ISSN 2277-2685 International Journal of Engineering ... Sumit...the flow through a plane...

*Corresponding Author www.ijesr.org 167

IJESR/April 2014/ Vol-4/Issue-4/167-180 ISSN 2277-2685

International Journal of Engineering & Science Research

FLOW THROUGH A SUDDEN EXPANSION: A REVIEW

S. Kumar*1, S. Chakrabarti

2, S. Majumder

3

1Dept. of Mechanical Engineering, Heritage Institute of Technology, Kolkata, West Bengal, India.

2Dept. of Mechanical Engineering, Bengal Engineering and Science University, Shibpur, West Bengal, India.

3Dept. of Mechanical Engineering, Jadavpur University, Kolkata, West Bengal, India.

ABSTRACT

A flow through sudden expansion configuration has been demanding area for researchers since last four

decades. Many researchers have done a lot of numerical and experimental work in this field. Review papers

available in this field are very limited. A bibliographical review on the flow through sudden expansion has been

presented in this paper. The numerical and experimental research activities appeared in the open literature are

critically analyzed. This review looks into the methodologies used to study the flow characteristics for various

channel geometrical parameters, types of fluid, flow conditions, plain and modified sudden expansion

configurations and other relevant parameters. The aim of this review is to summarize recent development in

research on the flow characteristics of the fluid through sudden expansion configuration for the purpose of

suggesting some possible reasons why this configuration can be used for industrial applications such as

combustor, diffuser, mixing devices, electronic cooling equipments, cooling of turbine blades, micro-fluidic

devices etc. and to provide a guide line or perspective for future research.

Keywords: Sudden expansion, Combustor, Diffuser, Aspect ratio, Expansion ratio, Back-ward facing step.

1. INTRODUCTION

Flows through sudden expansions are of interest from the view point of fundamental fluid mechanics as well as

practical applications. There is keen interest in the understanding of such flows due to their widespread

occurrence in many fluid applications including heat exchangers, dump combustors, diffusers, nuclear reactors,

in pipe-flow systems in the chemical, pharmaceutical and petroleum industries, in air-conditioning ducts and in

fluidic devices as well as in area of medical science. The flow of liquid through expansion geometries is also

relevant to a number of practical engineering applications, including extrusion processes, mold filling,

processing of food stuffs, creams and pharmaceutical matters, and in many other manufacturing processes.

During the last many years it has been of great interest to study the flow in channels with reversals and

experiencing the transition from symmetry to asymmetry. To aid in experimental and numerical investigations

of such a flows, the flow in a sudden expansion has been recognized as a representative test bed because it

involves a configuration which is regarded as having one of the most simple geometries. But on the other hand,

geometrical simplicity does not imply that the flow phenomena are also simple. Moreover, flow separation and

reattachment as well as multiple recirculating regions of fluid flow are those rich features that attracted the

interest of many researchers. The application of sudden expansion configuration is very vast. The number of

available literature on plain sudden expansion is very large; however the number of studies done on modified

sudden expansion is very limited. Thus, this literature review is intended to focus on the studies done on the

flow characteristics of fluid passing through plain sudden expansion and its modified configurations separately

for Newtonian and non-Newtonain fluids to obtain the best understanding of the topic.

2. A GENERAL LITERATURE REVIEW

2.1 Plain Sudden Expansion

The first numerical work in the field of plain sudden expansion was carried out by Abbot and Kline. Abbott and

Kline [1] are considered pioneers in the field of research of sudden expansion flows. They experimentally

investigated the subsonic turbulent flow over single and double backward facing steps. They studied separated


Copyright © 2013 Published by IJESR. All rights reserved 168

regions of turbulent, subsonic fluid flow system downstream of two-dimensional, backward-facing steps for the

Reynolds number range of 2×104 to 5 ×10

4. They observed that three different zones of flow exists in turbulent

separation: a three-dimensional zone immediately downstream of the step face and characterized by one or more

vortices rotating about an axis normal to the flow direction, a two-dimensional zone downstream of the earlier

zone, and a time dependent region which changed its size periodically. They further reported that the three zones

are of different length for area ratios greater than 1.5 for the double step configuration, which indicated the

presence of flow asymmetry, but for area ratios less than 1.5 the double step approaches the single step

configuration with symmetric stall regions. They also observed that Reynolds number and turbulence intensities

were strong effect on flow pattern or reattachment length. Macagno and Hung [2] studied flow visualization in

sudden expansion configuration in axisymmetric flows for a Reynolds number ranging from 36 to 4500, by

means of computational simulation, for an aspect ratio of 2 and of Reynolds number up to 200. They concluded

that, for laminar flow, the main role of eddy is that of shaping the flow with rather a small energy exchange.

Using the laser Doppler anemometry (LDA) Durst et al. [3] examined the Newtonian fluid flow in a 1:3 planar

symmetric expansion. In their experiments, two symmetric vortices along the walls of the expansion were

observed at Re = 56. At Re = 114, flow bifurcation was already observed with vortices of unequal size forming

at both salient corners. The experimental measurements of Chedron et al. [4] also relied on LDA, but are more

comprehensive and explored the flow patterns and instabilities in ducts with symmetric expansions. The effect

of aspect ratio of tested geometry was also investigated. Their study for channels with moderate expansion ratios

demonstrated that when Re is relatively low the flow in the channel was steady, two-dimensional (2D) and

symmetric with two separation zones near the expansion corners, the size of which increased with Re. However,

at higher values of Re, the flow stays 2D and steady but becomes asymmetric with two separation zones of

different lengths which attached on either the upper or the lower wall of the channel. At even higher Re,

additional recirculation zones appear along the channel walls. Armaly et al. [5] employed Laser Doppler

