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LIBRARYM
Michigan State
University

 

 

 

This is to certify that the
thesis entitled

CHARACTERIZATION OF A SHEAR LAYER THROUGH
PARTICLE IMAGE VELOCIMETRY

presented by

Kyle McHugh Bade

has been accepted towards fulfillment
of the requirements for the

Master of Science degree in Mechanical ErLcLineering

 

 

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Date

 

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_._.___..___.....___. ... ..

 

CHARACTERIZATION OF A SHEAR LAYER THROUGH

PARTICLE IMAGE VELOCIMETRY

By

Kyle McHugh Bade

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

CHARACTERIZATION OF A SHEAR LAYER THROUGH
PARTICLE IMAGE VELOCIMETRY

By
Kyle M. Bade

An experimental investigation of a shear layer using particle image velocimetty
(PIV) to acquire instantaneous realizations of the flow field was conducted. Detailed PIV
data were acquired across the primary flow inlet region as well as over a large downstream
domain. The instantaneous flow field observations were used to create ensemble flow field
statistics. The initial momentum thickness was 00 = 1.11mm. The mean inlet velocity of
the primary flow was Uo,x=0 = 4.51m/s. The Reynolds number, based on these scales, was
R690 = 321. Boundary layer results nominally agreed with the Blasius solution at x=0.

The experimental facility’s spatial constraints created a large scale recirculating
flow. The primary flow velocity was U0 = 4.6m/s in the downstream data region: 495 < x/
00 < 567. The growth rate of the downstream shear layer, within the range of KAI—0:0. 1 3 to
1.0, was dG/dx = 0.032. This growth rate is indicative of a single stream shear layer.

A topological ‘collapsed sphere’ surface was used to analyze across the single-
stream shear layer region over the downstream range noted above. Singular points (nodes
and saddles) were identified in the instantaneous velocity fields. Large scale coherent
motions were identified in a convection speed reference frame. The subset of these
motions, which could be fully characterized, exhibited the following quantities: i) mean
location of a coherent motion center: —u/I_JO=O.66 isotach, ii) size of the average

motion ((—L—) = 3.34) where L2 is the area bounded by the circulation contour, iii)

0 _
(x) . . (926(51800)
strength of the spatlally averaged motion ( (7 > = —20.4 .

0

 

ACKNOWLEDGEMENTS

First and foremost, I would like to thank Dr. John Foss for his guidance throughout
both my undergraduate and graduate careers. My academic and research accomplishments
were made possible through the support and the environment he has provided. The Turbu-
lent Shear F lows Laboratory and those that have worked there during my time at MSU
have helped to shape my accomplishments and my high career aspirations. I would like to
extend a special thanks to Doug Neal and Al Lawrenz who have been extremely helpful in
my endeavours while in the TSFL. I would also like to thank all those who have been in the
TSFL during my time there, specifically: Richard Prevost, Michael Dusel, Scott Morris,
Aren Hellum, Amanda Danielson, Matthew Norconk, Scott Treat, Matthew Maher, Jason
Peabody, Joy Reichbach, and Bob Morris.

I would like to thank my committee members, Dr. Manoochehr Koochesfahani and
Dr. Farhad Jaberi, for their influence and assistance in my academic and research efforts.

Finally, I would like to thank my parents, Richard and Suzanne Bade, for their end-
less love and support. Without their constant guidance and strength nothing I accomplish
in my life would be possible. I would also like to thank my brother Ryan Bade and the rest
of my family for their support in all that I have done. Lastly, I would like to thank all of my

friends who been with me through everything.

iii

 

 

TABLE OF CONTENTS

 

 

 

 

 

 

LIST OF TABLES _ vii
LIST OF FIGURES - - - viii
NOMENCLATURE xii
1.0 Introduction - 1
1.1 Initial Motivation .................................................................................................. 1

1.2 Motivation (for Present Experiments) .................................................................. 3

1.3 Shear Layer Mechanics ......................................................................................... 3

1.4 Topology of a Velocity Field ................................................................................ 4
1.4.1 Collapsed Sphere Topology ....................................................................... 4

1.4.2 SSSL Collapsed Sphere Geometry and Accounting .................................. 5

2.0 PIV Facility and Test-Section -- - - - - - - u 9
2.1 General Overview of the PIV Facility .................................................................. 9
2.1.1 PIV Facility Specifications and Key Features ............................................ 9

2.1.1.1 Closed-Loop Test Facility ................................................................ 9

2.1.1.2 Non-Reflective Surfaces ................................................................ 10

2.1.1.3 Removable Test-Section ................................................................ 11

2.1.2 Blower Specifications ............................................................................... 11

2.2 Shear Layer Test-Section Fabrication and Segment Specifics ........................... 12
2.2.1 Test-Section segments .............................................................................. 12

2.2.1.1 Inlet Segment .................................................................................. 12

2.2.1.2 Flow Conditioning Segment ........................................................... 13

2.2.1.3 Backstep Region Segment .............................................................. 14

2.2.1.4 Downstream Shear Layer Segment ................................................ 15

2.2.1.5 Final Test-Section Assembly ......................................................... 15

3.0 Measurement and Acquisition Equipment and Software - - 25
3.1 Pressure Transducer ............................................................................................ 25

3.2 PIV Equipment ................................................................................................... 25
3.2.1 Dual PIV Lasers ....................................................................................... 26

3.2.2 PIV CCD Camera ..................................................................................... 27

iv

3.2.3 Computer and Programmable Timing Unit .............................................. 27

 

 

 

3.2.4 Aspirator Flow Seeder .............................................................................. 28

3.3 DaVis PIV Software Calibration and Cross-Correlation Method ...................... 28
3.3.1 Camera Calibration ................................................................................... 29

3.3.2 PIV Image Plane ....................................................................................... 29

3.3.3 Image Processing Routines - Vector Field Calculation ............................ 30

3.4 MATLAB Post-Processing Routines .................................................................. 33
3.4.1 Ensemble Calculation ............................................................................... 33

3.4.2 Singular Point Mapping and Circulation Calculations ............................. 34

3.5 Tecplot 360 - Contour Plots and Streamlines ..................................................... 35

4.0 Boundary Layer PIV Results - - -- - -- , - - 43
4.1 Acquisition and Processing Specifications ......................................................... 43

4.2 Boundary Layer Velocity Contour PIV Results ................................................. 44

4.3 Discrete Boundary Layer Profiles from PIV Results ......................................... 44

5.0 Downstream Ensemble PIV Results 53
5.1 PIV Vector Field Converged Data Range .......................................................... 53
5.1.0.1 Downstream Image Plane Definition and Orientation ................... 53

5.1.0.2 Measurement Domain .................................................................... 54

5.2 Ensemble PIV Vector Field Statistics Contours ................................................. 55

5.3 Discrete Velocity Profiles and Isotach Levels .................................................... 56
5.3.1 Discrete velocity profiles at various downstream locations ..................... 56

5.3.2 Single-Steam versus Two-Stream Shear Layer System ........................... 58

5.3.3 Normalized Discrete Profiles ................................................................... 58

5.3.4 Isotach Definition Results ........................................................................ 59

6.0 Singular Point Identification _ - - - - - - - 71
6.1 Node-Saddle Identification ................................................................................. 71
6.1.1 Topological Discussion of Instantaneous Vector Fields .......................... 71

6.1.2 Locations of Nodes and Saddles ............................................................... 72

6.1.3 Collapsed Singular Point Statistics ........................................................... 73

6.2 Identification of Nodes at the Convection Speed ............................................... 74
6.2.1 Vorticity Calculations for Individual Convecting Nodes ......................... 75

7.0 Summary and Conclusions _ - -- - 99

 

APPENDIX A

101

 

A.0 Large Single Stream Shear Layer (SSSL) Seeding Efforts

A.1 Smokewire Seeding Method .....................................................................
A.2 Installed Seeding Plenum .........................................................................
A.3 Adjustable Seeding Unit ...........................................................................

REFERENCES

vi

 

“-102

102
104
104

114

LIST OF TABLES

Table 5.1 Utilized Correlation Parameters .................................................................... 52

Table 5.2 Slope to Isotach Fit Constants ....................................................................... 59

vii

Figure 1.1
Figure 1.2

Figure 2.1

Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 4.1

Figure 4.2

LIST OF FIGURES

Single-Stream Shear Layer Flow Model ........................................................ 7
Single-Stream Shear Layer Euler Characteristic ............................................. 8
PIV Facility (3D Model - 4 Perspectives) .............................................. 17-18
a) PIV Facility Front View ........................................................................... 17
b) PIV Facility Front View (Primary Hidden Lines) .................................... 17
c) PIV Facility Left Side View ..................................................................... 18
d) PIV Facility Bottom Angle View (Transparent Lower Floor) ................. l8
PIV Facility 2D Model ................................................................................. l9
Blower & Plumbing Connected to the PIV Facility Photo ............................ 20
Test-Section - 2D Profile with all Segments ................................................. 21
Test-Section - Dimensioned 2D Profile ........................................................ 22
Inlet-F low Conditioning Sub-Assembly Photo ............................................. 23
Refraction Demonstration (Air-Glass-Air) .................................................... 23
Installed Test-Section Photo .......................................................................... 24
PIV house with installed test-section and PIV equipment - Model ............... 36
PIV house with installed test-section and PIV equipment - Photo ................ 37
PIV Image Plane Locations ........................................................................... 39
Cross-Correlation Method ............................................................................. 40
Initial and Final Window Overlap Correlations ............................................ 40
Median Filter example Vector Field .............................................................. 41
Circulation Contour of a 7x7 Discrete Grid (6x6 Area) ............................... 41
Discrete Grid with Integrated Streamlines .................................................... 42
Boundary Layer PIV Image Definition ........................................................ 47
Representative Boundary Layer PIV Image .................................................. 48

viii

Figure 4.3
Figure 4.4

Figure 4.5

Figure 4.6
Figure 4.7
Figure 4.8
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8

Figure 5.9

Figure 5.10
Figure 5.11
Figure 5.12
Figure 5.13

Figure 5.14

Figure 6.1
Figure 6.2

Figure 6.3

Boundary Layer PIV Image - Reliable Image Range .................................... 49
Strearnwise Velocity - Ensemble Average of 400 vector fields .................... 50

Strearnwise Velocity and Turbulence Intensity Profiles

at the Inlet (x=2mm) .................................................................................... 50
Inlet Region Strearnwise Velocity Profiles ................................................... 51
Inlet Region Strearnwise Velocity RMS Profile ........................................... 51
Boundary Layer Data and Blasius Solution .................................................. 52
Downstream Image Plane .............................................................................. 61
PIV Image Frame with Illuminated Particles ................................................ 62
PIV Image Plane with Eliminated Data Regions .......................................... 63
Normalized Strearnwise Turbulence Intensity ( {I /U_o) ................................. 64
Normalized Strearnwise Velocity Contour (W0) ........................................ 65
Normalized Vorticity Contour (m*9(51860)/I—Jo) .......................................... 66
Dimensional Velocity and Turbulence Intensity Profiles ............................. 66
8 vs. xand 913 vs. x ....................................................................................... 67
Growth Rates at Various Isotach Levels ....................................................... 67
Modified Flow System with Smoke Trace Indications ................................. 68
Velocity Magnitude (Q) Contour with (0.13)Uo Division ............................ 69
Normalized Velocity and Turbulence Intensity Profiles ............................... 69
Isotach Levels ................................................................................................ 70
Isotach vs. Slope Curve Fit ............................................................................ 70
Representative Instantaneous Vector Field - Topologically Valid ................ 79
Representative Instantaneous Vector Field with “Edge Problems” .............. 80
Types of Singular Points (Descriptions from Perry & Chong (1986)) .......... 81

ix

 

Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7

Figure 6.8

Figure 6.9
Figure 6.10

Figure 6.11

Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15

Figure 6.16

Figure 6.17

Figure 6.18

Figure 6.19

 

Node (rhs) Type Examples with Saddles (top) .............................................. 82

Node and Saddle Map with Selected Isotachs ............................................... 83
Saddle Location Relative to its Associated Node .......................................... 84
Node-Saddle Pairing Example ...................................................................... 85
Distribution of Nodes in a given Isotach Range - For the

0.13<u/Uo<1.0 “single stream shear layer” domain ..................................... 86
Distribution of Node-to-Saddle Distance ...................................................... 87
Strearnwise Velocity Contour - Convection Velocity Reference Frame ....... 88

Strearnwise Velocity with Topological Considerations - Convection

Velocity Reference Frame ........................................................................... 89
Mean Vorticity vs. Area & Samples vs. Area ............................................... 90
Large Scale Node Centered Near the Data Range Border ............................ 91
Vorticity vs. Area for 10 Individual Nodes ................................................... 92
Distribution of Minimtun Vorticity Level ..................................................... 93

Cumulative Distribution of the Area at which the Minimum Vorticity
Level Occurs ................................................................................................. 94

Representative Circulation-Derivative (Mean Vorticity) vs. Circulation
Contour Area Traces ..................................................................................... 95

Distribution of the Normalized Circulation Contour Size where the Mean
Vorticity reaches a constant level ................................................................. 96

Distribution of the Maximmn Normalized Strength of Vorticity which
becomes Constant ......................................................................................... 97

Figure 6.20 Normalized Distance from Node Circulation Contour Center to the

Figure A]
Figure A.2

Figure A.3

Mean 0.560 Isotach ...................................................................................... 98
Installed Smokewire Seeder Prototype ....................................................... 107
Large Single Stream Shear Layer with Installed Seeding Plenum ............. 108
Adjustable Seeder Unit Schematic ............................................................. 109

Figure A.4

Figure A.5

Figure A.6

Figure A.7

Figure A.8

Installed Adjustable Seeder Unit seeding the large SSSL low speed
entraimnent flow ......................................................................................... 1 10

Inlet Fan Voltage versus Exit Flow Velocity .............................................. 111

Adjustable Seeder Unit - Positively Tuned (higher seeder exit velocity
than external flow velocity) ........................................................................ 112

Adjustable Seeder Unit - Negatively Tuned (lower seeder exit velocity
than external flow velocity) ........................................................................ 113

Adjustable Seeder Unit - Neutrally Tuned (approximately equal seeder
exit velocity and external flow velocity) .................................................... 114

xi

 

Roman:

dN/s

dt

1(0,1)

2N

ZN’

R690
ES

28’

I: |

 

