Project #4: Simulation of Fluid Flow in the Screen- Bounded
Channel in a Fiber Separator
By
Lana Sneath and Sandra Hernandez
4th Year, Biomedical Engineering
University of Cincinnati
Faculty Mentor: Dr. Urmila Ghia
Department of Mechanical and Materials Engineering
University of Cincinnati
Sponsored By the National Science Foundation
Grant ID No.: DUE-0756921
1
Abstract
The goal of this project was to verify the ability of the Bauer McNett Classifier (BMC) to
classify asbestos fibers in large batches for use in toxicology studies. Previous studies
have shown that fiber toxicity varies with changes in fiber length. In the present study,
the Bauer McNett Classifier was modeled using CFD (Computational Fluid Dynamics) to
analyze its potential use to classify fibers based on their length. The focus of this study
was to simulate the flow in the deep open channel of the BMC, with focus on the screen.
The channel geometry was first modeled in Gambit, and then the computational grid was
imported into FLUENT to solve the three-dimensional Navier-Stokes equations
governing the fluid flow. Turbulence in the channel was found using the Reynolds Stress
Model (RSM). Initial work was completed by modeling the screen with a solid wall
boundary to facilitate the computations. The results from this case concluded that the outplane angle of shear stress on the XY plane was around 8 degrees for the solid wall
model, inferring that the shear stress distribution of the flow was parallel to the screen.
Upon completion of the solid wall simulation, a verification study with a 2D porous plate
using the porous-jump boundary condition was conducted to see if this boundary
condition simulates flow through the screen correctly. The 2D results show that FLUENT
implements a pressure drop across the porous-jump surface using Darcy's law. Once the
correct boundary conditions were determined from the verification case, a portion of the
sidewall in the channel was replaced by a porous boundary to represent the screen
openings. The results showed that the shear stress on the screen approaches zero. The
next step in this study will be to obtain steady state results and further investigate the
shear stress on the screen.
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Contents
Abstract
Contents
Nomenclature
Chapter 1
Introduction
1.1 Bauer McNett Fiber Classifier
1.2 Objectives
1.3 Materials
1.4 Methods
Chapter 2
Flow in the BMC Open Channel with Two Solid Walls
2.1 Geometry and Computational Grid
2.2 Boundary Conditions
2.3 Results and Discussion
Chapter 3
Verification Case: Flow Across a Porous Plate
3.1 Geometry and Computational Grid
3.2 Boundary Conditions.
Two Wall Model
One Wall and One Pressure Outlet Model
Two Pressure Outlets Model
3.3 Results and Discussion
3
All Wall Model
Two Wall Model
One Wall and One Pressure Outlet Model
All Outlets Model
3.4 Conclusion
Chapter 4
Flow in the BMC Open Channel with a Screen on a Side Wall
4.1 Geometry and Computational Grid
4.2 Boundary Conditions
4.3 Results and Discussion
4.4 Conclusions
Future Work
Acknowledgements
Bibliography
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Nomenclature
The following symbols have been used in this document:
μ: Viscosity of the fluid
Re: Reynolds number.
Fr: Froude number.
d: Wire diameter.
K: Permeability
C2 : Pressure-jump coefficient
Ui: Velocity.
Elent: Entrance length number.
lentrance: Length to fully developed velocity profile.
ρ: density
τij : Shear stress
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Chapter 1
Introduction
Asbestos fibers are naturally found in the environment and have been used in many
commercial products such as insulation, flooring, plaster, and cloth materials. Asbestos is
a known carcinogen that can lead to one or more disorders if fibers in the air are inhaled
[3]. It has been proposed that alveolar macrophages (AM) are unable to completely
engulf longer asbestos fibers, leading to oxidants and enzymes leakage from the AM, in
turn causing cell damage [12]. The effect of asbestos can be determined by various
factors including fiber length, concentration, and duration of exposure. Previous
experiments conducted by the National Institute of Occupational Safety and Health
(NIOSH) have shown that asbestos toxicity varies with fiber length; longer fibers have a
greater chance of it being toxic compared to shorter fibers [1]. The current fiber classifier
being used is only able to separate small batches of fibers based on their length at a time,
making it difficult to conduct a large-scale toxicology study. In order to be able to
conduct large-scale studies, technologies that will be able to classify large batches of
fibers are being explored. The objective of this study is to determine the efficiency of the
Bauer McNett Fiber Classifier (BMC) as a fiber length-based classifier.