Anemometer to measure the velocity distribution and reattachment lengths downstream of a single backward-

facing step mounted in a two- dimensional channel. In their study laminar, transitional and turbulent flow of air

in a Reynolds-number range of 70 to 8000 are considered. They observed that the various flow regimes are

characterized by typical variations of the separation length with Reynolds number. Their study revealed that

even though the inlet flow was fully developed and two-dimensional, the flow downstream of the step only

remain two-dimensional at low and high Reynolds numbers. They observed that in addition to the main

recirculating flow region downstream of the step, secondary vortex forms on both the sides of the channel at

high Reynolds numbers. So and Ahmed [6] numerically investigated the effect of turbulent flow and

geometrical parameters on the performance of dump combustors. They studied two different step heights and

the effect of rotation on the flow behavior. They concluded that when all inlet geometrical and flow parameters

except step height are kept constant; the net effect of step height on the flow in the combustor is negligibly

small. Shapira et al. [7] studied the stability and existence multiple solutions for viscous flow in a suddenly

enlarged channel. Linear stability of a two dimensional flow through a symmetric channel was studied. They

performed numerical computation of the flow field and linear disturbances using time dependent finite element

algorithm. The channel semi angle considered was in the range of 100 to 90

0. Their study indicated the existence

of steady non symmetrical solutions for Reynolds number greater than a certain critical value The main feature

of their work was the manner in which the stability of the least-stable mode was determined, using an energy-

based method. In their work there was no evidence of multiplicity of stable, non-symmetric solutions, nor for

any further limit points on the non-symmetric branches. Durst et al. [8] studied the plane symmetric sudden-

expansion flow at low Reynolds numbers. They performed detailed measurements and numerical predictions for

the flow through a plane two-dimensional duct with asymmetric sudden expansion of area ratio 1:2. Both

experimental and numerical predictions confirmed a symmetry breaking bifurcation of flow leading to one long

and one short separation zone for Reynolds numbers above 125, based on the upstream channel height and the

maximum flow velocity upstream. They observed the increase in length of the long separation region while the

short region remains approximately constant as the Reynolds numbers increased above 125. They used laser-

Doppler anemometer to obtain the experimental data. Numerical predictions were made using finite volume

method. Foumeny et al. [9] performed a computational investigation into the bifurcations of incompressible

Newtonian flow through plane symmetric channel expansions. Their study was focused in determination of the



critical value of the Reynolds number, above which the flow became asymmetric with respect to the channel

geometry. They considered two systems, first, a channel model in which the channel walls downstream of the

expansion were modeled by the no-slip conditions and second one was the cascade model, in which cyclic

boundary conditions were specified. They compared the obtained results with the experimental and numerical

data obtained by previous investigators. Oliveira and Pinho [10] numerically studied Laminar flow of a

Newtonian fluid in an axisymmetric pipe expansion. They adopted a finite-volume approach for the

computational work. The results obtained from the numerical work for the overall flow characteristics, such as

recirculation length, its strength, and centre location, were compared with available experimental data and

correlations, and good agreement was found. The main motivation of this investigation was to evaluate the

pressure-loss coefficient for a range of Reynolds numbers and compared the results with existing simplified

theory, which was based on a one-dimensional (l-D) overall balance of energy and momentum. They observed

considerable differences in the comparison and formulated corrected theoretical equations for the 1-D

approximation. They proposed a correlation for calculating the local loss coefficient as a function of the

Reynolds number for the 1:2.6 sudden expansion and fully developed conditions. Drikakis [11] found that the

critical Reynolds number for the symmetry-breaking bifurcation was reduced when the expansion ratio was

increased. The experimental and numerical study of Fearn et al. [12] in 1:3 planar expansion had shown a

similar flow bifurcation at a Reynolds number of 40.5. In contrast to the few experimental investigations, there

was a large number of numerical works available in the literature and one of its advantages is that it was

possible to investigate truly 2D flows. Alleborn et al. [13] had examined the two-dimensional laminar flow of

an incompressible viscous fluid through a channel with sudden expansion. They used a continuation method to

study the bifurcation structure of the discretized governing equations. Arnoldi based iterative method was used

to investigate the stability of the different solution branches by calculating the most unstable eigenmodes of the

liberalized equations for the perturbation quantities. Additional solution branches and bifurcation points were

computed. They studied the behavior of critical eigen values in the neighborhood of these bifurcation points.

Numerical results for the limiting cases for the geometrical and flow parameters were compared with the

analytical solutions for these cases. The study revealed the presence of weak viscous eddies, known as Moffat

eddies, in the corners of the expansion in the creeping flow limit. The numerically computed stream function

was compared in the regions of the corner vortices with an approximation formula derived by Moffat, and a

good agreement with previous results was found. Lee and Mateescu [14] performed experimental and numerical

investigation of 2-d backward-facing step flow. They used, multi-element hot-film sensor arrays to measure the

lengths of separation and reattachment on the upper and lower walls for Re ≤ 3000 and expansion ratios of 1.17

and 2.0. The results obtained from their experiments show that, by the use of multiple hot-film sensor (MHFS)

arrays operated with a bank of constant-temperature anemometers, the locations of flow separation and

reattachment points on the upper and lower walls of the two-dimensional channel could be measured both non-

intrusively and simultaneously. They observed that the results obtained from this method were in good

agreement with results predicted from the numerical analysis. Hammad et al. [15] used real-time digital particle

image velocimetry (PIV) for experimental study on the laminar flow through an axisymmetric sudden expansion

with expansion ratio 2. In their experiment the measurements covered the regions of separation, reattachment

and re-development. Two dimensional velocity maps were obtained on the vertical center plane for six Reynolds

numbers between 20 and 211. They studied the dependence of reattachment length, redevelopment length and

recirculating flow strength on the Reynolds number. They observed that not only the reattachment length but

also the redevelopment length downstream of reattachment was a linear function of the Reynolds number, while

the recirculation eddy strength, on the other hand, was dependant nonlinearly on the Reynolds number. They

also observed that recirculation eddy strength became weaker as the Reynolds number increased. Khezzar et al.

