International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 03, March 2019, pp. 421-433. Article ID: IJMET_10_03_043
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
UNSTEADY THREE-DIMENSIONAL
NUMERICAL STUDY OF LAMINAR FLOW IN
SUDDEN EXPANSION CHANNEL (EFFECT OF
ASPECT RATIO)
Ahmed N. Naeyyf
Post Graduate Student, Engineering CollegeMechanical Engineering Department, Basra Iraq
Qais A. Rishack
Lecture Engineering CollegeMechanical Engineering Department, Basra Iraq
ABSTRACT
Three-Dimensional, Unsteady Laminar Flow through Sudden Expansion Channel
has been studied numerically. Used rectangular and symmetric sudden expansions
(ER=H/h) with different aspect ratio (AR=Wch/h). CFD software ANSYS FLUENT
15.0 was developed to solve the Naviar-Stokes equation by used the finite volume
method to transfer these equations from differential form to algebraic form which can
be solved by SIMPLE algorithm procedure. The results obtained were represented on
graphs and discussed the suitable parameters like: pressure drop, velocity
recirculation region and skin fraction coefficient. From the results founded the time
steady state increase with the increasing of the aspect ratio and this effects become
more clearly at the high of Reynolds numbers and the aspect ratio, so founded high
effect of the time on the hydrodynamic parameters, behavior of the flow, recirculation
region and the velocity profile, and this effect was clearly at high of Reynolds
numbers. Also observed the increasing both the Reynolds numbers and aspect ratio
leaded to increase the recirculation zone and streamwise velocity, the pressure drop
increase with Reynolds number increase but reduce with increasing the aspect ratio,
the results of the numerical study were compared with the other research and
obtained acceptable convergence.
Keywords: Unsteady, Laminar Flow, Sudden Expansion Channel, expansion ratio,
aspect ratio.
Cite this Article: Ahmed N. Naeyyf, and Qais A. Rishack, Unsteady ThreeDimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect
of Aspect Ratio), International Journal of Mechanical Engineering and Technology,
10(3), 2019, pp. 421-433.
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Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel
(Effect of Aspect Ratio)
1. INTRODUCTION
In many systems the flow separation and its subsequent reattachment to a solid surface are
occurred. The flow through duct with sudden expansion can be also occurred in different
industrial application such as environmental control system, combustion chamber, electronic
cooling equipment and many other devices. The characterization of flow could be done by
increasing the losses of pressure which is caused by the flow separation near the expansion
area, [1]. Based on the variation of the pressure losses, erosion rates are increased as well as
the heat and mass transfer rates in the area where flows are occurring, [2]. In order to focus
our studying on flow with separation region experimental and theoretical techniques have
been developed based on many conducted attempts and this is due to stress such flow in many
engineering equipment. Therefore, numerical and experimental methods for characterizing
these flow features are still far from perfect due to the complexity of the flow’s behavior
associated with the flow separation [2], [3]. An overview of the relevant available literature.
Ali J. Chamkha, [4], unsteady laminar flow and heat transfer in channel and circular pipe has
been studied numerically. It is used the hydro-magnetic fluid with particle suspension flow.
The finite difference method used to solve the non-linear equations. The graphical results
discussed the volumetric flow rate and the friction coefficient for the both fluid and particle
phases to show the influences of the Hartmann magnetic number, the viscosity ratio and the
particle loading on the solutions. The finite difference computation showed the effect of
temperature inverse stock number on the heat transfer and the temperature profile of both
phases. Radhi [5], numerical study has been conducted on the viscous incompressible laminar
and turbulent flow in two geometries through step channel, with time depended and two
dimensions. The Navier-Stokes equation is used to solve each laminar and turbulent flow
while the finite difference method is used to solve the equations using two models to study the
turbulent flow. The first one called zero-equation and the second called one-equation model.