NOMENCLATURE

Circulation Contour Area

Distance from a Node to the Associated Saddle
Image Frame-Pair Time Delay

Distance Traveled of Particles in PIV Correlation Window
Intermittency Function

Length of One Side of a Square Circulation Contour
Index of Refraction

Total Number of Samples (Vectors)

Sum of Nodes

Sum of Half-Nodes

Primary (highest) Cross-Correlation Peak

Secondary (second highest) Cross-Correlation Peak
Lowest Cross-Correlation Peak Level

Planar Velocity Magnitude (x-y plane)

PIV Vector Validation Minimum Required Peak Ratio
Reynolds Number based on 00

Sum of Saddles

Sum of Half-Saddles

Strearnwise Velocity

Mean Strearnwise Velocity

Strearnwise Turbulence Intensity

xii

 

YC

Y1/2

Greek:
d0

dx
1]

9130‘)
90

0(x)

Xsurface

A

r
a

(020)

13% of the Maximum Mean Strearnwise Velocity

Mean Strearnwise Convection Velocity

Maximum Mean Strearnwise Velocity at the Backstep
Maximum Mean Strearnwise Velocity Downstream
Spanwise Velocity

Velocity Vector of Particles in PIV Correlation Window
Strearnwise Coordinate

Spanwise Coordinate

Distance from a Node Center to the (0.5)U0 Mean Isotach
Spanwise Location where E = (Uo)/2

Out-of-Plane Coordinate

Shear Layer Growth Rate
Normalized Spanwise Coordinate
Momentum Thickness at a given Strearnwise Location (x), from U13 to U0
Initial Momentum Thickness

Momentum Thickness at a given Strearnwise Location (x)
Surface Euler Characteristic

Circulation

Vorticity

Time variant vorticity in the z-direction

xiii

Acronyms:

CCD

DEHS

LHS

NszAG

PIV

I’TU

RHS

RMS

SSSL

TSF L

Charge Coupled Device

Bis(2-ethylhexyl) Sebdecate

Left Hand Side

Neodymium-doped Yttrium Aluminium Garnet; Nsz3A15012
Particle Image Velocimetry

Programmable Timing Unit

Right Hand Side

Root mean square

Single-Stream Shear Layer

Turbulent Shear Flows Laboratory

Facility and Equipment Components (chapters 2 and 3 only):

[A]
[B]
[C]
[D]
[E]
[F]
[G]
[H]
[I]

[1]

Flow Inlet Portal

Flow Outlet Portal

Primary Blower

Lower Plenum

Receiver Plenum

Test-Section Opening

Lower Plenum Static Pressure Tap
Receiver Plenum Static Pressure Tap
Inlet Flow Bafiles

Inlet Flow Re-Entry Channels

xiv

 

[K]
[L]
[M]
[N]
[0]
[P]
[Q]
[R]
[S]
[T]
[U]
[V]
[W]
[X]
[Y]
[Z]
[AA]

[313}

Steel Test-Section Mounting Brackets
Support Frame

Support Frame Holes

Test-Section Support Board

Test-Section Support Board Holes for Threaded Positioning Rods
Threaded Positioning Rods

Laser Head x2

Laser Control Boxes x2

PIV Computer and PTU

PIV CCD Camera

Aspirator (PIV Flow Seeder)

Modular Focusing Lens for the Laser Beam
Differential Pressure Transducer

Divergent Lens for the Laser Sheet

Laser Cooling Lines

Focusing Lens for the Camera

Light Filter for the Camera

PIV Calibration Plate

XV

1.0 Introduction

1.1 Initial Motivation

The focus of this experimental investigation is to identify the physical phenomena
on the low speed side of a single-stream shear layer (SSSL). Specifically, the motivation
for this work was to acquire and analyze detailed PIV data across the superlayer of the
entrainment side flow and to use these data to characterize the intermittency region. Over
the course of these experiments many experimental techniques were used in evaluating
test setups and facility components including pressure measurements, hotwire measure-
ments, and PIV measurements. The primary data analyzed herein are derived from PIV
observations across the subject shear layer.

The majority of tests and time was spent in the large single stream shear layer
located in the Turbulent Shear Flows Lab (TSFL) at Michigan State University. This facil-
ity was originally constructed in 1999 by Scott C. Morris with the help of co-workers. Dr.
Morris conducted his Ph.D. research in the facility under the direction of Dr. John Foss.
The primary focus of those experiments was the transition region from a turbulent bound-
ary layer to a single-stream shear layer (Morris (2002) and Morris & Foss (2003)). This
unique SSSL facility has the attractive quality of possessing very large initial length
scales; the initial momentum thickness (00) at separation, for example, was 9.6m with a
Reynolds number based on this initial momentum thickness of Reg, = 4650.

Following the efforts by Dr. Morris in the large SSSL, an extensive hotwire inves-
ti gation of the intermittency region on the high—speed side of the downstream shear layer
was carried out by Aren Hellurn (Hellum (2006)). Hellurn defined the intermittency func-

tion (I =0,1) on the basis of (oz(t). A threshold and a dwell time were required for this

I=0,1 discrimination. This hot-wire investigation worked quite well in this region given
the strong streamwise component of the velocity field.

The logical focus for the next effort in the coordinated research effort of this single
stream shear layer, was an investigation of the low speed side entrainment region of the
SSSL. The proposed method for this investigation was to utilize PIV techniques which
would allow the intermittency region to be studied despite the large fluctuations in flow
direction and superlayer location that are experienced in this region. However, in practice
this proved to be quite difficult to accomplish without disrupting the non-vortical entrain-
ment fluid. This difficulty was primarily due to the need to introduce seed particles into
the system in order to acquire PIV images. The large SSSL facility employs a driven low
speed side flow which is calibrated to deliver the appropriate mass flow of entrained fluid
to the low speed side of shear layer (see Morris & Foss (2003)). The low speed side
entrainment flow is driven with four large, low pressure rise fans which are upstream of a
series of flow conditioning elements. This setup allows the majority of the driven entrain-
ment flow to escape upstream of the flow conditioners. By allowing a substantial portion
of this driven flow to escape, the low speed flow is provided to the shear layer, but is not
forced into the shear layer. Seed particles could not be distributed upstream of the flow
conditioners without clogging the conditioning screens, increasing the restriction, and
altering the entrainment flow calibration. Additionally, the majority of the seed would not
be present in the test-section. Distribution of the seed particles downstream of the flow

conditioners without disrupting the low speed side entrainment flow could not be accom-

plished for this work.

 

 

In addition to the low speed side entrainment flow seeding issues, the primary flow
is quite difficult to adequately seed due to large out-of-plane diffusion of the seeding fluid
prior to it reaching the downstream region of interest.

After extensive efforts to overcome the seeding difficulties, a more suitable PIV
facility was employed to complete this investigation. The efforts and results of the investi-
gations in the large SSSL are discussed firrther in Appendix A of this thesis. The new

facility is described in detail in chapter 2.

1.2 Motivation (for Present Experiments)

A single-stream shear layer test-section was built to allow for a PIV investigation
of a shear layer using the PIV facility. A uniform seed was achieved in all regions of the
shear layer test-section by utilizing the PIV facility. The PIV facility and the constructed
single stream shear layer test-section are discussed in great detail in chapters 2 and 3
respectively. The primary focus of the present investigation remains the low speed entrain-
ment side of the single-stream shear layer and the associated intermittency region. After
acquiring, processing, and investigating 1000 PIV images, extensive work was completed
to characterize the flow field, and specifically, the low speed side of the shear layer. The
investigations were ultimately based upon topological considerations that are further iden-

tified in section 1.4.

1.3 Shear Layer Mechanics
The dynamics of a single-stream shear layer are driven by a primary flow. The
resulting interaction of this primary flow with the entrained fluid creates the shear layer

which grows in the spanwise direction as the fluid convects downstream. Figure 1.1 dem-

onstrates the most notable components of a single-stream shear layer. The primary flow,
which is directly driven by the blower, provides a nearly uniform streamwise (+x) velocity
flow. When this flow reaches the backstep, it is suddenly and immediately bordered by the
un-forced low speed side entrainment flow. Once the primary flow encounters the back-
step, the interaction of these two flows results in the formation of the shear layer region.
For a comprehensive description of the entrainment and vorticity induction of low speed

side fluid see Dimotakis (1986).

1.4 Topology of a Velocity Field

. Topological analysis allows for the investigation of a continuous vector field with
an a—priori knowledge of the net basic flow structures based on the flow field geometry.
Analysis of a flow field geometry provides a surface Euler Characteristic (xsurface). This
constraint must also be satisfied by the net flow structures on that surface. A topological
surface may exist on a physical surface or within the flow field. For the investigations pro-
vided here, a topological sphere (or single deformable volume) will be collapsed in depth
to the mid-plane (x,y,z=0) of the test-section. The velocity field vectors will exist on the
internal surface of this ‘collapsed sphere’. Therefore, three holes allow the primary and
entrained flows to pass through the collapsed sphere and exit downstream. Some basic
topological descriptions are discussed here, for a more complete discussion, Foss (2004)
and Perry & Chong (1987) are recommended. For the purposes of these experiments it
will only be necessary to investigate a collapsed sphere surface and this collapsed sphere

will exist at the centerplane of the SSSL test-section.

1.4.1 Collapsed Sphere Topology

The accounting of singular points provides insight into the flow structures based
on the surrounding geometry. The first step is to determine the geometry-based Euler
Characteristic defined by:

Xsurface = 2 - 22handles - Zholes. (1,1)

Following the determination of this Euler Characteristic, the flow structures (singular
points), contained within the topological sphere, must agree with the Euler Characteristic.
Nodes and saddles may also exist as half-nodes and half—saddles on a collapsed sphere
surface. The topological accounting of singular points is demonstrated in equation 1.2.

xsurface = 22N + ZN’ - 22s - 23’ (1.2)

By first determining the Euler Characteristic based on the geometry (which provides the
topological constraint), the investigator is able to determine the proper number of net
nodes, half-nodes, saddles, and half-saddles. Using this Euler Characteristic, a flow which
is compatible with the determined Euler Characteristic constraint can be determined. This
method can be employed for an instantaneous flow image as well as for an averaged situa-
tion, however, an instantaneous flow field can be much more complex. The instantaneous
flow field will, however, still arrive at the same net singular point accounting and Euler

Characteristic.

1.4.2 SSSL Collapsed Sphere Geometry and Accounting

The topological assessment of this SSSL setup provides clear insight into the
ensemble average flow structure. As seen in Figure 1.2, there are three holes and no han-
dles for this geometry.

xsurface = 2 - 22handles - Zholes = 2 - 2(0) - 3 = -1 (1.3)

The surface in this setup is chosen so that the primary inlet and the low speed side
entrained flow both approach their respective in-flow holes uniformly, also, the down-
stream exit flow exits uniformly to its hole. The seams are chosen to be parallel with the
flow along strategic streamlines, seams connect holes and allow no flow to pass through
them. The obvious locations for this flow field are the sidewall and the backstep wall. The
third seam follows a streamline which, on average, the flow moves downstream without
crossing.
The only singular point to be inferred from this geometry comes immediately at

the backstep and is a half-saddle,

xsmface=2ZN+2N’-2)ZS-2S’=0+0-0-1=-1 (1.4)
this is demonstrated in Figure 1.2. Therefore, the total Euler Characteristic is xsurface = -1
based on both the geometry and the mean flow field singular point investigations. With an
educated assessment of the overall mean flow structure, detailed measurements can now
be carried out on the flow field and analyzed with a preconceived mean flow solution and

a known net topology.

 

_. Entrail-mdmyy

 

Backstep

 

\\\\\\\\\\\\\\\\Y\\\\\\\ \\\\\\\\\\\ \\\\ R K

/////////////////// /////////j

Figure 1.1 Single-Stream Shear Layer Flow Model

Outlet Hole

 
 
 
     

Entrainment
Flow Streamline

Entrainment
Flow Inlet Hole

Primary Flow
Inlet Hole

Figure 1.2 Single-Stream Shear Layer Euler Characteristic

2.0 PIV Facility and Test-Section

2.1 General Overview of the PIV Facility
2.1.1 PIV Facility Specifications and Key Features

The Particle Image Velocimetry (PIV) facility located in the TSFL at Michigan
State University was employed for all measurements contained in this experimental inves-
tigation. The PIV facility possess’ many qualities ideal for PIV measurements. The facil-
ity is a closed-loop, removable test—section facility which was designed and built in
December of 2002 with the explicit purpose of improving the PIV capabilities of the
TSFL. Figures 2.1(a-d) and 2.2 provide the general design of the PIV facility along with
labeled key elements which are described with greater detail in the remainder of this chap-

ter.

2.1 .1.1 Closed-Loop Test Facility

A closed-loop flow testing system provides an ideal situation for many PIV exper-
iments. By employing a closed—loop flow system, the seed (or particulate) material
required for PIV measurements is recirculated through the flow system. The flow inlet[A]
and outlet portals[B] to the PIV facility are labeled in Figure 2.1. Careful consideration
was taken in positioning the outlet portal as far away as possible from the test section, as
well as conditioning the flow as it returns to the test-section portion of the PIV facility.
Baffles[I] are located just past where the flow re-enters the PIV facility lower section.
These baffles, along with the re-entry channels[J], help to more evenly distribute the flow
across the entire lower plenum[D].

The primary benefit of employing a closed-loop flow system, for these experi-

ments, was the ability to seed both the primary and entrained flows with a single seeding

system. By recirculating the seeded flow through the flow system, a nearly steady-state
level of seed was achieved throughout the entire flow system. This made it possible to
achieve not only uniform seeding in each stream, but the same level of seeding in both the
primary and entrained streams. Achieving this balance can be difficult in multi-stream
flows.

A secondary benefit of the closed-loop flow system used here was the conserva-
tion of the seeding particulate. Over the course of these experiments, testing time for a sin-
gle data set ranged from a few minutes to nearly an hour. By initially filling the system to
the proper density of seed and then greatly reducing the seeding rate, very little seed was
added continuously once the proper seed density was achieved. It is assumed that the low—
ered level of seeding rate used approximately one-quarter the seeding material as the ini-

tial rate.