[16] experimentally performed to quantify the isothermal and combusting flows downstream of a plane sudden

expansion. They had used an area ratio of 2.86 and a Reynolds number of 20000. The equivalence ratios for

smooth and rough combustion measurements were 0.72 and 0.92 respectively. The results showed that the

extent of asymmetry of the isothermal flows was reduced by coupling the pressures between the two

recirculation regions. Mizushima and Shiotani [17] in their study of structural instabilities of bifurcation

diagram had found that a flow in a symmetric channel with a sudden expansion makes a transition from a

symmetric flow to an asymmetric one due to a symmetry-breaking pitchfork bifurcation on increasing the Re if



the system was perfectly symmetric. An infinitesimal imperfection of the system could render the pitchfork

bifurcation imperfect. The authors proposed a weakly non-linear stability analysis to investigate the structural

instability of the bifurcation observed in such flows. The authors derived an amplitude equation for a

disturbance by including the effect of imperfection of the systems. They emphasized that the weakly non-linear

stability theory showed the essential and skeleton dynamics of the bifurcation phenomena, from which it was

possible to study the underlying physics of instabilities. The equilibrium amplitude of the disturbance was

calculated from the amplitude equation and compared with both experimental results obtained in previous cases

and also with the numerical solution of the full non-linear equations for the flow in a slightly asymmetric

channel. Comparison of the results from the weakly non-linear stability analysis with the experimental and

numerical results was done and it was shown that the parameter range where the weakly non-linear stability

theory gave a very good approximation is limited in the vicinity of the critical point. Hawa and Ruzak [18]

performed bifurcation analysis, linear stability study and direct numerical simulations of the dynamics of a two-

dimensional, incompressible laminar flow in a symmetric long channel with a sudden expansion. The

bifurcation analysis of solutions of steady Navier-Stokes equations was concentrated on the equilibrium states

around a critical Re where asymmetric states appeared in addition to the symmetric states. The stability analysis

was based on the liberalized equations of motion for the evolution of infinitesimal two-dimensional disturbances

imposed on the steady symmetric as well as the asymmetric states. The simulations clarified the relationship

between the linear stability results and the time-asymptotic behavior of the flow as described by the asymptotic

steady-state solution. It was observed that the symmetric flows with Re < Rec are linearly stable to two-

dimensional disturbances, whereas the symmetric states with Re > Rec are unstable. The dynamics of both small

and large amplitude disturbances in the flow is described and the transition from symmetric to asymmetric flow

is demonstrated. Thus the author infers that the critical state is a point of exchange of stability for both

symmetric and asymmetric states. The broad picture of the studies is: when the Re was sufficiently low, the flow

cannot sustain any disturbance and any initial disturbance decayed through viscous dissipation. As the Re was

increased, viscous dissipation reduced and the symmetric flow became less stable. Kadja et al. [19] performed a

numerical investigation of bifurcation phenomena occurring in flows through planar sudden expansions. A new

convection scheme Variable-Order Non-Oscillatory Scheme (VONOS) along with a multi-grid algorithm was

used for an in-depth study of bifurcation phenomena which occurred in flows through planar sudden expansions.

This new scheme contributed to a considerable increase of accuracy and convergence rate. The predictions

offered a good qualitative behavior of the flow bifurcation parameters. For Reynolds numbers below Rec the

flow remained symmetric throughout all the period of its development, during which the recirculation lengths

increased monotonically with time towards their final stationary values. For Reynolds numbers above Rec. the

flow changed from a symmetric structure at the beginning to an asymmetric one at the steady state where one of

the main recirculation zones became longer than the other, and a third zone appeared on the same side as the

short primary recirculation zone. Chakrabarti et al. [20] made an extensive study on the performance of sudden

expansion from the perspective of a diffuser. They solved two-dimensional steady differential equations for

mass and momentum conservation equations for the range of 20<Re<100, aspect ratio from 1.5 to 4, for uniform

velocity profile and fully developed velocity profile at inlet, and for different inlet lengths. They studied the

effect of each variable on the diffuser efficiency and the stagnation pressure drop gradient in detail.

In many realistic situations the fluids flowing through flow devices were non-Newtonian and showed complex

rheological behavior. Specifically, theycould exhibit shear-thinning viscosity depending on the type of fluid and

thus it was relevant to investigate the non-Newtonian fluid flow in planar expansions starting with simple

rheological models in order to independently assess the impact of specific rheological features upon the flow

characteristics. If the non-Newtonian solutions were not too concentrated the flows tend to have a high Reynolds

number, even leading to turbulent flow. Since the sudden expansion is a well-known geometry for studies of

laminar flow instabilities at high Reynolds numbers, in recent years it has naturally started to attrach the

attention of researchers in the field of non-Newtonian fluid mechanics wishing to investigate the complex

interaction between these bifurcations and fluid rheology, namely viscoelasiticity. The non-Newtonian power –

law model is the simplest model for a purely viscous fluid that can represent the behavior of shear-thickening

and Newtonian fluids by varying the parameter of the model, n, known as the power law index. Mishra and

Jayaraman [21] had examined numerically and experimentally the asymmetric steady flow patterns of shear-



thinning fluids through planar sudden expansions with a large expansion ratio, ER = 16. Manica and De Bortoli

[22] studied numerically the flow of power-law fluids in a 1:3 planar sudden expansion for n = 0.5, 1 and 1.5.