1.1 Bauer McNett Fiber Classifier
The Bauer McNett Fiber Classifier is a device commonly used for paper fiber
classification based on length. The BMC is a system with 5 elliptical tanks arranged in a
cascade, as shown in Figure 1. An agitator slowly circulates the water flow within each of
the elliptical tanks. The water then flows past a screen in the channel within the tank,
causing separation of fibers based on their length, as shown in Figure 2. This fiber
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separation occurs due to the cross flow through the screen which allows fluid to escape
through the square apertures of the mesh, leaving behind the fibers that are too long to fit
lengthwise through the aperture. Fiber orientation upon passing through the screen is
governed by the shear stress distribution on the wire mesh screen. It is assumed that the
fibers flowing in the fluid align themselves in the direction of the shear stress on the
boundary, and any change in the direction of the shear stress vectors will result in a
change in the fiber orientation [1]. For successful length-based separation, the fibers must
be oriented parallel to the screen. If the fiber orientation is parallel to the screen and the
diameter is greater than the opening, it is expected that fibers larger in length than the
aperture size of the particular screen size will be filtered.
Figure 1: Bauer McNett Classifier
The flow across the cascading tanks is governed by gravity. This study
concentrates on modeling a portion of the deep, open channel within the BMC as a
porous boundary to replicate the wire mesh. The previous study on length-based fiber
orientation in the BMC apparatus found that the Reynolds number of the deep open
channel was greater than 4000, classifying the flow as turbulent. The Reynolds number is
a dimensionless number, which correlates the viscous behavior of Newtonian fluids [6].
7
The flow was also found to be subcritical as determined from the value of Froude
number, which was about 0.18 [1].
1.2 Objectives
The motivation behind this study is to understand the behavior of the fluid flow
within the deep open channel in the BMC apparatus. The goal of the present study is to
numerically simulate the three-dimensional flow in the BMC deep open channel of aspect
ratio (H/B) 10. In previous studies, the channel was modeled with both vertical side
boundaries as solid walls. In this study, a portion of one of the solid walls is replaced by a
porous-jump boundary condition, which represents the screen in the BMC apparatus. The
focus of the experiment is to analyze the shear stress distribution on the screen, modeled
as a porous boundary, and determine the effectiveness of the BMC for length-based
separation of fibers.
The objectives of the study are to:
a) Determine proper boundary conditions, inputs, and geometry
b) Conduct a verification case
c) Simulate and study the flow in the open channel of the BMC apparatus, modeling
the screen as a porous boundary
d) Interpret results and form conclusions
1.3 Materials
Commercially available Computational Fluid Dynamics (CFD) tools FLUENT
and Gambit are used for the simulations in this study.
1.4 Methods
8
The goal of this study is to numerically simulate the fluid flow in the screenbounded channel within the BMC fiber separator. In order to numerically study the fluid
flow, Computational Fluid Dynamic (CFD) software FLUENT and Gambit are used.
Computational Fluid Dynamics is defined as “concepts, procedures, and applications of
computational methods in fluids and heat transfer” [9]. CFD tools apply the principles of
engineering to the modeling of fluid flow. [10]. Using the CFD tool FLUENT, the 3D,
unsteady, incompressible Reynolds-Averaged Navier-Stokes Equations (RANS) are
solved to determine the three-dimensional flow in the deep open channel of aspect ratio
10. The Semi-Implicit Pressure-Linked (SIMPLE) algorithm is used to achieve pressurevelocity coupling. The solution is deemed converged, when the residuals of the continuity
equation and the conservation of momentum equation reach 10e-6.
Chapter 2
Flow in the BMC Open Channel with Two Solid Walls
2.1 Geometry and Computational Grid
The deep open channel geometry, within the BMC apparatus, is created and
meshed in Gambit and the mesh is later imported into FLUENT where the RANS
equations are solved to simulate fluid flow.
The channel geometry is created in gambit with dimensions of 0.217 x 0.02 x .2 m
in the x, z, and y directions, respectively, giving the channel geometry an aspect ratio of
10. A computational grid is created, with grid spacing of 50, 180, and 45 in the x, y, and z
directions, respectively. The first step size of the grid is 0.00005 m away from the
boundaries in the y direction, and 0.00007 m in the z direction. The small step sizes allow
9
for more computations to be taken along the boundary edges where the fluid flow has
greater variation. The grid spacing along the x direction has a successive ratio of 1,
meaning that the grid points are evenly spaced. The fluctuations in the fluid flow along
the distance of the channel are moderated as compared to the y- and z-directions, hence it
was not necessary to cluster the points around the edges. Figure 3 shows the
computational grid used for this study.
