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EXPERIMENTAL INVESTIGATION OF FLOW IN A

RECTANGULAR CAVITY WITH A POROUS OPENING

presented by

SAGAR RAYEPALLI

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6/07 p:/ClRC/DateDue.indd-p.1

EXPERIMENTAL INVESTIGATION OF FLOW IN A
RECTANGULAR CAVITY WITH A POROUS OPENING

By

Sagar Rayepalli

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Mechanical Engineering

2007

ABSTRACT

EXPERIMENTAL INVESTIGATION OF FLOW IN A
RECTANGULAR CAVITY WITH A POROUS OPENING

By

Sagar Rayepalli

The velocity ﬁeld within a nominally two-dimensional cavity is investigated in a water
channel. The Reynolds number based on cavity length and freestream speed is in the
range 245 — 410. The purpose of the study is to characterize the changes in the
recirculation ﬂow pattern inside the cavity caused by a porous surface (rectangular mesh)
covering the cavity opening. Both ﬂow visualization and quantitative results for the mean
and ﬂuctuating velocity ﬁeld are discussed for surfaces of different porosity ranging
between 64.8% and 37.3%. The total kinetic energy, vorticity distribution and related
circulation in the cavity are analyzed. The most signiﬁcant ﬁnding is the huge reduction
in total kinetic energy when the cavity opening was covered with the mesh for all cases.
It is observed that parameters such as positioning of mesh with respect to cavity, length
of mesh exposed to flow, gap between the cavity and mesh also affect the ﬂow ﬁeld
inside the cavity. And ﬁnally suggestions are made to minimize the flow ﬁeld inside the

cavity.

ACKNOWLEDGEMENTS

I take this opporttmity to express my deep sense of gratitude and profound thanks to Dr.
Manoochehr Koochesfahani, for the constant help, continual encouragement and
guidance given to me during the course of my Masters’ research. He has been a source of
inspiration throughout the course of this work. But for his continuous guidance and help,
I would not have completed this work successfully. I would also like to thank Dr.

Brereton and Dr. Rishi Gupta for reviewing my manuscript.

I am indebted to my current and past lab mates: Dr. Chee Lum, Dr. Douglas Bohl,

Shahram and Raj at Basu who provided me with valuable information regarding my work.

I dedicate this thesis to my family who unremittingly supported me and provided me

constant encouragement during my years of study. They made this work possible.

Finally, I wish to place on record my deep sense of gratitude to Dr. Manoochehr

Koochesfahani for all the help, guidance and encouragement extended by him for the

successful completion of this work and cherish to remember my association with him.

Sagar Rayepalli

iii

TABLE OF CONTENTS

LIST OF TABLES ................................................................................ vi

LIST OF FIGURES .............................................................................. vii

LIST OF SYMBOLS ............................................................................. x

1. INTRODUCTION ........................................................................... 1

1.1. Cavity Flows ........................................................................... 1
1.2. Brain Aneurysm .......................................................................

2. EXPERIMENTAL FACILITY AND INSTRUMENTATION ........................ 8
2.1. Experiment Facility ....................................................................

2.2. Diagnostics ............................................................................. ll

3. RESULTS AND DISCUSSION ........................................................... 17

3.1. Boundary Layer Thickness .......................................................... 17

3.2. Results for effect of percentage variation in mesh ................................ 18

3.2.1. Flow Visualization ........................................................... 19

3.2.2. Measured Quantities ....................................................... 21

3.2.3. Discussion .................................................................... 27

3.3. Results for effect of rectangle size of mesh ....................................... 32

3.3.1. Discussion ..................................................................... 32

3.4. Results for effect of positioning of mesh with respect to cavity ................ 35

3.4.1. Flow Visualization ........................................................... 35

3.4.2. Measured Quantities ....................................................... 35

3.4.3. Discussion ..................................................................... 37

3.5. Results for effect of length of mesh ................................................ 39

3.5.1. Flow Visualization ........................................................... 39

3.5.2. Measured Quantities ....................................................... 41

3.5.3. Discussion ...................................................................... 41

3.6. Results for effect of gap between the mesh and cavity .......................... 44

3.6.1. Flow Visualization ........................................................... 44

3.6.2. Measured Quantities ....................................................... 46

3.6.3. Discussion ..................................................................... 47

4. CONCLUSIONS .............................................................................. 50

iv

APPENDIX A. Timing data for all the experiments ........................................ 54

APPENDD( B. MTV in-house program for correlating DPIV data.. ........................... 56
APPENDD( C. Figures .......................................................................... 58
LIST OF REFERENCES ....................................................................... 101

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Table 1 1.

Table 12.

Table 13.

LIST OF TABLES

Reynolds number range for 6,8,10 Hz frequencies of water tunnel motor.
Mesh speciﬁcations .................................................................
Properties of silver—coated hollow glass spheres ...............................

Normalized space averaged total kinetic energy data from the study of
variation in percentage opening area and rectangle size .....................

F luctuating component of space averaged TKE data from the study of
variation in percentage opening area and rectangle size ......................

Normalized space averaged total kinetic energy data from the study of
effect of exposed length of mesh ..................................................

Fluctuation component of normalized space averaged TKE data from the
study of effect of exposed length of mesh .......................................

Normalized space averaged total kinetic energy data from the study of
effect of gap between the mesh and the cavity opening .......................

Fluctuation component of normalized space averaged TKE data from the
study of effect of gap between the mesh and the cavity opening ............

Timing data for the study of effect of percentage opening area and
rectangle size ........................................................................

Timing data for the study of effect of exposed length ofmesh. . . . . . ..

Timing data for the study of effect of gap between the mesh and the
cavity opening ......................................................................

Water tunnel calibration data .......................................................

vi

9

10

12

31

31

43

43

49

49

54

54

55

55

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.
Figure 6.
Figure 7.
Figure 8.

Figure 9.

Figure 10.

Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.

Figure 17.

Figure 18.

LIST OF FIGURES

Optical matching of aneurysm model (a) without optical matching (b)
with optical matching .............................................................

Comparison of velocity ﬁeld within the aneurysm (3) without stent (b)
with stent at a Reynolds number of 184 ........................................

Comparison of total kinetic energy within the aneurysm (a) without
stent (b) with stent at a Reynolds number of 184 ..............................

Comparison of vorticity within the aneurysm (a) without stent (b) with
stent at a Reynolds number of 184 ..............................................

Experimental Set up (a) Rear View (b) Front view ..............................

Schematic of ﬂat plate with the cavity ..........................................
Water Tunnel Calibration .........................................................
Deﬁnition of rectangle size and opening area ..................................

Schematic of test section for the experiment (a) Effect of percentage
opening areal rectangle size (b) Effect of exposed length of mesh. .

Schematic of test section for the experiment - effect of gap between the
mesh and the cavity (a) Front view (b) Top view of ﬂat plate ...............

Streamwise imaging arrangement for Pixelfly camera ........................
Schematic of timing diagram for Pixelﬂy camera ............................
Schematic of timing diagram for Pixelﬂy camera (cont) ....................
Streamwise imaging arrangement for Pulnix TM — 9701 CCD camera...
Schematic of timing diagram for Pulnix TM-970l CCD camera ...........
Schematic of timing diagram for Pulnix TM-970l CCD camera (cont)...

Comparison of measured velocity proﬁles with Blasius solution at a
section, (a) 1.8cm (b) 0.04cm upstream of the front edge of the cavity...

Flow visualization inside the cavity for no mesh case at Reynolds
number (a) 390 (b) 325 (c) 255 (d) 179 (e) 100 . .... .....

vii

6O

61

62

62

63

64

65

65

66

67

68

69

70

71

72

73

74

75

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

Figure 33.

Comparison of flow ﬁeld between the cavity and free stream, for no
mesh case at a Reynolds Number of 390. .....................................

Flow visualization inside the cavity, which is covered with the mesh of
0.1905 mm diameter, 64.8% opening area, at Reynolds number (a) 390
(b) 325 (c) 255. .......................................................................

Flow visualization inside the cavity, which is covered with the mesh
0.1651 mm diameter, 64.8% opening area, at Re (a) 390 (b) 325 (c) 255.

Vorticity distribution (cavity + freestrearn) for the no mesh case at
Reynolds number of 390 .........................................................

(a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for the no mesh case at Reynolds number of 390 ......................

(a) Mean kinetic energy (b) Fluctuating kinetic energy distribution
inside the cavity for the no mesh case at Reynolds number of 390. . . . .

(a) TKE distribution (b) Vorticity distribution inside the cavity for the
0.1905 mm diameter, 64.8% opening area mesh at Re of 390 ...............

(a) Mean kinetic energy distribution (b) F luctuating kinetic energy
distribution inside the cavity for the 0.1905 mm diameter, 64.8%
opening area mesh case at Reynolds number of 390 .........................

(a) TKE distribution (b) Vorticity distribution inside the cavity for the
0.1651 mm diameter, 64.8% opening area mesh at Re of 390 ...............

(a) TKE distribution (b) Vorticity distribution inside the cavity for the
0.1905 mm diameter, 39.1% opening area mesh at Re of 390 ...............

Result for effect of percentage opening area of mesh on normalized
space averaged total kinetic energy inside the cavity ........................

Result for effect of percentage opening area of mesh on normalized
mean component of space averaged TKE inside the cavity ..................

Result for effect of normalized rectangle size of mesh on normalized
space averaged total kinetic energy inside the cavity ........................

Result for effect of normalized rectangle size of mesh on normalized
mean component of space averaged TKE inside the cavity. . . . . . . . . .

Study of effect of positioning of mesh through particle streak flow
visualization inside the cavity ...................................................

viii

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

Figure 34.

Figure 35.

Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.

Figure 43.

Figure 44.

Figure 45.

(a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for the 0.1905 mm diameter, 64.8% opening area mesh at
Reynolds number of 390 whose ﬁrst wire is at a distance of 0.7 mm
from the downstream edge of the cavity .......................................

(a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for the 0.1905 mm diameter, 64.8% opening area mesh at
Reynolds number of 390 whose first wire is at a distance of 0.2 mm
from the downstream edge of the cavity .......................................

Result for effect of position of mesh with respect to cavity on
normalized space averaged total kinetic energy inside the cavity ..........

Study of effect of exposed length of mesh through particle streak ﬂow
visualization inside the cavity ...................................................

a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for 0 cm exposed length of mesh (0.1905 mm diameter, 64.8%
opening area) at Reynolds number of 390 .....................................

a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for 2 cm exposed length of mesh (0.1905 mm diameter, 64.8%
opening area) at Reynolds number of 413 .....................................

Result for effect of exposed length mesh on normalized space averaged
total kinetic energy inside the cavity ............................................

Study of effect of gap between the mesh and the cavity, through particle
streak ﬂow visualization inside the cavity .....................................

(a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for a gap of 0.508 mm between the mesh (0.1905 mm diameter,
64.8% opening area) and the cavity at Reynolds number of 392.7 .......

(a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for a gap of 0.127 mm between the mesh (0.1905 mm diameter,
64.8% opening area) and the cavity at Reynolds number of 406 ............

(a) Total kinetic energy distribution (b) Vorticity distribution inside the
cavity for a gap of 0 mm between the mesh (0.1905 mm diameter,
64.8% opening area) and the cavity at Reynolds number of 390 ............

Result for effect of gap between mesh and the cavity on normalized
space averaged total kinetic energy inside the cavity ........................

