Low Reynolds number flow over a plane symmetric sudden expansion

1974 ◽  
Vol 64 (1) ◽  
pp. 111-128 ◽  
Author(s):  
F. Durst ◽  
A. Melling ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Sudden Expansion ◽  
Main Stream ◽  
Plane Symmetric ◽  
Dimensional Effects ◽  
Separation Zones

Flow visualization and laser-anemometry measurements are reported in the flow downstream of a plane 3: 1 symmetric expansion in a duct with an aspect ratio of 9·2: 1 downstream of the expansion. The flow was found to be markedly dependent on Reynolds number, and strongly three-dimensional even well away from the channel corners except at the lowest measurable velocities. The measurements at a Reynolds number of 56 indicated that the separation regions behind each step were of equal length. Symmetric velocity profiles existed from the expansion to a fully developed, parabolic profile far downstream, although there were substantial three-dimensional effects in the vicinity of the separation regions. The velocity profiles were in good agreement with those obtained by solving the two-dimensional momentum equation. At a Reynolds number of 114, the two separation regions were of different lengths, leading to asymmetric velocity profiles; three dimensional effects were much more pronounced. At a Reynolds number of 252, a third separation zone was found on one wall, downstream of the smaller of the two separation zones adjacent to the steps. As at the lower Reynolds numbers, the flow was very stable. At higher Reynolds numbers the flow became less stable and periodicity became increasingly important in the main stream; this was accompanied by a highly disturbed fluid motion in the separation zones, as the flow tended towards turbulence.

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.

Bifurcated Forced Convective Heat Transfer of Supercritical CO2 Flow in Plane Symmetric Sudden Expansion Duct

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Bi-Li Deng ◽  
Xin-Rong Zhang ◽  
Hiroshi Yamaguchi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Thermal Effects ◽  
Supercritical Co2 ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Sudden Expansion ◽  
Recirculation Region ◽  
Plane Symmetric ◽  
Co2 Flow

This study presents a computational investigation of forced convection of supercritical CO2 flow in plane symmetric sudden expansion duct at an expansion ratio of 2 in flow asymmetric regime. Computations were conducted at various Reynolds numbers in flow asymmetric regime and low wall heat fluxes below 500 W/m2 to examine the Reynolds number and thermal effects on the flow and heat transfer of the bifurcated flow. General flow features and temperature distributions are presented. The transitional Reynolds numbers above, which a third recirculation region will appear at different wall heat flux are presented, and thus thermal effects on the flow stability are discussed. Reynolds number and thermal effects on distributions of wall skin friction, pressure coefficient, and Nusselt number are presented and discussed.

Three-Dimensional Forced Convection Flow in Plane Symmetric Sudden Expansion

2003 ◽  
Author(s):  
J. H. Nie ◽  
B. F. Armaly
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Forced Convection ◽  
Three Dimensional ◽  
Sudden Expansion ◽  
Recirculation Region ◽  
Number Range ◽  
Plane Symmetric ◽  
Reynolds Number Range

Simulations of three-dimensional flow and heat transfer in laminar incompressible forced convection in plane symmetric sudden expansion (backward-facing step in rectangular duct) are presented for different Reynolds numbers. The duct’s downstream (H) and upstream (h) heights are 0.04m and 0.02m, respectively, thus providing a step height (S) of 0.01m and an expansion ratio of 2. The duct’s width (W) is 0.08m, thus resulting in an aspect ratio of 4 before and 2 after the expansion, respectively. The incoming flow is considered to be isothermal, hydro-dynamically steady and fully developed. Uniform and constant heat flux is specified on the stepped walls, while the other walls are treated as adiabatic surfaces. The flow appears to be symmetric for the low Reynolds number range that is considered in this study (Re=150). A “jet-like” flow develops near the sidewall and its impingement on the stepped wall creates a swirling flow inside the primary recirculation region adjacent to the stepped wall, and that is responsible for creating a maximum in the Nusselt number distribution. The results reveal that the location where the streamwise component of wall shear stress is zero on the stepped wall does not coincide with the location of the outer edge of the primary recirculation region, especially in the region near the sidewall. Neither one of these boundary lines represents the reattachment region of the separated flow in the region adjacent to the sidewall. The maximum Nusselt number on the stepped wall is located inside the primary recirculation region and is not identical to the “jet-like” flow impingement point. The maximum friction coefficient on the stepped wall is located inside the primary recirculation region, and it is at the center of the duct for the Reynolds number range considered in this study. The minimum friction coefficient on the stepped wall is located at the impingement of the “jet-like” flow.