2.1 .1 .2 Non-Reflective Surfaces

All surfaces inside the PIV facility are painted to minimize all laser light reflec-
tions. All surfaces have a two-layered coating to maximize absorption of light, especially
light which is of the wavelength emitted from the PIV lasers. The undercoat is a flat-black
paint, the overcoat is a rhodarnine 6G dye and water mixture. The flat-black undercoat
pre-darkens the surfaces which reduces reflections of all light. The overcoat of rhodarnine
6G dye maximizes the absorbtion of light of the wavelength emitted by the lasers. Absorb-
ing laser light before it reflects greatly reduces any chance of secondary or tertiary image
planes that can occur with bright reflections. By eliminating the possibility of any intense
reflections, the illuminated seed particles are dominantly those within the primary image

plane.

10

A second desirable property of rhodamine 6G is a high resistance to photobleach-
ing by light with high intensity such as that used in PIV. By covering all permanent sur-
faces inside the PIV facility with rhodamine 6G, the PIV facility itself is protected from
the intense PIV laser light. The laser light would eventually burn through the flat-black

underlayer and expose more reflective material without this protective outer coating.

2.1 .1.3 Removable Test-Section

The PIV facility is built with an open-section with mounting brackets which are
used to secure the test-section in place between the lower and receiving plenurns, this
opening is labeled in Figure 2.2 as element [F]. This generic test-section opening allows
for many possible experimental test-sections to be installed. The mounting portion of the
test-section opening is constructed with steel angle brackets which are welded together at
the corners for added structural strength. The steel mounting brackets[K] have a 5mm
thick layer of foam weather stripping which is compressed when the test-section is
installed, this ensures there will be no flow leakage across this interface. The test section is
held in place with 16 mounting bolts which run through the installed test-section and
thread into the steel supports at approximately 18cm intervals on all four sides of the test-
section. The test-section constructed for these experiments is further discussed in section

2.2.

2.1.2 Blower Specifications
The primary flow in these experiments was driven by a single blower[C] located
outside of the PIV facility, its location can be seen in Figure 2.1. This blower was a Cin-

cinnati centrifugal blower with radial blades (zero blade curvature). The blower’s rotor

11

diameter was ~480m and its exit portal was ~11.5cm in diameter. The driving motor was
fully powered for all experiments and the limiting gate was in the fully-open position. F ig-
ure 2.3 provides a photo of the blower connected to the PIV facility system. It is worth
noting that the blower was positioned on its side, relative to its support base, in order to
properly orient the inlet and outlet of the blower with the PIV facility flow plumbing. Dur-
ing operation the pressure rise from the PIV facility lower plenum[D] to the receiver ple-
num[E] was monitored via static pressure taps at locations [G] and [H] respectively. The
pressure drop across this interface was monitored during all tests using a pressure trans-
ducer located inside the PIV Facility. The pressure level was observed to remain very reg-

ular throughout each test and fiom one test to the next.

2.2 Shear Layer Test-Section Fabrication and Segment Specifics

The test-section fabricated for these experiments consisted of multiple segments
which were assembled in place with the test-section opening of the PIV facility. The sin-
gle-stream shear layer that was created was meant to provide an idealized setup for PIV

measurements with uniform seeding throughout the test section.

2.2.1 Test-Section segments

The test-section was constructed in 4 segments which were pre-assembled into 2
sub-assemblies. These 2 sub-assemblies were then aligned and mounted to the PIV facility
test-section opening. Figure 2.4 provides a two-dimensional profile view of the test-sec-

tion. Each of the four segments is described in more detail in the following sections.

2.2.1.1 Inlet Segment

12

The inlet segment is the first portion of the test-section the flow encounters as it
leaves the lower plenum. Figure 2.6 shows the uninstalled inlet segment, also, Figure 2.4
provides a profile view of the inlet segment. This segment provides a smooth transition
from the lower plenum to the downstream segments. This segment consisted of a rounded
inlet and a contraction, see Figure 2.4. The key dimensions of this segment can be seen in
Figure 2.5. The lower edge of the rounded inlet was located approximately 50cm from the
lower plenum floor to allow for uniform, unobstructed flow entry. Immediately following
the rounded inlet was a smooth contraction to accelerate the flow and decrease the flow
channel area, this contraction was gradual to ensure that the flow remained attached to the

channel walls.

2.2.1.2 Flow Conditioning Segment

Once the flow has been reduced to the proper dimensions it is conditioned to have
nominally uniform streamwise velocity and minimal disturbances. This segment consisted
of a straight channel with a combination of screens and honeycomb. The screens create a
restriction which causes a pressure drop across each screen which aides in evenly distrib—
uting the flow velocity across the entire channel area. The initial screen also serves to sup-
port the honeycomb material. The screens also provide a uniform small scale disturbance
that can help to breakdown larger scale vortical motions and provide a disturbed, but uni-
formly disturbed, flow field. The honeycomb material is one-inch in depth and prohibits
any motions of a larger length scale than the diameter of each individual cell from exiting
the honeycomb. These cells were one-eighth of an inch wide in this case. Figure 2.4 dem-
onstrates the locations of screens and honeycomb, a photograph of the inlet segment as

well as the flow conditioning segment is provided as Figure 2.6. This segment provides a

13

nearly uniform velocity, uniform small-scale disturbance flow field to the backstep region

segment.

2.2.1.3 Backstep Region Segment

The purpose of these experimental data is to investigate a single-stream shear layer
and to examine the resulting low speed side entrainment region/ shear layer interaction.
This situation is created by constructing a four-walled channel with one of the walls mak-
ing a sharp perpendicular bend in the spanwise direction, often referred to as a backstep.
The resulting primary flow entrains fluid from the backstep opening and a single stream
shear layer is created. Figure 2.4 provides a planar representation of this setup. The pri-
mary flow opening (+y) in this case was 100m wide and the depth (+/-z) of the section was
50cm. The data collected here were acquired at the centerline of the testing-section (2:0),
25cm from the front and back walls. The smooth backstep extends 30cm in the spanwise (-
y) direction. The PIV facility wall, in the negative y-direction, is 119cm fi'om the backstep
location. There are multiple small steps as well as the PIV laser tripod legs between end of
the smooth backstep region and the PIV facility walls. The backstep itself is located 15cm
downstream of the final flow conditioning screen, see Figure 2.5 for clarification of these
dimensions.

Construction of the backstep region was done primarily with flat—black foam-
board. This material is 5mm thick and provided a light-weight, sturdy frame for the walls
of the backstep region. The entire front of the test-section was a single sheet of one-eighth
inch thick glass chosen to assist in obtaining an undistorted PIV image. By utilizing a very
thin, high quality sheet of glass, distortions due to refraction of light inside of the glass

medium was virtually eliminated. Refraction can be a serious problem in image acquisi—

l4

tion across multiple mediums with different indices of refraction (n). For an example of
refraction distortion see Figure 2.7. The light traveling to the camera has very little (negli-
gible in this case) distance over which to refract. The glass wall extends for 5cm below the
backstep (-x) in order to allow for an inlet flow investigation of the boundary layer, via

PIV.

2.2.1.4 Downstream Shear Layer Segment

The downstream region (+x) where the primary data were collected was con-
structed of the same materials as the backstep region. These two regions were constructed
from material that reached from upstream of the backstep to the furthest downstream
region in order to ensure the transition from the backstep to the downstream shear layer
was as smooth as possible. This downstream region extends 81cm downstream of the ini-
tial backstep, the primary PIV data were acquired from approximately 43.50m to 73.50m
downstream. Beyond the end of the downstream region there is no interference until the
flow reaches the PIV facility ceiling, this occurs at 131cm downstream of the backstep.
Figure 2.5 provides these dimensions concerning the test-section’s location and orienta-

tion within the PIV facility.

2.2.1.5 Final Test-Section Assembly

The final assembly of the Inlet/Flow-Conditioning segments (inlet sub-assembly)
and the Backstep/Downstream segments (backstep sub-assembly) was done inside the
PIV facility. This was done for two reasons; i) the fully assembled test-section could not

physically fit into the PIV facility and, ii) by assembling the two sub-assemblies in—place it

15

was possible to assure proper support and alignment of the inlet sub-assembly which was
located entirely within the lower plenum.

The assembly process was mildly complicated but allowed for careful alignment
of the two sub-assemblies in only a few steps. Initially the inlet assembly was placed on
the floor in the lower plenum, notice the threaded positioning rods[P] which are attached
to the inlet segment in Figure 2.8. Next the backstep sub-assembly was placed onto the
PIV facility steel test-section mounting brackets[K] and the positioning rods were slipped
through carefully placed holes[O] in the test-section support board[N]. The support
fiame[L] for the inlet sub-assembly was then positioned over the backstep sub-assembly.
The need for this support fi'arne was due to the light-weight and somewhat fiagile nature
of the backstep sub-assembly and the weight (~40 lbs.) of the inlet sub-assembly. Once the
support frame was in place, the positioning rods were placed through holes[M] in the sup-
port frame and nuts were threaded onto the positioning rods. As these nuts were tightened
they slowly drew the inlet sub-assembly up off the floor of the lower plenum and towards
the backstep sub-assembly. The nuts on all four rods located at the four corners of the inlet
segment were tightened until the two sub-assemblies met and compressed the foam
weather stripping which was placed on the top edge of the inlet sub-assembly. Fine adjust-
ments were then made to assure that the two sub-assemblies were firmly connected and
properly aligned. Figure 2.4 demonstrates the fully assembled, installed test-section in the
PIV facility, and Figure 2.8 provides an actual photo of the installed test-section in the PIV

facility.

16

 

a) PIV Facility Front View

 

 

A. Flow Inlet Portal

B. Flow Outlet Portal

C. Blower

D. Lower Plenum

E. Receiver Plenum

F. Test—Section
Opening

G. Pressure Tap
(Lower Plenum)

H. Pressure Tap
(Receiver Plenum)

L Inlet Flow Baffles

 

 

J. Re—Entry Channels

 

*: feature is hidden in
current view

 

A. Flow Inlet Portal

B. Flow Outlet Portal

C. Blower

D. Lower Plenum

E. Receiver Plenum

F. Test-Section
Opening

G. Pressure Tap
(Lower Plenum)

H. Pressure Tap
(Receiver Plenum)

I. Inlet Flow Baffles

J. Re-Entry Channels

 

 

 

*: feature is hidden in
current View

b) PIV Facility Front View (Primary Hidden Lines)

 

c) PIV Facility Left Side View

  

J

 

I

 

A. Flow Inlet Portal

B. Flow Outlet Portal

C. Blower

D. Lower Plenum

E. Receiver Plenum

F. Test-Section
Opening

G. Pressure Tap
(Lower Plenum)

H. Pressure Tap
(Receiver Plenum)

I. Inlet Flow Baffles

 

 

J. Re~Entr_v Channels

 

*: feature is hidden in
current view

 

A. Flow Inlet Portal

B. Flow Outlet Portal

C. Blower

D. Lower Plenum

E. Receiver Plenum

F. Test-Section
Opening

G. Pressure Tap
(Lower Plenum)

H. Pressure Tap
(Receiver Plenum)

I. Inlet Flow Baffles

 

 

J. Re-Entry Channels

 

*: feature is hidden in
current view

(1) PIV Facility Bottom Angle View (Transparent Lower Floor)

Figure 2.1 PIV Facility (3D Model - 4 Perspectives)

 

T Flow

F _.__. .

71/]

 

 

A. Flow Inlet Portal

B. Flow Outlet Portal

C. Blower

D. Lower Plenum

E. Receiver Plenum

F. Test-Section
Opening

G. Pressure Tap
(Lower Plenum)

H. Pressure Tap
(Receiver Plenum)

I. Inlet Flow Baffles

J. Re-Entry Channels

K. Mounting Brackets

 

 

 

*: feature is hidden in
current View

 

 

 

I]
*E. J |®|

Figure 2.2 PIV Facility 2D Model

19

0* G* H*

 

 

Figure 2.3 Blower & Plumbing Connected to the PIV Facility Photo

20

I I I I [J I I I I I I I I I I I I I I I I

Receiver Plenum Ceiling

 

 

 

 

 

 

   

 

Downstream Segme It
Receiver Plenum y
Lower Plenum

Backstep Segme it

Screen 2 \
Honeycomb Flow Conditioning Segme It

Screen 1k

Contraction Section
\ Inlet Segme It
Inlet Round\

/'//‘1\\\

Lower Plenum Floor

 

I I I I I 7 I I I I I I I I I I I I I I 7 7

Figure 2.4 Test-Section - 2D Profile with all Segments

21

All Dimensions
in centimeters

 

l—~20.5

 

    

 

 

Receiver Plenum
Lower Plenum

  

 

 

 

 

 

 

 

 

7 I I I I I I I I I I I I I I I I I I I

Figure 2.5 Test-Section - Dimensioned 2D Profile

22

 

Figure 2.6 Inlet-Flow Conditioning Sub-Assembly Photo

 

Air , Glass Air Index of Refraction:
Air: n==1.0003

Glass: n==1.51 7

 
 
 

 

 

 

  
  

Beam of Light

Error due to
refraction

Figure 2.7 Refraction Demonstration (Air-Glass-Air)

23

 

L. Support Frame

M. Support Frame Holes
N. Test—Section Support Board
0. Support Board Holes

P. Threaded Positioning Rods

 
   
 

 

 

Figure 2.8 Installed Test-Section Photo

24

3.0 Measurement and Acquisition Equipment and Software

The data acquisition and processing that was carried out for the present results was
primarily obtained through particle image velocimetry (PIV); the required equipment and
software is outlined in this chapter. The main components of the PIV system used here,
and in most systems, are the lasers, camera, computer with software, and a seeding device.
For these measurements a pressure transducer was used to monitor and ensure reliability
and repeatability of the data sets. Also, all post-processing was completed using programs
written for this work in MATLAB. Visual interogation and presentation of the data was

done primarily in Tecplot 360.

3.1 Pressure Transducer

The pressure drop fi'om the lower plenum to the receiving plenum was monitored
by a differential pressure transducer[W] in order to ensure that all experimental data
acquisitions operated under the same conditions. This pressure differential remained very
regular throughout all tests but it was a necessary check this to ensure the reliability and
consistency of the system. The pressure transducer used for this purpose was a 10 torr
Baratron differential pressure transducer type 398HD-00010 with a type 27OB-4 signal
conditioner. The accuracy of this device, as specified by MKS, was 0.05%. As previously

indicated, no sampling of pressure was taken, only a ‘real time check’ to ensure regularity.