Images in this thesis/dissertation are presented in color.

ix

91

92

93

94

95

96

97

98

99

100

101

102

Symbol

Re

3|

LIST OF SYMBOLS

Description (page or ﬁgure of ﬁrst reference)
Diameter of mesh wire (10)

Diameter of silver coated hollow spheres (12)
Digital particle image velocimetry (l l)
Gravitational acceleration (12)

Rectangle size (10)

Reynolds number based on cavity opening width (9)
Total kinetic energy (30)

Mean component of X — velocity (22)
Fluctuating component of X — velocity (22)
Settling speed of particles (12)

Mean component of Y — velocity (22)
Fluctuating component of Y — velocity (22)
Freestream velocity (17)

Distance from the ﬂat plate bottom surface (17)

Boundary layer thickness (17)
5y
— l7
6 ( )
Density of silver coated hollow spheres (12)

Density of water (12)

Kinematic viscosity (12)

1. INTRODUCTION

Research has been done on several aspects of cavity ﬂows both experimentally and
numerically. However, it is noted less or no research has been done on characterizing the
changes in the recirculation ﬂow pattern inside the cavity, caused by a porous surface
covering the cavity opening. The primary motivation for this investigation was ﬂow ﬁeld
analysis inside a brain aneurysm; minimization of ﬂow ﬁelds within the aneurysm using
a stent being one the aspects. Keeping this objective in mind, a fundamental study of ﬂow
ﬁeld inside a 2D rectangular cavity with a porous opening would be useful before starting

with analysis inside the aneurysm.

1.1 Cavity Flows

The study of cavity flows at low Reynolds numbers dates back several decades. Two

types of cavity ﬂows have been studied, both experimentally and numerically. They are:

1. Lid driven cavities

The problem geometry is simple and two-dimensional, and the boundary conditions are
also simple. The standard case is ﬂuid contained in a square domain with Dirichlet
boundary conditions on all sides, with three stationary sides and one moving side (with

velocity tangent to the side).

2. Shear driven cavities

For these types of flows, the lid is replaced with a moving ﬂuid. The two names (lid-
driven and shear-driven) are used interchangeably in spite of the fact that they are distinct

(and different) problems.

The problems of the cavity ﬂows have been studied by several investigators. The
streamlines have been analyzed theoretically by Moffatt (1963) and T akematsu (1966).
Moffatt (1963) studied some simple similarity solutions for the ﬂow of a viscous ﬂuid
near a sharp corner between two planes on which a variety of boundary conditions may
be imposed. Takematsu (1966) studied the steady ﬂow of a viscous incompressible ﬂuid
past a two—dimensional cavity of inﬁnite depth. His analysis is based on Stokes
approximation, i.e. the assumption that Re <<< 1 and the convection of vorticity is to be
neglected. In his analysis he assumed the oncoming stream to be a parallel ﬂow with
constant vorticity, its speed being U(y) = y. He found that the dividing streamline was not
consistent with the mouth of the cavity, although rather straight, but that it penetrates to a
considerable depth into the cavity. He mentions that as far as the Stokes approximation

was concerned, the separation of the ﬂow occurs, not at the corner, but on the cavity wall.

Kawaguti (1961) has studied the two-dimensional rectangular cavity ﬂows (lid driven
type) to obtain the distributions of stream function, vorticity and pressure. He computed
the results for low Reynolds numbers ranging from 0 (Stokes’ solution) to 64 and for
various cavity lengths. He concluded that in all cases, the pressure on the downstream
edge of the cavity is higher and that on the upstream was lower compared to middle point

of the bottom wall. He also found that as Reynolds number was increased, the centre of

the vortex moves downstream, and the pressure gradient in the region downstream

becomes steeper, while that in the region upstream less steep.

Kinoshita, O. and Ito, H. (1984) have experimentally studied the two-dimensional ﬂow of
an oblique cavity (lid driven type) for a very low Reynolds numbers (Re << 1) using
tracer techniques. They compared their results with numerical simulations of Kawaguti

(1961) and found solutions to be nearly consistent.

Manovski, P. (2005) experimentally investigated two-dimensional rectangular cavity for
several cavity lengths, for Reynolds numbers 90 — 730. Planar laser induced ﬂuorescence
(PLIF) was employed as a ﬂow visualization method and particle image velocirnetry
(PIV) provided quantitative measurements of the complex velocity ﬁelds. His analysis
was mainly related to an interesting aspect of cavity ﬂow that is the initiation of self-
sustained oscillations of the cavity shear layer between the freestream ﬂow and the cavity

ﬂuid.

1.2 Brain Aneurysm

The details about the brain aneurysm and the current available treatment options are
obtained from the website www.brainaneurysm.com. An aneurysm is an abnormal
widening or ballooning of a portion of a blood vessel. A cerebral aneurysm refers to a
blood vessel within the brain that weakens over time and undergoes such widening. This
usually occurs at the junctions of the large arteries at the base of the brain, in an area

called the Circle of Willis. As the blood vessel weakens, it begins to bulge out like a

balloon. Often, as an aneurysm develops, it forms a neck with an associated dome, or

balloon like structure. As the artorial wall weakens, the aneurysm may rupture.

Brain aneurysms are often discovered when they rupture, causing bleeding into the brain
or the space closely surrounding the brain called the subarachnoid space, causing a
subarachnoid hemorrhage. Subarachnoid hemorrhage from a ruptured brain aneurysm
often leads to signiﬁcant disability or death. It is estimated that up to one in 15 people in
the United States will develop a brain aneurysm during their lifetime 6-8 / 100,000

patients will present with subarachnoid hemorrhage.

Surgery or minimally-invasive endovascular coiling techniques can be used in the
treatment of brain aneurysms. Until recently, people with wide-necked aneurysms in the
brain would not have been candidates for coil embolization, a procedure in which tiny

coils are used to close off the aneurysm.

Historically, if the fundus to neck ratio was less than 2 then the coil embolization could
not be performed satisfactorily due to coil loop herniation. The recent introduction of
ﬂexible intracranial stents has provided a method of preventing the coil from migrating
out of wide-necked aneurysms. The stent is placed across the neck of the aneurysm prior
to introduction of coils into the aneurysm. Therefore, more patients can undergo
minimally invasive interventions to repair their cerebral aneurysms. The body responds
by forming a blood clot thrombosis around the coils and new tissue growth around the
stent to prevent blood ﬂow into the aneurysm cavity. Coiling introduces the risk of

perforation of the aneurysm when the coils are introduced. There is also a risk of

thrombus formation that can dislodge into the parent vessel and also of coil protrusion

into the parent vessel.

Recently, intravascular porous tubular-shaped stents are being considered for the
endovascular treatment of intracranial aneurysms. Flow ﬁeld analysis inside a brain
aneurysm in the presence of stent is one of the interesting areas. Research in this area is
being done for the past decade by several researchers. They have studied the effect of

stent porosity and inﬂuence of aneurysm geometry on the ﬂow inside the aneurysm.

Lieber, B.B., Stancarnpiano, AP. and Wakhlooo, AK. (1997), investigated the changes
in local hemodynarnics resulting from stent implantation. They used woven nitinol stents
of porosities 76%, 80%, 82% and 85%. Womersley number was 5.3 for large arteries and
2.7 for small arteries. The mean, maximum, minimum Reynolds number for large arteries
was 180, 490, and 30 respectively and 90, 230 and 2 respectively for small arteries. They
found that for both large and small arteries placement of a stent of lowest porosity across
the aneurysm oriﬁce resulted in substantial reduction of aneurysmal vortex speed and
decreased interaction with parent vessel. Their results are based on ﬂow visualization
(qualitative analysis) using laser-induced ﬂuorescence of Rhodamine dye. Measurements

related to kinetic energy reduction due to the presence of stent were not studied.

Yu, S.C.M., Zhao, J.B. (1999) have done steady ﬂow analysis on the stented and non
stented sidewall aneurysm models using particle image velocirnetry techniques. They
found that the highest wall shear stresses (derived from near wall velocity measurements)
always appear at the distal neck of the aneurysmal pouch. Their investigations are limited

to only steady state ﬂow analysis and haven’t made any measurements for pulsatile

ﬂows. Rhee, K., Han, M.H. and Cha SH. (2002) studied the changes of ﬂow
characteristics by stenting in aneurysm models for a pulsatile ﬂow. In addition to
inﬂuence of stent porosity, they also studied the effect of aneurysm geometry. In their
study they clariﬁed the velocity and wall shear stress changes that are caused by stenting
in fusiform and lateral aneurysm models. Even, their results are also completely based on
ﬂow visualization of photochromic dye that was 1’, 3’, 3’-trimethyl-6-nitroindoline-6-
spiro-benzospyran (TNSB). Their analysis is purely qualitative in nature and they haven’t

commented on total kinetic energy reduction caused by the placement of stent.

Chee Lum (2007) has made quantitative measurements inside a glass model (Figure 1) of
brain aneurysm. The stent used in that experiment has a diameter of 5 mm and the wire
thickness of it is 0.1077 mm. The aneurysm opening was 6.5 mm wide and the
percentage opening area of the stent was 80%. This experiment was done at Reynolds
number of 184 (based on tube diameter) and 267 (based on aneurysm opening diameter).
The measured velocity ﬁeld inside the aneurysm with/without the stent is shown in
Figure 2. He reported that the average total kinetic energy decreased to 9.6% (Figure 3)
when the aneurysm opening was covered with the stent. He observed that the vortex core

lies towards the downstream edge of the aneurysm cavity (Figure 4).

The ﬂow characteristics inside the aneurysm pouch could be signiﬁcantly affected by the
selection of stent, the shape of aneurysm and the type of ﬂow. To the best knowledge of
author very little research has been done to estimate reduction (from quantitative
measurements) in total kinetic energy for pulsatile ﬂows. Therefore, a detailed study of

velocity ﬁeld, total kinetic energy distribution, vorticity distribution, wall shear stress

changes inside the aneurysm pouch for a pulsatile ﬂow caused by stenting, is felt to be of
importance. The results from these experiments would comprehend the results from little

known research.

At present in the Turbulent Mixing and Unsteady Aerodynamics Laboratory (Michigan
State University, East Lansing), stents of different porosity are not available to carry out
the experimental analysis on the glass model of brain aneurysm. So, as a starting point, a
fundamental study of ﬂow ﬁeld inside a 2D rectangular cavity with a porous opening it is
felt to be of use. Furthermore, it is limited to steady state analysis. The results from 2D
rectangular cavity experiment are compared with the aneurysm result of Chee Lum
(2007), to check whether the porous surface near the cavity opening has similar effect on

aneurysm and 2D rectangular cavity.

2. EXPERIMENTAL FACILITY AND INSTRUMENTATION

All of the experiments used for this study were performed in the Turbulent Mixing and
Unsteady Aerodynamics Laboratory’s (Michigan State University, East Lansing) small
water tunnel facility. The present study is based on the results from streamwise imaging.
This chapter will explain the experimental facility and diagnostics. Images in this

thesis/dissertation are presented in color.

2.1 Experimental Facility

All of the experiments were performed in a water tunnel, which was driven by Baldor
electric motor attached with a Fincor 5200 adjustable frequency ac motor control as
illustrated in Figure 5. The test section used in this study had inside dimensions of 19 cm
(height) x 15.3 cm (width) x 43.4 cm (length). During the experiment the water tunnel
was ﬁlled with deionized water with a hose up to a height of 14.2 cm from the test
section base. Extreme care was taken in ﬁlling the test section to reduce bubbles that
could upset the ﬂow characteristics of the approach stream. Uniform, laminar ﬂow was
ensured in the test section by using a series of honeycombs and ﬁne screens upstream of

the contraction.

