Project #5: Simulation of Fluid Flow in the Screen-

Bounded Channel in a Fiber Separator

By

Lana Sneath and Sandra Hernandez

3rd Year, Biomedical Engineering

University of Cincinnati

Faculty Mentor: Dr. Urmila Ghia

School of Dynamic Systems

University of Cincinnati

Sponsored By the National Science Foundation

Grant ID No.: DUE-0756921

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Abstract

The goal of this project is to classify asbestos fibers in large batches to use in toxicology

studies. Previous studies have shown that fiber toxicity depends on fiber length. In the

present study, the Bauer McNett Classifier (BMC) is modeled using CFD (Computational

Fluid Dynamics) to analyze its potential use to classify fibers based on length. The focus

of our study is to simulate the flow in the deep open channel of the BMC, with focus on

the screen (wire mesh). As a first step, the screen is replaced by a solid wall boundary to

facilitate the computations. The channel geometry is modeled in Gambit, and the

computational grid is imported into FLUENT to solve the three-dimensional Navier-

Stokes equations governing the fluid flow. Turbulence in the channel is founded using the

Reynolds Stress Model (RSM). As a second step, a portion of a sidewall is replaced by a

porous boundary to represent the screen openings in order to determine the flow

behavior. The results conclude the out-plane angle of shear stress on the xy plane is

around 8 degrees for the solid wall model, inferring that the shear stress distribution of

the flow is parallel to the screen.

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Contents

Abstract................................................................................................................................2

Contents...............................................................................................................................2

Chapter 1..............................................................................................................................6

Introduction......................................................................................................................6

1.1 Bauer McNett Fiber Classifier...............................................................................6

1.2 Objectives..............................................................................................................8

1.3 Materials................................................................................................................9

1.4 Methods.................................................................................................................9

Chapter 2............................................................................................................................10

Flow in the BMC Open Channel – Solid Side Walls....................................................10

2.1 Geometry and Computational Grid.....................................................................10

2.2 Boundary Conditions...........................................................................................11

2.3 Results and Discussion........................................................................................12

Chapter 3............................................................................................................................18

Flow in the BMC Open Channel with a Screen on a Side Wall....................................18

3.1 Geometry and Computational Grid.....................................................................18

3.2 Boundary Conditions...........................................................................................19

Conclusion.........................................................................................................................24

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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.

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d: Wire diameter.

K: Permeability

C2: Pressure-jump coefficient

Ui: Velocity.

Elent: Entrance length number.

lentrance: Length to fully developed velocity profile.

ρ: densityτ ij: 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. The use of

asbestos is a problem because asbestos is a known carcinogen that can lead to one or

more disorders if inhaled [3]. It has been proposed that alveolar macrophages (AM) are

unable to completely engulf long fibers and oxidants and enzymes leak from the AM,

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; the longer the fibers the greater the

chance of it being toxic [1]. Currently, studies are limited due to having only small

quantities of fibers available at a time, so it is difficult to conduct a large-scale toxicology

study. 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 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 the elliptical tanks.

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The water then flows through the screen in each of the tanks, causing separation of fibers

based on their length, as shown in Figure 2. This fiber 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.

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Figure 1. The Bauer McNett Fiber Classifier [13]

Figure 2. Top View of a Single Tank of the Bauer McNett Classifier

= Region of focused study

The flow within the tanks is governed due to gravity in the tank cascade. This

study concentrates on modeling the deep, open channel within the BMC as a porous

boundary to determine the shear stress distribution on 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]. 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. The BMC deep open channel is first modeled as a channel with both

vertical side boundaries as solid walls. Next, 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) Learn the fundamentals of fluid dynamics.

b) Learn the fundamentals of solving fluid dynamic problems numerically.

c) Simulate and study the flow in the open channel of the BMC apparatus, modeling

the screen as a solid wall boundary (i)

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d) Model the screen as a porous boundary (ii)

1.3 Materials

Commercially available Computational Fluid Dynamics (CFD) tools FLUENT

and Gambit are used for the simulations in this study.

1.4 Methods

The goal of this study is to numerically simulate the fluid flow in the screen-

bounded channel within the BMC fiber separator. To numerically study the fluid flow,

Computational Fluid Dynamic (CFD) software FLUENT and Gambit are used.