3.2 PIV Equipment
A LaVrsion PIV system was employed for these measurements. The system con-
sists of four primary components which are i) 2 laser heads[Q] with control boxes[R], ii) a

PC[S] with timing control electronics, iii) CCD camera[T] and, iv) an aspirator[U] flow

25

seeder. In addition to the core components just listed, there are two high-precision posi-
tioning tripods used to support and orient the lasers and camera. Each element is discussed
in detail in the following sections. The positioning of each element is demonstrated in Fig-

ures 3.1 and 3.2; all main components are labeled.

3.2.1 Dual PIV Lasers

The lasers employed by the PIV system used here are New Wave Research model
Minilase-III lasers. These NszAG lasers emit a 1064nm wavelength (infrared) laser
which is frequency-doubled to achieve a visible 532nm wavelength (green) laser beam.
These lasers may operate at up to 15 Hz at 50 ml with a pulse width of 5-7ns. The dual
head design provides for a variable time between the firing of each laser which can be
manually or remotely controlled. The laser heads are housed in a single assembly which
orients and redirects each beam to the same point when exiting the housing. A Rodenstock
modular-focusing lens[V] is mounted to the fi'ont of the dual-laser housing. This allows
for focusing the laser sheet thickness and it also provides the ability to orient the diverged
laser sheet to any angle. The laser sheet thickness was approximately 1mm across the
image plane. The final component attached to the laser heads, mounted after the Roden-
stock lens, was an interchangeable divergent lens[X] which is used to spread the laser into
a sheet suitable for PIV measurements. The divergent lens used here had a focal length of
6mm which supplied a relatively large angle of divergence. The dual laser heads allowed
for the acquisition of high frequency cross-correlation double-frame images.

Each laser head has an associated laser control box[R] which controls the laser fir-
ing. The control boxes can be used to control the laser pulses manually (usually for setup)

or they can be connected to a PC and controlled by timing components and software. This

26

software is discussed further in section 3.2.3. In addition to controlling the pulsing of the
lasers, the control boxes supply the cooling lines[Y] and filters for the laser heads which
are cooled by recirculated deionized water.

The lasers were originally manufactured and calibrated in December of 1997 and,
after many years of both heavy use and prolonged storage, the laser beams became weak-
ened and misaligned. Prior to this research effort, both lasers were returned to New Wave
and reconditioned to optimum intensity and alignment specifications. It is worth noting
here that this process is usually unneccesary if the lasers are run for a minimum of 30 min-

utes per week.

3.2.2 PIV CCD Camera

For these measurements, double-flame images were acquired with a prescribed
delay time (dt) using a Flowmaster 28 type CCD camera[T]. The 12-bit camera provides a
2kx2k pixel resolution and a maximum acquisition rate of 11.8 double-frames/s. The lens
mounted to the front of the acquisition camera was a Nikon AF Nikkor 50mm focal length
lens[Z]. This provides the ability to adjust the focus and aperture of the light scatter image
reaching the CCD. The frame-transfer style CCD employed in this camera allows for two
image frames to be captured over a very low time delay.

A light filter[AA] was utilized while acquiring data in order to inhibit ambient
light from reaching the camera CCD. This band-pass light filter only allows light within

the range emitted by the PIV laser to pass to the CCD, near the 532nm wavelength.

3.2.3 Computer and Programmable Timing Unit

27

The computer supplied with the LaVision PIV system is a dual Intel Xeon proces-
sor machine with an internal Programable Timing Unit (PTU). The PTU onboard the PC
was used to control and synchronize the camera’s double-frame image acquisition with the
pulse of each laser. One image (two frames) per laser pulse cycle (one pulse from each
laser head) was acquired. The PTU incorporates all the features of the LaVision PIV soft-
ware, DaVrs. The DaVis software was used to set the image frame-pair time delay (dt), as

well as many other settings discussed in Section 3.3.

3.2.4 Aspirator Flow Seeder

The flow seeder[W] used to supply seeding particles to both the primary flow as
well as the entrainment flow was a Topas brand Aerosolgenerator ATM 210/H. This aspi-
rator uses high pressure air with a Venturi nozzle to create a very high velocity outside the
seeding fluid reservoir and, as a result, draws in the liquid seeder fluid out of the reservoir
in a gaseous state. The fluid used here is Bis(2-ethylhexyl) Sebacate (DEHS) which pro-
vides a very steady, non-toxic vapor when used with the aspirator. The particle sizes gen-
erated, according to the manufacturer specifications, are within the range of 0.2um and

0.3 pm.

3.3 DaVis PIV Software Calibration and Cross-Correlation Method

The LaVision PIV program, DaVis, was used to acquire all images and ultimately
process the image frames into vector fields in these experiments. After the initial align-
ment of the PIV lasers and camera, there is very little activity which is necessary but not
controlled via the computer software, i.e. DaVis. DaVis controls every aspect necessary

for proper PIV acquisition and processing including camera calibration, image acquisi-

28

tion, vector calculation, and vector validation. These processes are outlined and describe
in this section. DaVls also offers a multitude of post-processing routines and calculations;
however, these post-processing tasks were completed outside of the pre-written LaVision

software for these experimental results.

3.3.1 Camera Calibration

Proper calibration of the PIV camera is of utmost importance given that any mis-
calibration will be unknown and possibly un-noticeable until much later in the analysis of
the results. This process is the only physical link between the real flow field and the ulti-
mate vector field which is calculated. The process begins by constructing a calibration
plate[BB] that, when oriented in the desired plane of the data, can be imaged by the PIV
camera and used to link the real image plane to that which is recorded by the camera. This
calibration grid supplies a known reference distance and location to the acquired calibra-

tion image.

3.3.2 PIV Image Plane

The data discussed herein were acquired in two separate image planes. The initial
data were acquired at the backstep location (x=0) to analyze the boundary layer and pri-
mary inlet flow. The inlet image plane was large enough to span the entire inlet of the pri-
mary flow. The second image plane (downstream image plane) was located downstream at
432.5mm<x<734.6mm and spanned from the wall on the high speed side to the low speed
side entrainment flow region (-195mm<y<106mm). This downstream image plane pro-
vided the data that is of primary interest in these experiments. These image planes are

demonstrated in Figure 3.3.

29

3.3.3 Image Processing Routines - Vector Field Calculation

The images acquired in these experiments were taken using a double—flame dou-
ble-exposure method. In practice this means that each ‘image’ acquired is actually two
frames which have a set time delay, dt=3 00p.s for these data. A cross-correlation technique
is used to map the movement of small clusters of seed particles, within correlation win-
dows, and to assign a distance traveled (D ), see Figure 3.4. This distance and the pre-

scribed time delay combine to form a velocity vector P :

V = (61-12), (3.1)

assigned to the interrogated window. Initially, each frame is divided into windows which
are cross-correlated with the corresponding window from the other frame. This two-
dimensional cross-correlation method provides a correlation map over each window area
and the peak correlation level is selected as the most appropriate vector. There are addi-
tional methods employed during this process to not only ensure that the most appropriate
vector is calculated, but also to ensure that spurious vectors are disallowed or more appro-
priately calculated as described below.

When processing PIV images it is often useful to have an initial shift of the corre-
lation windows so that the most appropriate vector may be calculated. One method for
accomplishing this is to start with a larger window size than is ultimately desired. By first
calculating vectors over a larger window, the area is smoothed and a general vector over
that area can be used as an initial shift for smaller correlation windows. This larger win-
dow is then split into 4 smaller windows and the correlation is calculated again using the

initial shift from the larger window, this helps to ensure that the same particle groups are

30

correlated for each iteration. For these data, the initial window size was 128 pixels and the
final window size was 16 pixels, each reduction in size is a one-half side-length reduction
(128 --> 64 -->32 --> 16 pixels). Another method used to increase the accuracy of the ini-
tial shift vector is a re-run of the cross-correlation at each window size using the result of
the initial run at that window size. This allows the correlation to take into consideration an
initial ‘guess’ that is of the same window size and increases distance over which the peak
correlation search is performed. Also, correlation overlap allows the correlation map to
include a percentage of the surrounding area which can aide in proper correlation when
particle groups have partially passed into the surrounding windows. For these data the ini-
tial correlations were overlapped 25%, and the final correlation windows were overlapped
50%. The final correlation overlap also serves as a method to increase vector resolution
(calculated vector density). It allows the correlation windows to be overlapped in order to
create more vectors with the same window size. Figure 3.5 demonstrates this increase in
vector density with a 50% final interogation window overlap. In the end, the data acquired
here provided cross-correlation vector fields comprised of 65536 vectors (2562).

There are many vector validation routines which can help to identify and eliminate
spurious vectors incorporated into the DaVis software. Two of these routines were
employed during these calculations. They are termed the minimum peak ratio and the
median filter. The minimum peak ratio validation method ensures that there are no second-
ary correlation peaks which are near the magnitude of the primary correlation peak. If, for
example, there are two local-maximum peaks in the correlation map, and they are of the
same order of magnitude, then it is possible that either of the peaks could be the correct

correlation. Therefore, the primary correlation peak cannot be validated with confidence.

31

The ratio of the primary peak to the secondary peak for these validations was required to
be greater than 1.2. It is worth noting that the primary and secondary peaks a have the
minimum peak subtracted from their levels, this eliminates the influence of any noise that

may exist within the image. Therefore, the final calculation of peak ration (Q) is:

P —P .
1 mm
>1.2 (3.2)

mm

 

Q:

A second validation method used here, the median filter, examines the results of the corre-
lations surrounding each window and verifies that there is some continuity in the vector
field results. For all vectors, the median of the eight surrounding vectors is calculated.
Then, from this median, the RMS of the eight surrounding vectors is calculated. Figure 3.6
provides an example vector field that may, depending on the level of acceptable relative
RMS, remove and replace the center vector. The median value is used, rather than the
mean value, so that the most extreme values do not influence the comparison vector. Also,
when the RMS is calculated, the two most outlying points are not included as to not
greatly sway the result. For the validations employed here, a vector was removed if the
vector was not within the median of its neighbors plus/minus two-times the RMS of its
neighbors. Also, the median vector was inserted if the calculated vector was within the
median of its neighbors plus/minus 3 times the RMS of its neighbors. These parameters
are demonstrated for a non-specific streamwise velocity component vector in equations

3.3 and 3.4.

+ 2U (3.3)

remove: Um edian rms

—2UrmssU_<_Um

edian

replace: Um —3UrmsS US Umedian+3U (3.4)

edian rms

32

3.4 MATLAB Post-Processing Routines

After calculating and validating complete vector fields from 1000 images, these
vector fields were exported from DaVis into MATLAB. Numerous post-processing calcu-
lations were completed using MATLAB. From DaVis the coordinates (x, y) as well as the
calculated two components of velocity (u, v) were exported, {x, y, u, v}. All other calcula-

tions were completed with code written specifically for these experiments by the author.

3.4.1 Ensemble Calculation

Several statistical and numerical calculations were carried out that required infor-
mation from all 1000 vector fields. One difficulty in calculating the statistical results is the
available memory of the processing computer. Due to the large amount of information
contained in each vector field (65536x4) and the large number of total data files (1000),
each vector field was loaded and summed pointwise. The total value for each vector was
then divided by the total number of summed values at each location to find the mean.
Once the mean vector field was determined, other field contour variables could be calcu-
lated such as the turbulence intensity and vorticity fields.

The vorticity field was calculated from the mean velocity field of all 1000 images.
A circulation contour method was used in which a 24-point contour (7x7 discrete grid of
points) was used to calculate the circulation. The circulation value was then divided by the
area (~43mm2 area square block) to arrive at the vorticity at a given central grid point; see
Figure 3.7. One caveat of this method arises at the comer points. In essence, each discrete
grid point, located at a circulation contour corner, represents a velocity value one-half a
grid spacing distance on either side of its location. This means that at the corners, these

points only represent one-half a grid spacing in one direction. To account for this, a mean

33

value was calculated and reorganized halfway between each grid point. In practice, this
was accomplished by adding all discrete points around the contour, but only adding half of
the value at each comer. The described contour and area calculation is demonstrated, for a
non-specific representative 7x7 grid, in Figure 3.7. By using the circulation contour
method, each vorticity value was smoothed over a larger area than represented by a single
grid-point but the loss in resolution was offset by the gain in data that was included in each
calculation. Vorticity calculations were completed using a derivative method as well as
circulation integrals with small contour areas, however, these methods proved less effec-

tive than the described technique.

3.4.2 Singular Point Mapping and Circulation Calculations

Following thorough ensemble vector field calculation, instantaneous images were
investigated to map the location of all singular points. Singular points, as described in sec-
tion 1.4, are points of discontinuity in a planar flow field. The node and saddle occur-
rences were mapped fiom the instantaneous vector field. Also, in a separate investigation,
the nodal points traveling at the convection velocity were located from instantaneous
images with the convection speed subtracted. By locating these singular points in these
two types of instantaneous realizations, statistical representations and characterizations
were calculated. The vorticity was also calculated around the nodal points traveling at the
convection velocity to represent the size and strength of these large scale, convecting vor-
tical motions.

In order to accurately and efficiently calculate the vorticity around a node at differ-
ent circulation areas, MATLAB was used for the circulation contour calculations about

each node center. The node centers of the data images were manually located and recorded

34

using streamlines created in Tecplot (discussed in section 3.5), next MATLAB was used to
evaluate these points. MATLAB code was written to load these locations, load the appro-
priate velocity vector field files, and calculate the circulation at increasing square contour
areas. The area spacing was increased one grid point in each direction at a time, and the

circulation ( F )and thus the vorticity (Vb ) was calculated based on the contour area (A).

(3.5)

St
II
Alp”

The vorticity versus the area, as well as other relationships, were then plotted and evalu-
ated. By using MATLAB, many circulation areas were able to be calculated efficiently and
precisely as well as introducing a degree of regularity in the calculations, i.e. square con-

tour areas located at the discrete grid points.

3.5 Tecplot 360 - Contour Plots and Streamlines

Tecplot was used to plot all field contours presented in these discussions, the high
quality and customization that this program offers allowed for very professional and
appropriate representations of these complicated data sets. One of the most attractive fea-
tures of the Tecplot software is its streamline integration routine. The software includes
the ability to, based on 2 specified variables (11 and v here), integrate across discrete grid
points and calculate smooth traces that follow the flow path based on the discrete grid
points. Figure 3.8 provides a portion of one representative discrete vector field with
streamlines which pass between grid points. Discrete data are located only at the orthogo-
nal grid intersections (thick lines), but the streamlines (thin lines with arrows) clearly pass
smoothly between many discrete points. This feature was used to manually map all singu-

lar points located within the image planes. By mapping these singular points, statistical

35

investigations of singular point locations, spacings, consistency, and types within each

vector field were completed.