They presented the vortex characteristics for these values of n and for 30≤Re≤ 125, and observed that the flow

bifurcation for shear-thinning fluids occurred at a critical Reynolds number higher than for Newtonian fluids,

and that shear-thickening fluids exhibited the lowest critical Reynolds number. Considering again purely

viscous fluids represented by the power-law and Casson models, Neofytou [23] analysed the transition from

symmetric to asymmetric flow of power-law fluids with power-law indices in the range 0.3≤n≤3 in 1:2 planar

sudden expansion and also studied the effect of Reynolds number on the flow patterns. Ternik et al. [24] studied

the flow through a 1:3 planar symmetric expansion of non-Newtonian fluids with shear-thickening behavior

using the quadratic and power-law viscosity models. They compared the results of both models with those of

Newtonian fluids and concluded that the occurrence of flow asymmetry was greatly affected by the shear-

thickening behavior. Later, Ternik computed the flow of shear-thinning fluids with power-law indices n = 0.6

and 0.8 in a 1:3 planar sudden expansion. After the first bifurcation, from a symmetry to asymmetry flow, a

second flow bifurcation, marking the appearance of a third vortex, was investigated as the generalized Reynolds

number was further increased, with shear-thinning delaying the onset of this second bifurcation. More recently,

Ternik [25] revisited the generalized Newtonian flow in a two-dimensionmal 1:3 sudden expansion using the

open source open FOAM CFD software. The fluid was again represented by the powe-law model with power-

law index in the range of 0.6≤n≤ 1.4 and the simulatons were performed for generalized Reynolds numbers in

the range 10-4≤Regen≤10 with the emphasis on the analysis of low Reynolds number flows, below the critical

conditions for the onset of the pitchfork bifurcation. Small recirculation, typical of creeping flow was observed

for all fluids with shear-thinning behavior reducing the size and intensity of the secondary flow. Numerical

simulations of the flow of power-law fluids in a planar 1:3 sudden expansion using commercial or open source

codes were also attempted by several authors. It has been found that the solution convergence was often a major

limitation when utilizing these codes especially when the non-Newtonian behavior was enhanced. For instance,

Poole and Ridley [26] used Fluent software to numerically calculate the development-length required to attain

fully developed laminar pipe flow of inelastic power-law fluids and were unable to attain a converged solution

for n<0.4. Ternik [27] reported that the iterative convergence had become increasingly time consuming with a

reduction in power-law index, and for n<0.6. No converged solutions were obtained using the open FOAM

SOFTWARE. Mistrangelo and Buhler [28] had investigated MHD flows in sudden expansions of rectangular

ducts numerically and by an asymptotic- numerical approach. The numerical tool was consisted in an extended

version of the commercial code CFX and gave accurate results for Hartmann numbers up to 1000. The

asymptotic method had been employed for creeping MHD flow at very strong magnetic fields. Numerical

results were presented for a constant Reynolds number and increasing imposed magnetic field. They had shown

that for moderate Hartmann numbers vortices may form behind the expansion. However, they were suppressed

already at Ha > 60. Moreover, regions with very small velocities were detected close to the outer corners of the

cross-section enlargement. For strong magnetic fields an internal layer developed at the expansions, which

collects the flow from the upstream core and distribute a large fraction towards the side layers. The additional

pressure drop caused by 3D induced currents and the flow rate carried by the side layers and the internal layer

was quantified. Buhler et al. [29] had done experiments on MHD flows in electrically conducting sudden

expansions of rectangular ducts performed for high Hartmann numbers. The pressure distribution along the

Hartmann wall and the distribution of wall potential was measured up to values above Ha = 5000. Results for

pressure measurements gave a clear indication that the total pressure drop contained an inertial distribution that

might be quite significant for moderate N but which vanished asymptotically as N tends to infinity. However,

even at the highest value investigated in this work, i.e., N = 39,151, a weak inertial contribution was still

observable. For N tends to infinity the measurements confirm quite well inertia less asymptotic predictions for

pressure distribution. Based on inspection of wall potential it was possible to identify the decreased velocity in

center of the cores and the increased velocity closer to the side walls, when approaching the expansion. The

profiles of side wall potential gave further information about the distribution of the local side layer flow rates

and indicated a strong side layer jet immediately behind the expansion. A comparison between measured and

calculated surface potentials was performed at the symmetry plane of the side wall which showed good

agreement. Lima et al. [30] reported numerical simulations of the two-dimensional laminar flow over a



backward-facing step channel using two commercially-available computational fluid dynamics (CFD) code.

They analyzed the three recirculation regions of the flow in a unilateral sudden expansion. Results were

presented for laminar air flow for Reynolds number lower than 2500. The mathematical model equations (mass

conservation and momentum) were solved with finite element (FEM), finite volume (FVM) methods and a

segregated approach. To get the grid independent, intensive refinement studies were carried out. Results

obtained were compared to experimental data presenting a good agreement. Aloui and Madani [31] studied the

flow characteristics of aqueous foam through a horizontal sudden expansion localized in the middle of a

horizontal duct. With a square section 21× 21 mm2 in the upstream and a rectangular section 21× 42 mm2 in the

downstream, this singularity was an aspect ratio of 0.5. Through this sudden expansion, they determined the

static drainage, the regular pressure loss, the wet foam flow dynamics in the vicinity of the singularity using