A ﬂat two — dimensional ﬂat plate of 1.7 cm thickness was placed in the water tunnel at a
distance of 8.5 cm (measured from the bottom face of ﬂat plate to the bottom of the test
section) with the help support rods as shown in Figure 6(a). The rounded leading edge of

the ﬂat plate is half circular while the trailing edge is tapered. An arrangement was

provided within the ﬂat plate to place a two — dimensional rectangular cavity of different
sizes. The length of the cavity used in the experiment is 0.5 cm and depth of is 0.52 cm.
The front edge of the cavity is located at a distance of 17.3 cm from the leading edge of

the ﬂat plate.

The experiments were done at three different motor frequencies namely 6 Hz, 8 Hz and
10 Hz. The motor has the capability to reach a maximum of 60 Hz. The Reynolds
number (Re) of the freestream (with ﬂat plate in the test section) was measured based on
the cavity length of 0.5 cm. The experiments were done over a period of several months
and so the knob (used to adjust the water tunnel motor frequency) position may not
exactly coincide with the previous lcnob positions. 80, for a particular motor ﬁ'equency
the free stream velocity is not a constant value but, varies within a certain range. The
range of Reynolds numbers for 6 Hz, 8 Hz, and 10 Hz frequencies are listed in Table 1.
Table 13 in Appendix A shows the water tunnel calibration data up to a motor frequency

of 18 Hz and is plotted in Figure 7.

Table 1. Reynolds number range for 6,8,10 Hz frequencies of water tunnel motor

 

 

 

 

 

Re olds Number
Water Tunnel Motor Frequency (Hz) (based on 3:1,“), length = 0.5 cm)
6 245 - 265
8 310 - 340
10 370 - 410

 

 

 

Seven different sizes of stainless steel woven mesh are used in the cavity ﬂow
experiments. Their speciﬁcations namely, wire diameter, percentage opening area,

rectangle size and cell per inch are listed in Table 2. The diameters of the wire meshes are

chosen in such a way that they are roughly about the same wire diameter as that of the
stent (0.1077 mm) used by Chee Lurn (2007) in his experiments. Rectangle size is
deﬁned as the distance between adjacent wires in the wire mesh as shown in Figure 8.

The percentage opening area of mesh is given by equation 2.1.

2

 

 

 

 

 

 

 

 

 

Percentage opening area = 2 x100 (2.1)
+ d)
Table 2. Mesh speciﬁcations
Wire diameter Percentage open Rectangle size (mm) Cell per inch

(mm) area

0.1397 49.4 0.3302 54 x 54
0.1397 59.1 0.4572 42 x 42
0.1651 37.3 0.2540 60 x 60
0.1651 56.7 0.5080 38 x 38
0.1651 64.8 0.6807 30 x 30
0.1905 39.1 0.3302 50 x 50
0.1905 64.8 0.7874 26 x 26

 

 

 

 

 

 

Five different sets of experiments involving the mesh were conducted namely, study of
effect of percentage opening area of mesh (Figure 9(a)), study of effect of rectangle size
(Figure 9(a)), study of effect of positioning of mesh with respect to the cavity, study of
effect of exposed length of mesh (Figure 9(b)) and study of effect of gap between the

mesh and cavity (Figure 10).

For all experiments, expect the experiments involving the study of the effect of length of

mesh, the length of the mesh used was 2 cm. The mesh was attached to the ﬂat plate

symmetrical to the cavity using a black vinyl electrical tape of 0.215 mm thickness as

10

shown in Figure 9(a). Except the cavity opening length of 0.5 cm, the mesh was covered
with a tape of length 0.75 cm upstream and downstream to the cavity edges. Three
experiments involving a gap between the cavity and mesh were performed and the gap

was maintained using shim stocks of thiclcness 0.127 mm, 0.254 mm and 0.508 mm.

2.2 Diagnostics

Digital Particle Image Velocimetry (DPIV) technique was used to measure two
components of velocity in a plane parallel to the streamwise direction and perpendicular
to spanwise direction. The DPIV apparatus consisted of a light source (laser), camera and
a PC equipped with a frame grabber. The laser acts as a photographic ﬂash for the
camera, and the particles in the ﬂuid scatter the light. It was this scattered light that was

detected by the camera.

In order to measure the velocity at least two exposures are needed. They are recorded on
two separate frames. The frames were split in a large number of interrogation areas, often
called tiles/windows. It was then possible to calculate a displacement vector for each tile
with help of cross-correlation program. This was converted to a velocity using the time
between image exposures. Spacing between image exposures was controlled by timing
electronics. The electronics also permitted image pairs to be acquired at various times
along the ﬂow. These digital delay and pulse generators provided several outputs that can

be delayed and referenced to each other.

11

The ﬂuid under investigation (deionized water) was ﬁrst seeded with tracer articles that
followed ﬂow ﬁeld. It is the motion of these seeding particles that is used to calculate
velocity information. The seed particles used in the experiment are CONDUCT-O-FIL®
silver-coated hollow glass spheres (Potter Industries Inc. - SH400820). The properties of

the particles are mentioned in Table 3.

Table 3. Properties of silver-coated hollow glass spheres

% metal 20
D10 6

D90 33
True Dens' 1.6

 

In Table 3 D10 implies 10 percent of particles are smaller than 6 pm and similarly D90
implies 90 percent of particles are smaller than 33 um. Eames (2004) in his paper showed
the settling speed of a particle, 01 to be equation 2.2. In equation 2.2, assuming diameter
of the particle to be D50 i.e. 19.5 pm, the settling speed of the particles in water was
measured to be 0.124 mm/s. The settling speed could affect the results of ﬂow ﬁeld
inside the cavity, when dealing with either low Reynolds numbers or low percentage
opening areas of mesh. The effect of the settling speed will be discussed in detail in the
later chapters while dealing with quantitative results of ﬂow ﬁeld inside the cavity.

may

8
v =
T 181)

 

(2.2)

A 500 mW Lasiris Magnum SP Laser operating at a wavelength of 680nm was used as
the light source. It was mounted on top of the test section with the help of 80/20® Inc.'s

aluminum T-slotted proﬁles (20 series). Laser line patterns are often generated by

12

cylindrical optics that produce a Gaussian line proﬁle with a bright centre and fading
ends. Lasiris optics spread the laser beam into an evenly illuminated line along the
streamwise direction. The laser is focusable and was adjusted to produce a focus line at
desired distance. In addition the line was collimated so that its thickness (approximately

200 um thickness) remains fairly constant over a long projection distance.

The imaging was done using two different cameras. Pixelﬂy camera was used to make
ﬂow measurements inside the cavity because of its higher resolution and Pulnix TM-9701

CCD camera was used to make freestream speed measurements.

The streamwise imaging arrangement for Pixelﬂy camera is shown in Fig 11. A Pixelﬂy
camera with a resolution of 1392 (horizontal) x 1024 (vertical) pixels (focus area - 0.928
cm x 0.683 cm) was used to image the cavity in the setup. It was operated with an
exposure of 400 ms (2.5 frames/s) for particle streak ﬂow visualization within the cavity
and laser was shot continuously. Since the exposure was maintained same for all cases
during the experiment, one can ﬁgure out the difference in velocities qualitatively based
on streak lengths. Using a Pixelﬂy camera the maximum frame rate that can be achieved
was 11.5 fps. So, for velocity measurements the camera exposure was maintained at 100
ms (10 fps) but, the actual exposure was given by laser pulse width. It was operated in
video mode. Table 10—12 shows the pulse widths used for different sets of experiments.
Micro-Nikkor 105 mm f/2.8 lens was mounted on the camera. Nikon Teleconverter (TC —
201), Quantaray Double Ranger 7 EL were also mounted between the lens and the

Pixelﬂy camera, to multiply the primary lens's focal length by a factor of 2X each. While

13

on the other hand, they decrease the effective aperture of the primary lens by two f-stops

each.

Camware was the control software for Pixelﬂy camera. It’s a 32-bit application for the
Windows 9x/ME/2000/NT operating systems. The image acquired using Camware was
stored as 16 bit TIFF image (2.72 MB each). It was converted to 8-bit TIFF image (1.36
MB) using Image-Pro Plus 5.0 software. 125 image pairs are acquired for quantitative

analysis i.e. 125 velocity ﬁeld samples.

Schematic of timing diagram for Pixelﬂy camera is illustrated in Figure 12-13. In case of
cavity ﬂow measurements, the timing and duration of light pulses was attained with the
help of 3 SRS 4-Channe1 digital delay/pulse generators (Model DG535) and one 2 —
channel AND gate. The ﬁrst delay generator was used to generate an internal 10 Hz
signal which was provided to both camera and second delay generator. In video mode
setting of Pixelﬂy camera there is an intrinsic + system delay of 130 us. So, the ﬁrst
delay generator is operated at 9.987 H2 (100130 us) so that the resultant output would be
10 Hz (105 us) signal. The second delay generator converts that 10 Hz signal to 5 Hz. The
third produces two pulses of desired pulse width and delay, such that ﬁrst pulse lies at the
end of ﬁrst camera frame and second pulse at the beginning of the next camera frame.
The AND gate combines the 2 pulses and then transmits the combined signal to the laser.
The separation time between light pulses depends on the velocity range and the size of

the interrogation region. This is because accurate PIV velocity estimates require that the

14

majority of the particles located in the interrogation region in the ﬁrst image remain

within the corresponding region in the second image.

In this case the light source was pulsed with a pulse width in the range 2 — 50 ms for an
incavity maximum speed of 3.80 - 0.19 cm/s respectively. And the delay periods between
pulses vary in the range 15 — 900ms. For a delay period of more than 200 ms, a slightly
different strategy was adopted. The ﬂow was imaged at 10 fps with a delay period of
lOOms and every second or third or fourth so on images were correlated depending on the
ﬂow speed. If every second image was correlated it implies the delay period was 200ms.
Similarly, if the delay period was 300ms then, every third image was correlated. Table
10-12 in Appendix A gives the complete list of pulse widths and delay periods for

various experiments.

Figure 14 illustrates the arrangement for freestream speed imaging using Pulnix TM-
9701 CCD camera. Pulnix TM-9701 CCD camera with a resolution of 640 (horizontal) x
480 (vertical) pixels (focus area - 5.07 cm x 3.8 cm) was used for this. Standard video
framing rate (30 frames/s or 60 ﬁelds/s) was digitized to 8 bits (300 KB) and recorded
onto hard disk (as TIFF image) in real time by an image acquisition system (Mutech
MV1000 Capture Sequence). 30 image pairs were recorded for freestream velocity

calculations using digital particle image velocirnetry.

Schematic of timing diagram for the Pulnix TM-9701 CCD camera is illustrated in Figure

15-16. In the case of freestream measurements, the timing and duration of light pulses

15

was attained with the help of Color Sync, 2 SRS 4-Channel digital delay/pulse generators
(Model DG535) and a 2 — channel AND gate. The Color Sync was used to generate the
30 Hz (60 VD) reference signal. It was provided to both camera and ﬁrst delay generator.
The ﬁrst delay generator converts that 30 Hz signal to 15 Hz. The second produces two
pulses of desired pulse width and delay, which was combined by AND gate and then
transmitted to laser. Table 13 in Appendix A gives the list of pulse widths and delay

periods for freestream velocities measured.

The DPIV data were processed using the in-house MTV processing programs. The
program was broken down into three categories: pre-processing, processing, post-
processing. The preprocessing step readies the data and the inputs for the correlation step.
The post-processing step allows the user to extract statistics and prepare the output for
plotting. All images used in the MTV processing routines are TIFF images. The typical

sequence of steps used for processing the DPIV data is listed in Appendix B.