36

 

Q. PIV Lasers

R. Laser Control Boxes
S. PC with PTU

T. PIV Camera

U. Aspirator

V. Laser Focusing Lens
W. Pressure Transducer

*: component is hidden
in current view

 

 

 

 

MWM «3‘31th :eytwmmwzmirnmnwmameu . d‘k’itfit‘fiy‘fl‘iw m

Figure 3.1 PIV house with installed test-section and PIV equipment - Model

37

 

Q. PIV Lasers

R. Laser Control Boxes

T. PIV Camera

V. Laser Focusing Lens

X. Laser Divergent Lens

Y. Laser Cooling Lines

Z. Camera Focusing Lens

AA. Light Filter

BB. Installed PIV Calibration Plate

 

 

 

Figure 3.2 PIV house with installed test-section and PIV equipment - Photo

38

All dimensions are in
centimeters

106.8

  
      
         
     

Downstrea . . .
[ma _e Plane

734.6

432.5

 

 

 

Receiver Plenum
Lower Plenum

Inlet (Boundary
Layer) Image Plane

 

 

// \ \\

Figure 3.3 PIV Image Plane Locations

39

16x16 Window Image Plane, 2 Frames (256 Total Vectors)

 

 

 

 

 

 

 

 

 

\
=> /
Frame 1 Frame 2 Distance of Peak Window Centered
\Vindow \Vindow Correlation Vector

Figure 3.4 Cross-Correlation Method

Initial Overlap 0% Initial Overlap 50% Initial Overlap 0%
Final Overlap 0% Final Overlap 0%

        

 

 

 

 

Interrogation Window
Overlap Area

.4 Calculated Vector

Figure 3.5 Initial and Final Window Overlap Correlations

40

Final Overlap 50 %

 

 

 

 

 

Figure 3.6 Median Filter example Vector Field

 

+1
+ Discrete Vectors
(i+3, j+3) O Circulation Contour Center
X lVIean of Adjacent

Discrete Vectors

(i-3, j+3)

 

— Circulation Contour Boundary

 

 

(1+3, j+1.r2)

—...
+1

 

(i-3, i-3) (H3. i-3)

Figure 3.7 Circulation Contour of a 7x7 Discrete Grid (6x6 Area)

41

 

 

590

585

.580
CD

X]

575

570

 

yle

 

Figure 3.8 Discrete Grid with Integrated Streamlines

42

 

4.0 Boundary Layer PIV Results

An initial investigation into the boundary layer separation region, at the backstep
region of the shear layer test-section, was carried out for two purposes. The first was to
characterize the quality of the inlet flow entering the shear layer test-section. It was impor-
tant to verify the inlet flow contained minimal disturbances as well as possessed a mostly
uniform streamwise velocity profile across the backstep interface (x=0). A uniform inlet
condition is an important criteria for the desired downstream canonical shear layer. The
second purpose of the boundary layer investigation was to quantitatively define the initial
momentum thickness in order to aide in properly characterizing the downstream shear
layer. Specifically, the initial momentum thickness was investigated and found to be
00:1.11mm at x=2mm. (This small x>0 value was required to obtain reliable PIV observa-

tions.)

4.1 Acquisition and Processing Specifications

As demonstrated in Figure 4.1, the boundary layer PIV image plane was posi-
tioned to capture both upstream and downstream of the backstep. Due to obstructions in
the PIV camera’s view, the usable data range was from -20mm<x<9mm, the blockages
can be seen in any representative PIV image such as that presented in Figure 4.2. Due to
the positioning of the laser, the data range was ultimately reduced firrther due to both laser
light blockage and reduced laser light intensity, the final data range can be seen in Figure
4.3. All boundary layer PIV results were calculated from the ensemble of 400 vector
fields. As discussed earlier, the PIV image discrete grid size was (256)2 points, this pro-
vides a resolution of 0.58mm spacing between each discrete grid point. Topologically this

image plane has an identical setup to that described in the introduction for the entire sin-

43

gle-stream shear layer region. This orientation results in three holes in the collapsed
sphere on the mid-plane of the test-section. One half-saddle is located at the separation

edge of the backstep and, hence, the topological constraint is satisfied as xsurface=2-3= -1.

4.2 Boundary Layer Velocity Contour PIV Results

The boundary layer PIV data results provide a clear indication of the quality of the
inlet flow and they adequately define the initial scale for the description of the down-
stream shear layer. The mean strearnwise velocity ( r7 ) calculated over the entire validated
data range is presented in Figure 4.4. It is apparent fi'om the representative PIV image in
Figure 4.2 that there is high intensity light reflection interference with the results at the
backstep (x=0, y=0). This interference appears to be non-existent when moving down-
stream from x = 0m to a location of x = 2m. These data are further investigated in the
following section by extracting discrete velocity profiles at multiple downstream locations

in close proximity to the backstep.

4.3 Discrete Boundary Layer Profiles from PIV Results

Extracting a streamwise velocity profile across the inlet span fi'om the PIV images
allows for firrther detailed boundary layer profile examination. Figure 4.5 gives the inlet
(x=2mm) streamwise velocity profile. Also provided in Figure 4.5 is the streamwise tur-
bulence intensity profile at x=2mm downstream. In examining the inlet profile, there are
deviations from a perfectly uniform free stream region profile. However, the detailed mea-
surements will be taken downstream and will focus on the entrainment side of the shear
layer, therefore, the slight streamwise inlet velocity profile unevenness will be demon-

strated to dissipate upstream of the downstream measurements. Qualitatively, a more uni-

44

form inlet flow could be achieved, however, this inlet profile will suffice for the intended
measurements. The mean streamwise velocity level in the inlet free stream, from point b
to point c as denoted in Figure 4.5, is calculated to be Uo,x=0 = 4.51 m/s. This is within 2%
of the free-stream streamwise velocity (U0 = 4.6 m/s) at the downstream data region
investigated in chapter 5.

Figure 4.6 provides boundary layer profiles at four streamwise locations in the
immediate region of the backstep (-10mm<y<25mm). At downstream locations of x =
2mm, 3mm, 4mm, and 5mm the profiles appear to be very similar both qualitatively and
quantitatively. Calculating the momentum thickness, defined by,

9(x)= {(zfirijo gem ).y (4..)

at both x=2mm and x=3mm downstream arrives at 00:1.11mm. For these calculations b
was taken to be the location of the local maximum velocity, as seen in Figure 4.6, this
occurred at y=10mm. Also, a was taken at y=-0.3mm or slightly to the negative y-side of
the backstep location, this is also the location where all four profiles meet and reach a
nearly minimum and constant level. This range is supported by Figure 4.7 which repre-
sents the associated streamwise turbulence intensities ( i} ) levels at the various down-
stream locations, the spanwise range of -0.3mm<y<l 0mm roughly defines where the
turbulent intensity values arrive at near minimum values of {r = 0.1 m/s.

The boundary layer results nominally agree well with the Blasius solution with a
small negative pressure gradient. Figure 4.8 presents the boundary layer data at x=2mm

normalized to Blasius coordinates F’ and n.

45

(4.2)

n = (0664);,1 (4.3)

0
The boundary layer’s agreement with the Blasius solution determines that the inlet flow is
adequately prepared by the upstream flow conditioning elements.

With the inlet flow sufficiently characterized, it is now possible to investigate the
primary region of interest for these data; the downstream entrainment side of the self-sim-
ilar single-stream shear layer. From the inlet region PIV results, the initial momentum
thickness has been determined to be 00:1 .11mm, and the inlet profile has been shown to

be sufficiently uniform.

46

 
   
   
 
    

aser Light Plane

Side Wall

'.L. Image Plane

Backstep Wall

Figure 4.1 Boundary Layer PIV Image Definition

47

ill“ 88061‘fraltne‘

 

 

 

 

Figure 4.2 Representative Boundary Layer PIV Image

48

 

 

Figure 4.3 Boundary Layer PIV Image - Reliable Image Range

49

 

x(mm)

 

 

 

 

 

 

 

 

(Ms)
M
l

 

 

 

 

yawn)

Figure 4.5 Streamwise Velocity and Turbulence Intensity Profiles at the Inlet
(x=2mm)

50

J (rer)

u',ms (m/s)

 

CD

 

«in

 

4L

 

 

 

 

 

 

-15

 

 

 

 

 

3 +x=2rrrn
+x=3rrm
—+—x=4mn
2 +x=5mn
41
-10 -5 5 1O 15 20 25 30
NM“)

Figure 4.6 Inlet Region Streamwise Velocity Profiles

 

:0.
db

 

 

 

 

 

 

 

44 fl
1"
41')
l.‘
l
41 t
1 if
+x=2rrm
1
' ‘ -o-x=4rrrn
I +x=5rrrn

 

 

 

 

g:
C»

 

 

 

 

 

 

 

I T I T l’

5 10 15 20 25 30
Y (m)

 

Figure 4.7 Inlet Region Strearnwise Velocity RMS Profile

51

 

14

 

12

 

 

 

 

 

A x=2data
+blasius

 

 

 

 

“0564”“
a) CD
K"inn-L

 

 

 

 

 

‘A
‘A
A‘ ‘
2 . ‘ ‘
‘ I
a ‘ ‘ ‘
0 r r r T r
0 0.2 0.4 0.6 0.8 1 1.2
Pauli»

Figure 4.8 Boundary Layer Data and Blasius Solution

52

5.0 Downstream Ensemble PIV Results

Detailed investigations of downstream PIV data were conducted to examine the
interaction of the shear layer with the associated entrained fluid. The complete data set
consisted of 1000 dual-frame images, acquired in order to calculate converged statistical
characterizations of the shear layer. These images were processed as described in chapter
2 and all 1000 vector fields, representing 65536 (2562) discrete vectors per image, were
utilized in the present calculations. The cross-correlation parameters and the employed

settings are presented in Table 1.

Table 1: Utilized Correlation Parameters

 

Initial Initial Initial Final Final Final
Window Window Window Window Window Window
(pixels) Overlap Iterations (pixels) Overlap Iterations

Correlation Median
Peak Ratio Filter

 

1282 50% 2 322 50% 3 Q>l.2 23 & 3b

 

 

 

 

 

 

 

 

a. Velocity vector must be greater than 2 times the RMS of the surrounding vectors in order to be
removed (firrther description in Section 3.3.3)
b. Velocity vector must be less than 3 times the RMS of the surrounding vectors in order to be replaced
with the median of the surrounding vectors (further description in Section 3.3.3)
5.1 PIV Vector Field Converged Data Range
5.1.0.1 Downstream Image Plane Definition and Orientation
The image plane utilized for these data is defined by Figure 5.1, which demon-
strates the location and orientation of the downstream image plane and the major sur-
rounding geometry. The positive x-direction is in the primary flow’s streamwise direction
du
and the positive y-direction is oriented such that 7y >0 in the shear layer, this is demon-
strated in Figure 5.1. Note that, the PIV laser light sheet divergence is not capable of illu-

minating the entire image plane, as is shown in Figure 5.2. The most-divergent lens

(defined in section 3.2.1) was utilized for these measurements, also, the laser head was

53

maximally displaced in the negative y-direction to allow for the largest area of illuminated
particles as possible. The total image area was not reduced due to the existence of reliable
data across the entire span of the image. Therefore, the properly illuminated region in the

image plane must be identified. A new, smaller measurement domain is defined below.

5.1.0.2 Measurement Domain

Figure 5.2 supplies clear insight into why some of the measurement domain is
inadequately illmninated for PIV measurements. Figure 5.3 defines the four regions to be
omitted from the inadequately illuminated image in Figure 5.2. Eliminating these regions
from the measurement domain assures that the inadequately lit data regions will not influ-
ence the nearby regions.

Region #1 defines the upper range of the laser light plane divergence. In the same
sense, region #2 defines the lower limit. Region #4 is on the right-hand—side of the image
plane, the laser light in this region is directly impinging on the sidewall. In Figure 5.2 it is
possible to see not only the highly reflected light near the wall, but the back-comer of the
test-section is also affecting the image. The intense light in region #4 prevents proper vec-
tor correlations and must be eliminated. Region #3 contains particles that are dimly lit due
to the attenuation of the laser light as it passes through the densely seeded primary flow.

The defined region of reliable data is supported by the normalized streamwise tur-
bulence intensity (é) contour plot presented as Figure 5.4. In Figure 5.4, the levels in
regions 1-4 give an inaccurately high value. Figure 5.5 provides an example of the final,
converged data vector field domain to be investigated. This normalized streamwise veloc-

ity vector field and its usefulness will be discussed in further detail in the following sec-

tions.

54

5.2 Ensemble PIV Vector Field Statistics Contours

Using the Tecplot program, contour plots were created by loading the discrete data
grid values and using Tecplot’s contouring integration routines to smooth across the
spaces between the discrete data points. Several statistical and numerical contour fields

were calculated including i) the velocity magnitude,

q = x/u2+v2a (5-1)

ii) the streamwise( {r ) and spanwise( i3 ) turbulent intensities,

1/2
N

i} = F171 2 (ii—17)].2 (5.2)
j=1

where N is the total number of samples (N =1000 for these data) and iii) vorticity,

.3
(DZ

APT»

= l . (5.3)
A (V d3)

C

Figure 5.5 provides the normalized streamwise velocity (E/Uo) contour. The contour levels
represent the normalized streamwise velocities. The streamlines, which are overlaid on the
contour plot, are computed fi'om the V and 5 components of velocity. Topologically, if '
seams are placed at the streamline locations as demonstrated in Figure 5.5, then a col-
lapsed sphere with two holes is defined for analysis. The Euler Characteristic of this sur-
face equals zero, therefore, there should be no net singular points contained within the
ensemble average of this flow geometry. This is clearly the case in Figure 5.5 where each
streamline continuously passes through the image plane. In the following section (section

5.3) the streamwise velocity contour plot will be used to extract discrete streamwise veloc-

55

ity profiles at various downstream locations in order to investigate the self-similar nature
of this shear layer.