Figure 2. Computational Grid [1]
Total Size
X
Y
Z
∆Y
∆X
405000
50
180
45
0.00005
0.0007
Table 1. Computational Grid Spacing
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2.2 Boundary Conditions
The boundary conditions used for modeling the wire-mesh wall as a solid
boundary are shown in Figure 4. The two sidewalls and the bottom wall are specified as
no-slip stationary walls, where the values of the u, v, and w components of velocity are
zero. The average velocity at the inlet is specified to be 0.25 m/s. The Reynolds number
for the BMC apparatus is equal to 9982, classifying it as a turbulent flow. Turbulent
flows contain fluctuations, whereas laminar fluid flows are smooth without many
irregularities. The fluid flow is computed in FLUENT at every discrete grid point, and the
Reynolds-stress model includes the effects of turbulence. The Reynolds-stress model
takes into account the fluid rotation, curvature, and rapid changes in strain rate more
rigorously than one or two-equation models and, therefore, is an ideal model to use when
analyzing the complex flow within the BMC apparatus [7]. The turbulence boundary
conditions were specified in the form of turbulence intensity and viscosity of 5% and 10,
respectively, for the inlet and outlet boundaries.
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Figure 3. Boundary Conditions for Solid Wall Model
The non-dimensional entrance length, Elent , for turbulent flow is expressed as
Elent = 4.4(Re)1/6
(3)
For a Re of 9844, the non-dimensional entrance length is:
Elent = 4.4(9844)1/6 = 20.37
(4)
Elent =
lentrance
Dh
= 20.37
(5)
Therefore the entrance length for the flow is:
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lentrance = 20.37 ∗ 0.01 = 0.2 m
(6)
Entrance length is defined as the length of the inlet to the point where the flow
becomes fully developed. It is assumed that the fluid does not undergo any further
changes in velocity along x, after the entrance length. The velocity and vorticity results
are analyzed in cross planes at x= 0.2 m, y = 0 to 20 m, and z= 0.02 m.
2.3 Results and Discussion
The objective of this study was to numerically study the flow through the deep open
channel of the BMC with an aspect ratio of 10. The BMC channel geometry is initially
modeled as two sidewalls and the bottom wall that are no-slip stationary walls, where the
u, v, and w components of velocity are equal to zero.
Initially it was found in the first model with solid sidewalls that the x-velocity contours
were highest in magnitude towards the center of the channel and lowest at the stationary,
non-porous sidewalls.
The bulges in the x-velocity contour plots can be attributed to the presence of a free
surface attracting higher momentum fluid, pushing the lower momentum fluid towards
the center of the channel [1]. The shear stress distribution on the vertical sidewalls near
the free surface is affected by this circulatory effect. Furthermore, the circulation of fluid
is observed in the x-vorticity contour plots, which show the highest vorticity in the
corners near the free surface.
In the solid side walls channel geometry, the off-plane angle is greatest at the inlet
and drops down and remains around 8 degrees as the x-position increases. These results
indicate that the shear stress is mainly aligned tangential to the fluid flow.
13
Figure 4. Total Shear Stress along (left y-axis) and off plane shear stress angle (right yaxis); line at y= 0.1 m (mid-plane), z= 0.02 m
2.4 Conclusion
The objective of this study was to numerically study the flow through the deep
open channel of the BMC with an aspect ratio of 10. The BMC channel geometry was
modeled as two sidewalls and the bottom wall that are no-slip stationary walls, where the
u, v, and w components of velocity are equal to zero.
The results indicated that the x-velocity contours were highest in magnitude
towards the center of the channel and lowest at the stationary, non-porous sidewalls. In
the solid side walls channel geometry, the off-plane angle was greatest at the inlet and
drops down and remained around 8 degrees as the x-position increases. These results
indicated that the shear stress was mainly aligned tangential to the fluid flow.
