HYDRODYNAMICAL INSTABILITY OF NEWTONIAN FLOW BEFORE AN AXISYMMETRIC SUDDEN CONTRACTION

The sizes of the vortex region before the axisymmetric sudden contraction of the circular pipe at the Newtonian flow have been investigated. Area ratios 0.250 and 0.500 were considered. The sizes of the vortex region have the extreme dependence with a maximum at the transition of the laminar flow into a turbulent flow one. When the Reynolds number at the laminar flow increase, these sizes also increase, and they decrease at the turbulent flow. In both cases, the sizes of the vortex region are proportional to the Reynolds number. A transition region between laminar flow and turbulent flow lies in the range of the Reynolds number from 3000 to 5300 and 750…1300, determined by the diameter of a bigger pipe of sudden expansion and a step height correspondingly

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Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2005-77098 ◽

2005 ◽

Cited By ~ 2

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.

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

10.1115/imece1999-1230 ◽

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.

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A Study of Flow of Plastics Through Pipes

Journal of Applied Mechanics ◽

10.1115/1.4009533 ◽

1946 ◽

Vol 13 (2) ◽

pp. A101-A105

Author(s):

R. C. Binder ◽

J. E. Busher

Keyword(s):

Experimental Data ◽

Reynolds Number ◽

Friction Coefficient ◽

Laminar Flow ◽

Turbulent Flow ◽

Dynamic Viscosity ◽

Apparent Viscosity ◽

Turbulent Viscosity ◽

Yield Value

Abstract The pipe friction coefficient for true fluids is usually expressed as a function of Reynolds number. This method of organizing data has been extended to tests on the flow of different suspensions which behaved as ideal plastics in the laminar-flow range and as true fluids in the turbulent-flow range. In the laminar-flow range, Reynolds number below about 2100, the denominator in Reynolds number is taken as the apparent viscosity. The apparent viscosity can be determined from the yield value and the coefficient of rigidity. In the turbulent-flow range, the denominator in Reynolds number is an equivalent or turbulent viscosity equal to the dynamic viscosity of a true fluid having the same friction coefficient, velocity, diameter, and density as that of the plastic. The various experimental data on plastics correlate well with this extension of the method for true fluids.

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Experiments on Backward-Facing Step Flows Preceding a Filter

Volume 2: Fora, Parts A and B ◽

10.1115/fedsm2007-37204 ◽

2007 ◽

Author(s):

S. Yao ◽

C. Krishnamoorthy ◽

F. W. Chambers

Keyword(s):

Reynolds Number ◽

Turbulent Flow ◽

Separated Flow ◽

Reynolds Numbers ◽

Velocity Profiles ◽

Step Height ◽

Reattachment Point ◽

Backward Facing Step ◽

Air Filters ◽

Air Filter

The resistance of automotive air filters alters upstream pressure gradients and thereby affects flow separation, the velocity distributions over the filter, and the performance of the filter. Air filters provide a resistance sufficient to alter flows, but not enough to make face velocities uniform. The backward-facing step flow is an archetype with a separation that resembles those found in automotive air filter housings. To gain insight to the problem of separation and filters, experiments were conducted measuring velocity fields for air flows in a 10:1 aspect ratio rectangular duct with a backward-facing step with and without the resistance of an air filter mounted downstream. The expansion ratio for the step was 1:2. The filter was mounted 4.25 and 6.75 step heights downstream of the step; locations both upstream and downstream of the nominal 6 step-height no-filter reattachment point. Experiments were performed at four Reynolds numbers between 2000 and 10,000. The Reynolds numbers were based on step height and inlet maximum velocity. The inlet velocity profiles at the step were developed. A Laser Doppler Anemometer (LDA) was used to measure velocity profiles and map separated regions between the step and the filter. The results indicate that the filter tends to decrease the streamwise velocity on the non-separated side of the channel and increase it on the separated, step, side compared to the no-filter flow. Non-separated flow tends to separate due to the deceleration and separated flow reattaches before the filter, whether the filter is placed at 4.25 or 6.75 step heights. The literature shows that without a filter the reattachment location depends on the Reynolds number in the laminar and transitional regimes, but is constant for turbulent flow. However, the area of the reversed flow may vary with Reynolds number for turbulent flow. With the filter at 4.25 step heights, the area of reversing flow is reduced significantly, and the Reynolds number has little effect on the main properties of the flow. With the filter at 6.75 step heights, the reversing flow area decreases as the Reynolds number increases though the reattachment point is fixed just upstream of the filter.