The normalized mean vorticity field, given in Figure 5.6, represents a well con-
verged shear layer region. Equation 5.4 demonstrates the method by which the vorticity
was normalized.

_20(51800)

Normalized Vorticity =
U0

(5.4)

The mean flee-stream velocity (U0 = 4.6 m/s) and the momentum thickness 51800 down-
stream (0(51800) = 0.0196 m) were used as characteristic values for the vorticity normal-
ization. These vorticity levels are calculated using a 7x7 discrete point contour around a
center discrete grid point as described in section 3.4.].

As a point of interest, it is noted that the angle from which the low speed side
entrainment fluid approaches the shear layer has a much larger streamwise velocity com-
ponent outside the shear layer than was expected. It was expected that the entrained fluid
would approach from a much more spanwise direction and undergo a more aggressive turn

as it came in close proximity to the edge of the shear layer.

5.3 Discrete Velocity Profiles and Isotach Levels
Discrete data, distinctions: i'r(y) and {202), were extracted from the smooth con-
tours described in section 5.2. These distributions allow the quality of the single-stream

shear layer to be assessed.

5.3.1 Discrete velocity profiles at various downstream locations

56

Velocity profiles were extracted from the smoothed streamwise velocity contours
at streamwise locations of x=49500, 51300, 53100, 54900, and 56700. These profiles
stretch from y=-1690o to y=850o in the spanwise direction. There were 200 discrete,
evenly spaced points extracted for each profile and therefore the point—to-point spacing
was 1.2800. These dimensional profiles can be seen in Figure 5.7 along with the associ-
ated turbulence intensities at the same locations, note the separate ordinates for the mean
(LHS) and rms (RHS) levels. It is worth noting that the maximum streamwise velocity
level is U0 = 4.6 m/s. It was expected that the streamwise velocity in the far field entrain-
ment fluid would be very near zero; the data do not appear to fully satisfy this expectation
and this will be discussed in further detail later. It will suffice for now to say that the
domain bounded by the isotachs: fi=(0.13)U0=0.6 m/s to the free stream (6:11,), the shear
layer can be thought of as single-stream in nature.

The momentum thickness at various streamwise locations, 0(x), is calculated from
each of these profiles. The momentum thickness versus downstream location is plotted for
five downstream locations in Figure 5.8. Focusing on the momentum thickness calculated
from U0 to 13% of U0, the growth rate is d0/dx=0.032. This growth rate is indicative of a
single-stream shear layer. Morris (2003) reported that for a self similar single-stream shear
layer, the growth rate d0/dx, was found to be 0.035, and Hussain & Zaman (1985) found a
value of 0.032. The present results agree with the latter value. As was pointed out earlier,
the streamwise component of velocity in the entrainment region does not appear to
approach a constant, nearly zero, level. When the momentum thickness is calculated
across the entire spanwise data range, dG/dx decreases to 0.019. These observations and

calculations lead to the assertion that, to the high speed side of the (0.13)U0 isotach, the

57

flow is a single-stream shear layer in character. Figure 5.9 demonstrates the grth rate
for isotach levels very near the (0.13)Uo isotach. The growth rate (slope) of increases from
the higher isotachs to a level of 0.032, which is appropriate as more of the shear layer
region is included in the momentum thickness integration. However, to the grth rate
(slope) for the isotach levels lower than (0.13)Uo begin to decrease which is inappropriate
for a single stream shear layer. Therefore Figure 5 .9 supports the assessment that flow sys-

tem is single-stream shear layer in nature from W0 = 0.13 to 1.0.

5.3.2 Single-Steam versus Two-Stream Shear Layer System

After initial analysis of the data acquired from the experimental setup, it becomes
clear that the flow system is not a simple, single-stream shear layer. Figure 5.10 provides
the, now modified, assessment of the flow system that has been developed. Due to the spa-
tial constraints within the PIV facility, it appears that the primary flow has caused a sec-
ondary driven flow which recirculates within the receiver plenum of the PIV facility. The
existence of this recirculation was confirmed with a smoke trace placed at the locations
shown in Figure 5.10. As demonstrated by the growth rate calculations, the region to the
+y side of the (0.13)Uo isotach can be analyzed as a single-stream shear layer, and any
analysis completed outside this range must be done with this secondary flow structure
taken into consideration. The mean velocity magnitude contour is presented in Figure 5.11

with the distinction of the range which is to the high speed side of the (0.13)Uo isotach.

5.3.3 Normalized Discrete Profiles
By normalizing the streamwise profiles by U0 at each streamwise location and

transforming the y-coordinate to 11, defined by:

58

= y‘yl/z

9130‘) , (5-5)

the streamwise velocity profiles collapsed to a single profile. 0] 3(x) is defined as the
streamwise location’s momentum thickness from the free stream to 13% of the free
stream. The variable, Y1/2, is defined to be the y-location where one-half of the free stream
velocity (TIC/2) occurs. Figure 5.12 presents the normalized velocity profiles as well as the
normalized turbulence intensities, both quantities are normalized by the maximum mean
streamwise velocity (U0 = 4.6m/s). These normalized profiles collapse and agree very well
both qualitatively and quantitatively with published results such as those in Spencer (1970
Ph.D. Thesis) and Jones eta]. (report). Specifically, the maximum normalized turbulence
intensity in the present data is {MI-10 = 0.18 which is in agreement, albeit on the high end,
with published results such as Jones (il/ £70= 0.19), Wignanski and Fiedler (1970) (52/ (70:
0.176), and Liepman and Laufer (1947) (ii/ (70: 0.15). From these results, the shear layer
inside of (0.13)IJ-0 and between streamwise distances of x=49500 to x=5670o demon-

strates the features of a self-similar single-stream shear layer.

5.3.4 Isotach Definition Results

Isotach levels were created using discrete points from the smooth streamwise
velocity contour in order to firrther characterize the present flow in relation to a SSSL and
the outer region. In order to create the isotach levels, discrete points were extracted at
9.0100 intervals starting at x=4860o and continuing to x=56700, these ten points were
taken at the location of an isotach at each streamwise location. From these ten points a lin-
ear fit was then applied and the linear trendline was extrapolated to x=0. These data show

that all isotachs from (0.13)Uo to (0.95)Uo converge to a “point” very near the separation

59

lip. It should be noted that some discrete points seemed unindicative of the general 10-
point trend and these points were discarded, however, a minimum of 7 points were
employed for all isotachs. Figure 5.13 presents these isotachs for 10, 11, 12, 13, 14, 15, 20,
30, 40, 50, 55, 60, 65, 90, and 95 percent of U0. These data clearly, combined with the
growth rate assessment, support the single-stream shear layer’s existence within the
described range: (0.13)Uo —+ U0.

Isotach levels were developed to provide a method by which to interpolate
between determined isotachs and collapse singular point locations in the downstream
region. By developing this downstream point isotach fit, the singular point locations are
allowed to be based solely the associated spanwise location. An exponential fit was devel-
oped based on the slope from a downstream point location to the origin (x=0,y=0). These
slopes were then used to develop an interpolated fit. Figure 5.14 presents this fit overlaid
on the discrete isotach vs. slope points. The developed fit involves the sum of two expo-

nential functions in the form demonstrated below:

isotach = a x e(b—Slope) + c x ew—Slope) (5'6)

Equation 5.6 is utilized in conjunction with the fit constants located in Table 2 to reduce

the singular points in chapter 6 to a normalized streamwise location.

Table 2: Slope to Isotach Fit Constants

 

 

 

 

 

Constant Value
a -57.72
b 0.00118
c 81.01
(1 -0.07305

 

 

60

 

+X All dimensions are in

    
    
     
 

 

 

centimeters
1 75 0o 95 0o
Ima1e Plane .
661 0.,
389 0.,
fir

 

 

 

ReerceiVPLIen

Lower Plenum

Figure 5.1 Downstream Image Plane

61

 

 

-150 —100 —50 0 50 100
34M)

Figure 5.2 PIV Image Frame with Illuminated Particles

62

x(mm)

 

     
  

Region #1

 

Region #3

 

Region #4

Region #3

  

Region #2

 

-730
-710
-690
-670
-650
-630
~610
'590
>570
'550
-530
'510
[490
*470

'450

 

 

—1so —1'oo —§o ['1 5'0 100

Figure 5.3 PIV Image Plane with Eliminated Data Regions

63

x(mm)

 

0.08 0.12 0.16
0.04 0.06 0.10.14

 

650

 

400
100

 

 

 

Figure 5.4 Normalized Streamwise Turbulence Intensity ( 17 lie)

64

 

 

650

600

550

 
   

 

 

 

¢° '
i _
500
450 ‘-
E 1.0 1.0
400- lllllllllLJJIIlllll
-150 -100 -50 0 50
we,

 

Figure 5.5 Normalized Strearnwise Velocity Contour (We)

65

 

 

 

_J_L_L,L r41 1 l r r r r I r I r r I l L4 1
450 -100 -50 0 50
we

 

 

 

 

Figure 5.6 Normalized Vorticity Contour (6*0(51800)/Uo)

5.0
4.5
4.0
3.5
3.0
a (ma)
2.5

2.0

0.5

 

0.0
-250 -2(Il -150 4(1) -50 0 50 100 150

Figure 5.7 Dimensional Velocity and Turbulence Intensity Profiles

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
  

    

 

 

 

 

 

 

 

 

 

 

 

 

30.00 _ .1
_ +
' y = 0.0192x + 17.505
25.00
.. 20.00 - - = =
E " y = 0.0319x + 1.3015 n meta
K o theta13
15.00
10.00
5.00
0.m I I I *I I I j I I
540550560570580590603610620630640
sou-nut. Loedlon (x (M)
Figure 5.8 0 vs. x and 013 vs. x
24
/ y = 0.0241x + 8.3005
23
y = 0.027451 + 5.3207
2 _
y =0.0319x + 1.3015 . 10%
21 - / _ - 11%
y - 0.002: + 0.7354
F / s 12%
;' I A . / y =0.0294X +1.84% . 130/0
20 / . . 14%
o 15%
A . .
19 W
15 .
17 r r r I r r
540 550 550 500 500 640 660 680

M London (x(mfi)

Figure 5.9 Growth Rates at Various Isotach Levels

67

n
‘

N

\ Receiver Plenum '7"
Lower Plenum \Smoke Trace

I I I II I I I I I I I I I I I I I

c—o \
Recirculating Flow\ Smoke Trace

Primary

Smoke Trace FIOW

 

 

 

Figure 5.10 Modified Flow System with Smoke TYace Indications

68

 

650

600

         

 

 

550
@0
R
500
450 -
; - i>(o.13)0.
400 _ I I I I l I I I I I I l l I I I I I I l
-150 -100 -50 0 50
we"

 

 

 

Figure 5.11 Velocity Magnitude (E) Contour with (0.13)fio Division

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2 0.24
1.0 0.20
0.8 0.16
in]. u'...JU.
0.6 O. 12
0.4 0.05
0.2 4‘ 0.04
0.0 I I I r n r 1 ‘ (1m
-10 -8 -6 -4 -2 0 2 4 6 8

Figure 5.12 Normalized Velocity and Turbulence Intensity Profiles

69

10 111211415 20 30 40 5055665 90 95

 

-110 -90 -70 50 -30 -1o 10 30 50
Mom)

Figure 5.13 Isotach Levels

U fitpoints
—-curvefit

 

-120 -100 -80 -60 40 -20 O
dope

Figure 5.14 Isotach vs. Slope Curve Fit

70

6.0 Singular Point Identification

The identification of singular point locations was carried out for 1000 instanta-
neous PIV vector fields. This identification involved manually locating and recording the
centers of all isolated singular points. The investigations were done in two parts: (i) identi-
fication of nodes and saddles within instantaneous vector fields and (ii) the identification

of large-scale nodes traveling downstream at the convection speed.

6.1 N ode-Saddle Identification
6.1.1 Topological Discussion of Instantaneous Vector Fields

The identification of nodes and saddles is demonstrated in Figure 6.1 which pro-
vides a representative instantaneous PIV vector field. Figure 6.1 also demonstrates
streamlines based on the vector field and the associated topological considerations. As can
be seen in the collapsed sphere assessment of Figure 6.1, there is a clear inlet-hole and an
outlet-hole and the seams here are represented by streamlines that clearly bound the iso-
lated domain. In Figure 6.1, the streamlines provide insight into the flow path, all stream-
lines clearly enter and/or exit their respective holes. The addition of two holes and no
handles to the collapsed sphere yields an Euler Characteristic of zero, xsurface = 0. That is,
there can be no net nodes or saddles, or more explicitly, nodes and saddles must exist in
pairs. Therefore, for proper singular point accounting, every node must have an associated
saddle or vice-versa. This topological accounting cannot be properly carried out if the
flow does not both enter and exit uniformly to the inlet and outlet holes. Figure 6.2 offers
an instantaneous vector field which does not provide a uniform inlet hole. It is possible to
analyze the highlighted region and utilize many holes and seams, which will result in

many nodes and half-saddles. For the present analyses, images which did not properly sat-

71

isfy this simple, uniform inlet and exit condition were discarded. There were a total of 151
of the original 1000 images that were not investigated further due to their complexity near
the border of the data range.

In addition to the identification of all singular points contained within a properly
collapsed sphere, all nodal singular points were characterized by their type as defined by
Perry & Chong (1987). In this reference nodal points are described to have five possible
definitions, Figure 6.3 demonstrates these five types of nodes as they apply to two-dimen-
sional fluid flow. These descriptions of node types are taken from Perry & Chong (1987).
Figure 6.4 provides a blown-up view of the singular points contained within Figure 6.1. A
collapsed sphere is developed again in Figure 6.4 and by the same assertions as outlined
for Figure 6.1, all singular points must exist in pairs. There are a total of five nodes located
in Figure 6.4 and each has an associated saddle. The nodal points are labeled according to
their node-type in Figure 6.4, labeling appears on the right-hand-side of the figure, outside
of the data range. The saddle points in Figure 6.4 are also labeled, these are labeled “S” on

the top of the image. As expected, there are 5 saddles within the collapsed sphere.

6.1.2 Locations of Nodes and Saddles

After manually locating and logging the location of all singular points, their loca-
tions were plotted as seen in Figure 6.5. Nodes are represented by circles and saddles are
represented by crosses. It is clear from Figure 6.5 that singular points exist at all stream-
wise locations. Figure 6.5 also provides isotachs, as defined and discussed in chapter 5, as
a relative reference. A distinct feature of these results is the complete lack of any singular

points in the positive-y-region through all 1000 images.