Chapter 3
Verification Case: Flow Across a Porous Plate
14
The objective of this verification study was to determine the proper boundary
conditions to model in the model with a portion of the wall replaced by a screen. The case
was also used to determine how the porous plate affected axial flow and the laminar fluid
flow behavior. The verification case was modeled as a laminar flow to simulate the ideal
case and to facilitate computations.
3.1 Geometry and Computational Grid
Reynolds number was calculated in the beginning of the verification case to
classify the proper fluid flow to be laminar or turbulent. The original inlet velocity was
divided by 10 to ensure that the flow would be laminar. The Reynolds Number, Re, was
calculated to be 5500 with a velocity of 0.025 m/s, classifying the verification case as a
laminar flow.
Calculating Reynolds Number (Re):
Re =
Re =
ρVL
(7)
μ
1000×0.025×0.22
(8)
1.002×10−3
Re = 5500
(9)
With ρ signifying the density of the water, V for the velocity, and μbeing the viscosity of
fluid.
ANSYS Gambit was used to create a 2D geometry of a porous plate and a
computational domain. The geometry in the 2D case was modeled to reflect the actual
BMC apparatus dimensions with a decreased velocity by 10 to simulate a laminar flow.
Figure 5. labels the dimensions accordingly. The computational grid spacing can be seen
15
in Table 2. Grid points were clustered at the inlet using a First Length distance in Gambit
to better capture the fluid flow fluctuations.
Three different cases were simulated to determine the effect of the various
boundary conditions on the fluid flow behavior. The three cases change the boundary
conditions on the sides and bottom of the computational domain after the porous-jump.
Figure 5. Verification Case Geometry
Total Size
X
∆X
Y
16
∆Y
20000
100
200
0.01
0.01
Table 2. Computational Grid Spacing
3.2 Boundary Conditions.
In order to model a face or line with a porous-jump boundary condition, FLUENT
requires the Permeability (K), thickness, and Pressure-Jump Coefficient (C2 ) to be
entered. In the actual BMC apparatus, the screen portion is a 16 Mesh with wire diameter
(d) of 0.0004572m. All calculations for permeability, thickness, and Pressure-Jump
Coefficient were done using the corresponding values for a 16 mesh found in literature.
Calculating Permeability (K) and Pressure-Jump Coefficient (C2 ):
The standard wire diameter (d) for a 16 Mesh is 0.0004572m. The screen being
modeled is woven, making the thickness of the screen 2*d, which is equivalent to
K
0.0009144 m. When evaluating through-plane flow through a 2D planar structure, the d2
value is given in Table 3 to equal 0.0046 with F=0.118. The equation used to calculate
the permeability (K) and the pressure-jump coefficient are:
C2 =
2F
√K
and
K
K
d2
= d2
(10)
K
To first solve for K, the given wire diameter (d) and the d2 value for a through-plane flow
through a planar 2D structure are imputed into the equation
K
0.0046 = (0.0004572)2
(11)
K = 9.6154e−10 m2
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This means the face permeability (K) of the screen mesh is 9.6154e−10 m2
The pressure-jump coefficient (C2 ) is calculated by replacing F with the given 0.118
value and using the calculated K
C2 =
2(0.118)
√(9.6154e−10 m2 )
1
= 7610.739 m
(12)
These values are then entered into FLUENT along with the overall screen thickness of
0.0009144 m to analyze the flow behavior across the porous plate.
Table 3. Empirical relations to estimate permeability and inertial coefficient [15]
The following three diagrams represent the boundary conditions modeled in
Fluent of the 2D porous plate model. Each of the boundary conditions is labeled and
explained in the key
All Walls Model
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Figure 5. Boundary Conditions on All Walls Model
Two Wall Model
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Figure 6. Boundary Conditions on Two Walls Model
One Wall and One Pressure Outlet Model
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Figure 7. Boundary Conditions on One Wall and One Pressure Outlet Model
Two Pressure Outlets Model
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Figure 8. Boundary Conditions on All Pressure Outlets
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3.3 Results and Discussion
All Wall Model
According to Darcy’s law, the calculated pressure drop across the porous-jump
boundary condition should be equivalent to the pressure drop observed in the simulation.
To verify the porous-jump boundary condition provided the needed pressure drop, the
change in pressure across the porous-jump boundary was calculated via Darcy’s Law and
from numerical data directly from the simulations.
