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 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.

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.

LOW REYNOLDS NUMBER FLOW OVER A SQUARE RIB

1997 ◽  
Vol 21 (4) ◽  
pp. 371-387
Author(s):  
D.A Billenness ◽  
N. Djilali ◽  
E. Zeidan
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Recirculation Region ◽  
Number Range ◽  
Reynolds Number Flow ◽  
First Results ◽  
Region Length ◽  
Number Flow

Laminar flow over a square rib placed in a fully developed channel flow is investigated over the Reynolds number range 80-350. The effect of Reynolds number on the flow and the variation of the primary reattachment length with Reynolds number are investigated using flow visualization and laser-Doppler velocimetry. The primary recirculation region length is found to increase in a slightly non-linear fashion with Reynolds number up to Reh = 250, at which point shear layer instabilities first appear downstream of the rib. Increasing the Reynolds number further, first results in continuing growth of the separation bubble, and then for Reh ≳ 300, in the appearance of three dimensional vortices and gradual shortening of the bubble. The measurements are complemented by two- and three-dimensional numerical simulations using a finite volume method with a high-order descretization scheme. These simulations yield excellent agreement with the measured reattachment lengths and velocity profiles over the steady laminar flow régime.

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.

The wake behind a cylinder rolling on a wall at varying rotation rates

2010 ◽  
Vol 648 ◽  
pp. 225-256 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Number Range ◽  
Rotation Rates ◽  
Transition Mechanism ◽  
Three Dimensional Simulations

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers

2004 ◽  
Vol 126 (3) ◽  
pp. 362-374 ◽  
Author(s):  
G. Biswas ◽  
M. Breuer ◽  
F. Durst
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Wall Jets ◽  
Number Range ◽  
Reynolds Number Range ◽  
Concave Corner

This paper is concerned with the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0. A literature survey was carried out and it was found that the flow shows a strong two-dimensional behavior, on the plane of symmetry, for Reynolds numbers ReD=ρUbD/μ below approximately 400 (Ub=bulk velocity and D=hydraulic diameter). In this Reynolds number range, two-dimensional predictions were carried out to provide information on the general integral properties of backward-facing step flows, on mean velocity distributions and streamlines. Information on characteristic flow patterns is provided for a wide Reynolds number range, 10−4⩽ReD⩽800. In the limiting case of ReD→0, a sequence of Moffatt eddies of decreasing size and intensity is verified to exist in the concave corner also at ReD=1. The irreversible pressure losses are determined for various Reynolds numbers as a function of the expansion ratio. The two-dimensional simulations are known to underpredict the primary reattachment length for Reynolds numbers beyond which the actual flow is observed to be three-dimensional. The spatial evolution of jet-like flows in both the streamwise and the spanwise direction and transition to three-dimensionality were studied at a Reynolds number ReD=648. This three-dimensional analysis with the same geometry and flow conditions as reported by Armaly et al. (1983) reveals the formation of wall jets at the side wall within the separating shear layer. The wall jets formed by the spanwise component of the velocity move towards the symmetry plane of the channel. A self-similar wall-jet profile emerges at different spanwise locations starting with the vicinity of the side wall. These results complement information on backward-facing step flows that is available in the literature.

Asymmetry and transition to turbulence in a smooth axisymmetric constriction

2008 ◽  
Vol 607 ◽  
pp. 351-386 ◽  
Author(s):  
J. VÉTEL ◽  
A. GARON ◽  
D. PELLETIER ◽  
M.-I. FARINAS
Keyword(s):  
Reynolds Number ◽  
Wavelet Transforms ◽  
Transition To Turbulence ◽  
Sudden Expansion ◽  
Recirculation Region ◽  
Discrete Wavelet ◽  
Spectral Structure ◽  
Mean Flow ◽  
Number Range ◽  
Structure Of Flow