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Performance Analysis of High Speed Floating Ring Hybrid Bearing in the Laminar and Turbulent Regimes

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.197-198.1776 ◽

2011 ◽

Vol 197-198 ◽

pp. 1776-1780 ◽

Cited By ~ 3

Author(s):

Hong Guo ◽

Bo Qian Xia ◽

Shao Qi Cen

Keyword(s):

Reynolds Number ◽

Laminar Flow ◽

Turbulent Flow ◽

Dynamic Characteristics ◽

High Speed ◽

Load Capacity ◽

Flow Equation ◽

The Finite Element Method ◽

Static And Dynamic Characteristics ◽

Hybrid Bearing

This paper presents a theoretical study concerning the static and dynamic characteristics of high speed journal floating ring hybrid bearing compensated by interior restrictor under laminar flow and turbulent flow respectively. The turbulent flow fluid film control equations and the pressure boundary conditions of this floating ring bearing together with the restrictor flow equation are solved by using the Finite Element Method. The variation regularity of static and dynamic characteristics such as load capacity, friction power loss, stiffness, damping etc. is analyzed. By comparing the laminar flow results and turbulent flow results, it is found that the characteristics coefficients are adjacent under small Reynolds number (laminar flow is dominant). But the characteristics coefficients are discrepant under big Reynolds number (turbulent flow is dominant). So turbulence lubrication theory is more accurate to high speed floating ring bearing.

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Entropy Generation Minimization of Fully Developed Internal Convective Flows With Constant Heat Flux

Heat Transfer: Volume 1 ◽

10.1115/ht2003-47389 ◽

2003 ◽

Cited By ~ 1

Author(s):

Eric B. Ratts ◽

Atul G. Raut

Keyword(s):

Heat Transfer ◽

Heat Flux ◽

Reynolds Number ◽

Laminar Flow ◽

Turbulent Flow ◽

Entropy Generation ◽

Cross Sections ◽

Constant Heat Flux ◽

Constant Heat ◽

Entropy Generation Minimization

This paper addresses the thermodynamic optimum of single-phase convective heat transfer in fully developed flow for uniform and constant heat flux. The optimal Reynolds number is obtained using the entropy generation minimization (EGM) method. Entropy generation due to viscous dissipation and heat transfer dissipation in the flow passage are summed, and then minimized with respect to Reynolds number based on hydraulic diameter. For fixed mass flow rate and fixed total heat transfer rate, and the assumption of uniform heat flux, an optimal Reynolds number for laminar as well as turbulent flow is obtained. In addition, the method quantifies the flow irreversibilities. It was shown that the ratio of heat transfer dissipation to viscous dissipation at minimum entropy generation was 5:1 for laminar flow and 29:9 for turbulent flow. For laminar flow, the study compared non-circular cross-sections to the circular cross-section. The optimal Reynolds number was determined for the following cross-sections: square, equilateral triangle, and rectangle with aspect ratios of two and eight. It was shown that the rectangle with the higher aspect ratio had the smallest optimal Reynolds number, the smallest entropy generation number, and the smallest flow length.

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STUDY OF THE BEHAVIOURS OF SINGLE-PHASE TURBULENT FLOW AT LOW TO MODERATE REYNOLDS NUMBERS THROUGH A VERTICAL PIPE. PART I: 2D COUNTERS ANALYSIS

EUREKA Physics and Engineering ◽

10.21303/2461-4262.2020.001538 ◽

2020 ◽

pp. 108-122

Author(s):

Akeel M. Ali Morad ◽

Rafi M. Qasim ◽

Amjed Ahmed Ali

Keyword(s):

Reynolds Number ◽

Laminar Flow ◽

Turbulent Flow ◽

Single Phase ◽

Static Pressure ◽

Fluid Velocity ◽

Mixing Length ◽

Shearing Force ◽

Vertical Pipe ◽

Moderate Reynolds Number

This study presents a model to investigate the behavior of the single-phase turbulent flow at low to moderate Reynolds number of water through the vertical pipe through (2D) contour analysis. The model constructed based on governing equations of an incompressible Reynolds Average Navier-Stokes (RANS) model with (k-ε) method to observe the parametric determinations such as velocity profile, static pressure profile, turbulent kinetic energy consumption, and turbulence shear wall flows. The water is used with three velocities values obtained of (0.087, 0.105, and 0.123 m/s) to represent turbulent flow under low to moderate Reynolds number of the pipe geometry of (1 m) length with a (50.8 mm) inner diameter. The water motion behavior inside the pipe shows by using [COMSOL Multiphysics 5.4 and FLUENT 16.1] Software. It is concluded that the single-phase laminar flow of a low velocity, but obtained a higher shearing force; while the turbulent flow of higher fluid velocity but obtained the rate of dissipation of shearing force is lower than that for laminar flow. The entrance mixing length is affected directly with pattern of fluid flow. At any increasing in fluid velocity, the entrance mixing length is increase too, due to of fluid kinetic viscosity changes. The results presented the trends of parametric determinations variation through the (2D) counters analysis of the numerical model. When fluid velocity increased, the shearing force affected directly on the layer near-wall pipe. This leads to static pressure decreases with an increase in fluid velocities. While the momentum changed could be played interaction rules between the fluid layers near the wall pipe with inner pipe wall. Finally, the agreement between present results with the previous study of [1] is satisfied with the trend