PIV, the thickness of the underlying liquid film, and finally local void fraction and bubble sizes. In the vicinity

of the expansion, singular pressure rise was deduced by extrapolation using the linear static pressure

measurement evolutions obtained in the upstream and downstream far from the singularity. However, the

average and fluctuating velocities using PIV method near the singularity, were obtained from a series of 150

instantaneous snapshots for each chosen quality of the foam low reorganization. They had shown the influence

of the presence of such a singularity on the underlying liquid film thickness, for the three cases of study (case A:

U = 2 cm/s, case B: U = 3 cm/s and case C: U = 4 cm/s). In mono-dimensional flow, and when the gravitational

drainage was completed, the underlying liquid film thickness becomes independent of the foam velocity. In two-

dimensional flow, this thickness decreased when the foam velocity increased. Concerning the gravitational

drainage, they had noted that the quantity of drained liquid decreased with the quality of foam β and with the

foam velocity. Downstream of the expansion, the bubble sizes and the local void fraction were influenced by the

presence of the singularity. These results showed that the presence of such singularities in the foam flow

systems could have serious effects on the end-of-duct structure of the foam. Zdanski et al. [32] presented

numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The

mathematical model includes the mass, momentum and energy conservation laws within the framework of a

generalized Newtonian formulation. Two constitutive relations were adopted to describe the non-Non-

newtonian behavior of flow, namely Cross and Modified Arrhenius Power-law models. The governing equations

were discretized using the finite difference method based on central, second-order accurate formulas for both

convective and diffusive terms. The pressure-velocity coupling was treated by solving a Poisson equation for

pressure. They presented the results for two commercial polymers and demonstrate the important flow

parameters, such as pressure drop and viscosity distribution, were strongly affected by heat transfer features.

They concluded that for both polymers subjected to the same boundary conditions, despite the similarity of the

flow topology, the pressure variation computed was markedly different due to viscosity effects. In this class of

problems, viscosity was closely related to temperature, thereby introducing a strong coupled character to the

problem. The parametric analysis had shown that the pressure distribution inside the channel was strongly

related to both the expansion ratio and the inlet polymer temperature. For a given expansion ratio, the pressure

coefficient decreased linearly with increasing inlet temperatures. For the conditions modeled in this work, as

expansion ratio decreased from 4.0 to 2.0, the pressure loss computed along the channel was reduced by 40%.

Zhang et al. [33] presented a computational investigation of laminar forced convection of supercritical CO2 flow

in horizontal duct with plane symmetric sudden expansion and its bifurcation phenomenon. The computations

were conducted at various Reynolds numbers for cases of different wall heat fluxes. They introduced a

parameter named recirculation disturbance intensity aimed to shed some light on the reduction of flow stability

when Reynolds number or wall heat flux increased. The Nusselt number distribution in the symmetric flow

regime was presented, the variation of peak Nusselt number and its relative location were discussed. Wall

friction coefficient and pressure coefficient distributions were presented and discussed. They observed that

unlike the gas flow, the size of the recirculation region increased with the increase of wall heat flux due to

thermal induced enhancement of reverse pressure difference. The peak Nusselt number increased as the

Reynolds number or wall heat flux increased. With the increase of Reynolds number, the location of peak

Nusselt number didnot not seem always in the recirculation region and its relative location moved into the

recirculation region from downstream and shifts upstream towards the inlet. As the wall heat flux increased, the

movement of the relative location appeared irregular. With the larger temperature gradient at the wall for higher



heating intensity, this irregularity might arise from the interaction of the sharp change of thermo-physical

properties near the wall. The critical Reynolds number decreased as wall heat flux increased. The increasing

recirculation disturbance intensity strengthens the flow disturbance and thus flow got less stable and the critical

Reynolds number decreased. Balakhrisna et al [34] studied the change of flow patterns during the simultaneous

flow of high viscous oil and water through the sudden contraction and expansion in a horizontal conduit. They

found that these sudden changes in cross-section had significant influence on the downstream phase distribution

of lube oil-water flow. The observation suggested a simple technique to establish core flow as well as a way to

prevent pipe wall observed a number of interesting differences during low viscous oil-water flow through the

same test rigs. While several types of core annular flow were observed for the former case, a wider variety of

interfacial distribution characterizes kerosene water systems. They also studied the pressure profiles during the

simultaneous flow of lube oil and water through the sudden contraction and expansion and had compared with

low viscous oil-water flows. The pressure profiles were found to be independent of liquid viscosity and the loss

coefficients were observed to be independent of flow patterns in both the cases. Zohir et al. [35] had studied the

heat transfer characteristics and pressure drop for turbulent airflow in a sudden expansion pipe equipped with

propeller type swirl generator or spiral spring with several pitch ratios. The investigation was performed for the

Reynolds number ranging from 7500 to 18500 under a uniform heat flux condition. The experiments were done

for three locations for the propeller fan (n = 15 blades and blade angle of 650) and three pitch ratios for the spiral

spring (P/D = 10, 15 and 20). The influences of using the propeller rotating freely and inserted spiral spring on

heat transfer enhancement and pressure drop were reported. In the experiments, the swirl generator and spiral

spring were used to create a swirl in the tube flow. They determined mean and relative mean Nusselt numbers

and compared with those obtained from other similar cases. The experimental results indicated that the tube with

the propeller inserts provided considerable improvement of the heat transfer ratio over the plain tube around

1.69 times for X/H = 5. While for the tube with the spiral spring inserts, an improvement of the heat transfer rate

over the plain tube was around 1.37 times for P/d = 20. The increase in pressure drop using the propeller was

found to be three times and for spiral spring 1.5 times over the plain tube. They developed correlations for mean