Darcy’s Law pressure drop calculations:
μ
1
∆p = −(∝ v + C2 2 ρv 2 )∆m
1.002x10−3
(13)
1
∆p = −( 9.6x10−10 v + 7650.739 x 2 x 1000 x v 2 )0.0009
(14)
∆p = −(1.04x106 v + 3.424x102 v 2 )0.0009
(15)
For the All Wall model, v = (9.18x10−6 )
∆p = −(1.04x106 (9.18x10−6 ) + 3.424x102 (9.18x10−6 )2 )0.0009
(16)
∆p = −(9.5472 + 2.8854x10−8 )0.0009
(17)
∆p = −(85.9248x10−4 )
(18)
∆p = −0.008592
(19)
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The variable V is the radial velocity normal to the fluid flow. This radial velocity
was obtained from FLUENT calculations for each case, using the value of radial velocity
on the porous plate. Δρ according to Darcy’s law is -0.008592, while the pressure drop
from the FLUENT experimental data was -0.00868. The percent error is 1.10% between
the two calculated values. Due to the low percentage error, the approximation can be
made that the porous-jump boundary condition works in our model as expected and the
porous-jump boundary condition applies for this case. The low percentage error was
calculated for each case and hold true for all of the cases of this verification study.
Figure 9. Velocity Magnitude Contours for All Walls
Two Wall Model
The first case modeled the computational domain past the Porous-Jump boundary
condition with both sides modeled as pressure outlets, as seen in Figure 10. The results
show that the boundary conditions do allow fluid flow to pass across the porous plate,
which is modeled with a Porous-Jump condition. The boundary layer formation is clearly
24
seen at the beginning of the channel and throughout the length, which is the proper
behavior for a laminar flow across a porous plate. The left side of the lower
computational domain is modeled as a wall, preventing fluid from entering at that point.
Figure 10.Velocity Magnitude Contours for Two Walls and One Pressure Outlet
One Wall and One Pressure Outlet Model
In this model, it is observed that some of the flow is leaving the domain through
the sidewall that is modeled as a pressure outlet. The physical case of the 3D channel in
the BMC apparatus does not allow for this type of flow, and thus this combination
boundary conditions cannot be used. Delta p must be the same for all boundary
conditions
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Figure 11.Velocity Magnitude Contours for One Wall and One Pressure Outlet
All Outlets Model
The model with two pressure outlets shows a change in the boundary layer
formation and fluid flow velocity. Results are similar to previous cases.
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Figure 12.Velocity Magnitude Contours for All Outlets
Pressure Drop Calculated
Pressure Drop Fluent
Percent Error
3.48E-03
0.00351781
1.19%
-3.73E-03
-0.003679068
1.25%
2.54E-03
2.53E-03
0.32%
-0.008593229
-0.00868129
1.01%
Table 4. Pressure Drop Calculations
3.4 Conclusion
The purpose of this verification case was to determine how the porous boundary
jump condition behaves and how to properly implement it into the 3D deep open channel
model. These verification cases also helped verify that the porous-jump boundary
condition worked exactly the same for different set of boundary conditions inside the
computational domain.
From the results, it can be determined that the flow wasn’t within the porous
media, but instead was across the porous-jump condition. These results helped verify that
the area after the porous boundary jump condition was a computational domain and not
the thickness of a porous media.
27
Additionally, this verification case helped determine the proper boundary
conditions needed to run the 3D open channel model with a screen. After analyzing the
results, it was concluded that the case with both sides of the computational domain
modeled as walls was the best fit for the 3D open channel model with a screen. This was
concluded because there was an observed pressure drop across the porous-jump boundary
condition and no fluid was seen entering the channel from the sides. Thus, the resulting
boundary layer formed was consistent with literature.
Chapter 4
Flow in the BMC Open Channel with a Screen on a Side Wall
4.1 Geometry and Computational Grid
In order to further understand and analyze the fluid flow in the deep open channel
of the BMC apparatus, a portion of the sidewall of the channel containing the screen was
replaced with a porous boundary. A porous boundary was chosen as a method to model
the screen within the BMC channel rather than a wire-screen to facilitate computation.
The porous boundary represents the screen in the BMC apparatus.
The porous boundary is modeled with 1 inch (0.0254 m) margins lengthwise and
a 1 inch margin from the bottom of the channel. The dimensions of the boundary are x=
0.1662 m, y= 0.1746 m, and a wire diameter 0.0004572 m. The grid spacing for the
channel with a porous boundary maintains the same grid spacing and ratio of points per
inch as the previous mesh. Figure 13 shows the computational mesh that was used to
analyze the fluid flow in FLUENT.
