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VELOCITY-FIELD MEASUREMENTS OF AN
AXISYMMETRIC SEPARATED FLOW SUBJECTED TO
AMPLITUDE-MODULATED EXCITATION

presented by

Barry James Trosin

has been accepted towards fulfillment
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VELOCITY-FIELD MEASUREMENTS OF AN AXISYMMETRIC SEPARATED
FLOW SUBJECTED TO AMPLITUDE-MODULATED EXCITATION
By

Barry James Trosin

A THESIS
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
MASTERS OF SCIENCE

Department of Mechanical Engineering

2006

ABSTRACT

VELOCITY-FIELD MEASUREMENTS OF AN AXISYMMETRIC SEPARATED
FLOW SUBJECTED TO AMPLITUDE-MODULATED EXCITATION

By

Barry James Trosin

Active ﬂow control was applied at the point of separation of an axisymmetric, backward-
facing-step ﬂow. The control was implemented by employing a Helmholtz resonator that
was externally driven by an amplitude—modulated, acoustic disturbance from a speaker
located upstream of the wind tunnel. The velocity ﬁeld of the separating/reattaching ﬂow
region downstream of the step was characterized using hotwire velocity measurements

with and without ﬂow control.

Conventional statistics of the data reveal that the separating/reattaching flow is affected
by the imposed forcing. Triple decomposition along with phase averaging was used to
distinguish periodic disturbances from random turbulence in the ﬂuctuating velocity
component. The outcome of this analysis showed that the forcing triggered large-scale,
organized structures that formed at regular intervals near the separation point. The
structures convect downstream and grow to a size comparable to the step height at a
location approximately half way to reattachment. A signiﬁcant outcome of the present
study is that it demonstrates that amplitude-modulated forcing of the separated ﬂow alters

the ﬂow in the same manner as the more conventional method of periodic excitation.

Copyright by
Barry James Trosin

2006

To my Mom, Dad, and Sister,

- Thank you so much.

iv

ACKNOWLEDGMENTS

There are many people that played a large role in getting me where I am today. I would
like to acknowledge my family, advisor, committee, colleagues, lab members, and
friends, without your help and support completing my degree would not have been

possible.

This work was partially supported by the National Science Foundation contract
#CTSOI 16907. I would also like to thank NASA and the Graduate Student Researchers

Program for their support.

I would like to thank Dr. Naguib for guiding me through graduate school. I don’t know if
I could have made it through without your wisdom and patience. I could not have asked

for a better advisor and friend, thank you.

I would like to thank Dr. Radcliffe for taking the time to be on my committee. Dr. Foss,
thank you for sparking my interest in ﬂuid dynamics, for being on my committee and

being my faculty advisor when I studied in Germany.

The members of the Flow Physics and Control Laboratory have set the foundation of my
work and provided insight and help throughout my Masters. Chad, Tony, Laura, Ke, and
Brendan thank you for your willingness to help, the countless hours spent in the lab

together and fun we had along the way.

I have made many good friends throughout my life and at Michigan State that have

supported me and imparted their wisdom. Zack, you are a life long friend and will remain

that way no matter what happens. We have been through a lot; we have shared many
successes and failures, thank you for being such a great friend. Paul, you have been a
great friend and have always been there for me. I will never forget all the time we spent
on the water, the ﬁshing was great, thanks kid. Drew, you and your family have taken
me in and given me a second family, even if that meant being put to work sometimes,
your friendship has meant a lot to me. Tina, somehow you are always happy, you will
always be able to put a smile on my face, thanks for everything. Chad you were a great
roommate and friend, thanks for helping me through all the tough classes and hard times

and tailgates.

My family has always been a huge support. Aunt Colleen, Uncle Chris, Nora and Erin,
thank you for all the support you have given over the years, all the letters you have
written and phone calls made, you have been more of a help than you could ever know.
Aunt Deb, Uncle Tim, and Jenny, you have always looked out for me and believed in me,
your support helped me get through my masters and get me to where I am today. Aunt
Denise and Uncle Bill, your unparalleled knowledge in ﬂuid dynamics has always
astonished me, it was a great help with my degree. But seriously all the jokes help make
the long hours in the lab pass just a bit quicker, thank you. Grandma Trosin, your support
has been constant and welcome, thank you for always telling me to follow my dreams.
Grandma and Grandpa Gimpel, your support has been nothing short of amazing, I will
forever remember getting a letter a week keeping me up to date with family business and
how the petanque tournaments are going, I have saved everyone of them. Thank you for

being a compassionate ear for me to talk to even when you are so far away.

vi

Christa, you have been a great sister, I have always been able to count on your help,
fashion advice, and moral support. Even through you have been across the country while
I have worked on this degree you were always willing to talk to me and lend a

sympathetic ear when needed. Thank you for being an amazing sister.