Nusselt number, fan location and spiral spring pitch. Mandal et al. [36] presented the numerical analysis and

performance simulation of a sudden expansion with fence viewed as a diffuser. SIMPLE algorithm was used to

solve two-dimensional steady differential equations for conservation of mass and momentum. The Reynolds

number was in the range of 20 to 100 and fence subtended angle (FSA) between 100 to 300. The location of

fence from throat varies from 0.2 to 2.6. An aspect ratio for all computations was taken to be 2. They studied the

effect each variable on average static pressure, diffuser effectiveness, distance of maximum static pressure rise

and average stagnation pressure and also compared with respect to simple sudden expansion without fence. It is

revealed from the computation for lower Reynolds number regime that the effectiveness with fence offered

benefit depending on the positioning of the fence and fence subtended angle. Fence at any location always

offered benefit at relatively higher Reynolds number at any value of fence subtended angle. They found that

fence subtended angle and location of fence had no appreciable impact on distance of maximum static pressure

rise from throat and average stagnation pressure drop at a particular value of Reynolds number. Sousa et al. [37]

investigated the three-dimensional flow of Newtonian and viscoelastic fluids through square-square expansions.

Visualizations of the flow patterns were performed using streak photography, the velocity field of the flow was

measured in detail using particle image velocimetry and additionally, pressure drop measurements were carried

out. They investigated the Newtonian fluid flow for the expansion ratios of 1:2.4, 1:4, and 1:8 and compared the

experimental results with numerical predictions. For all expansion ratios studied, a corner vortex was observed

downstream of the expansion and an increase of the flow inertia leads to an enhancement of the vortex size.

They found a good agreement between experimental and numerical results. The flow of the two non-Newtonian

fluids were investigated experimentally for expansion ratios of 1:2.4, 1:4, 1:8 and 1:12, and compared with

numerical simulations using the Oldroyd-B, FENE-MCR and sPTT constitutive equations. For both the Boger

and shear-thinning viscoelastic fluids, a corner vortex appeared downstream of the expansion, which decreaseed

in size and strength when the elasticity of the flow was increased. For all fluids and expansion ratios studied, the

recirculation that were formed downstream of the square-square expansion exhibit a three-dimensional structure

evidenced by a helical flow, which was also predicted in the numerical simulations. Nassar et al. [38] used a

recently proposed constitutive model that addresses the elastic behavior of viscoplastic liquids. They used the



equation in an expansion-contraction axisymmetric flow, and compared the results with experimental data found

in the literature. Steady, inertialess numerical solutions were obtained by solving the balance equations of mass

and momentum via the finite element method. They obtained the velocity and stress fields for different

combinations of the governing parameters. It was observed that elasticity lead to significant changes in the

shape and position of the yield surface, affecting both the extra-stress and the rate of deformation fields in the

cavity. The trends observed were in qualitative agreement with visualization results available in the literature.

Kaushik et al. [39] performed a computational fluid dynamic simulation to investigate core annular flow through

sudden contraction and expansion. They simulated core annular flow of lubricating oil and water using VOF

technique and a satisfactory match between simulated data and experimental results was obtained. A detailed

study was performed to generate the profiles of velocity, pressure and volume fraction over a wide range of oil

and water velocities for an abrupt expansion and contraction. They observed the asymmetric nature of velocity

across the radial plane for both the cases. Zohir and Gomaa [40] studied the heat transfer and pressure drop

characteristics for turbulent air-flow in a sudden expansion pipe (d/D = 0.72) equipped with propeller swirl

generator with different blade angles. They performed the investigation for the Reynolds number ranging from

10000 to 40000 under a uniform heat flux condition. Three propeller fans of five blades with swirl anlgles � =

150, 300, 450 for upstream flow and one propeller fan with swirl angle 450 for downstream flow were inserted

separately inside the test section. The swirl propeller fan was located at different locations inside the tested pipe,

where S = 10H, 20H and 40H for both upstream of the tube provides considerable improvement of the heat

transfer rate up to 190% for all swirl angles with higher values obtained at � = 450. They found that inserting the

propeller down-stream of the tube provides more improvement in heat transfer rate than inserting the propeller

upstream of the tube provides more improvement in heat transfer rate than inserting the propeller upstream of

the tube at swirl angle � = 450, the heat transfer rate increased up to 225%. The maximum enhancement factor

for the downstream swirler was about 326% while it was about 213% for the upstream one. They also presented

correlations for relative mean Nusselt number and enhancement factor for different fan locations, swirl angle

and Reynolds number.

2.2 Sudden Expansion with Some Modifications

Some research activities have also been initiated to study the flow characteristics and performance of sudden

expansion configurations with some modifications e.g., incorporation of suction on the wall, incorporation of

fence in the diffuser zone, incorporation of blowing on the wall, incorporation of diverging channel after sudden

expansion, incorporation of swirling devices with sudden expansion etc. Among them, diffuser such as vortex

bleed diffuser, a duct bleed diffuser, a diffuser with simple boundary Walker et al. [41] experimentally and

numerically studied the operation of a diffuser. They studied several geometric variations of a bleed layer bleed,

and a duct bleed diffuser with no fence. In a recent work Chakrabarti et al. [42] performed a numerical

simulation to study the performance of a of sudden expansion configuration with multiple number of steps for

Reynolds number in the range of 20 to 100. Aspect ratio for each configuration used was fixed at 2. The authors

studied the effects of Reynolds number and multiple steps on static pressure rise, diffuser effectiveness and

distance to the location of maximum static pressure rise. Authors noticed benefits on both diffuser effectiveness

and stagnation pressure drop for the multiple step configuration. They observed that the average stagnation

pressure drop was less in case of multistep sudden expansion than that of a plain sudden expansion for a

particular value of Reynolds number. Their study revealed that increase in number of steps did not have much

impact on the effective length for a particular Reynolds number. From literature, it appeared that the first

experimental work on the performance study of vortex-controlled diffusers was reported by Heskestad [43].