16

 

3. RESULTS AND DISCUSSION

This chapter presents visual and quantitative results of the effect of several parameters
namely, percentage opening area, rectangle size, length of mesh, positioning of mesh
with respect to cavity and also effect of gap between mesh and cavity at three different
water tunnel motor frequencies. The corresponding Reynolds number of those 3
frequencies is mentioned in Table 1. Details of the boundary layer thickness, upstream of
the cavity are also discussed. Images in this thesis/dissertation are presented in color. In
the analysis the direction of positive vorticity is considered to be into the plane, which is

opposite to the standard convention i.e. out of the plane.

3.1 Boundary layer Thickness

The upstream edge of the cavity is located at a distance of 17.3 cm from the leading edge
of the ﬂat plate. The boundary layer starts developing at the leading edge and its
thickness was measured at 2 locations upstream of the cavity, for three different Reynolds
numbers. Using the measured boundary layer thickness (at 99% U0), dimensionless
measured velocity proﬁles were plotted and compared with Blasius solution (Equation

3.1).

far) =3}, where n =3} (3.1)

Case 1: Upstream Length = 1.8 cm (15.5 cm from the leading edge of ﬂat plate)
Figure 17 (a) shows the velocity proﬁles measured at a length of 1.8 cm upstream to the
upstream edge of the cavity. The measured velocity proﬁles are slightly off from the

Blasius solution.

17

 

For a free stream velocity, Uo of 7.48 cm/s (Re = 374.15), 6.5 cm/s (Re = 325.1), 5.031
cm/s (Re = 251.56) the boundary layer thickness was measured to be 0.74 cm, 0.774 cm,

0.851 cm respectively.

Case 2: Upstream Length = 0.04 cm (17.26 cm from the leading edge of ﬂat plate)

Figure 17(b) shows the velocity proﬁles measured at a length of 0.04 cm upstream to the
upstream edge of the cavity. The measured velocity proﬁles at an upstream length of 0.04
cm deviates from the Blasius solution, more compared to the velocity proﬁles at an
upstream length of 1.8 cm. The velocities are higher through out the measured velocity
proﬁles compared to Blasius solution. In all the three measured velocity proﬁles, points
very near to the wall (ﬁrst 4 points) behave slightly different compared to remaining part
of the proﬁle. The reason for this behavior could be because of the presence of cavity,

just 0.04 cm downstream of this measured point.

For a free stream velocity, U0 of 7.57 crn/s (Re = 378.49), 565 cm/s (Re = 328.26), 5.077
cm/s (Re = 253.87) the boundary layer thickness was measured to be 0.72 cm, 0.74 cm,

0.842 cm respectively.

3.2 Results of effect of percentage opening area of mesh
This part of the section presents the visual and quantitative results of the effect of
percentage Opening area. The results will be discussed only for Re A? 390, since the ﬂow

patterns are found to be similar at other Reynolds numbers too for most of the cases.

18

First for several cases, the particle streak ﬂow visualizations will be presented which is

followed by numerical results and ﬁnally the results will be discussed.

3.2.1. Flow Visualization

Figures 18-22 show the particle streak ﬂow visualization of ﬂow inside the 2—dimensional
cavity. Flow visualizations are shown only for no mesh case and two mesh cases at all
three Reynolds number. For other meshes the ﬂow patterns are similar. Trajectories of
particles are photographed in a long exposure. The exposure time was 400 ms for all

images. The freestream in each image ﬂows from right to left. The cavity is 5 cm

(length) x 5.2 cm (depth).

Case 1: Percentage opening area = 100 (No mesh case)

Figure 18 shows the flow visualization for no mesh case at 5 different Reynolds numbers
390, 325, 255, 180 and 100 approximately. In every case, a circulating ﬂow is observed
inside the cavity. The centre of circulating ﬂow appeared to move towards upstream
direction with decrease in the Reynolds number. Vortex centre can be deﬁned as the
region which has maximum vorticity. So only from the vorticity distribution plot, one can
decide whether this centre of circulating ﬂow can be called a vortex centre or not. The
ﬂow near the top edge of the cavity appeared to be very small. As expected, the ﬂow
velocities inside the cavity appeared to decrease with decreasing Reynolds number,

which can be visualized from the length of the streaks.

l9

Figure 19 compares the ﬂow ﬁeld between the cavity and free stream regions, for no
mesh case at a Reynolds number of 390. In ﬁgure 19(a), the lengths of the streaks in the
freestream region are much bigger and so the streak lengths in the ﬁ'eestream region
cannot be seen clearly seen. So the exposure time was decreased from 400 ms (Figure
19(a)) to 20 ms (Figure 19(b)). From ﬁgure 19(b) one can get a clear picture of the
difference in magnitudes of velocity between the two regions. Now it can be seen that the
lengths of the streaks in the free stream region are much bigger compared to the cavity
region. It can be clearly seen that the length of streaks keep increasing in the free stream
as you move away from the intersection of the cavity and the free stream, implying that

region is still within the shear layer.

Case 2: Percentage Opening area = 64.8 (Diameter = 0.1905 mm, Rectangle size =
0.7874 mm)

Figure 20 shows the ﬂow visualization for the mesh of 0.1905 mm diameter, 64.8%
percentage opening area at 3 different Reynolds numbers 390, 325 and 255. In every case
a circulating ﬂow is observed inside the cavity. The centre of the circulating ﬂow appears
to be located on the mesh. The centre of the circulation moved upstream as the Reynolds
number was decreased. The most signiﬁcant observation was the huge reduction in the
length of streaks inside the cavity region as compared to no mesh case. The velocities
near the intersection of the cavity and the free stream appeared less compared to no mesh

case. This is due to the hindrance caused by the mesh to the ﬂow.

20

Case 3: Percentage Opening area = 64.8 (Diameter = 0.1651 mm, Rectangle size =
0.6807 mm)

Figure 21 shows the ﬂow visualization for the mesh of 0.1651 mm diameter, 64.8%
percentage opening area at 3 different Reynolds numbers 390, 325 and 255. The
characteristics of the ﬂow are similar to previous case. In every case a circulating ﬂow is
observed inside the cavity. The centre of the vortex appears to be located on the mesh.
Again, the centre of the vortex moved upstream as the Reynolds number is decreased, but
this movement was less. The velocities appeared lower compared to previous case, which
could be due to the smaller rectangle size. These differences will be described in detail,

quantitatively later.

The ﬂow patterns are similar for remaining meshes at all Reynolds number. The lengths

of streaks keep decreasing as the percentage opening area decrease.

3.2.2. Measured Quantities

Figure 22 — 26 shows the kinetic energy and vorticity distributions for the no mesh case
and one mesh case at Reynolds number of 390. The mean velocity vectors are shown
over the total kinetic energy distributions. The distributions are similar at other Reynolds
number and also for remaining meshes. The details with regard to pulse width and delay
between pulses used for measurements are listed in Table 10-13 in Appendix A. Even
though the cavity is of size 5 cm (length) x 5.2 cm (depth) but due to the presence of light
reﬂections very near to the mesh, the results are presented only for 5 cm (length) x 5 cm

(depth). The total kinetic energy was calculated using the formula Equation 3.2. Then it

21

was averaged over the 5 cm (length) x 5 cm (depth) space to get the space averaged total
kinetic energy. This space averaged total kinetic energy for every mesh was then
normalized with space averaged total kinetic energy of no mesh case at the corresponding

Reynolds number to get the normalized space averaged total kinetic energy.
Total Kinetic Energy, TKE = iii-2 + V2 + (u')2 + (v')2) (3.2)

Kinetic energy distributions based only on mean and ﬂuctuating velocity components are
also shown separately. The mean component of total kinetic energy (MKE) and

ﬂuctuating component of total kinetic energy (FKE) are given equations 3.3 and 3.4

respectively.
Mean component of Total Kinetic Energy, MKE = -;-(172 + V2) (3.3)
. . . l ,
Fluctuating component of Total Kinetic Energy, FKE = 3 ((u')2 + (v )2) (3.4)

The normalized space averaged total kinetic energy and normalized average vorticity data

for all cases is listed in Table 4.

Case]: Percentage opening area = 100 (No mesh case)

Figure 22 shows the vorticity distribution for both the cavity and freestream. The
vorticity distribution looks qualitatively similar at other Reynolds numbers. The vorticity
has a maximum value at the corners, near the intersection of the cavity and freestream.
The vorticity in the shear region is much larger than the vorticity in the cavity, and there
by there is no peak vorticity within the cavity which implies the centre of the circulating
ﬂow cannot be termed as vortex centre. The vorticity values keep increasing as one move

away from the top edge of cavity except near the side walls. The vorticity is negative near

22

the side walls and its magnitude is more near the downstream edge of the cavity
compared to the upstream edge of the cavity. This is because of large velocity gradients
near the downstream edge of the cavity. The magnitudes of vorticity are higher in the
half, which is towards the downstream edge of the cavity. Figure 23 (b) shows the

vorticity distribution only for the cavity region.

The maximum magnitude of vorticity in the region is 10.09 s", 7.71 s", 6.82 s'1 and
average vorticity in the region is 0.53 s", 0.46 5'], 0.395"1 at Reynolds number of 390,
325, and 255 respectively. These average values of no mesh case are used as reference to
normalize the vorticity for the cases where the cavity is covered with the mesh, at

corresponding Reynolds numbers.

Figure 23(a) shows the total kinetic energy distribution for the no mesh case at Reynolds
number of 390. The distribution is not symmetrical about the central axis, which is
midway between the upstream and downstream edges of the cavity. The magnitudes of
total kinetic energy are higher in the half, which lies towards the downstream edge of the
cavity. As expected a circulating ﬂow is observed. The total kinetic energy distribution
looks qualitatively similar at other Reynolds numbers too, except that there is a shift in
the position of centre of circulating ﬂow. One would expect the region around point x =
2, y = 4.3 in the Figure 23(a), to be the centre of the vortex. But from the vorticity
distribution it is seen that the peak vorticity does not lie in that region because of high

vorticity in the shear layer.

23

The maximum value of total kinetic energy is 7.96 mmz/sz, 5.34 mmZ/sz, 3.69 mmZ/s2
and average value in the region is 0.78 mmZ/sz, 0.525 mmz/sz, 0.34 mmz/s2 at a Reynolds
number of 390, 325 and 255 respectively. These average values of no mesh case are used
as reference to normalize the total kinetic energy for the cases where the cavity is covered
with the mesh at corresponding Reynolds numbers. So, the normalized value of total

kinetic energy for the no mesh case is l at all Reynolds number.

Figure 24(a) shows the mean component of total kinetic energy distribution with mean
velocity vectors on top of it. And Figure 24(b) shows the ﬂuctuating component of total
kinetic energy distribution with ﬂuctuating component of velocity vectors on top of it.
From the distributions it can be seen that the ﬂuctuating component of total kinetic
energy is higher near intersection of cavity and freestream, especially towards the

downstream edge of the cavity.

The ﬂuctuating component of space averaged total kinetic energy was found to be 1.86%,

2.17%, 2.69% at Reynolds number of 390, 335, and 255 respectively.

Case 2: Percentage Opening area = 64.8 (Diameter = 0.1905 mm, Rectangle size =
0.7874 mm)

Figure 25(b) shows the vorticity distribution at Re 2 390. The vorticity is negative in the
region near the side walls close to the mesh. The distribution is almost symmetrical about
the central axis which is midway between the upstream and downstream edges of the

cavity.

24

The maximum magnitude of vorticity in the region is 2.57 5'], 1.376 5", 0.761 s'1 and
average vorticity in the region is -0.02$" (Normalized value = -3.78%), -0.011s'l
(Normalized value = -2.33%), -0.00455'1 (Normalized value = -l.l7%) at Reynolds

number of 390, 325, and 255 respectively.