72

Figure 6.6 represents the location of the saddle points relative to their associated
node. The associated node was located at the plot origin. This node-to-saddle spacing will
be investigated further in section 6.1.3 where all singular points have been collapsed to a
single relative streamwise level. It is worth noting here that the node/ saddle combination
is one selected during the singular point identification, there is no ‘right’ answer for which
node should combine with any specific saddle. In general, as a convention, the nearest
saddle was chosen to combine with a node unless there was a clear flow-field reason to
choose a different pairing combination. An example of this, see Figure 6.7, involved a
very large node with a nearby saddle which was very close to the node center. However, a
different saddle is clearly “more-involved” in the node’s flow structure. Specifically, node
#1 is clearly closer to both saddles #2 and #3 than to saddle#l. However, node #1 is
clearly the major contributor to the large flow structure and therefore saddle #1 was cho-

sen as it’s pair. Nominally 5% of the assessed pairs required such judgements to be made.

6.1.3 Collapsed Singular Point Statistics

Statistical characterizations of the singular point locations were made using the
slope-to-isotach fit developed and described in section 5.3.4. This fit was used to interpo-
late between manually deterrnined isotach levels and eliminate the dependence of the data
upon its streamwise dimension. In reducing the singular points to a single streamwise
level, the location is based purely upon the singular points’ spanwise location or, more
appropriately, the associated isotach for a given streamwise and spanwise location. Figure
6.8 presents the normalized distribution of nodes versus the assigned isotach. The nodes in
this distribution were limited to those that were within the single-stream shear layer

region1 and below the x=5850o streamwise level. After this subset of nodes was deter-

73

 

 

mined, the total number of usable nodes was 1154, as opposed to the 2560 total nodes that
were identified.

Figure 6.9 provides the normalized distribution of node-to-saddle distance. The
abscissa in this figure is presented on a logarithmic scale. Once again, the 1154 single-
stream shear layer node subset was used. The mean of this distribution was calculated to

be dN/S/9(X) = 0.1884.

6.2 Identification of Nodes at the Convection Speed

In order to properly identify the location of nodes moving downstream at the con-
vection velocity, the convection velocity was subtracted from the streamwise velocity con-
tours. This convection velocity was calculated from the 0.13Uo level to U0:

(7 +0
13 0 = O.6+4.6 = 2.611-

Ucz 2 2 s

(6.1)

The streamlines, which were created using the relative streamwise velocity, quite clearly
revealed the large scale nodes in the convecting reference fi’ame. Figure 6.10 provides a
representative instantaneous vector field in the convecting reference frame. These new
contours were investigated to map the large scale convecting nodes such as that seen in
figure 6.10. Figure 6.11 provides the topological considerations for these convection
velocity contours. In these flow fields there are 4 total holes, 2 inlet holes and 2 outlet
holes. Since the vector field at a topological hole must be unidirectional, there are seams
located along streamlines at the top, bottom, and sides of the contour. The Euler Charac-

teristic is -2 for the indicated surface. The half-saddles at the central region streams have

 

1. As described in section 5.3, this region is bounded by the isotachs: u/Uo=0.l3 and 1.0.

74

been described by Foss (2007). Alternatively, it would be possible to simply identify a col-

lapsed sphere surrounding the node for an Euler Characteristic of 2.

6.2.1 Vorticity Calculations for Individual Convecting Nodes

There were 917 total large-scale, convecting nodes located in the 1000 vector
fields investigated in the absolute reference frame. The focus of these identification data
will be on the large scale nodes, therefore, no saddle locations are documented. Contour
circulation calculations were completed by mapping the node centers. Using MATLAB
code written for these investigations, the vorticity as the circulation contour area was
increased was quantified, see equation 6.2 for this relationship.

(3,: F/A (6.2)

The method by which these mean vorticity calculations were completed over various areas
is outlined in chapter 3. This method involved calculating the circulation about a 7x7 dis-
crete grid of data points which arrives at a mean vorticity value over the circulation con-
tour area. Figure 6.12 presents the mean vorticity level as the area increases, Figure 6.12
also provides the total number of samples that were incorporated into the mean at each
area. This total level changes due to the fact that the node centers are often not in the cen-
ter of the image plane, therefore circulation calculations could only be completed until one
comer of the square circulation contours reached the edge of the data range. The circula-
tion level was no longer calculated once an edge of the data domain was encountered. F ig-
ure 6.13 demonstrates a non-centered node with the associated largest circulation contour
area that could be calculated. Consider, if this node had been centered within the data
domain, many larger circulation areas could have been calculated and included in the

mean vorticity for those areas. It is expected that the vorticity values would reach a con-

75

stant level as the area increases, this appears to occur where the area reaches 1x104 mmz.

This area would correspond to a contour side length of 100 mm. As can be seen in the rep-
resentative velocity profiles in Figure 5.7, this is very nearly the width of the shear layer in
measurement domain.

When analyzing individual image contours, the vorticity level, as the circulation
contour area is increased, seems to nearly always reach a constant level when large
enough contour areas are available. However, this minimum vorticity level and the area at
which it is finally realized varies for each node. This would seem to account for the slow
decrease in the mean vorticity level in Figure 6.12. Figure 6.14 provides traces for a group
of ten vorticity vs. contour area investigations and clearly supports the assertion that indi-
vidual vorticity levels seem to reach a stable level as the area increases. However, in some
cases, the computational domain reaches the edge of the data domain prior to reaching the
stable level. In these traces, the vorticity value was immediately set to zero once a data
domain edge was encountered. Note that these zero levels were not included in the calcu-
lated mean vorticity. Figure 6.14 demonstrates two highlighted cases, A and B. Case A
involved sufficient contour area evaluations to reach a nearly constant minimum vorticity.
In contrast, case B encounters a data domain edge prior to reaching a constant vorticity.

In analyzing these mean vorticity vs. contour area results, the minimum vorticity
level as well as at what contour area this level occurs provide insight into the character of
the convecting nodes. Figure 6.15 provides the distribution of the minimum vorticity level
reached for the investigated set of nodes. This demonstrates the large range of values for

the minimum (maximum magnitude) vorticity level. The normalized mean minimum vor-
5,0(x = 51800)

 

ticity is ( )= —17.6 . Also, Figure 6.16 demonstrates the area at which the

0

76

minimum vorticity level is reached. In these cumulative levels, a large portion of the min-
ima (~30%), occur at very small areas. This high number of instances at the lower areas is
most likely a relic of the node centers encountering a domain edge, this will result in a
minimum level which is still increasing but cannot be calculated further. Therefore, an
investigation which first determines if -- a large enough circulation contour area was uti-
lized to reach a constant vorticity level -- was carried out.

In order to determine if a constant vorticity level was attained for a given node cir-
culation contour area range, a third-order polynomial fit was applied for each circulation
vs. area (L2) investigation. The derivative with respect to the circulation contour area of
this fit was taken to arrive at a second-order ‘circulation-derivative’ polynomial function.
The relation of circulation contour area, circulation value, and mean vorticity is provided

in equation 6.2.

r = (coz)(L2) (6.3)

The derivative of this relation with respect to circulation contour area is given in equation

6.3.

15— - <m,> (6.4)

d(L2) —
It is clear fiom Equation 6.3 that this circulation derivative is representative of the mean
vorticity for a given circulation area. Figure 6.17 provides five representative circulation-
derivative vs. area conditions. Employing Equation 6.3 it is apparent that, where these
quadratic polynomial traces reach a minimum level, the mean vorticity has reached a con-
stant level. For these results, there were a total of 917 nodes identified. Of these nodes,

394 circulation contours reached a constant vorticity level according to this method. Fig-

77

ure 6.18 provides the distribution of normalized circulation contour size at which the con-

stant mean vorticity was reached. The mean size, normalized by the momentum thickness

at the streamwise location of the node center, is (5%) = 3.34. Figure 6.19 provides the
x

normalized mean vorticity strength, at the level where the circulation-derivative reached a
5,0(x = 51800)

U

0
tive measure, Figure 6.20 provides the normalized distance of the location of the node

 

constant level. The mean of this distribution is ( ) = —20.37. As a rela-

centers relative to the (0.5)Uo isotach. The mean of this normalized distance is

y c
0(x)

 

( )=0.26.

78

 

650

  

Seam
Hole (Inlet)

‘logular Point Pelt: (See Flgure 6.4)
400 .

-150 -100 -50 0 50 100
we

 

 

 

Figure 6.1 Representative Instantaneous Vector Field - Topologically Valid

79

 

650 '-

    

/
\Slnguler Polnte

I I I I l l l I l l I I Ll IALLL I l I L J
-150 -100 -50
we

 

I I I I l
l l

400
100

 

 

 

Figure 6.2 Representative Instantaneous Vector Field with “Edge Problems”

80

 

1. Stable Foci (node) 2. Unstable Foci (node)

 

3. Stable Nodes 4. Unstable Nodes

 

5. Concentric Nodes Standard Saddle

JIL

_.—>

VIK—

Figure 6.3 Types of Singular Points (Descriptions from Perry & Chong (1986))

 

 

 

 

81

 

 

(as seen In Figure 6.1)

  
         
   

5 ss (Outlet)

530
525
520

@O

§515
510

505

We. Hole (Inlet)

 

Figure 6.4 Node (rhs) Type Examples with Saddles (top)

82

 

 

 

 

 

 

20

 

 

 

 

 

 

j

-100 -80 -60 -40

-140 -120

-160

 

-180

 

 

 

 

 

 

 

-200

.5 § § § § E5

((uw)x) uonaoq asymuaans
Figure 6.5 Node and Saddle Identification with Selected Isotachs

83

 

25

1.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

X
to. v- v.- m.
\"' fu—
x I
X
X
x x
X
I: I:
x t x _ ‘1'
x x x
X x
‘0.
x " ‘7
’ X
Ex 0']
X
x l0.
8 “J
m
I
(me/Xe

Figure 6.6 Saddle Location Relative to its Associated Node

_5L =_ 5_x =
(600) 0.0933 (9(x) 0.0415

84

8y/9(x)

 

 

 

54o -- \

 

 

 

 

 

 

 

 

 

 

Figure 6.7 Node-Saddle Pairing Example

85

 

 

0.08

0.07 ‘ d

l

x5;
(‘1
9.
.3

[LEE

I

f fi-i Te“

r ..W.?:~.kvl~'-'~Lff".

.
"my; min-w 1‘1””"5733 '3‘ ’
__ .

,4 3.33559;

    

p
E

n(isotach)lN

0.03

I
.‘..1ca‘-*.t¢3‘n:-;’.rx' enigma-neg-

   
    
   

 

”.591. fps.

0.02

I

J!

0.01

I

rpm»; ywl;~‘.rf.:u

 

 

 

 

 

 

 

 

 

 

 

. ...4-..~r-
- .-

3,1,“?!

 

 

'4‘ tL‘L’}.’.‘."' '

U 8&1“; Ii Eli-H. a; t . J y
10 20 30 4° - 5° 50
Isotach (1UUXG/Uo)

Figure 6.8 Distribution of Nodes in a given Isotach Range - For the 0.13<-u-/fio<1.0
“single stream shear layer” domain

86

n(distance)fN

[109 - ....,.... e
m. -.

0.07

 

0.EB

p
8

5::
E

P
D
m

0.02

0.01

 

 

 

1o 10'2 10‘ 10° 10
Distance Magnitude from Node to Saddle (dmf0(x))

Figure 6.9 Distribution of Node-to-Saddle Distance

87

 

     
  
    

700

u (mls)

1.75
1.25
0.75
0.25
-0.25
-0.75
-1.25
-1.75
-2.25

llllllii

650

 

    

 

 

K
550
500 L
450 l
— i l l [ALA 1 l LLJ_LI l l i
-150 -100 -50 0 50 100
y (mm)

 

 

 

Figure 6.10 Streamwise Velocity Contour - Convection Velocity Reference Frame

88

 

 

 

 

 

 

 

 

 

 

 

 

 

700 '_ Hole1(ln|et) Sum
- HoleZlOutlet)
- T all-Saddlet
" Ill-Saddle!
650 - I
I ’ l
E600 _- " ‘ Node‘l
E, -
x I t
550 -
' Ill-Saddle:
I ~ - - Ill-Saddlet
500 - / Yl
- HoleHOutlet)
- Hohallnlet)
' Sum
450 -
billlllllllllllllllllllllllllj
-150 -100 -50 0 50 100
y (mun)

 

 

 

Figure 6.11 Strearnwise Velocity with Topological Considerations - Convection
Velocity Reference Frame

89

 

-2000
-2500
-3000

Vorticity (1 Is)

 

 

 

 

 

% of total included

 

 

 

U l L l L l l l l f

U 0.2 0.4 0.5 0.8 1 1.2 1.4 1.5 1.3 2
Area (mmz) x 104

 

Figure 6.12 Mean Vorticity vs. Area & Samples vs. Area

90

 

700

IITjr

 

rill
U

650

x (mm

IIITITTFII

 

550

 

 

500 - Deslrod Clteuhtlon Node Center

" Contour Ana \

h-

" Maximum Calcuhtoda
' cnuhtlonCOntout
450 '-Aru

~1lllllllllL11 l;r114‘xlllll

-150 -100 I-s'oi H 0 50 100
Ylmml

 

 

A

 

 

 

 

 

Figure 6.13 Large Scale Node Centered Near the Data Range Border

91

Vorticity (Vs)

4000

1000

 

 

 

f
R
Case A

l Case B
h

 

 

‘r‘ I

l l l

 

 

M—

05 1 15
Area (mmz)

Figure 6.14 Vorticity vs. Area for 10 Individual Nodes

92

2.5
x 10

n(v0rticity)/N

0.12

 

0.1 F

.0

0

CD
I

0.05 -

p

D

A
l

0.02 -

 

0
—1 2000

-10000

Figure 6.15

     

0000 95000 9 4000 -2000

Minimum Vorticity Level

Distribution of Minimum Vorticity Level

93

 

 

 

 

 

gamicw

1(104

Area (mmz) Level where Minimum Vorticity occurs

16 Cumulative Distribution of the Area at which the Minimum Vorticity
Level Occurs

Figure 6

94

 

 

 

 

 

 

U "v‘¢¢;¢¢¢¢¢¢¢¢¢¢‘§¢¢¢¢¢¢ 3?: “ ‘ 3 t t fr 3,: ¢ ¢ :47:
’33 -1[lIl -
g l
t l
O
> 'i
E 2013': .
a”.
5 ..
as 3000‘ -
h
i=3 ~\
0 ‘ r
t \0
LI.
I: 40]]- -
9 5“! ......
.0—0
2
3
8
'5 -5lI]J- -
b
_m l 1 l J
0 0.5 1 1.5 2 2.5
4
Area(mm2) x10

Figure 6.17 Representative Circulation-Derivative (Mean Vorticity) vs. Circulation
Contour Area Traces

95

 

 

0.076 . T u I u .