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Heat and mass transfer from rotating cones

Journal of Fluid Mechanics ◽

10.1017/s0022112063001142 ◽

1963 ◽

Vol 17 (1) ◽

pp. 105-112 ◽

Cited By ~ 35

Author(s):

C. L. Tien ◽

D. T. Campbell

Keyword(s):

Heat Transfer ◽

Mass Transfer ◽

Reynolds Number ◽

Laminar Flow ◽

Turbulent Flow ◽

Heat And Mass Transfer ◽

Flow Characteristics ◽

Sublimation Rate ◽

Semi Empirical ◽

Good Agreement

Heat transfer by convection from isothermal rotating cones is investigated experimentally by measuring the sublimation rate from naphthalene-coated cones and using the analogy between heat and mass transfer. Measurements are made for a range of conditions from entirely laminar flow to conditions when the outer 70% of the surface area is covered by turbulent flow. Mass-transfer measurements for laminar flow over cones of vertex angles 180°, 150°, 120° and 90° are in good agreement with the theoretical prediction. For turbulent flow, experimental results for cones of the above vertex angles also agree very well with the semi-empirical analogy calculations for the disk case. A different heat- and mass-transfer relationship with the rotational Reynolds number is observed in the measurements on the 60° cone, and is believed to be due to a change of flow characteristics. The instability and the transition of flows over different cone models are also discussed.

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The dynamics of a laminar flow in a symmetric channel with a sudden expansion

Journal of Fluid Mechanics ◽

10.1017/s0022112001004086 ◽

2001 ◽

Vol 436 ◽

pp. 283-320 ◽

Cited By ~ 60

Author(s):

T. HAWA ◽

Z. RUSAK

Keyword(s):

Reynolds Number ◽

Laminar Flow ◽

Numerical Simulations ◽

Direct Numerical Simulations ◽

Sudden Expansion ◽

Asymptotically Stable ◽

Two Dimensional ◽

Stable Mode ◽

Symmetric States ◽

Asymmetric Equilibrium

Bifurcation analysis, linear stability study, and direct numerical simulations of the dynamics of a two-dimensional, incompressible, and laminar flow in a symmetric long channel with a sudden expansion with right angles and with an expansion ratio D/d (d is the width of the channel inlet section and D is the width of the outlet section) are presented. The bifurcation analysis of the steady flow equations concentrates on the flow states around a critical Reynolds number Rec(D/d) where asymmetric states appear in addition to the basic symmetric states when Re [ges ] Rec(D/d). The bifurcation of asymmetric states at Rec has a pitchfork nature and the asymmetric perturbation grows like √Re − Rec(D/d). The stability analysis is based on the linearized equations of motion for the evolution of infinitesimal two-dimensional disturbances imposed on the steady symmetric as well as asymmetric states. A neutrally stable asymmetric mode of disturbance exists at Rec(D/d) for both the symmetric and the asymmetric equilibrium states. Using asymptotic methods, it is demonstrated that when Re < Rec(D/d) the symmetric states have an asymptotically stable mode of disturbance. However, when Re > Rec(D/d), the symmetric states are unstable to this mode of asymmetric disturbance. It is also shown that when Re > Rec(D/d) the asymmetric states have an asymptotically stable mode of disturbance. The direct numerical simulations are guided by the theoretical approach. In order to improve the numerical simulations, a matching with the asymptotic solution of Moffatt (1964) in the regions around the expansion corners is also included. The dynamics of both small- and large-amplitude disturbances in the flow is described and the transition from symmetric to asymmetric states is demonstrated. The simulations clarify the relationship between the linear stability results and the time-asymptotic behaviour of the flow. The current analyses provide a theoretical foundation for previous experimental and numerical results and shed more light on the transition from symmetric to asymmetric states of a viscous flow in an expanding channel. It is an evolution from a symmetric state, which loses its stability when the Reynolds number of the incoming flow is above Rec(D/d), to a stable asymmetric equilibrium state. The loss of stability is a result of the interaction between the effects of viscous dissipation, the downstream convection of perturbations by the base symmetric flow, and the upstream convection induced by two-dimensional asymmetric disturbances.

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