Even though in this case the ﬂow is circulating in the same direction as the no mesh case,
the average vorticity value has opposite sign compared to no mesh case. In no mesh case
the large velocity gradients near the intersection of cavity and freestream dominated the
velocity gradients near the downstream and upstream edges of cavity. But in the case
where the cavity is covered with the mesh, the large velocity gradients are absent near the
intersection of cavity and freestream. So, the velocity gradients near the downstream and

upstream edges of cavity dominate, making the average vorticity negative.

Figure 25(a) shows the total kinetic energy distribution for the mesh of 0.1905 mm
diameter, 64.8% percentage opening area. Its magnitude is high near the corner regions
just where it enters and leaves the cavity through the mesh. The distribution is almost
symmetrical about the central axis which is midway between the upstream and

downstream edges of the cavity.

The maximum value of total kinetic energy is 0.433 mmZ/sz, 0.118 mmZ/sz, 0.036 mmZ/s2
and average value in the region is 0.048 mmz/s2 (Normalized value = 6.1%), 0.0122
mmz/sz (Normalized value = 2.33%), 0.0036 mm2/52 (Normalized value = 1.07%) at

Reynolds number of 390, 325 and 255 respectively.

25

Figure 26(a) shows the mean component of total kinetic energy distribution with mean
velocity vectors on top of it. And Figure 26(b) shows the ﬂuctuating component of total
kinetic energy distribution with ﬂuctuating component of velocity vectors on top of it.
From the distributions it can be seen that the ﬂuctuating component of total kinetic
energy is higher near intersection of cavity and freestream, especially near the upstream

and downstream edges of the cavity.

The ﬂuctuating component of space averaged total kinetic energy was found to be 5.14%,
4.04%, 4.75% at Reynolds number of 390, 335, and 255 respectively. The ﬂuctuating

components are relatively higher compared to no mesh case.

Case 3: Percentage Opening area = 64.8 (Diameter = 0.1651 mm, Rectangle size =
0.6807 mm)

Figure 27(a) and 27(b) shows the total kinetic energy and vorticity distribution at Re 2
390 respectively. The distribution patterns are qualitatively similar to the above case.

The maximum value of total kinetic energy is 0.223 mmz/sz, 0.085 mmz/sz, 0.024 mmZ/s2
and average value in the region is 0.024 mmZ/s2 (Normalized value = 3.07%), 0.0089
mmz/s2 (Normalized value = 1.7%), 0.0013 mmz/s2 (Normalized value = 0.38%) at

Reynolds number of 390, 325 and 255 respectively.

26

The ﬂuctuating component of space averaged total kinetic energy was found to be 8.89%,
3.62%, 9.19% at Reynolds number of 390, 335, and 255 respectively. The ﬂuctuating

components are relatively higher compared to above two cases.

Case 4: Percentage Opening area = 39.1 (Diameter = 0.1905 mm, Rectangle size =
0.3302 mm)
Figure 28(a) and 28(b) shows the total kinetic energy and vorticity distribution at Re 2

390 respectively. The distribution patterns are qualitatively similar to the above case.

Case 5: Remaining meshes

The normalized space averaged total kinetic energy and normalized average vorticity data
for all cases is listed in Table 4. The trends are similar for other percentage opening areas.
The ﬂuctuating components of space averaged total kinetic energy for all cases are listed
in Table 5. The ﬂuctuating components are found to be less than 10% for all the cases,

which implies almost steady ﬂow.

3.2.3. Discussion

Figure 29 shows the effect of percentage opening area on normalized space averaged
total kinetic energy. It can be clearly seen from the plot that the normalized space
averaged total kinetic energy decreases with percentage opening area at all Reynolds
numbers. The normalized space averaged total kinetic energy decreases with decrease in

Reynolds number at all percentage opening areas.

27

By covering the cavity surface with a mesh of 0.1905 mm diameter, 64.8% percentage
opening area, the normalized space averaged total kinetic energy decreased to 6.04%,
2.3%, and 1.07% at Reynolds number of 390, 325 and 255 respectively. This shows how
rapidly the normalized values decrease with decrease in percentage opening area, which
implies the slope of the curves will be too large at percentage opening areas greater than
64.8%. At 64.8% opening area the slope of curve at Reynolds number of 390 and 325
already started growing rapidly, but relatively the slope of the curve at Reynolds number

of 255 is less.

At 64.8% two data sets can been seen and they don’t overlap on each other. This is
because those meshes are of different diameters and rectangle sizes. The comparison

between those two meshes will be discussed in the next section.

The ﬂuctuating component of space averaged total kinetic energy is calculated to be less
than 10% for all cases. From ﬂuctuating component calculations, it is seen that the effect

of percentage Opening area on the ﬂuctuating components has no particular trend.

As mentioned previously, the results will be compared with the aneurysm result of Chee
Lum (2007). The stent used in that experiment has a diameter of 5 mm and the wire
thickness of it is 0.1077 mm. The aneurysm opening was 6.5 mm wide and the
percentage opening area of the stent was 80%. The normalized total kinetic energy
decreased to 9.6% (Figure 3) when the aneurysm opening was covered with the stent.

This experiment was done at Reynolds number of 184 (based on tube diameter) and 267

28

(based on aneurysm opening diameter). But, he calculated the total kinetic energies based
on only mean velocities (equation 3.3). So in Figure 30 the mean components of space

averaged total kinetic energies are compared with the aneurysm result.

As mentioned before the slope of the curve at Re of 255 is relatively less at 64.8%, so by
looking at trends the slope for a curve at Re of 184 will be less at this percentage opening
area. The result from the brain aneurysm experiment doesn’t quite ﬁt on these curves.
From the trends it appears that at 80% opening area the normalized space averaged total
kinetic energy on the curve, Re = 184 will be less than the value from aneurysm
experiment. But if Re of the aneurysm experiment is considered as 267 then there appears
a high probability for the aneurysm experiment result to follow the trends of rectangular

cavity experiment results.

It is assumed that the ﬂuctuation component of space averaged total kinetic energy in the
aneurysm experiment is small, which implies trends will be similar even if one were to
compare the aneurysm result and rectangular cavity results based on space averaged total

kinetic energies and not just its mean components.

As mentioned in the previous chapter the settling speed of silver coated hollow spheres is
0.124mm/s for a particle of diameter 19.5um and density 1.6g/cc. The settling speed is
more or less equivalent to the peak speed in the cavity for extremely low percentage
opening area meshes especially at Re of 263. So this phenomenon could have affected the

result at very low speeds. But since the diameters of the particles range between 6pm and

29

32pm and similarly the particle density is also distributed and not exactly 1.6g/cc, so
there will always be particles whose settling speeds are very low and hence their
trajectories are not inﬂuenced by their settling speed. Whenever new particles were added
to the ﬂow, atleast 30 min was given for the water tlmnel to come to a steady state. And
while changing speeds, atleast 10 - 15 min was given for the water tunnel to settle.
During that period of time, the denser particles would have settled down. So settling

speed issue would not affect the results very much.

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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3.3. Results of effect of rectangle size of mesh

Cavity opening length of 0.5 cm is used to normalize the rectangle size for the
rectangular cavity experiments. For the aneurysm, the cavity opening diameter is about
0.65 cm whose equivalent rectangular cavity opening length is 0.576 cm. The meshing
structure was not rectangle in the aneurysm. So based on the percentage opening area
(80%) and diameter of the wire (0.1077mm) in the stent, the equivalent rectangle size
was estimated as 0.9124mm. The normalized rectangle size of the aneurysm was

calculated to be 0.1584 after normalizing with 0.57 6 cm.

The numerical data for the effect of normalized rectangle size on normalized space
averaged total kinetic energy is shown in Table 4. This is the same data that has been

used to study the effect of percentage opening area on normalized space averaged TKE.

3.3.1. Discussion

Figure 31 shows the effect of normalized rectangle size on normalized space averaged
total kinetic energy. It can be seen that normalized space averaged total kinetic energy
decreases with decrease in normalized mesh size. This trend is not followed at a
normalized mesh size of 0.091 and 0.102. The values of normalized space averaged total
kinetic energy are larger at a normalized mesh of 0.091 compared to the values at 0.102
for all Reynolds numbers. This could be because of higher percentage opening area of

59.1% for a mesh size of 0.091 case compared to 56.7% for a mesh size of 0. 102.

32

In the previous section it is seen that the meshes with same percentage opening area
(64.8%) do not have the same normalized space averaged total kinetic energy at all three
Reynolds numbers. For the case with normalized rectangle size of 0.157, the normalized
space averaged total kinetic energy was 6.09%, 2.3%, and 1.07% and for the case with
normalized rectangle size of 0.136, the normalized space averaged total kinetic energy
was 3.07%, 1.7%, 0.38% at Reynolds number of 390, 325 and 255 respectively. This
difference in normalized rectangle size should be the cause for the difference in

normalized space averaged total kinetic energy.

The positioning of mesh with respect to cavity could have also affected the result. The
details about the effect of positioning of mesh will be discussed in the next section. For
the case of rectangle size 0.157, the ﬁrst wire of the mesh is a bit far away from the
downstream edge of the cavity, compared to the mesh whose rectangle size is 0.136. But
here the meshes are of different rectangle size and diameter, so it’s not easy to compare

this positioning of mesh effect in these meshes.

As mentioned before for comparing the rectangular cavity results with aneurysm result,
only mean component of space averaged total kinetic energy has to be considered. Figure
32 shows the effect of normalized rectangle size of mesh on normalized mean component
of space averaged total kinetic energy inside the cavity. Even in this plot the aneurysm
data point doesn’t follow the trend of rectangular cavity experiment results. From the

trends it is very clear that at 80% opening area the normalized space averaged TKE on

33

both the curves, Re of 184 and Re of 267 will be deﬁnitely less than the value from

aneurysm experiment.

This difference could be because of few differences between the experiments. In
rectangular cavity experiment, the edges of cavity are perpendicular to the freestream
direction while the edges are round in the brain aneurysm experiment. Secondly, the
cavity is rectangular compared to almost circular in the aneurysm experiment. Thirdly,
the ﬂow in the rectangular cavity experiment is open cavity type compared to pipe ﬂow
type in the aneurysm experiment. Fourthly, the mesh used in the rectangular cavity
experiment is rectangular in nature compared to a different shape of stent (Figure 1) in
the aneurysm experiment. Fifthly, the ﬂow is nominally 2-dimensional in nature in

rectangular cavity experiment compared to 3-D in aneurysm experiment.

34

3.4. Results for effect of positioning of mesh

The mesh used for this part of experiment has a diameter of 0.1905mm, 64.8%
percentage opening area and rectangle size of 0.7874mm. In the 2 cases, the Reynolds
number varies slightly by 10 - 20 at all three Reynolds number. Except positioning of
mesh, remaining experimental setup was maintained same. The discussion will be done

only for Re 3 390. Similar patters are seen at other Reynolds numbers too.

3.4.] Flow Visualization

Figure 33 shows the ﬂow visualization of the effect of position of mesh with respect to
cavity at a Reynolds numbers of z 390. Inside the cavity region, the ﬁrst wire of the
mesh is closer to the downstream edge of the cavity in the ﬁgure 33(b) compared to
ﬁgure 33(a). The length of the streaks in the region near to downstream edge of the cavity
is smaller in ﬁgure 33(b) compared to ﬁgure 33(a). So it appears there is less amount of
total kinetic energy inside the cavity for the case where ﬁrst wire of mesh is closer to

downstream edge of the cavity.