Heskestad experimented with a suction slot at the convex discontinuity of a strep expansion in a circular pipe.

Two 300

included-angle wedges were formed the suction gap. He considered two area ratios with flow Reynolds

number varying between 2×104 and 20 ×104. He used uniform inlet velocity profile with a thin boundary layer in

his experiment. It was found that the flow turned in the corner in a manner that significantly decreased the

recirculation length. Hahn et al. [44] studied the use of suction for prevention of transition of flow downstream

of a backward facing step. They adopted distributed suction approach through closely spaced slots in the near

throat region. They investigated the effect of Reynolds number and step height on transition of the boundary

layer for both with and without suction. They observed that the reattachment length gradually increased with



step height Reynolds number in the regime of pure laminar separation. The turbulent intensity of the flow

downstream of the reattachment region was largely controlled by the suction rate and suction location. They

reported that prevention of premature transition caused by the separated flow over a backward facing step could

be achieved by suction in the neighborhood of the reattachment region that occurred without suction. Verigin

[45] experimentally investigated the influence of porous injection and suction on the drag and pressure recovery

and efficiency of a conical diffuser. Author had used a vacuum pump for application of the suction force. Area

ratio and divergence angle considered by him were 5.15 and 120 respectively. Both primary and secondary flows

were subsonic with Mach number of 0.34. Reynolds number ranges considered for suction and injection are (1-

5) x 105 and (.5-4) x 10

5 respectively. He observed a very interesting feature that injection and suction hadvery

little influence on upstream and downstream position of the separation zone but there was a considerable change

in the static wall pressure distribution. He observed that the pressure recovery in the diffuser configuration

considered in the study, lowers with porous injection, but it helped in protection the structural element from

thermal stresses. He also reported that with porous suction the pressure recovery increased over the entire

length. Spall [46] performed a numerical study of a prototypical vortex controlled diffuser. The geometry of the

diffuser used consists of a step expansion in a pipe with a area ratio 2.25:1. He solved the incompressible

Reynolds averaged Navier-Stokes equations, employing the K-� turbulence model in his numerical analysis.

Bleed rates used are in the range of 1 to 7 percent. He obtained diffuser efficiency in the excess of 80 percent.

The results revealed in the study put light on the mechanism of operation of a vortex-controlled diffuser. The

results obtained do not support the hypotheses that the increase turbulence generated at the suction slot inhibits

flow separation along the wall downstream of the fence. Rather the results supported the proposal put forth by

Heskestad [43] that the effectiveness of the diffuser was a consequence of the turning of the flow around the

sharp corner, thus diminishing the length of the recirculation zone. Yang et al. [47] presented a numerical study

on fluid flow characteristics within the recirculation zone for a backward-facing step with uniform normal mass

bleed in the turbulent flow regime. The turbulent governing equations were solved by a control-volume-based

finite-difference method with power-law scheme. Non-uniform staggered grids were used. The channel

expansion ratio ER = 1.3, and the working medium was air. The attachment point extended to downstream.

From the computational results, normal injection significantly affected the flow field of the recirculation zone

behind the step. The horizontal velocity near the wall in the recirculation zone decreaseed with increasing the

injection rate. With normal injection, both the maximum reverse velocity and reverse flow rate in the

recirculation zone were found to be decreased. Janour and Jonas [48] studied the prospect of suction and

blowing through a gap at the foot of the step on a straight channel with rectangular cross-section in controlling

the separation region. They observed that the narrower channels had smaller recirculation zone than the broader

ones. They reported that Reynolds number affected the length only in the case of a narrow channel. The authors

also studied the effect of inlet turbulence on separation zone length and reveals that the turbulence level didnot

affect the recirculation length significantly except for very small suction rate. They reported that both outer

stream turbulence and the suction decreased the dissipation losses in the separation zone. Finally they concluded

that it is possible to control the occurrence of vortices by means of suction. Batenko et al. [49] numerically

investigated the influence of suction and blowing on friction and on heat transfer in separated laminar flow

behind a backward-facing step. Their study was covered with both unconfined and duct flow condition. Their

study revealed that the blowing and the suction were powerful factors affecting on friction and heat transfer

inside the recirculation zone. The local characteristics of friction and of heat transfer in separation zone were

more sensitive to suction than to blowing. They observed that when intense injection was applied the

recirculation bubble just behind the step diminishes. They also reported that just behind the step regions of

negative shear stresses were formed due to the combined action of separation and injection. They also observed

that for low Reynolds numbers, the transverse wall flow through the permeable wall had very little influence on

the reattachment length. Uruba et al. [50] experimentally investigated different flow separation control method

like suction and blowing in a narrow channel flow behind a backward-facing step. The flow considered was

inherently turbulent at a Reynolds number of 5.104. They examined the effect of blowing/suction slot shape on

flow control effectiveness. For this purpose they used various slots which differ in both shape (rectangular or

serrated) and cross-section. They concluded that both suction and blowing were effective in controlling flow

separation in turbulent backward-facing step flow. Their study revealed that suction effectiveness was relatively



insensitive to the orifice profile but blowing was strongly dependent on the slot profile as blowing completely

relayed on entrainment of high momentum fluid in the recirculation region. They also observed that suction

influenced the vortex structures near the back step. Layek et al. [51] performed a numerical simulation study of

the laminar separated flow in a symmetric sudden expansion channel to see the effect of uniform porous suction

and blowing on it and also on the symmetry breaking flow bifurcation. Authors used finite difference method to

solve the Navier-stokes equation in a staggered grid arrangement. They observed that with increasing blowing

speed there was a considerable decrease in the wall shear stresses in the recirculation and the reattachment point