0.053

0.051

0.030

"(UWWN

0.025

0.013

 

 

 

LM(x)

Figure 6.18 Distribution of the Normalized Circulation Contour Size where the
Mean Vorticity reaches a constant level

96

 

0.114 I I I I I

0.102

0.009

0.075

0.053

0.051

"(MOW

0.035

0.025

0.013

 

 

 

-35 -30 -25 -20 -15 -10 -5

Figure 6.19 Distribution of the Maximum Normalized Strength of Vorticity which
becomes Constant

97

 

0.087

0.075

0.055

0.055

0.044

n(dW‘BO‘W‘l

0.033

0.022

0.011

 

 

 

0
-2 4.5 -1 -05 0 0.5 1 1.5 2 2.5 3
ch|()()

Figure 6.20 Normalized Distance from Node Circulation Contour Center to the
Mean 0.5Uo Isotach

98

7.0 Summary and Conclusions

A detailed experimental investigation of a shear layer using PIV techniques has
been conducted. Detailed data were acquired across the inlet of a backstep test section to
assess the details of the inlet flow field. Additional PIV data were acquired to characterize
the downstream shear layer. Singular points were identified in the instantaneous down-
stream PIV images. They were used to form statistical characterizations of the locations,
sizes, and strengths of the singular point regions. The following items represent the impor-
tant results.

1. The inlet velocity field is nominally uniform with small irregularities in the free
stream region. The boundary layer velocity profile was in nominally good agreement with
the Blasius boundary layer solution and exhibited a small negative pressure gradient. The
mean streamwise velocity was Umxzo = 4.51m/s at x = 2m. The initial momentum thick-
ness was 60 = 1.11mm. The Reynolds number of this flow based on the initial momentum
thickness and the mean fiee stream velocity is R690 = 321.

2. The downstream data revealed a self-similar single-stream shear layer from
(495)0o to (567)60 within the (O.13)l—J'o to 00 isotach range. The flow system has a second-
ary, recirculating flow caused by the spacial constraints within the experimental facility.
The growth rate, within the single-stream shear layer range, was dex = 0.032. This is in
agreement with published literature concerning single stream shear layers; see Hussain
and Zaman (1985). The complete flow field, including the low speed side of the (013)-60
isotach, somewhat resembled a two-stream shear layer. This interpretation was based on

the reduced growth rate of dG/dx = 0.019 over this larger domain.

99

3. The maximum mean streamwise velocity was calculated to be 60 = 4.6 m/s. The
downstream acceleration, Uo,x=0 = 4.51m/s to 00 = 4.6m/s, is attributed to the global recir-
culating flow.

4. Singular points exist throughout the entire downstream measurement domain.
The sum of their indices (node = +1, saddle = -1) was in agreement with a Euler Charac-
teristic constraint of xsurfacc = 0 for the associated collapsed sphere with two holes.

5. For the domain described in (2) above, the mean spacing of node-saddle pairs

was ( EL) = —0.0933 in the spanwise direction and < E- = 0.0415 in the stream-

9(x) 9(X)
wise direction. The observed node occurrences were greatly reduced toward the center of
the shear layer with no node centers existing in the y > 0 (isotach 2 0.6800).

6. Coherent motions, surrounding a distinct node and traveling downstream at the
convection speed: me = 0.565, reach a maximum size and strength which is related to the
shear layer momentum thickness. A total of 91 7 large-scale coherent motions were located
and characterized. The location of these convecting node centers was, relative to the
(0.5)Uo isotach, on average determined to be ( yc ) = 0.26 (~0.66Uo isotach) and with

9(X)
a standard deviation of 0.64. 43% of the circulation investigations reached a constant

 

value within the measurement domain before encountering a domain edge. The mean nor-

malized circulation contour side length, where constant circulation occurred, was

L
<93")

which reached a constant circulation was (

= 3.34 with a standard deviation of 1.16. The normalized mean vorticity of nodes
6,0(51800)

 

) = —20.4.

0

100

 

APPENDIX

101

APPENDIX A

A.0 Large Single Stream Shear Layer (SSSL) Seeding Efforts

Extensive efforts were made in attempting to adequately seed the low speed side
entrainment flow of the large SSSL. This appendix will serve to outline the major efforts
which were conducted toward this end. Three primary methods were experimentally
tested and proven ineffective in supplying proper seed particle density and distribution for
the intended measurements. These three primary methods were: a smokewire/hotwire, an

installed seeding plenum, and an adjustable seeding unit.

A.1 Smokewire Seeding Method

The smokewire seeding method was experimentally tested in two forms. First a
heated wire was used to vaporize fogging fluid which was then carried with the entrain-
ment flow; see Figure A.1. The second form employed the same heated wire to burn a
smoke stick. For the first investigation, a thin (D=0.007mm) tungsten wire was wound
across 2 supports, located 50cm apart, and stretched taut. The Reynolds number around
this wire was much less than 40 which ensured no downstream vortex shedding from the
smokewire. The efiecfive Reynolds number around this wire was Re=0.1 l , based on the
flow velocity (V = 0.245 m/s) and the wire diameter. A thin layer of fogging fluid was
applied to the wire and an electrical current was supplied in order to heat the wire and
vaporize the fogging fluid. This method worked well but did not supply a continuous seed
to the flow. This method did however supply a low-density, instantaneous ‘line’ of seed

which could prove useful in an alternative application.

102

 

The second smokewire method utilized smoke sticks (incense sticks) which were
burned using the heated wire. The smoke sticks were initially reduced in diameter in order
to ensure that no vortex shedding would occur on the downstream side of the smoke
sticks, this was accomplished by lightly sanding the smoke sticks with a low gauge sand-
paper. In order to keep the Reynolds number below 40, with the low speed side entrain-
ment flow velocity of V=O.245m/s, the diameter of the smoke sticks was reduced to less
than D=2.5mm. The reduced diameter smoke sticks were then tightly wound with tung-
sten wire; approximately two revolutions per smoke stick was used. An electric current
was then applied and the heated wire caused the smoke sticks to ignite. This supplied a
continuous sheet of seed particulate for approximately 30 seconds. One major problem
with this method was with the inherently heated smoke particulate matter. Due to the very
low flow speed in this region, the buoyancy of the smoke carried the smoke vertically
about one-quarter as fast as it was convected towards the shear layer. In other words, for
every meter towards the shear layer the smoke traveled, it traveled approximately one-
fourth of a meter out-of-plane in the positive z-direction. Additionally, the smoke sheet
supplied by the smoke stick was not simply two-dimensional. The smoke which was
burned off the smoke sticks was not burned evenly, and therefore the smoke sheet had
very pronounced non-uniform density as well as ‘waves’ in the sheet. There was a negligi-
ble likelihood that this sheet would pass precisely and uniformly through the PIV image
plane. However, this method provided a sheet of seeded flow which, in a slightly stronger
passing flow field, could provide a fairly clean sheet of seed particulate matter for planer

observations.

103

A.2 Installed Seeding Plenum

The installed seeding plenum was the most elaborate of the methods which were
attempted. Figure A.2 provides a demonstration of the proposed setup for this method. By
intent, this large suspended plenum would be allowed to fill with seeding fluid, then the
vertical walls would be dropped and the large volume of seeded fluid within the seeding
plenum would convect as part of the entrainment flow. Thin steel cables were stretched,
very tightly, across the length of the large single stream shear layer facility. These cables
were then used to support a thin sheet of material called ‘Monokote’. Monokote is a thin
plastic which constricts when heated. The Monokote sheets were designed to make up the
horizontal (x-y plane) walls of the seeded plenum. The monokote would then be heated to
create a tight, flat, horizontal plenum wall which would only minimally influence the
entrainment flow. In practice the light weight Monokote was not able to stretch tight

enough to be nominally two-dimensional and therefore this method was abandoned.

A.3 Adjustable Seeding Unit

The adjustable seeding unit (ASU) provided a removable, tunable seeding mecha-
nism which worked moderately well. This unit was, essentially, a small version of the
large SSSL’s entrainment system. However, unlike the large SSSL the ASU has the capa-
bility for seed to pass through it’s flow conditioning screens. Figure A.3 provides a sche-
matic of this unit. Figure A.4 supplies a picture of the installed unit in the process of
seeding the large SSSL low speed entrainment flow, the seed particulate is illuminated by
the PIV laser in this image. By design, this unit would ingest entrainment flow to offset
the blockage it presents, then add seed to the flow within the seeding plenum, and finally

digest a seeded flow. Minimal disruption to the external flow which was not ingested was

104

the goal. In practice this was accomplished by tuning the inlet fans to ingest the proper
amount of flow in order to match the momentum of the external (unseeded) flow. Figure
A.5 supplies a plot of the supplied fan voltage versus flow velocity exiting the seeding
unit. According to this linear fit, the ideal fan voltage was 6.22 volts in order to match the
entrainment flow speed of 0.245m/s. However, even after tuning the inlet fans to this level
and other levels, the exiting flow became unstable and coherent motions were observed.
These coherent motions could be seen to rotate clockwise or counterclockwise depending
on the speed of the inlet fans. Figures A.6-A.8 provide representative images of the flow
field with clockwise (positive), counterclockwise (negative), and nearly stable (neutral)
motions near the exit of the seeding unit in the y-z plane. The least disruptive level of inlet
fan speed was determined and investigated further, however, this method proved insuffi-
cient for the intended PIV measurements. Specifically, the seeded entrainment flow pos-
sessed a level of disturbance that precluded the desired vortical/non—vortical

discrimination method to define the intermittency states: 1:] and 1:0 respectively.

105

ungsten Wise
D=0.007"
L=500mm

 

Figure A.1 Installed Smokewire Seeder Prototype

106

    

Seeder

Monokote Layers

Support Cables

PIV Laser

Monokote Layers PIV Laser
Sup ort Cables

 

PIV Camera

Figure A.2 Large Single Stream Shear Layer with Installed Seeding Plenum

107

Inlet Fans

 
   
  
  

Seeded
Flow Exit

Seed Generator

Figure A.3 Adjustable Seeder Unit Schematic

108

 

Figure A.4 Installed Adjustable Seeder Unit seeding the large SSSL low speed
entrainment flow

109

8.5
8 /
y = 17.48x + 1.9351 /

 

 

.‘l
or

 

 

 

O)
0) 0|

 

Inlet Fan Voltage (V)
' N

-/
./

v

 

.01
or

 

 

 

 

4.5 r I I I I I l I
0.17 0.19 0.21 0.3 0.25 0.27 0.29 0.31 0.33 0.35

mmwmmwoatyrnu)

Figure A.5 Inlet Fan Voltage versus Exit Flow Velocity

110

 

Figure A.6 Adjustable Seeder Unit - Positively Tuned (higher seeder exit velocity
than external flow velocity)

11]

 

Figure A.7 Adjustable Seeder Unit - Negatively Tuned (lower seeder exit velocity
than external flow velocity)

112

 

 

Figure A.8 Adjustable Seeder Unit - Neutrally Tuned (approximately equal seeder
exit velocity and external flow velocity)

113

REFERENCES

114

REFERENCES

Dimotakis, RE, (1986), “Two-Dimensional Shear Layer Entrainment,” AIAA J. 24, 1791-
1796.

Foss, J.F., (2004), “Surface selections and topological constraint evaluations for flow field
analyses,” Experiments in Fluids, vol. 37, pp. 883-898.

Foss, J.F., (2007), Handbook of Experimental Fluid Mechanics, Ed C. Tropea, J Foss, A
Yarin, Springer Verlag.

Hellum, A.M., (2006), “Intermittency and the Vrscous Superlayer in a Single Stream
Shear Layer,” MS. Thesis, Department of Mechanical Engineering, Michigan State Uni-
versity, East Lansing, MI.

Hussain, A.K.M.F. & Zaman, K.B.M.Q., (1985), “An experimental study of organized
motions in the turbulent plane mixing layer.”, J. Fluid Mech., vol. 159, pp. 85-104.

Jones, B.G., Hammersley, R.J., Planchon Jr., HR, and Spencer, B.W., “The Turbulence
Structure in the Plane Two-Stream Mixing Layer,” Nuclear Engineering Program, Univer-
sity of Illinois at Urbana-Champaign, (Report).

LaVrsion GmbH., (2002), F lowMaster Manual, Gottingen, Germany, p. 50-67.

Liepmann, H.W., & Laufer, J. (1947), “Investigation of free turbulent mixing”. N.A. CA.
Tech. Note, no. 1257.

Morris, SC, (2002), “The Velocity and Vorticity Fields of a Single Stream Shear Layer,”
Ph.D. Dissertation, Department of Mechanical Engineering, Michigan State University,
East Lansing, MI.

Morris, S.C., Foss, J.F., (2003), “Turbulent boundary layer to single-stream shear layer:
the transition region,” J. Fluid Mech., vol. 494, pp. 187-221.

Perry, A.E. and Chong, MS, (1987), “A description of eddying motions and flow patterns
using critical-point concepts,” Annu. Rev. Fluid Mech, 19:125-155.

Spencer. B.W., (1970), “Statistical Investigation of Turbulent Velocity and Pressure Fields
in a Two-Stream Mixing Layer,” Ph.D. Thesis, Nuclear Engineering Program, University
of Illinios.

Wmant, CD. and Browand, F.K., (1974), “Vortex Pairing: The Mechanism of Turbulent
Mixing Layer Growth at Moderate Reynolds Number,” Journal of Fluid Mechanics, Vol.
63, Part 2, pp. 237-255.

115

Wignanski, I. and Fiedler, HE, (1970), “The Two-Dimensional Mixing Region,” Journal
of Fluid Mechanics, vol. 41, pp. 327-361.

 

 

116

 

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