At Re=100000, it is observed stable and convergent results with acceptable accuracy. Rathish
Kumar.et al., [6], in this paper, the unsteady laminar flow through three dimensional doubly
constricted has been studied numerically, the flow with pulsatile condition. Time accurate
finite volume method is used to solve the non-linear partial differential equation. The
computational showed the effect of Reynolds number and the spase between the two
constrictions on the pressure drop through the constrictions. At
the pressure drops
near the constriction increased with increasing of Reynolds number. For a small distance
between the constrictions, they observed the drop of the total pressure was large in the first
section of the flow acceleration and the second section of the flow deceleration phases. But
for the large distance between the constrictions, they observed in the second section of the
flow acceleration and the first section of the flow deceleration phases, the drop of the total
pressure was large. Hassan AL-Abode .et al [7], the laminar and turbulent flow through
expansion channel have been studied numerically with three-dimensional flow and different
aspect ratio, used the finite volume to solve the continuity and momentum equations. The
results illustrated the maximum reattachment length is located in the laminar flow and it's
observed in the upper stepped wall, and in the turbulent flow observed the kinetic energy,
friction factor and streamwise velocity inside the reverse flow increase with increasing
Reynolds number. The result also showed the critical Reynolds numbers increase as the
aspect ratio decrease and the revers flow region increase with aspect ratio increase. Finally, in
the laminar flow the recirculation flow region is increased but it is approximately constant in
the turbulent flow. Vijayalakshmi R. et al., (2017) [8], unsteady flow, heat and mass transfer
of a casson fluid in vertical expansion and contraction channel has been studied numerically.
They used the Runge-Kutta method to solve the reduced ordinary differential equations that is
derived from the governing partial differential equations. The pivotal velocity, temperature
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and the concentration distribution are showed in different graphs and discussed their behavior
for variable parameters casson parameter, magnetic field parameter, Reynolds number,
expansion ratio, heat source parameter, Prandtl number, Groshoff number, Chemical reaction
parameter, Schmidt s number. The obtained results showed multi case, firstly for the
expansion region (
) lead to high axial velocity in the center and low velocity vicinity
the walls, secondly for the contracting region (
) increasing the
lead to low axial
velocity in the center even invert the direction near the walls, thirdly for (
) the axial
velocity in the center increases with increasing the casson parameter even it reduces vicinity
the walls. Also, the result showed the heat source parameter for (
) lead to increase the
Nusselt-number at the left wall, and at the right wall the Sherwood number increase with the
high value of chemical reaction. Khudheyer S. et al., (2015) [9], in this paper research, the
laminar flow through an obstacle sudden expansion channel has been studied numerically.
The obstacles position is behind the expansion region for the geometry on the upper and
lower wall of the used channel. In this research, they showed that the influence of the length,
thickness and the number of obstacles on the flow and the thermal fields for different
parameters such as expansion ratio and Reynolds number. The results illustrated the obstacles
have important effect on the dynamic flow and edification on the heat rate. In other word the
heat transfer rate increases with increasing the thickness and the number of the obstacles
while its decreases with increasing of the obstacles length.
2. MODELING AND THEORETICAL
The present section introduces the physical model of laminar flow through sudden expansion
channel configurations and its mathematical analysis; includes the, governing equations that
describe flow, boundary conditions and assumptions. Also, this chapter contains the
procedure of simulation; the employed method in this work for numerical attaining of
hydraulic behaviors of the present problems. ANSYS 15 was used in simulations and
computations of problems that included in this thesis.
2.1 Description of Model
The physicals model that was study is shows in the figure (1). This exhibits the threedimension horizontal channel have symmetric sudden expansions. The heights of channel
downstream, upstream of the expansion are (H) and (h) consecutively. The height of step is
preserved as (s). The geometry prepare an arrangement within expansions ratio (ER=2), and
"aspect ratio" (AR=W/h) are different, the location of the coordinates axes at the center of the
inlet channel; the direction of the stream wise (x), transverse (y), and span wise (z)
coordinates are showed in figure (3.1), the inlet duct length (Li) selected to make sure that
inlet flow through the channel is fully developed [10], [11].