Computational Fluid Dynamics is the “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 pressure-

velocity coupling. The solution is deemed converged, when the residuals of the continuity

equation and the conservation of momentum equation reach 10e-6.

Continuity Equation (Equation of Mass Conservation):

(1)

Conservation of Momentum:

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(2)

Chapter 2

Flow in the BMC Open Channel – Solid Side 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

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.

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Figure 3. Computational Grid [1]

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

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Table 1. Computational Grid Spacing

Total Size X Y Z ∆Y ∆X

405000 50 180 45 0.00005 0.0007

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.

Figure 4. Boundary conditions applied on the BMC open channel

2.3 Results and Discussion

This study focuses on understanding the fluid behavior in the BMC deep open

channel in order to analyze the effectiveness of the system as a large-scale fiber

separator. Results examined in this study include the x-velocity contours, tangential

velocity vectors, x-vorticity, and the shear stress distribution.

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Outlet, pstat = 0

Inlet, u = U, v = w =0

No-Slip Wall, u = v = w = 0

Free-Slip Wall, v=0, du/dy=0, dw/dy=0

The non-dimensional entrance length, Elent, for turbulent flow is expressed as

Elent=4.4 (ℜ)1/6 (3)

For a Re of 9844, the non-dimensional entrance length is:

Elent=4.4 (9844)1 /6=20.37 (4)

Elent=lentranceDh

=20.37 (5)

Therefore the entrance length for the flow is:

lentrance=20.37∗0.01=0.2m (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.

Figures 5 and 6 show the x-velocity contours on the cross plane of the open

channel near the free surface and the channel base, respectively. Velocity is lowest at the

edges of the channel due to friction of the stationary wall. The velocity contours are

bulged towards the corners near the free surface at the top of the channels, while

elsewhere along the vertical wall boundaries, the contours gradually shift towards the

center of the plane. The shift and bulge in the velocity contours are attributed to the

secondary flows [1]. The free surface at the top of the channel is modeled by a zero-shear

stress wall, which attracts the high-momentum fluid from the center of the open channel.

In order to preserve the channel continuity, low momentum fluid from the corner regions

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flows towards the center of the channel. This motion of fluid flow creates a circulatory

effect near the corners, which causes the bulge in velocity contours near the free surface.

Figure 5. Top and Bottom Halves of X-Velocity Contours

Figure 6 shows the x-vorticity on the cross plane of the BMC open channel.

Vorticity is defined as the tendency of a fluid to rotate [11]. The vortices represent the

secondary flows within the channel. The vortices are different near the free surface than

near the channel base. In the corners near the free surface, the vortex pair is not

symmetrical about the angle bisector. The vortex near the channel base is symmetrical

about the angle bisector. There are noticeably more vortices near the free surface than the

channel base. The variation in vorticity along the top and bottom of the channel is due to

the different boundary conditions which changes the behavior of the fluid flow.

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Figure 6. X-Vorticity Contours of the bottom and top halves of BMC open channel flow

Shear stress, as shown in Figure 8, was computed along the x-direction of the

channel. Total shear stress, including τ zx , τ zy, and τ zz, was calculated along the z=0.02 m

sidewall at x = 0 to 0.217 m, y = 0.1 m (mid-plane). The computations from FLUENT for

each partial derivative in respect to z were written out as a text file, and uploaded into

Microsoft Excel in order to calculate τ for each shear stress component on the sidewall.

Each of the three components was squared and added together. The square root of the

summation is taken to obtain the total shear stress along the x- direction acting on the

sidewall at y = 0.1m. The shear stress is highest at the inlet (x = 0m), reaching around 1.7

Pascal. Along the x-axis, the shear stress steeply decreases between 0 and ~ 0.02 m. After

around 0.02 m in the x-direction, the shear stress levels off and gradually approaches 0.2

pascals.