was shifted towards upstream direction. From this they came with the opinion that blowing shrinks the large

recirculation zone. They noted that application of blowing from the step walls increased the stability to

asymmetric perturbation by increasing the critical Reynolds number for flow symmetry bifurcation. But the

authors noticed a completely opposite nature of flow when suction was applied from the porous step wall. They

observed that with increasing value of suction velocities the length of the recirculation zone also increased. They

further reported asymmetry creeping into the flow with increasing suction velocity. They proposed that suction

could be used as an asymmetry generator. Sano et al. [52] studied the separation control of turbulent channel

flow over a back-step by applying continuous suction through a slit placed at the bottom corner of the step. The

authors measured the local heat transfer coefficient and wall static pressure by applying suction in both

perpendicular and horizontal direction separately. They observed that turbulence intensity and Reynolds shear

stress increased with increasing suction that result in improvement of local heat transfer coefficient near the

step. They reported that application of suction on a turbulent channel flow over a backward-facing step

enhanced the pressure recovery. Their study revealed that the direction of suction had no significant effect on

wall static pressure and heat transfer coefficient. Zheng et al. [53] numerically investigated Separation control

over a backward-facing step (BFS) flow by continuous suction using the turbulence model of large eddy

simulation (LES). They studied the effect of suction control on the flow fields by altering the suction flow

coefficient. Their study revealed that suction was not only very effective in shortening the reattachment length

but also very influential in reducing the tangential velocity gradient and turbulence fluctuations of the reattached

flows. Bakhshan et al. [54] had done flow separation study of a turbulent flow through a sudden expansion in a

rectangular channel with the provision of suction and blowing. They used different turbulent models in their

study. They observed increased pressure drop in turbulent flow at the bottom of the step. From streamlines of

the flow, they observed that the circulation of flow after the step with no suction or injection created due to

pressure drop at the step increases the risk of flow separation from the wall. Their study revealed that injection

from the wall affected the size of generated wake at the bottom of step which decreases the risk of flow

separation from wall. They further reported that among various turbulence model the standard K- € model was

the most suitable for separation flow studies. McManus and Bowman [55] experimentally investigated the use

of flow control methods to improve the performance of air-breathing combustors by considering modified

sudden expansion configuration. They observed that the introduction of stream wise vorticity into the inlet flow

of combustor caused the shear layer to become corrugated and results in a three dimensional flame structure.

The modification of flame structure was accompanied by increase in volumetric energy release of up to 75%.

Chakrabarti et al. [56] made a numerical study of the performance of a diffuser with bleed slot in different

locations at vertical and horizontal walls of plain sudden expansion. They achieved the best performance when

suction slot was placed at the top corner in the vertical wall. Forliti and Strykowski [57] described the

application of countercurrent shear control to the nonreacting flow in a combustor with modified sudden

expansion geometry. They used a suction (approximately 10% of the primary flow) base approach to achieve

countercurrent shear control, which induced through a gap at the sudden expansion plane. They observed that

the effect of counter flow was dramatic on both the mean and turbulent flow statistics but peak turbulence levels

increased with suction. Jochmann et al. [58] numerically studied a gas turbine combustor with modified sudden

expansion configuration. The realistic gas turbine combustor was consist of the swirler and the axisymmetric

combustion chamber. Ubertini and Desideri [59] experimentally investigated a three-dimensional

characterization of the flow path inside a model of an annular exhaust diffuser for gas turbines. They presented

their results in terms of mean and fluctuating components of velocity in seven axial stations inside the model.

They investigated the flow field inside the diffuser by means of the turbulence scale of dissipating eddies

calculated with the Kolmogorav theory. Shyy [60] numerically investigated 2-D axisymmetric steady flow for a



modified sudden expansion configuration. Depending upon the value of the Reynolds number and

characteristics of the central and corner recirculation zones for typical flow patterns were classified. These are

open annular flow, closed annular flow, vortex shedding, and stable central flow. An experimental investigation

of separated flows in fully stalled wide-angled diffusers was carried out by Kibicho and Sayers [61]. The effect

of the diffuser angle on the flow and heat transfer was studied by Lan et al. [62] in a plane symmetric diffuser

with an expansion ratio of 4.7. Chakrabarti et al. [63] carried out a performance simulation of a sudden

expansion with fence for the Reynolds number in the range of 20 to 100, non-dimensional distance of fence

from throat for 0 to 2 and fence subtended angle of 100 for the aspect ratio of 2. They obtained the best

performance of sudden expansion viewed as a diffuser, when the position of the fence was located from the

throat, at a non-dimensional distance of around 1 for higher flow Reynolds number in the case of fence

subtended angle of 100. They obtained the best performance of the diffuser, when the position of the fence

waslocated from the throat, at a non dimensional distance of around 1 for higher Reynolds number in the case of

fence subtended angle of 100.

3. CONCLUSION

From the presented literature study, it is obvious that many researchers have performed numerical and

experimental studied on plain sudden expansion as well as sudden expansion with some modification like

incorporation of suction on the wall, with single fence or double fence on the wall, incorporation of suction with

fence, incorporation of the blowing on the wall, induction of diverging channel after sudden expansion,

incorporation of swirling devices etc. Both Newtonian and non-Newtonian fluid have been considered for

numerical investigations. From the detailed review of available literatures, it has been observed that a

comprehensive investigation on the flow through plain sudden expansion as well sudden expansion with some

new modification is still lacking. Further, literatures are very scarce on numerical study of non-Newtonian flow

through sudden expansion with various modified configurations. The flow characteristics through modified

sudden expansion viewed as a combustor with Non-Newtonian fluid is very limited and therefore, it may be

mentioned that there are tremendous scope for further research in the same field.

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