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Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel
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Figure 1 explain the schematic sudden expansion with the boundary condition [12]
2.3 Assumption
For carrying out the numerical simulations of the present work, the bellow assumptions are
considered for the flow:
1. The fluid of work is air.
2. Three dimension, laminar and unsteady state flow.
3. The flow is Incompressible.
4. Neglected the effect of gravity.
5. The flow assumed is Non-slip.
2.4 Governing Equations
The motion equations of the laminar flow are used in Cartesian coordinates as the follows
[11], [13], [14]:
Equation of continuity:
Equation of momentum:
x-direction
(
)
(
)
y-direction
(
)
(
)
z-direction
(
)
(
)
2.5 Boundary Condition
When looking at figure (1) which explain the boundary condition for the presented model
(sudden expansions channel), and based on the last presumptions the boundary conditions of
the laminar flow can be summed as ahead:
The velocity in the walls of channel equal zero (no slipping). i.e u, v, w=0 with the x, y,
and z directions.
The velocity in the inlet of channel is known (u= uin, v=0, w=0).
The Pressure at the outlet equal zero.
3. VERIFICATION
To check the validity of the present numerical model, verification was made by comparing the
results of the present model with numerical results reported in the literature. The verification
was made by comparison the present results and Abdu Latif et al. [8]. The model is presented
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in [14] is Finite element model for unsteady open channel flows with sudden
contraction/expansion, the used two unsymmetrical channels of different lengths with
contraction and expansion to study the flow behavior. The numerical results found using the
present model and that found by [14] are shown in Figure (1) which shows the velocity profile
with Re=60 and different position, before contraction(X/B=1) and during contraction
(X/B=1.2), from this figure, the agreement is acceptable, and the error is 13.11 %. From the
past verification, we deduction that, the present numerical model is dependable and can be
used accurately to simulate the flow in the expansion channel and study the variable
parameters affecting.
4. MESH INDEPENDENCY
It is very important to specify the elements number that obtains the accurate results. So, the
grid refinement was tested for every studied case through dividing the domain into many
different grids and comparing their results of x-velocity (U) and friction coefficient (Cƒ). As
shown in figure (2), the deviation between results that obtained from each two consequent
grids is decreased at finer grids due to the convergence in these results. For all studied cases
in present work, the deviation less than 1 % in both x-velocity (u) and friction coefficient (Cƒ)
is considered for selecting the grid at which the results will be stable and grid independent.
5. RESULTS AND DISCUSSED (EFFECT OF ASPECT RATIO)
This thesis will explain the aspect ratio on varicose of hydrodynamic parameters (velocity, the
zones of recirculation flow, pressure and the fraction coefficient) for presented flow (laminar
type).There is important conditions must be insured prior discussion the last parameters or the
influence, which is the required condition for the entry and the exit of the sudden expansion.
The inlet condition for the sudden expansion channel included known velocity, and the out let
condition included the static pressure equal zero.
A study was performed to verify the influence of aspect ratio on the time steady state and
the flow state after the stepped walls.
Figure (3) shows the effect of the aspect ratio on the time steady state at constant
Reynolds numbers, observed at AR=2 the effect of the time was little so the period to
approach to the steady state its short, by increase the aspect ratio (AR=4) the time become
longer, so at AR=6 The effect has become clearer and the time to approach to steady state
become more, all the last study at constant Reynolds number (Re=500). The reason for this
behavior; increase the AR mean increase the area of the fluid motion and this will take more
freedom for the partial fluid motion and this will cause more random for the fluid, and the
increase the random need more time for the stability and a approach to the steady state
Figure (4) shows the influence of the aspect ratio on the distribution of the velocity profile
at the center of channel and at position x=3, from this figure observed same recirculation zone
in the upper and lower wall for same the aspect ratio, also the value of velocity in the center
of channel increase with the AR increasing.
Figure (5) shows the effect of the aspect ratio on the distribution of the velocity profile
with the z axis, the center of channel and at position x=2, observed the value of velocity
decrease with the increasing of aspect ratio this for 30% of the first width after this the
velocity will increase with aspect ratio increasing, that’s mean the flow will become twodimensional velocities due the large of aspect ratio.
Figure (6) explain the boundary for the reattachment line on the lower of channel for
different aspect ratio, by observed the figure will find the increasing of the aspect ratio lead to
reattachment line increasing by decreases the pressure, so the result show the reattachment
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Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel
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line it be symmetric through the center of channel then has gradually increasing as a head to
the wall.