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Figure 8: Total of All X-Wall Shear Stress Components along the X-direction

Table 2 shows the calculated off-plane and in-plane angles. The off-plane angle is

the angle between resultant shear stress vectors and the xy plane, whereas the in-plane

angle is the angle between the resultant shear stress vectors and the x-axis. These results

show the shear stress angle between the free surface and the wall in the BMC channel

with respect to the x-position in the channel geometry. Several data points were selected

to showcase the shear stress angle trend, as the entire data set was rather large. From

these calculations, it is shown that the shear stress angle is greatest at the inlet, and

quickly drops down to around 8 degrees as the x-position increases. In the actual channel

in the BMC apparatus, the screen is on the z = 0.02 m wall and has one-inch margins

from the inlet, outlet, and bottom wall. The highest off-plane angle occurs at the inlet, x=

0m, and quickly drops down to 8.36 degrees around x = 0.0116 m. It can be inferred from

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this table that the shear stress is mostly aligned tangential to the fluid flow, which is the

ideal situation.

Table 2. Shear Stress Angles along the X-position at y = 0.1 m, z = 0.02 m

In the deep open channel within the BMC apparatus, shear stress distribution on

the wire mesh governs the orientation of the fibers [14]. It is expected that the fibers align

themselves in the direction of shear stress, and any changes or fluctuations of shear stress

will result in a change in orientation. The ideal shear stress distribution would be parallel

to the wire mesh so the fibers are properly filtered by size.

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Chapter 3

Flow in the BMC Open Channel with a Screen on a Side Wall

3.1 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 side wall 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 9 shows the computational mesh that was used to analyze the fluid

flow in FLUENT.

Figure 9. Computational mesh with porous boundary on a side wall

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3.2 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 9. In Fluent, the sides of

the screen were specified as a porous-jump boundary condition, and the other as a

pressure-outlet. In order for FLUENT to solve the Reynolds Stress Equations for the fluid

flow in the channel with a porous boundary, the permeability, pressure-jump coefficient,

and the thickness of the porous boundary need to first be determined.

Calculating Permeability (K) and Pressure-Jump Coefficient (C2):

The standard screen thickness for a 16 Mesh is 0.0009144 m (0.036 Inch) and the

wire diameter is 0.0004572m (0.0180 Inch). When evaluating through-plane flow

through a 2D planar structure, the Kd2 value is given to be 0.0056 with F=0.118. The

equation used to calculate the permeability (K) and the pressure-jump coefficient are:

C2=2 F√K and

Kd2=

Kd2 (7)

To first solve for K, the given wire diameter (d) and the Kd2 value for a through-plance

flow through a planar 2D structure are imputed into the equation

0.0046= K(0.0004572)2

(8)

K=9.6154 e−10m2

This means the face permeability (K) of the screen mesh is 9.6154 e−10m2

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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)

√(9.6154 e−10m2) = 7610.739

1m

(9)

These values are then entered into FLUENT along with the overall screen thickness of

0.0009144 m to analyze the flow in the 3D open channel with the screen modeled as a

porous-jump boundary.

Figure 9. Boundary Conditions of Channel with Porous Boundary

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Outlet, pstat = 0

Inlet, u = U, v = w =0

No-Slip Wall, u = v = w = 0

Free-Slip Wall, u= v = w = 0

Porous-Jump, K = 9.6e-10, C2=7610.7 1/m, thickness = 9e-4 m

The turbulence boundary conditions were specified in the form of turbulence

intensity and viscosity of 0.5% 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 0.0004572 m, which is the set

value of the wire diameter for a 16 mesh.

3.3 Results and Discussion

Figures 10 shows the x-velocity contours on the cross plane of the open channel

near the free surface and the channel base, respectively. The velocity is similar to the two

wall case with the velocity being highest towards the center and lowest at the edges of the

walls. The velocity contours are bulged towards the corners near the free surface at the

top of the channels, while elsewhere along the vertical wall boundaries, the contours

gradually shift towards the center of the plane. However, unlike the previous case, the

velocity contours along each wall are not symmetric. This can be attributed to the

addition of the porous boundary.

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Figure 10. Top and Bottom Halves of X-Velocity Contours

Figure 11 shows the x-vorticity on the cross plane of the BMC open channel.

Similar to the results with the solid wall boundaries, the vorticies at the bottom corners

are symmetrical about the angle bisectors. The porous boundary is modeled from x=

0.0254 m to 0.1916 m. The vorticity contours were taken at a plane at x= 0.20m in line

with the outlet, right after the porous boundary ends. The addition of the porous

boundary greatly increased the vorticity along the side wall of the channel.