3.4.2 Measured Quantities

Case 1: First wire of the mesh at a distance of z 0.7 mm from the downstream edge
of cavity

Figure 34(a) shows the total kinetic energy distribution for the case whose ﬁrst wire is at
a distance of z 0.7 mm for Reynolds number of z 390. Its magnitude is high near the

corner regions just where it enters and leaves the cavity through the mesh. The

35

distribution is almost symmetrical about the central axis which is midway between the

upstream and downstream edges of the cavity.

The maximum value of total kinetic energy is 0.433 mmz/sz, 0.118 mmz/sz, 0.036 mmz/s2
and average value in the region is 0.048 mmz/s2 (Normalized value = 6.1%), 0.0122
mmZ/sz (Normalized value = 2.33%), 0.0036 mm2/32 (Normalized value = 1.07%) at

Reynolds number of 390, 325 and 25 5 respectively.

Figure 34(b) shows the vorticity distribution at Re 2 390. The vorticity is negative in the
region near the side walls close to the mesh. The distribution is almost symmetrical about
the central axis which is midway between the upstream and downstream edges of the

cavity.

The maximum magnitude of vorticity in the region is 2.57 3", 1.376 5'], 0.761 s"1 and
average vorticity in the region is -0.023'1 (Normalized value = -3.78%), -0.Olls’l
(Normalized value = -2.33%), -0.00455'1 (Normalized value = -1.17%) at Reynolds

number of 390, 325, and 255 respectively.

Case 2: First wire of the mesh at a distance of z 0.2 mm from the downstream edge
of cavity

Figure 35(a) and 35(b) shows the total kinetic energy distribution and vorticity
distribution for the case whose ﬁrst wire is at a distance of z 0.2 mm for Reynolds

number of 384.4 respectively.

36

The maximum value of total kinetic energy is 0.204 mmz/sz, 0.01 mmz/sz, 0.036 mm"’/s2
and average value in the region is 0.019 mmZ/s2 (Normalized value = 2.4%), 0.008
mm2/s2 (Normalized value = 1.54%), 0.003 mmz/s2 (Normalized value = 0.89%) at

Reynolds number of 384.4, 316.6 and 245.5 respectively.

The maximum magnitude of vorticity in the region is 1.4 5", 1.225 s'l, 0.818 s'I and
average vorticity in the region is -0.019s'l (Normalized value = -3.78%), -0.008s'l
(Normalized value = -1.753%), -O.0043s'l (Normalized value = -1.11%) at Reynolds

number of 384.4, 316.6 and 245.5 respectively.

3.4.3 Discussion
Figure 36 shows results for effect of positioning of mesh with respect to cavity. The ratio
of normalized total kinetic energies at 10 Hz frequency of motor for Case A and B (Re =

390 for Case 1, Re = 384.4 for Case 2) is 2.54.

In no mesh case (Figure 18) the region (1.4 mm from the downstream edge of the cavity)
very close to the downstream edge of the cavity has regions of high total kinetic energy.
In ﬁgure 33(b) both the ﬁrst and second wires were present in this region of high total
kinetic energy. But in ﬁgure 33(a) only the ﬁrst wire was present in this region.
Considering only a length of 1.4 mm from the downstream edge of the cavity, the local
percentage opening area for case 33(a) is calculated to be 69.6% and 58.61% for case

33(b). Since the experiment setups for both the cases were same except the positioning of

37

mesh with respect to cavity, this was the only reason that could explain the reason behind

decrease in normalized space averaged total kinetic energy.

38

3.5. Results of effect of exposed length of mesh

The mesh used for this part of experiment has a diameter of 0. 1905mm, 64.8%
percentage opening area and rectangle size of 0.7874mm. A mesh of length 6 cm is
symmetrically placed with respect to the cavity. The length of the mesh that is exposed to
the ﬂow has been varied using a black tape and the effect of this exposed length on the
cavity ﬂow has been studied in the next two subsections. Figure 9(b) shows the schematic
for this part of the experiment. Altogether 5 different exposed lengths namely 2 cm, 1 cm,
0.5 cm, 0.2 cm and 0 cm have been studied The exposed length is deﬁned as the length
of mesh exposed to the ﬂow, upstream to the upstream edge of the cavity. Except

exposed length of the mesh, remaining experimental setup was maintained same.

3.5.1 Flow Visualization

Figure 37(a) and (b) shows the particle streak ﬂow visualization for exposed lengths of 0
cm and 2 cm respectively. In a movie sequence it is observed that for remaining 3 cases,
the ﬂow is a lot unsteady in nature and so particle streak ﬂow visualization images aren’t
shown. The ﬂow patterns are described only Re 3 390. The ﬂow patterns are similar at

other Reynolds numbers too.
Case 1: Exposed length = 0 cm

Figure 37(a) shows the ﬂow visualization for the case where exposed length is 0 cm. The

ﬂow direction is clockwise inside the cavity.

39

Case 2: Exposed length = 2 cm

Figure 37(b) shows the ﬂow visualization for the case where exposed length is 2 cm. The
ﬂow direction is anti-clockwise inside the cavity. This ﬂow pattern was opposite to
previous case (exposed length = 0) where the ﬂow direction is clockwise. The only
reason to explain this ﬂow behavior is because of the exposure to 2 cm of mesh length
upstream to the upstream edge of the cavity. In this case the ﬂow is ﬂowing over a
rugged surface (because the mesh is exposed to ﬂow), compared to smooth surface
(because of presence of black tape) in the case of zero exposure length. The mechanism

which caused this ﬂow pattern is not yet known.

Case 3: Exposed length = 1 cm and 0.5 cm

From movie sequence of these ﬂow visualizations, the ﬂow inside the cavity is observed
to be unsteady in nature. So the ﬂow visualizations were not presented. The ﬂow
direction inside the cavity kept changing from clockwise to counterclockwise, but for
most part of the time the direction was counterclockwise in direction. This shows that the
ﬂow direction is slowly transforming from counterclockwise direction to clockwise

direction with decrease in exposed lengths.

At an exposed length of 1 cm, the ﬂow appeared unrealistic. This is because the ﬂuid
entering and ﬂuid leaving the mesh does not appear to balance. The ﬂuid leaving the
mesh appears to be a lot more compared to ﬂuid entering the mesh. Probably the ﬂow has

become 3D in nature.

40

Case 4: Exposed length = 0.2 cm

Even for this case the ﬂow observed was unsteady in nature. So the ﬂow visualization
was not presented. The velocities appeared to be very low because of small streak
lengths. The ﬂow direction pattern kept changing very rapidly. It appears that the critical
point for the ﬂow direction pattern to change from counterclockwise to clockwise pattern

appears to be around 0.2 cm of exposed length.

3.5.2 Measured Quantities

Table 6 shows the numerical quantities for effect of exposed length of mesh on
normalized space averaged total kinetic energy at all three speeds. Figure 38, 39 shows
the total kinetic energy and vorticity distributions for an exposure lengths of 0 and 2 cm
respectively at a motor frequency of thz (Re z 390). Table 7 shows the ﬂuctuating
component of space averaged total kinetic energy for all the ﬁve cases at all three
Reynolds numbers. The ﬂuctuations are as high 70% for the exposed lengths of 0.5 cm

and 0.2 cm. This show how unsteady the ﬂow patterns are inside the cavity.

3.5.3 Discussion
From the movie sequences of particle streak ﬂow visualizations it is observed that the
ﬂow direction inside the cavity changes from counterclockwise to clockwise as the

exposed length is decreased.

41

Figure 40 shows the effect of exposed length of mesh on the ﬂow ﬁeld. For a water
tunnel motor frequency of 10 Hz, the normalized space averaged total kinetic energy
decreased ﬁom 1.397% to 0.3% as the exposed length decreased from 2 cm to 0.5 cm and
then later it increased from 0.3% to 6.09% as the exposed length decreased from 0.5 cm

to 0 cm. Almost similar trends are observed for the other two Reynolds number.

From the numerical results it can be seen that the critical length (deﬁned as the length
where the normalized space averaged total kinetic energy is minimum) could be between
an exposed lengths of 0.2 to 0.5 cm. The critical length could vary with variation in
Reynolds number. To ﬁnd this out, data have to be collected for every 0.1 cm of exposed
length and to see a large difference in the position of critical point, the Reynolds number

range has to be increased.

42

 

 

 

 

 

 

 

 

 

 

 

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3.6. Results of effect of gap between the mesh and cavity

The mesh used for this part of experiment has a diameter of 0.1905mm, 64.8%
percentage opening area and rectangle size of 0.7874mm. A mesh of length 2 cm is
symmetrically placed over the stainless steel shim stocks. The thickness of the
shimstocks has been varied and the effect of the gap between the cavity and mesh, on the
cavity ﬂow has been studied in the next two subsections. Figure 10 shows the schematic
for this part of the experiment. Altogether 3 different gaps namely 0.127 mm, 0.254 mm
and 0.508 mm have been studied Except the gap, remaining experimental setup was
maintained same. Since the mesh was not perfectly ﬂat, maintaining desired gap between

the mesh and cavity was a bit difﬁcult.

3.6.1 Flow Visualization

Figure 41 (a), (b), (c) shows the ﬂow visualization for gaps of 0.508 mm, 0.254 mm and
0 mm respectively. The ﬂow pattern for a gap of 0.254 mm is similar to the case where
the gap is 0.508 mm. The ﬂow patterns are described only for 10 Hz frequency of the

water tunnel motor (Re == 390).

Case 1: Gap = 0.508 mm

Figure 41 (a) shows the ﬂow visualization for a gap of 0.508 mm. The ﬂow inside the
cavity is counterclockwise in nature. The ﬂow enters the cavity from the gap on the right
bottom side of the cavity and it leaves though the gap on the left bottom side of the cavity
and also through the mesh. The ﬂow in the bottom half of the cavity was a lot faster

compared to upper half implying large velocity differences between the 2 halves. The

44

ﬂow pattern was similar at other Reynolds numbers too. Only for Reynolds number of

392 a very slow circulating ﬂow was seen on top right comer of the cavity.

Case 2: Cap = 0.127 mm

Figure 41 (b) shows the ﬂow visualization for a gap of 0.127 mm. The ﬂow pattern for
this gap was different compared to previous gap cases. For this case two types of ﬂow
patterns are observed. The ﬂow inside the cavity is counterclockwise in the right half of
the cavity and clockwise in the left half of the cavity. The ﬂow enters the cavity from the
gap on the right bottom side of the cavity and also enters from the left bottom comer of
the cavity through the mesh and it leaves though the through the middle cells of the mesh.
This different ﬂow pattern could be because the gap was so low that the mesh might have

touched the surface of the ﬂat plate on the downstream side of the cavity.

Case 3: Gap = 0 mm
Figure 41 (c) shows the ﬂow visualization for zero gap case. The ﬂow inside the cavity is

from clockwise in nature.

Case 4: Cap = 0.254 mm

The ﬂow pattern was similar to the case where gap was 0.508 mm. The ﬂow inside the
cavity is counterclockwise in nature. The ﬂow enters the cavity from the gap on the right
bottom side of the cavity and it leaves though the gap on the left bottom side of the cavity
and also through the mesh. The ﬂow in the bottom half of the cavity was a lot faster

compared to upper half

45

3.6.2 Measured Quantities

Table 8 shows the numerical quantities for the effect of gap between the mesh and cavity
on normalized space averaged total kinetic energy at all three speeds. Table 9 gives the
ﬂuctuating components of normalized space averaged total kinetic energy. The

ﬂuctuations are less 10% for all cases.