Figure (7) show the reattachment length with the Reynolds numbers for the upper and
lower step wall with different aspect ratio, the figure explains the effect of the aspect ratio and
Reynolds numbers on the flow reattachment length. The results show the symmetric flow
increase with the decreasing of aspect ratio (at AR=2 the symmetric observed clearly), so the
flow behavior after the bifurcation point increase in the upper step wall and decrease in the
lower, the last observed point seen the zone of reverse flow increase with the aspect ratio
increasing.
Figure (8) explain the distribution for the static pressure along the length of channel at
different of aspect ratio at constant Reynolds number, observed at high aspect ratio (AR=6)
the drop pressure was lowest from the other cases (AR=2, AR=4), so for AR=4 and AR=6 the
value of the pressure ware closely but for low aspect ratio AR=2 the pressure value far from
the others. The pressure still dropping at arrived to zero at the out let of channel and this
dropping increase with decreasing of aspect ratio.
60
present study
[40] Abdul Latif et al.,
50
40
y(m) 30
20
10
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
u (m/s)
Velocity profile at X/B=1
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[40] Abdul Latif et al.,
40
35
y(m) 30
25
20
15
10
u(m/s)
0
0.5
1
1.5
2
2.5
Velocity profile X/B=1.2
Figure 2 Verification of the present numerical model using the numerical results of [8]
Averag
e
velocity
(m/s)
No. of elements
(a)
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Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel
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Cƒ
(b)
No. of elements
Figure (3) computing results for the expansion channel at different grids at Re=2000 (a) Average
velocity. (b) Friction coefficient
Average velocity
(m/s)
AR=2
4.007
4.0065
4.006
4.0055
4.005
4.0045
4.004
4.0035
4.003
4.0025
t(s)
4.002
0
5
10
15
20
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40
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Figure (4) variation of the average velocity with the time at different aspect ratio and Re=500
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Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel
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1
# 10
-3
AR=2
AR=4
AR=6
0.8
0.6
0.4
y (m)
0.2
0
-0.2
-0.4
Re=250
X=3
t=120 s
-0.6
-0.8
-1
0
0.5
1
1.5
2
2.5
3
U (m/s)
Figure (5) velocity profile with the high of channel at different aspect ratio
Figure (6) velocity profile with the width of channel at different aspect ratio
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0.0045
AR=6
0.004
AR=4
0.0035
AR=2
𝑋𝑢
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
0
0.2
0.4
0.6
0.8
1
1.2
z(mm)
Figure (7) Diagram of the upper reattachment length at different Aspect ratio, Re=250, z=0 and
t=120s
AR=4 lower wall
AR=6 lower wall
AR=2 lower wall
0.008
AR=4 upper wall
AR=6 upper wall
AR=2 upper wall
0.007
𝑋𝑢
0.006
0.005
0.004
0.003
0.002
0.001
0
0
250
500
750
1000
Z (mm)
1250
1500
1750
2000
Figure (8) Diagram of the lower and upper reattachment length at different Aspect ratio, z=0 and
t=120s
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Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel
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80
AR=2
AR=4
AR=6
70
Re=250
t=120 s
60
y (m)
50
40
30
20
10
0
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
U (m/s)
Figure (9) variation of the static pressure along the channel with different aspect ratio
5. CONCLUSIONS
A numerical study has been conducted to investigate the three-dimensional, unsteady state,
laminar flow through sudden expansion channel; CFD software ANSYS FLUENT 15.0 was
developed to solve the Naviar-Stokes equation by used the finite volume method. Had been
Investigated the influence for many parameters on the fluid in present model,
The conclusions presented below have been obtained by the results obtained: Increase the
time of the steady state as the aspect ratio increasing with fixed the Reynolds numbers.
Founded high effect of the time on the hydrodynamic parameters, behavior of the flow,
recirculation region and the velocity profile. The reverse flow region increases with the aspect
ratio increasing. The drop of the pressure increases with Reynolds number increasing but its
decrease with the aspect ratio increase
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