Three-Dimensional Mixed Convection in Plane Symmetric-Sudden Expansion: Bifurcated Flow Regime

2006 ◽  
Vol 129 (7) ◽  
pp. 819-826 ◽  
Author(s):  
M. Thiruvengadam ◽  
B. F. Armaly ◽  
J. A. Drallmeier
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Regime ◽  
Three Dimensional ◽  
Wall Heat Flux ◽  
The Other ◽  
Sudden Expansion ◽  
Plane Symmetric

Simulations of three-dimensional laminar mixed convection in a vertical duct with plane symmetric sudden expansion are presented to illustrate the effects of the buoyancy-assisting force and the duct’s aspect ratio on flow bifurcation and heat transfer. The stable laminar bifurcated flow regime that develops in this geometry at low buoyancy levels leads to nonsymmetric temperature and heat transfer distributions in the transverse direction, but symmetric distributions with respect to the center width of the duct in the spanwise direction. As the buoyancy force increases, due to increases in wall heat flux, flow bifurcation diminishes and both the flow and the thermal fields become symmetric at a critical wall heat flux. The size of the primary recirculation flow region adjacent to the sudden expansion increases on one of the stepped walls and decreases on the other stepped wall as the wall heat flux increases. The maximum Nusselt number that develops on one of the stepped walls in the bifurcated flow regime is significantly larger than the one that develops on the other stepped wall. The critical wall heat flux increases as the duct’s aspect ratio increases for fixed Reynolds number. The maximum Nusselt number that develops in the bifurcated flow regime increases as the duct’s aspect ratio increases for fixed wall heat flux and Reynolds number.

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.

Three-Dimensional Forced Convection in Plane Symmetric Sudden Expansion

2004 ◽  
Vol 126 (5) ◽  
pp. 836-839 ◽  
Author(s):  
J. H. Nie and ◽  
B. F. Armaly
Keyword(s):  
Nusselt Number ◽  
Forced Convection ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Flow Region ◽  
Outer Edge ◽  
Sudden Expansion ◽  
Recirculation Flow ◽  
Plane Symmetric ◽  
Laminar Forced Convection

Simulations of three-dimensional laminar forced convection in a plane symmetric sudden expansion are presented for Reynolds numbers where the flow is steady and symmetric. A swirling “jetlike” flow develops near the sidewalls in the separating shear layer, and its impingement on the stepped wall is responsible for the maximum that develops in the Nusselt number adjacent to the sidewalls and for the reverse flow that develops in that region. The maximum Nusselt number on the stepped wall is located inside the primary recirculation flow region and its location does not coincide with the jetlike flow impingement region. The results reveal that the location where the streamwise component of wall shear stress is zero on the stepped walls does not coincide with the outer edge of the primary recirculation flow region near the sidewalls.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Measurement of Velocity Profiles of Laminar to Turbulent Water Flows in a Tube Using Particle Image Velocimetry

2004 ◽  
Author(s):  
Meredith R. Martin
Keyword(s):  
Reynolds Number ◽  
Particle Image Velocimetry ◽  
Particle Image ◽  
Glass Tube ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Reynolds Number Flow ◽  
Image Velocimetry ◽  
Dye Visualization ◽  
Number Flow

The transition from laminar to turbulent in-tube flow is studied in this paper. Water flow in a glass tube with an inside diameter of 21.7 mm was investigated by two methods. First, a dye visualization test using a setup similar to the 1883 experiment of Osborne Reynolds was conducted. For the dye visualization, Reynolds numbers ranging from approximately 1000 to 3500 were tested and the transition from laminar to turbulent flow was observed between Reynolds numbers of 2500 and 3500. For the second method, a particle image velocimetry (PIV) system was used to measure the velocity profiles of flow in the same glass tube at Reynolds numbers ranging from approximately 500 to 9000. The resulting velocity profiles were compared to theoretical laminar profiles and empirical turbulent power-law profiles. Good agreement was found between the lower Reynolds number flow and the laminar profile, and between the higher Reynolds number flow and turbulent power-law profile. In between the flow appeared to be in a transition region and deviated some between the two profiles.

Experimental characterization of three-dimensional corner flows at low Reynolds numbers

2012 ◽  
Vol 707 ◽  
pp. 37-52 ◽  
Author(s):  
J. Sznitman ◽  
L. Guglielmini ◽  
D. Clifton ◽  
D. Scobee ◽  
H. A. Stone ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Channel Cross Section ◽  
Experimental Characterization ◽  
Low Reynolds Numbers ◽  
Low Reynolds

AbstractWe investigate experimentally the characteristics of the flow field that develops at low Reynolds numbers ($\mathit{Re}\ll 1$) around a sharp $9{0}^{\ensuremath{\circ} } $ corner bounded by channel walls. Two-dimensional planar velocity fields are obtained using particle image velocimetry (PIV) conducted in a towing tank filled with a silicone oil of high viscosity. We find that, in the vicinity of the corner, the steady-state flow patterns bear the signature of a three-dimensional secondary flow, characterized by counter-rotating pairs of streamwise vortical structures and identified by the presence of non-vanishing transverse velocities (${u}_{z} $). These results are compared to numerical solutions of the incompressible flow as well as to predictions obtained, for a similar geometry, from an asymptotic expansion solution (Guglielmini et al., J. Fluid Mech., vol. 668, 2011, pp. 33–57). Furthermore, we discuss the influence of both Reynolds number and aspect ratio of the channel cross-section on the resulting secondary flows. This work represents, to the best of our knowledge, the first experimental characterization of the three-dimensional flow features arising in a pressure-driven flow near a corner at low Reynolds number.

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.

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