Case 1: Gap = 0.508mm

Figure 42(a) and 42(b) shows the total kinetic energy and vorticity distribution
respectively, for a gap size of 0.508 mm at Reynolds number of 392.7. The distribution
patterns are almost similar at other Reynolds numbers too. Figure 45 shows that the
normalized space averaged total kinetic energy decreased with decrease in Reynolds

number for the gap of 0.508 mm. Similar patters are observed for gap of 0.254 mm.

Case 2: Gap = 0.127mm

Figure 43(a) and 43(b) shows the total kinetic energy and vorticity distribution
respectively, for a gap size of 0.127 mm at Reynolds number of 406. The distribution
patterns are almost similar at other Reynolds numbers too. Figure 45 shows that the
normalized space averaged total kinetic energy increased with decrease in Reynolds
number for the gap of 0.127 mm. But the total kinetic energy decreased with decrease in

Reynolds number.

46

Case 3: Gap = 0mm

Figure 44(a) and 44(b) shows the total kinetic energy and vorticity distribution
respectively, for a gap size of 0mm at Reynolds number of 384. The distribution patterns
are almost similar at other Reynolds numbers too. Figure 45 shows that the normalized
space averaged total kinetic energy decreased with decrease in Reynolds number for the

gapomem.

3.6.3 Discussion

From particle streak ﬂow visualizations it was clearly seen that the ﬂow direction inside
the cavity changes from clockwise to counterclockwise as the gap between the cavity and
mesh was increased. For no mesh case the ﬂow pattern was clockwise, which implies as
the gap is still increased the ﬂow direction changes back to clockwise. Figure 45 shows
the effect of gap on normalized space averaged total kinetic energy at all three Reynolds

numbers.

For a Reynolds number of =-- 390, the normalized space averaged total kinetic energy has
decreased from 2.4% to 1.4% as the gap was increased from 0mm to 0.127 mm and then

it increased from 1.4% to 15.23% as the gap increased from 0.127 mm to 0.508 mm.

The normalized space averaged total kinetic energy is highest for a gap of 0.508 mm at

all three Reynolds numbers. The normalized space averaged total kinetic energy is higher

at 0.254mm and 0mm gap compared to 0.127mm gap at water tunnel motor frequencies

47

of Re 2 390 and Re 2 325. But at Re 2 255 the case with 0.127mm gap has higher total

kinetic energy compared to 0.254mm and 0mm gap.

The normalized space averaged total kinetic energy decreased with decrease in Reynolds
number at gaps except for the case with gap 0.127 mm. The normalized space averaged
total kinetic energy increased with decrease in Reynolds number for the gap of 0.127

mm. But the total kinetic energy decreased with decrease in Reynolds number at this gap.

48

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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4. CONCLUSION

Characterized the changes in the recirculation ﬂow pattern inside the cavity caused by a
porous surface (rectangular mesh) covering the cavity opening. The effect of several
parameters namely, percentage opening area, rectangle size, length of mesh, positioning
of mesh with respect to cavity and also effect of gap between mesh and cavity on the

cavity ﬂow ﬁeld have been studied using digital particle image velocimetry technique.

At 1.8cm upstream to the upstream edge of the cavity the boundary layer thiclmess is
measured to be 0.74am, 0.774cm, 0.851cm for Reynolds numbers of 378.49 (U0 = 7.57

cm/s), 325.1 (U0 = 6.5 cm/s), and 251.56 (U0 = 5.031 cm/s) respectively.

A circulating ﬂow pattern is observed inside the cavity for no mesh case and the centre of
circulating ﬂow moved towards upstream direction with decrease in the Reynolds
number. The most signiﬁcant ﬁnding is the huge reduction in total kinetic energy when

the cavity opening was covered with the mesh for all cases.

Even though the cavity is of size 5 cm (length) x 5.2 cm (depth) but due to the presence
of light reﬂections very near to the mesh, the results are presented only for 5 cm (length)
x 5 cm (depth). The results will vary by few percentages because data analysis is done
only up to a depth of 5 cm. In all calculations the space averaged total kinetic energies
and vorticity are normalized by the corresponding no mesh case values. Since the values

of total kinetic energy and vorticity are high in region between depth of 5 cm and 5.2 cm,

50

all the normalized values are estimated slightly high. So choice of region for averaging

will affect the results slightly.

A clockwise ﬂow pattern is observed inside the cavity, when the cavity is covered with
the mesh for all cases. The normalized space averaged total kinetic energy decreased with
decrease in percentage Opening area at all Reynolds numbers. The normalized space
averaged total kinetic energy decreased with decrease in Reynolds number at all
percentage opening areas. At 64.8% two data sets can been seen and they don’t over lap
on each other. This is because those meshes are of different diameters and rectangle sizes.
Numerical results showed that the ﬂuctuating component of space averaged total kinetic
energy is high near the corners close to downstream and upstream edges of cavity (near

the intersection of cavity and freestream).

It was seen that normalized space averaged total kinetic energy decreases with decrease
in normalized mesh size. This trend is not followed at a normalized mesh size of 0.091
and 0.102. The values of normalized space averaged total kinetic energy are larger at a
normalized mesh of 0.091 compared to the values at 0.102 for all Reynolds numbers.
This could be because of higher percentage opening area of 59.1% for a mesh size of

0.091 case compared to 56.7% for a mesh size of 0.102.

The result from the brain aneurysm experiment doesn’t follow the trend of rectangular

cavity experiment results (normalized mean component of space averaged total kinetic

energy vs percentage opening area & normalized mean component of space averaged

51

kinetic energy vs normalized rectangle size) if the Re for aneurysm experiment is
assumed to be 184. This is because of few differences between the experiments as
explained in previous chapters. But if Re = 267, then the aneurysm result appears to
follow the trend of rectangular cavity experiment results when TKE is plotted against

percentage opening area.

It is observed that the positioning of mesh with respect to cavity affects the cavity ﬂow
ﬁeld. The closer the ﬁrst wire of the mesh to the downstream edge of the cavity, the
lesser is the normalized space averaged total kinetic energy. This is because the local

percentage opening area very near to the downstream edge of the cavity becomes lesser.

From ﬂow visualizations it is clearly seen that the ﬂow direction inside the cavity
changes ﬁom counterclockwise pattern to clockwise pattern as the exposed length was
decreased. From the numerical results it is seen that the normalized space averaged total
kinetic energy decreased as the exposed the length decreased from 2 cm to 0.2 em, but
then the normalized space averaged total kinetic energy drastically increased when the
exposed length was decreased from 0.2 cm to 0 cm. This shows that the critical length is
around an exposed length of 0.2 cm. The critical length could vary with variation in
Reynolds number. From movie sequences of particle streak flow visualization it is
observed that at the point of critical length the ﬂow is unsteady in nature. The ﬂuctuation
component of space averaged total kinetic energy increased with increase in exposed
length. As this exposed length is increased beyond the critical length, the fluctuations will

decrease.

52

From ﬂow visualizations it was clearly seen that the ﬂow direction inside the cavity
changes from clockwise pattern to counterclockwise pattern as the gap between the cavity
and mesh was increased. For no mesh case the ﬂow pattern was again clockwise, which
implies as the gap keeps increasing the ﬂow direction changes back to clockwise. The
experimental results showed that the normalized space averaged total kinetic energy is
highest for a gap 0.508mm at all three Reynolds numbers. The normalized space
averaged total kinetic energy is higher for at 0.254mm and 0mm gap compared to
0.127mm gap at water tunnel motor frequencies of 10 Hz and 8 Hz. But at 6 Hz the case

with 0.127mm gap has higher total kinetic energy compared to 0.254mm and 0mm gap.

From the qualitative and quantitative analysis, it was found that for any chosen mesh the
total kinetic energy inside the rectangular cavity can be decreased by 2 methods. First
method was to have the ﬁrst wire of the mesh as close as possible to the downstream
edge of the cavity and second method was to have the length of mesh exposed to the ﬂow
to be critical length. Unless experiments are done on aneurysm, it is difficult to say
whether the two proposed methods will be able to reduce the total kinetic energy inside

the aneurysm or not, because of the difference in experimental setups.

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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55

APPENDIX B

interest _piv -d 15 -c 41 -s 61 -x 48,1098 -y 0,932 0 0 seq.in

seq_corr -o seq.out -a 10f_003.tif 123 < seq.in

seq2tec seq.out tec.dat

seq_dice -Q 0.75 -R 255646787,0,0 -x 48,1098 -y 0,200 seq.out seq_dice1.out
seq2tec seq_dicel .out tec_dice1.dat

seq_dice -Q 2 -R 2556467 87 ,0,0 -x 48,1098 -y 200,400 seq.out seq_dice2.out
seq2tec seq_dice2.out tec_dice2.dat

seq_dice -Q 5 -R 255646787 ,0,0 -x 48,1098 -y 400,600 seq.out seq_dice3.out
seq2tec seq_dice3.out tec_dice3.dat

seq_dice -Q 9 -R 255646787,0,0 -x 48,1098 -y 600,932 seq.out seq_dice4.out
seq2tec seq_dice4.out tec_dice4.dat

combine_bin seq_dice1.out sechice2.out seq_dice3.out seq_dice4.out seq_dice.out
seq2tec seq_dice.out tec_dice.dat

rm_bad -l l -p 2 -z seq_dice.out seq_rm.out

seq2tec seq_rm.out tec_rm.dat

make_off > scale.txt

seq_scale seq_rm.out seq_scale.out < scale.txt

seq2tec seq_scale.out tec_scale.dat

irreg2reg -x -0.1, 0.1,5 -y 0, 0.1,5 -2 -w 8 -W wall_file.dat seq_scale.out seq_reg.out

seq2tec seq_reg.out tec_reg.dat

56

seq_avg seq_reg.out seq_avg.out seq_rms.out
seq2tec seq_avg.out tec_avg.dat

seq2tec seq_rms.out tec_rms.dat

57

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58

60mmls

milimeter

(a)

 

 

_ _ o 2
milimeter

milimeter

(b)

 

 

_ _1o
mIlImeter

Figure 2. Comparison of velocity field within the aneurysm (a) without stent (b) with
stent at a Reynolds number of 184. The arrow shows the flow direction in the tube. Inside

the aneurysm cavity the flow is in counter-clockwise direction.

59

 

Figure 3. Comparison of total kinetic energy within the aneurysm (a) without stent (b)

with stent at 21 Reynolds number of l84

vr when“;

'vmti'illv

 

Figure 4. Comparison of vorticity within the aneurysm (a) without stent (b) with stent at a

Reynolds number of 184

60

   
   

Lasiris Magnum
SP laser

  

Flat plate
and cavity

 

 

 

Fincor 5200 adjustable
ﬁequency ac motor control

 
 

 

 

 

 

Baldor electric motor

 

 

Figure 5. Experimental Set up (a) Rear View (b) Front view

61

 

 

 

MAGNUM SP LASER

 

 

 

 

 

 

 

 

 

 

 

TRAILING EDGE

    

WIRE MESH ‘

(LENGTH = 2 cm) {-—

BLACK TAPE

X

Y

WATER TUNNEL TEST SECTION BASE

 

Figure 6. Schematic of ﬂat plate with the cavity. The dimensions of cavity are 0.5 cm

(length) x 0.52 cm (depth). The dimensions in the schematic are not shown to scale.

62

d-L—l—l—l
o—‘Nw-h

Velocity (cm/s)

 

CANOO#UIO)\IQCO

2 3 4 5 6 7 8 9101112131415161718
Frequency of Motor (hz)

Figure 7. Water Tunnel Calibration

d/2

    
 
   

7‘ Rectangle size (1)

Wire Diameter (d)

Figure 8. Deﬁnition of rectangle size.