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Figure 13. Computational mesh with porous boundary on a side wall
4.2 Boundary Conditions
The boundary conditions for all parameters except a portion of a side wall are the
same as the previous case with solid side walls, as seen in Figure 14. In Fluent, the side
of the screen in line with the deep open channel was modeled with a porous-jump
boundary condition. After the screen was modeled with a porous-jump boundary
condition, a computational domain was extruded from that face. All sides of the
computational domain were modeled as walls, with the back face being modeled as a
pressure outlet. These boundary conditions were chosen after interpreting the results from
the verification case.
29
In order for FLUENT to solve the Reynolds Stress Equations for the fluid flow in
the channel the permeability, pressure-jump coefficient, and the thickness of the porous
boundary need to first be determined. The equations and calculations can be found in
Section 3.2 of the Verification Case. The final values are as followed:
Permeability,K = 9.6154e−10 m2
1
Pressure-Jump CoefficientC2 = 7610.739 m
Screen thickness = 0.0009144 m
The turbulence boundary conditions were specified in the form of turbulence
intensity and viscosity of 5% and 1, respectively, for the inlet and outlet boundaries. The
edges surrounding the porous boundary are modeled as solid no-slip walls with u= v=
w=0. The thickness of the porous boundary is equal to 0.0009144 m, which is the set
value of the wire diameter for a 16 mesh multiplied by 2, due to the screen being woven.
30
Figure 14. Boundary Conditions on Porous Wall Model
4.3 Results and Discussion
Fluid within the deep open channel will take approximately 0.87 seconds to fully
travel the length of the channel, as calculated in the equations below. The Reynolds
Stress Time-Averaging equations and continuity equations were unable to run for the
appropriate time period.
31
Time (seconds) for fluid to travel the length of the channel calculations:
Time = Length/Velocity
Time = 0.217m/0.25s
Time = 0.87s
Due to time constraints, FLUENT was only able to calculate up to 0.5s of the fluid flow,
which is approximately ½ of the channel. Our results are accurate up to 0.5s, but results
for second half of the channel are incomplete.
The flow time that was obtained is 0.5 seconds. This means that the fluid has not
traveled across the entire channel. This is reflected in figure 15, which shows a certain
jump at x position 0.2 m. In addition, the peaks at 0.09m can be attributed to the flow not
traveling across the entire channel. The goal of the study was to obtain steady state
results, and a flow time of 0.5s does not suffice this goal.
Close to the inlet section of the channel, the total shear stress decreases with the
axial distance. As expected, the shear stress is maximum at the inlet, and the as the
velocity profile develops, the wall shear stress decreases, as seen in Figure 15.
32
Figure 15. Axial Variation of Shear Stress on the Back Wall at y=0.1 z= 0
As discussed previously, the shear stress is also seen to be maximum at the inlet
section. The shear stress decreases as the velocity profile develops downstream. At
x=0.2m the screen starts, and an increase in area at x=0.2m causes a dip in the shear
stress. The end portion of Figure 16 clearly reflects that the flow has not traveled across
the channel completely. According to Figure 16, the shear stress around the wire mesh
drops down to zero. This can be attributed to the porous boundary condition, or due to the
fact that the simulation has not yet reached steady state results. Further analysis is
required to understand the implementation of the porous-jump boundary condition by
FLUENT.
33
Figure 16. Axial Variation of Shear Stress on Screen at y=0.1 z= 0.2
Velocity contours along the X direction were visualized in Figures 17a and 17b.
In these figures, high velocity corresponds to warmer colors, while lower velocity
corresponds to cool colors. The highest velocity is seen in the red portion of the channel,
and the lowest velocity of zero is seen at the bottom no-slip wall. At the bottom no-slip
wall, boundary layer formation was observed that was in similar to that in the verification
case. The higher velocity near the central bottom of the channel could be due to the
smaller area at that region, leaving an increase in velocity when using the conservation of
mass equation. An increase in centerline velocity before the porous-jump boundary starts
is due to the velocity profile development of the axial velocity, giving rise to a higher
velocity. At the screen, the area increases due to which it is expected that there will be a
corresponding decrease in the overall velocity. Also, some mass escapes the channel
through the porous boundary contributing to smaller axial velocity. At the end of the
34
porous-jump boundary condition, area decreases again, thus a resultant increase in axial
velocity and further development of the velocity to the end of the channel will likely
occur. The yellow velocity contours at the beginning of the channel complement the
predictions made, as that slower velocity starts right after the porous-jump boundary
condition, where the channel has an increased velocity.
