section 300 × 30mm2, in the middle of which is located a cylindrical or a square obstacle. In the case of the cylindrical configuration and due to the confinement, PIV measurements in the range of 40 < Re < 200 clearly show that the von Karman vortex shedding appears at a critical Reynolds number which is about 66. A post-processing of these PIV measurements using the Proper Orthogonal Decomposition (POD) technique is by keeping only the first most energetic six modes, can be used as a filtering process to remove noise from instantaneous velocity signals. In the case of the square obstacle, PIV measurements obtained in the range of 30 < Re < 350 show the absence of vortex detachments and the chaotic behavior of the wake behind the obstacle beyond a certain Reynolds number. By examining the POD post-possessing results, the existence of a dynamic detachments’ regime (instantaneous breaking and coalescence of vortices), can be clearly observed. Given the chaotic behavior of the wake behind the obstacle, the application of the POD filtering process to only the first most energetic modes, cannot lead to good results.

J057014 Critical Reynolds number in channel flow

2013 ◽  
Vol 2013 (0) ◽  
pp. _J057014-1-_J057014-3
Author(s):  
Masaki SHIMIZU ◽  
Hiro ARAKO ◽  
Takahiro KANAZAWA ◽  
Genta KAWAHARA
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Critical Reynolds Number

Curvature- and rotation-induced instabilities in channel flow

1990 ◽  
Vol 210 ◽  
pp. 537-563 ◽  
Author(s):  
O. John E. Matsson ◽  
P. Henrik Alfredsson
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Channel Flow ◽  
Stability Theory ◽  
Critical Reynolds Number ◽  
Secondary Instability ◽  
Linear Stability Theory ◽  
Curved Channel ◽  
Dean Vortices ◽  
Coriolis Effects

In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.

Experimental Analysis of Microchannel Entrance Length Characteristics Using Microparticle Image Velocimetry

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Tariq Ahmad ◽  
Ibrahim Hassan
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Entrance Region ◽  
Working Fluid ◽  
Parallel Plates ◽  
Entrance Length ◽  
Number Range ◽  
Micro Piv ◽  
Image Velocimetry ◽  
Microparticle Image Velocimetry

The study of the entrance region of microchannels and microdevices is limited, yet important, since the effect on the flow field and heat transfer mechanisms is significant. An experimental study has been carried out to explore the laminar hydrodynamic development length in the entrance region of adiabatic square microchannels. Flow field measurements are acquired through the use of microparticle image velocimetry (micro-PIV), a nonintrusive particle tracking and flow observation technique. With the application of micro-PIV, entrance length flow field data are obtained for three different microchannel hydraulic diameters of 500 μm, 200 μm, and 100 μm, all of which have cross-sectional aspect ratios of 1. The working fluid is distilled water, and velocity profile data are acquired over a laminar Reynolds number range from 0.5 to 200. The test-sections were designed as to provide a sharp-edged microchannel inlet from a very large reservoir at least 100 times wider and higher than the microchannel hydraulic diameter. Also, all microchannels have a length-to-diameter ratio of at least 100 to assure fully developed flow at the channel exit. The micro-PIV procedure is validated in the fully developed region with comparison to Navier–Stokes momentum equations. Good agreement was found with comparison to conventional entrance length correlations for ducts or parallel plates, depending on the Reynolds range, and minimal influence of dimensional scaling between the investigated microchannels was observed. New entrance length correlations are proposed, which account for both creeping and high laminar Reynolds number flows. These correlations are unique in predicting the entrance length in microchannels and will aid in the design of future microfluidic devices.

A Theory of Transitional and Turbulent Flow of Non-Newtonian Slurries Between Flat Parallel Plates

1971 ◽  
Vol 11 (01) ◽  
pp. 52-56 ◽  
Author(s):  
Richard W. Hanks ◽  
Maheshkumar P. Valia
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Frictional Resistance ◽  
Newtonian Fluids ◽  
Transitional Flow ◽  
Parallel Plates ◽  
Bingham Plastic ◽  
Turbulent Transition ◽  
Large Width

Abstract A theoretical model is developed which Permits prediction of velocity profiles and frictional prediction of velocity profiles and frictional resistance factors for the isothermal flow of Bingham plastic non-Newtonian slurries in laminar, transitional, and turbulent flow between that parallel walls, in rectangular ducts of large width-to-height ratios, or in concentric annuli with radius ratios approaching unity. The theory is tested with available frictional resistance data for a range of Hedstrom numbers from 10(4) to 10(8) and a set of theoretical design curves of friction factor vs Reynolds number is developed. The model indices that for certain ranges of Hedstrom number (the non-Newtonian index) turbulence is suppressed relative to Newtonian flow behavior, whereas for other ranges of Hedstrom number, the converse is true. Introduction The handling of non-Newtonian fluids in turbulent motion is an important operation in many modern technological processes. Despite this fact, however, little has been done to develop models which are comparable to those available for Newtonian turbulent flow. In particular, a model of the transitional flow regime is notably lacking. Recently, a theory of laminar-turbulent transition for non-Newtonian slurries flowing in pipes and parallel plates was presented. A theory of parallel plates was presented. A theory of transitional and turbulent flow of Newtonian fluids in pipes and parallel plate ducts has also recently been developed. This theory permits the analytic calculation of the friction factor-Reynolds number curves as a continuous function of Reynolds number from the critical Reynolds number of laminar turbulent transition to any condition of turbulent flow. In this paper these two theories will be combined in order to develop a theory for the transitional and turbulent flow of non-Newtonian slurries in parallel plate ducts, rectangular ducts of large width-to-height ratio, or concentric annuli with radius ratios approaching unity. THEORETICAL ANALYSIS The rheological model which will be used to represent the non-Newtonian slurry behavior is the linear Bingham plastic model, ..............(1) ............(2) For this model the laminar flow curve is given by ..............(3) where q = 2v/b, b is one-half the distance between the plates, w = b(−dp/dz) is the wall shear stress, and D = o/ w. The end of the laminax flow, region is determined by the equations ........(4) .........(5) where N Rec = 4bp vc/ p is the critical Reynolds number, Dc is the critical transitional value of D and N He -16bp o/ p is the Hedstrom number expressed in terms of the hydraulic diameter for parallel plates. parallel plates. The calculation of the transitional flow field for this type of fluid will be based upon the model developed by Hanks for Newtonian fluids. SPEJ P. 52

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