The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

2015 ◽  
Vol 30 (11) ◽  
pp. 1718-1726 ◽  
Author(s):  
Jiazhong Qian ◽  
Lei Ma ◽  
Hongbin Zhan ◽  
Qiankun Luo ◽  
Xiao Wang ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Single Fracture ◽  
Fracture Flow

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.

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.

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.

scholarly journals Augmented of turbulent heat transfer in an annular pipe with abrupt expansion

2016 ◽  
Vol 20 (5) ◽  
pp. 1621-1632 ◽  
Author(s):  
Hussein Togun ◽  
Tuqa Abdulrazzaq ◽  
Salim Kazi ◽  
Ahmad Badarudin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Surface Temperature ◽  
Local Nusselt Number ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Inner Diameter ◽  
Annular Pipe

This paper presents a study of heat transfer to turbulent air flow in the abrupt axisymmetric expansion of an annular pipe. The experimental investigations were performed in the Reynolds number range from 5000 to 30000, the heat flux varied from 1000 to 4000 W/m2, and the expansion ratio was maintained at D/d=1, 1.25, 1.67 and 2. The sudden expansion was created by changing the inner diameter of the entrance pipe to an annular passage. The outer diameter of the inner pipe and the inner diameter of the outer pipe are 2.5 and 10 cm, respectively, where both of the pipes are subjected to uniform heat flux. The distribution of the surface temperature of the test pipe and the local Nusselt number are presented in this investigation. Due to sudden expansion in the cross section of the annular pipe, a separation flow was created, which enhanced the heat transfer. The reduction of the surface temperature on the outer and inner pipes increased with the increase of the expansion ratio and the Reynolds number, and increased with the decrease of the heat flux to the annular pipe. The peak of the local Nusselt number was between 1.64 and 1.7 of the outer and inner pipes for Reynolds numbers varied from 5000 to 30000, and the increase of the local Nusselt number represented the augmentation of the heat transfer rate in the sudden expansion of the annular pipe. This research also showed a maximum heat transfer enhancement of 63-78% for the outer and inner pipes at an expansion ratio of D/d=2 at a Re=30000 and a heat flux of 4000W/m2.

Instability of a Curved Pipe Flow With a Sudden Expansion

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Michael Shusser ◽  
Artyom Ramus ◽  
Oleg Gendelman
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Oscillatory Flow ◽  
Outer Wall ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Straight Pipe ◽  
Periodic Oscillations ◽  
Curved Pipe ◽  
Flow Variables

Numerical calculations of laminar flow of an incompressible fluid through an axisymmetric sudden expansion followed by a curved pipe recently done by the authors discovered an early instability of this flow for a certain expansion ratio, as it becomes unsteady with periodic oscillations of the flow variables at a Reynolds number when both curved pipe flow and flow in a straight pipe with an axisymmetric sudden expansion remain stable. This study describes in detail the created oscillatory flow and suggests that the early instability of the ratio 3 flow could be caused by the higher velocity gradient near the outer wall of the bend.

MODELING OF BIFURCATION PHENOMENA IN SUDDENLY EXPANDED FLOWS WITH A NEW FINITE VOLUME LATTICE BOLTZMANN METHOD

2011 ◽  
Vol 22 (09) ◽  
pp. 977-1003 ◽  
Author(s):  
AHAD ZARGHAMI ◽  
MOHAMMAD JAVAD MAGHREBI ◽  
STEFANO UBERTINI ◽  
SAURO SUCCI
Keyword(s):  
Reynolds Number ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Critical Reynolds Number ◽  
Expansion Ratio ◽  
Lattice Boltzmann Model ◽  
Finite Volume Scheme ◽  
Flow Through ◽  
The Stability ◽  
Stability And Accuracy

A lattice Boltzmann model using upstream finite volume scheme has been employed in the investigation of bifurcation and transition of flow through suddenly-expanded channels. To enhance the stability and accuracy of simulation, a fifth-order Runge–Kutta method is used for the time-marching and upwind biasing factors based on pressure are used as flux correctors in the lattice Boltzmann equation. 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. Comparisons are found to be quantitatively accurate. Furthermore, the results show that the critical Reynolds number decreases with increasing channel expansion ratio. At a fixed supercritical Reynolds number, the location at which the jet first impinges on the channel wall grows with the expansion ratio.

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.

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.

Stability of thermocapillary flows in non-cylindrical liquid bridges

2002 ◽  
Vol 458 ◽  
pp. 35-73 ◽  
Author(s):  
CH. NIENHÜSER ◽  
H. C. KUHLMANN
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Critical Reynolds Number ◽  
Volume Fraction ◽  
Thermocapillary Flow ◽  
Surface Shape ◽  
Liquid Bridges ◽  
Gravity Level ◽  
Neutral Curves ◽  
Prandtl Numbers

The thermocapillary flow in liquid bridges is investigated numerically. In the limit of large mean surface tension the free-surface shape is independent of the flow and temperature fields and depends only on the volume of liquid and the hydrostatic pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape is axisymmetric. A differential heating of the bounding circular disks then causes a steady two-dimensional thermocapillary flow which is calculated by a finite-difference method on body-fitted coordinates. The linear-stability problem for the basic flow is solved using azimuthal normal modes computed with the same discretization method. The dependence of the critical Reynolds number on the volume fraction, gravity level, Prandtl number, and aspect ratio is explained by analysing the energy budgets of the neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number exhibits a smooth minimum near volume fractions which approximately correspond to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4) the intersection of two neutral curves results in a sharp peak of the critical Reynolds number. Since the instabilities for low and high Prandtl numbers are markedly different, the influence of gravity leads to a distinctly different behaviour. While the hydrostatic shape of the bridge is the most important effect of gravity on the critical point for low-Prandtl-number flows, buoyancy is the dominating factor for the stability of the flow in a gravity field when the Prandtl number is high.

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