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Figure 11. Top and Bottom Halves of X-Vorcitity Contours

In Figure 12 shows the total shear stress profile for a deep open channel with a

porous boundary on one of the sidewalls to represent a screen. The total shear stress,

τ zx , τ zy, and τ zz, was calculated along the z=0.02 m sidewall at x = 0 to 0.217 m, y = 0.1 m

(mid-plane). It can be seen that the total shear stress profile at the beginning of the

channel is similar to that of the channel with non-porous sidewalls. Once the fluid flow

encounters the porous boundary, the total shear stress profile changes drastically. On

leaving the porous boundary wall, the shear stress reaches a value of approximately 0.22,

which is equal to the shear stress value in a non-porous wall.

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Figure 12. Total of All X-Wall Shear Stress Components along the X-direction

The off-plane and in-plane angles for the channel with a porous boundary are

displayed in Table 3. The shear stress angles at the beginning and end of the channel are

similar to those from the previous case. However, the off plane shear stress angle in

between is different because the porous boundary is present. The in plane shear stress

angle is relatively small, which means that the in plane shear stress angle is nearly

horizontal.

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Table 3. Shear Stress Angles along the X-position at y = 0.1 m, z = 0.0

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 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. As a second step, the

BMC channel geometry is modified to have one of the side walls contain a porous

boundary condition. The channel geometry is created in the CFD software Gambit with

grid spacing of 50, 180, and 45 grids in the x, y, and z directions. To determine the fluid

flow, FLUENT calculates the fluid flow at each discrete point along the grid. The

Reynolds-stress model accounts for effects of fluid rotation, curvature, and rapid changes

in strain rate of the fluid within the BMC apparatus.

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. In the second porous wall model, it was found that the

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x-velocity contours followed the same behavior as the previous case. However, once the

flow reaches the porous boundary, the x-velocity of the flow begins to fluctuate. In both

of the x-velocity contour plots, bulges are observed near the free surface.

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-vorticiy contour plots, which show the highest

vorticity in the corners near the free surface.

Looking at the shear stress of the fluid flow 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.

In the actual channel in the BMC apparatus, the screen is on the z = 0.02 m wall

and has one-inch margins from the inlet, outlet, and bottom wall. In the porous-wall case,

the screen is placed between x = 0.0254m and x = 0.1916m. The total shear stress

gradient at the beginning of the channel is similar in both the non-porous wall and the

porous wall cases. In the porous boundary case, once the flow encounters the porous

boundary, the shear stress changes drastically. On passing the porous boundary wall, the

shear stress nears a value of 0.22 pascals, which is similar to that observed in the solid

wall case.

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Future Work

The future work of this study is to further analyze the off-plane and in-plane shear stress

angles of the channel modeled with a porous boundary. Due to time constraints, this

study was not able to fully determine the effects of the porous boundary results. As a

further step, the results of both geometries will be compared with similar case studies.

Additionally, literature research will be performed to further investigate the fluid flow

through a porous boundary.

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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 out

project on numerous occasions and assisted us in learning the CFD software. Thank you

to Chandrima, Deepak, 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.

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Bibliography

1. Jana, C. (2011), “Numerical Study of Three-Dimensional Flow Through a Deep Open

Channel-Including a Wire-Mesh Segment on One Side Wall.” M.S. Mechanical

Engineering Thesis, University of Cincinnati.

2. Dodson, R., Atkinson, M., Levin, J. (2003), “Asbestos Fiber Length as Related to

Potential Pathogenicity: A Critical Review.” American Journal of Industrial Medicine,

Vol. 44, p. 291-297

3. http://www.nlm.nih.gov/medlineplus/asbestos.html

4. Guo, J., Julien, PY. (2005). “Shear stress in smooth rectangular open-channel flows.”

American Society of Civil Engineers, 131(1), 30-37.

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

12. Blake, T., Castranova, V., Baron, P., Schwegler-Berry, D., Deye, G.J., Li, C., and

Jones, W., (1998), “Effect of Fiber Length on Glass Microfiber Cytotoxicity,” Journal of

Toxicological Environmental Health, Part A, Vol. 54, Issue 4.

13. www.uceindia.com/fiber-classifier-bauer-mcnett-type.htm

29

14. Paschkewitz, J.S., Dubiel, Y., Shaqfeh, E., (2005), “The dynamic mechanism for

turbulent drag reduction using rigid fibers based on Lanrangian conditional statistics”,

American Institute of Physics, Vol. 17.

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