63

 

 

 

MAGNUM SP LASER

 

 

  
     

 

 

 

 

 

 

 

L. ‘—

4..—
TCAVITY DEPTH = 0.52 an"—
+—
‘—

 

 

(a) TRAILING EDGE

WIRE MESH

  
    

BLACK TAPE

X

(LENGTH = 2 cm)

Y

WATER TUNNEL TEST SECTION BASE

 

 

 

 

MAGNUM SP LASER

 

 

LEADING EDGE

mm B
LENGTH = ‘—
0.5 cm
I
L ‘
I! I <—
+——

       
    
 

 

 

 

 

 

 

 

CAVITY DEPTH = 0.52 cm
4—

LENGTH +—
BLACK TAPE ‘—

TRATLING EDGE

WIRE MESH <—
X

(LENGTH = 6 cm)

Y FREESTREAM

WATER TUNNEL TEST SECTION BASE

 

Figure 9. Schematic of test section for the experiment (a) Effect of percentage opening

area/ rectangle size (b) Effect of exposed length of mesh

 

 

 

L'\ MAGNUM SP LASER

 

 

WATER LEVEL

 

 

 

 

 

 

 

Y

 

 

  
      
   

CAVITY DEPTH = 0.52 cm ‘
TRAILING EDGE

SHIMSTOCK (USED TO
(a) MAINTAIN GAP BETWEEN

MESH AND CAVITY) WIRE H

(LENGTH = 2 cm)

WATER TUNNEL TEST SECTION BASE

 

 

(b) SHIMSTOCK
LASER SHEET ‘—

. E <——-—

I

T : ¢:————— CAVITY 4—

| ------ I FREE STREAM

TAPERED END ROUND LEADING EDGE
OF FLAT PLATE OF P LAT PLATE

 

 

 

 

 

Figure 10. Schematic of test section for the experiment - effect of gap between the mesh

and the cavity (a) Front view (b) Top view of ﬂat plate

65

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1,2 8 - a a . . - - . . - . -
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(a) 3 05 _ BIasnus solution
a
0.4 -
0.2 ~
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o 2.5 5.0 7.5 10.0 12.5
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3
a
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o 2.5 5.0 7.5 10.0 12.5
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(a) 1.8cm (b) 0.04cm upstream of the front edge of the cavity

72

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76

Downstream cavity edge

5 mm/s

 

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V(mm)

 

Centre of circulation Represents ﬂow '4
— . .
7 direction _8

 

llllllll|lllllIllllIlllllllllllllllllJ

 

 

#1 o 1 2 3 4 5 6 7
x (mm)

Figure 22. Vorticity distribution (cavity + freestream) for the no mesh case at Reynolds
number of 390. The flow circulates in the clockwise direction inside the

cavity.

77

5 mmls

 

TKE (mm/5M2

y(mm)

(a)

 

 

 

 

3
x(mm)

5 mmls

 

vorticity (Us)
10

(b)

y(mm)
:bc'nLac'nL'nisdoriaito—‘mwbmm‘imco

 

 

 

 

0 1 2

3
x(mm)

Figure 23. (a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity

for the no mesh case at Reynolds number of 390.

78

5 mmls

 

MKE (mm/5V2

y(mm)

(a)

 

 

 

 

 

FKE (mm/s)’\2

0.44
0.42
0.4

0.38
0.36
0.34
0.32
0.3

0.28
0.26
0.24
0.22
0.2

0.13
0.16
0.14
0.12
0.1

0.08
0.06
0.04
0.02

(b)

y(mm)

 

 

 

 

3
x(mm)

Figure 24. (a) Mean kinetic energy distribution (b) Fluctuating kinetic energy distribution

inside the cavity for the no mesh case at Reynolds number of 390.

79

(a)

(b)

Figure 25. (a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity

V (mm)

v (mm)

for the 0.1905 mm diameter, 64.8% opening area mesh at Re of 390.

2 mmls

 

2 mmls

2 3
x (mm)

I

80

 

 

TKE (mm/5V2

0.42
0.4

0.38
0.36
0.34
0.32
0.3

0.28
0.26
0.24
0.22
0.2

0.18
0.16
0.14
0.12
0.1

0.08
0.06
0.04
0.02

 

 

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2 mmls

 

MKE (mm/SY‘Z

0.4

0.38
0.36
0.34
0.32
0.3

0.28
0.26
0.24
0.22
0.2

0.18
0.16
0.14
0.12
0.1

0.08
0.06
0.04
0.02

V (mm)

(a)

 

 

 

 

 

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0.048
0.046
0.044
0.042
0.04

(b)

V (mm)

 

 

 

5

 

0 1 2 3 4 5

x (mm)
Figure 26. (a) Mean kinetic energy distribution (b) Fluctuating kinetic energy distribution
inside the cavity for the 0.1905 mm diameter, 64.8% opening area mesh at Re

of 390.

81

1 mmls

 

TKE (mm/s)"2

0.22
0.21
0.2

0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1

0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01

Y (mm)

(a)

 

 

 

 

3
x (mm)

1 mmls

 

vorticity (1/s)

(b)

V (mm)

 

 

 

 

0 1 2 3 4 5
x (mm)
Figure 27. (a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity

for the 0.1651 mm diameter, 64.8% opening area mesh at Re of 390.

82

0.5 mmls

 

TKE (mm/s)"2

0.017
0.016
0.015
0.014
0.013
0.012
0.011
0.01

0.009
0.008
0.007
0.006
0.005
0.004

(a)

y(mm)

 

 

 

 

3
x(mm)

0.5 mmls

 

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0))

Wm“)

 

 

 

 

0 1 2

3
x(mm)
Figure 28. (a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity

for the 0.1905 mm diameter, 39.1% opening area mesh at Re of 390.

83

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88

(a)

(b)

Figure 34. (a) TKE distribution (b) Vorticity distribution inside the cavity for the mesh

V (mm)

V (mm)

(0.1905 mm diameter, 64.8% opening area) at Re of 390 whose ﬁrst wire is at

2 mmls

 

 

TKE (mm/SY‘Z

0.42
0.4

0.38
0.36
0.34
0.32
0.3

0.28
0.26

 

 

 

 

vorticity (1/s)

2.4
2.2

 

 

a distance of 0.8 mm from the downstream edge of the cavity.

 

2 mmls

  

 

TKE (mrn/s)’\2

0.2
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1

y(mm)

(a)

 

 

 

 

vorticity (1/s)

V(mm)

(b)

 

 

 

3
x(mm)

Figure 35. (a) TKE distribution (b) Vorticity distribution inside the cavity for the mesh
(0.1905 mm diameter, 64.8% opening area) at Re of 390 whose first wire is at

a distance of 0.2 mm from the downstream edge of the cavity.

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TKE (mm/s)"2

0.42
0.4

0.38
0.36
0.34
0.32
0.3

V (mm)

(a)

 

 

 

 

 

vorticity (1/s)

y (mm)

 

 

 

o 1 2 3
x (mm)

Figure 38. (a) TKE distribution (b) Vorticity distribution inside the cavity for 0 cm
exposed length of mesh (0.1905 mm diameter, 64.8% opening area) at Re of

390.

93

1 mmls

 

 

TKE (mm/5)”?
0.24

(a)

y(mm)

 

 

 

 

(b)

V (mm)

 

 

 

2

3
x (mm)

Figure 39. (a) TKE distribution (b) Vorticity distribution inside the cavity for a 2 cm

exposed length of mesh (0.1905 mm diameter, 64.8% opening area) at Re 2
390.

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3 mmls
0
vorticity (Us)
1 7.5
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6.5
6
5.5
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3
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2
1.5
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5

o 1 2 3 4 5
x(mm)
(a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity

for a gap of 0.508 mm between the mesh (0.1905 mm diameter, 64.8%

opening area) and the cavity at Reynolds number of 392.7.

97

2 mmls

TKE (mm/s)"2

y(mm)

(a)

 

 

 

vorticity (US)

0.7
0.6
0.5
0.4
0.3
0.2
0.1

y(mm)

(b)

 

 

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3
x(mm)

Figure 43. (a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity
for a gap of 0.127 mm between the mesh (0.1905 mm diameter, 64.8%

opening area) and the cavity at Reynolds number of 406.

98

2 mmls

  

 

TKE (mm/5V2

Vlmm)

(a)

 

 

 

 

vorticity (1/5)

1.2
1.1

y(mm)

(b)

 

 

5 o 1 2 3 4 "'3
x(mm)

 

Figure 44. (a) Total kinetic energy distribution (b) Vorticity distribution inside the cavity
for a gap of 0 mm between the mesh (0.1905 mm diameter, 64.8% opening

area) and the cavity at Reynolds number of 406.

99

 

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LIST OF REFERENCES

Aydin, M. and Fenner, R. T. (2001), “Boundary element analysis of driven cavity ﬂow for
low and moderate Reynolds number,” International Journal for Numerical Methods in
Fluids, Vol. 37, pp. 45-64

Chee Lum (2007), “Experimental investigation of ﬂow ﬁeld inside a glass model of a brain
aneurysm”

Chiang, T.P., Sheu, W.H. and Robert R. Hwang (1998), “Effect of Reynolds number on the
eddy structure in a lid-driven cavity,” International Journal for Numerical Methods in
Fluids, Vol. 26, pp. 557-579.

Eames, I. and Gilbertson, MA. (2004), “The settling and dispersion of smell dense particles
by spherical vortices,” Journal of Fluid Mechanics, Vol. 498, pp 183-203.

Kawaguti, M. (1961), “Numerical Solution of the Navier—Stokes equations for a ﬂow in a
two-dimensional cavity,” Journal of the Physical Society of Japan, Vol. 16, pp. 2307-
2315.

Kinoshita, O. and Ito, H. (1984), “Experimental analysis of two-dimensional cavity ﬂow at
very low Reynolds numbers,” Journal of Fluid Control (ISSN 0015-4687), vol. 15,
pp. 65-77.

Lieber, B.B., Stancampiano, AP. and Wakhlooo, AK. (1997), “Alteration of hemodynamics
in aneurysm models by stenting: Inﬂuence of stent porosity,” Annals of Biomedical
Engineering, Vol. 25, pp. 460-469.

Manovski, P. (2005) “Experimental characterization of low Reynolds number ﬂow past a
cavity,” Graduate yearbook 2005, Department of Mechanical Engineering, Monash
University

Moffatt, H.K. (1964), “Viscous and resistive eddies near a sharp comer,” Journal of Fluid
Mechanics, Vol. 18, pp. 1-18.

Power, H. and Botte, V. (1998), “An indirect boundary element method for low Reynolds
number Navier—Stokes equations in a three-dimensional cavity,” International J oumal
for Numerical Methods in Engineering, Vol.41, pp. 1485—1505.

Rhee, K., Han, M.H. and Cha SH. (2002), “Changes of Flow Characteristics by stenting in

aneurysm models: Inﬂuence of Aneurysm geometry and stent porosity,” Annals of
Biomedical Engineering, Vol. 30, pp. 894-904.

101

Takematsu, M. (1966), “Slow viscous flow past a cavity,” Journal of the Physical Society of
Japan, Vol. 18, pp. 1816-1821.

Yu, S.C.M., Zhao, J.B. (1999), “A steady ﬂow analysis on the stented and non-stented
sidewall aneurysm models,” Medical Engineering & Physics, Vol. 21, pp. 133-141.

Zhoul, Y.C., Patnaik, B.S.V., Wan, BC. and Wei] G.W. (2003), “DSC solution for ﬂow in a
staggered double lid driven cavity,” International Journal for Numerical Methods in

Engineering, Vol. 57, pp. 21 1-234.

102

     
 

         
 

  

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