The flow through a smooth axisymmetric constriction (a stenosis in medical applications) of 75% restriction in area is measured using stereoscopic and time-resolved particle image velocimetry (PIV) in the Reynolds number range Re ~ 100–1100. At low Reynolds numbers, steady flow results reveal an asymmetry of the flow downstream of the constriction. The jet emanating from the throat of the nozzle is deflected towards the wall causing the formation of a one-sided recirculation region. The asymmetry results from a Coanda-type wall attachment already observed in symmetric planar sudden expansion flows. When the Reynolds number is increased above the critical value of 400, the separation surface cannot remain attached and an unsteady flow regime begins. Low-frequency axial oscillations of the reattachment point are observed along with a slow swirling motion of the jet. The phenomenon is linked to a periodic discharge of the unstable recirculation region inducing alternating laminar and turbulent flow phases. The resulting flow is highly non-stationary and intermittent. Discrete wavelet transforms are used to discriminate between the large-scale motions of the mean flow and the vortical and turbulent fluctuations. Continuous wavelet transforms reveal the spectral structure of flow disturbances. Temporal measurements of the three velocity components in cross-sections are used with the Taylor hypothesis to qualitatively reconstruct the three-dimensional velocity vector fields, which are validated by comparing with two-dimensional PIV measurements in meridional planes. Visualizations of isosurfaces of the swirling strength criterion allow the identification of the topology of the vortices and highlight the formation and evolution of hairpin-like vortex structures in the flow. Finally, with further increase of the Reynolds number, the flow exhibits less intermittency and becomes stationary for Re ~ 900. Linear stochastic estimation identifies the predominance of vortex rings downstream of the stenosis before breakdown to turbulence.

Experimental Investigation of Heat Transfer in Low Frequency Pulsating Turbulent Flow in Circular Pipe

2010 ◽  
Author(s):  
Chang Wang ◽  
Puzhen Gao ◽  
Chao Xu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Turbulent Flow ◽  
Low Frequency ◽  
Relative Amplitude ◽  
Pulsation Frequency ◽  
Number Range ◽  
Nusselt Numbers ◽  
Reynolds Number Range

Heat transfer characteristic of low frequency pulsating turbulent water flow in a vertical circular pipe which is heated at uniform heat flux, are experimentally studied under different conditions of Reynolds number, pulsation frequency and relative amplitude. The experiments are performed with the Reynolds number range of 3000 to 20000, pulsation frequency range of 0.033 to 0.1 Hz, and the relative amplitude range of 0.1 to 0.8. This pulsating flow situation is used to simulate the phenomenon happened in the ship power system which is induced by ocean conditions. The effects of pulsation on heat transfer characteristics are presented in terms of relative local and mean Nusselt numbers defined as the ratio of the local and mean Nusselt numbers for pulsation flow to that of the ordinary steady turbulent flow with the same time-averaged Reynolds number Reta. The results show that the relative local Nusselt number is strongly affected by Reynolds number, pulsation frequency and relative amplitude. The phenomena that the Nusselt number would increase or decrease with the increase of the Reynolds number are both observed and the variation is more notable in the entrance region than that in the fully developed region. The relative mean Nusselt number decreases initially as the Reta increases, and then recovers gradually, but finally it has the tendency to decrease again. With the increase of pulsation relative amplitude, the relative mean Nusselt number increases at first and then decreases. And for the Reynolds number range of 3176 to 6670, heat transfer enhancement is observed as the pulsation frequency raises, but complete contrary phenomena appears at Reynolds number range of 11904 to 15844. The obtained heat transfer results are analyzed and seem to be qualitatively in accordance with previous investigations.

Heat Transfer Enhancement by Imposed Pulsation in a Channel With Sudden Expansion

1999 ◽  
Author(s):  
E. Tandogan ◽  
N. K. Mitra
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Cross Section ◽  
Sudden Expansion ◽  
Navier Stokes ◽  
Transfer Enhancement ◽  
Channel Axis ◽  
Number Range ◽  
Field Symmetry ◽  
Energy Equations

Abstract A numerical investigation of laminar pulsating flows in a channel with sudden expansion in the cross section has been performed by solving two dimensional Navier-Stokes and energy equations for an incompressible fluid. A sinusoidal pulsation has been imposed on the axial velocity at the inlet. Results show that the flow field symmetry at the channel axis vanishes at even a Reynolds number of 100. The time averaged Nusselt number of pulsating flow increases sharply over the nonpulsating flow in the Reynolds number range of 400 and 500. The time averaged Nusselt number on the two walls can be different.

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