Figure 17a. Isometric View of Axial Variation of Velocity on Central Plane
35
Figure 17b. Front View of Axial Variation of Velocity on Central Plane
The X-velocity (Axial velocity) components are plotted in Figure 18. The
beginning of the inlet and near the free slip wall there is non-zero velocity. The first half
of the channel is the region that the fluid flow simulation has covered so far with 0.5s of
flow computations completed.
36
Figure 18. Axial Variation Plot of Velocity at Line y=0.1, z=0.01
4.4 Conclusions
The 3D geometry of this case was created in Gambit and run in FLUENT with the
appropriate boundary conditions. However, the results from the 3D porous boundary
model were incomplete due to time constraints and computationally intensive
simulations. The results obtained were obtained for only 0.5 seconds of the fluid flow
through the channel. This means that only 57% of the channel was solved
computationally. An approximate time required for the flow to travel across the channel
was obtained by dividing the length of the channel by the inlet bulk velocity. This time
period for the flow to fully travel across the channel was computed to be 0.87 seconds. In
order to achieve steady state results, the fluid should completely flow across the channel
4 or 5 times. Hence, it is expected that the results will be significantly different than the
results obtained from steady state solution. The current results demonstrate the initial
37
variation of the shear stress and axial magnitude correctly. However, the effect of the
porous-jump boundary condition on the shear stress still requires more analysis.
Future Work
In the future, the simulation should run the complex simulations in FLUENT until the
fluid flow solution has been calculated for at least 3 minutes. Additionally, further
research needs to be conducted to determine the reasoning behind the zero shear stress at
the porous boundary. Ultimately, final results need to be compared with literature
resources and verified for accuracy.
38
Acknowledgements
We would like to thank our faculty mentor, Dr. Urmila Ghia. She has devoted
much of her time to have us fully understand the concepts behind this project. We came
into this project with no background in fluid mechanics and improved knowledge of this
subject. Her mentorship has been a valuable aspect of our research project. Dr. Ghia’s
graduate students have been great resources to us as well, as they have helped us with our
project on numerous occasions and assisted us in learning the CFD software. Thank you
to Prahit, Deepak, Nikhil, Chandrima, and Santosh for taking time out of your busy
schedule to teach us the software and help us with our problems along the way.
We would also like to thank the National Science Foundation for sponsoring this
study. Without the program in place we would have not had this great opportunity for
part time research.
Throughout the length of this research project, our understanding of fluid
mechanics has grown exponentially. We both are studying biomedical engineering, and
began this project with absolutely zero background in fluid mechanics and dynamics.
Though the learning curve was steep, with the assistance of Dr. Ghia we were able to get
a solid understanding of the fluid dynamic properties and were able to conduct research
studying the fluid flow within a channel. Through this project we also learned how to use
CFD tools Gambit and FLUENT, as well as how to interpret the results from FLUENT.
Bibliography
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Channel-Including a Wire-Mesh Segment on One Side Wall.” M.S. Mechanical
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4. Guo, J., Julien, PY. (2005), “Shear stress in smooth rectangular open-channel flows.”
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5. Janna, W. S. (2009), “Introduction to Fluid Mechanics”, CRC press, 4th Edition.
6. White, F. M. (2003), “ Fluid Mechanics”, McGraw-Hill, 5th Edition.
7. Fluent 6.3 User’s Guide.
8. Gambit 2.4 User’s Guide.
9. Chung, T. J. (2010), “Computational Fluid Dynamics”, Cambridge University Press,
2nd Edition.
10. Birchall, D. (2009), “Computational fluid dynamics”, The British Institute of
Radiology, 82, S1-S2.
11. “Vorticity.” Def. 1. Meriam Webster Online, Merriam Webster
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Jones, W., (1998), “Effect of Fiber Length on Glass Microfiber Cytotoxicity,” Journal of
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14. Paschkewitz, J.S., Dubiel, Y., Shaqfeh, E. (2005), “The dynamic mechanism for
turbulent drag reduction using rigid fibers based on Lanrangian conditional statistics”,
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