Mom and Dad, your love support and guidance has made everything I have accomplished
possible. I will be forever grateful for giving me the opportunity to succeed. Your never
ending love and support kept me going when times got hard. You have made it possible

for my dreams to come true. Thank you.

vii

TABLE OF CONTENTS

List of Tables ...................................................................................................................... x
List of Figures .................................................................................................................... xi
Nomenclature ................................................................................................................... xiv
1 Introduction ................................................................................................................. l
1.1 Background ......................................................................................................... l

l .2 Motivation ........................................................................................................... 5

1 .3 Objectives ............................................................................................................ 7

1 .4 References ........................................................................................................... 8

2 Experimental Setup ................................................................................................... 10
2.] Wind Tunnel and Facility ................................................................................. 10
2.2 Axisymmetric Backward Facing Step Model ................................................... 12
2.2.1 Model Dimensions .................................................................................... 12
2.2.2 Measurement Region ................................................................................ 15
2.2.3 Resonator .................................................................................................. 1 6
2.2.4 Forcing System ......................................................................................... 18

2.3 Data Acquisition Systems ................................................................................. 23
2.3.1 Mean Static Pressure ................................................................................. 24
2.3.2 Pitot Tube .................................................................................................. 24
2.3.3 Temperature .............................................................................................. 25
2.3.4 Hotwire Velocity ....................................................................................... 25
2.3.5 Positioning Camera System ...................................................................... 28

2.4 Experimental Procedure .................................................................................... 28
2.4.1 Testing Parameters .................................................................................... 29

viii

2.4.2 F orcing-Signal Parameters ........................................................................ 29

2.4.3 Mean-Pressure Proﬁles ............................................................................. 35
2.4.4 Velocity Acquisition Procedure ................................................................ 37

2.5 References ......................................................................................................... 42

3 Conventional-statistics Results and Discussion ........................................................ 43
3.1 Mean Velocity ................................................................................................... 43
3.2 Fluctuating Velocity .......................................................................................... 46
3.3 Velocity Probability Density Function ............................................................. 56
3.4 References ......................................................................................................... 59

4 Phase-average Results and Discussion ..................................................................... 60
4.1 Phase averaging ................................................................................................. 60
4.2 Triple decomposition ........................................................................................ 71
4.3 Reference .......................................................................................................... 85

5 Conclusions and Recommendations for Future Work .............................................. 86
5.1 Conclusions ....................................................................................................... 86
5.2 Recommendations for Future Work .................................................................. 87
5.3 References ......................................................................................................... 89
A. Appendix ................................................................................................................... 90

ix

LIST OF TABLES

Table 2.1 Function generator settings for the forcing signal ............................................ 32

LIST OF FIGURES

Figure 1.1 A Schematic drawing illustrating the geometry and some ﬂow features of the

separated ﬂow over a backward-facing step ............................................................... 2
Figure 2.1 Schematic of wind tunnel (demission in meters) ............................................. 10

Figure 2.2 Schematic of the axisymmetric backward-facing-step model (dimensions in m)
................................................................................................................................... 13

Figure 2.3 Close up of the measurement region ............................................................... 14

Figure 2.4 Cross section of the measurement region downstream of the back step (ﬂow is

out of the paper) ........................................................................................................ 15

Figure 2.5. Cross section drawing of the resonator and step region (note drawing is not to

scale; dimensions in mm) .......................................................................................... 17
Figure 2.6 Geometry of the resonator’s outer shell supports (dimensions in mm) ........... 18

Figure 2.7 Location of the speaker used to drive the resonator relative to the wind tunnel

(dimensions in meters) .............................................................................................. 18
Figure 2.8 Example of an amplitude-modulated sine wave with MI = 2/3 ...................... 22
Figure 2.9 Picture of Hotwire Traverse System ................................................................ 26

Figure 2.10 Sample image of the hotwire above model wall during positioning procedure

................................................................................................................................... 28
Figure 2.11 Location of hotwire for carrier frequency determination .............................. 30
Figure 2.12 Amplitude modulated resonator’s jet velocity ............................................... 32
Figure 2.13 Hotwire trace of the ﬂow velocity above the resonator’s slit ........................ 33

Figure 2.14 F orced- and unforced-ﬂow mean-pressure proﬁles downstream of the step 36
Figure 2.15 Sample Hotwire calibration curves ................................................................ 38

Figure 2.16 Forward ﬂow probability from PIV measurements of Hudy (color map); and

hotwire measurement locations for the present investigation (black dots) ............... 39

xi

Figure 2.17 Block diagram of experimental setup ............................................................ 41

Figure 3.1 Normalized mean-velocity plots ...................................................................... 44
Figure 3.2 Normalized mean-velocity proﬁles at selected x/h locations .......................... 46
Figure 3.3 Normalized turbulent-velocity rrns contour plots ............................................ 47
Figure 3.4 Normalized turbulent-velocity rms proﬁles at selected x/h locations ............. 49
Figure 3.5 Peak q’rms location at different streamwise positions ...................................... 50
Figure 3.6 Streamwise evolution of the maximum q'nns values ........................................ 51

Figure 3.7 Power spectral density of q' for the unforced ﬂow at selected x/h locations... 52
Figure 3.8 Power spectral density of q' for the forced ﬂow at selected x/h locations ...... 53

Figure 3.9 Power spectral density of q' for the unforced ﬂow at Selected x/h Locations

(broken line shows sub-harmonic of the forcing frequency) .................................... 55

Figure 3.10 Power spectral density for the forced ﬂow at selected x/h locations (broken

line shows sub-harmonic of the forcing frequency) .................................................. 56

Figure 3.11 Velocity properties at y/h = 0.6833 and x/h = 1.5: (a) sample velocity trace

for unforced case, (b) sample velocity trace for forced case, (c) PDF’s ................... 57

Figure 4.1 Sample time series illustrating different forcing-cycle phases for phase

averaging: (a) forcing signal; (b) ﬂow velocity ........................................................ 61
Figure 4.2 Phase-average-velocity contour plots at selected phases of the forcing cycle 64

Figure 4.3 Close up of the phase-average-velocity contour plots in the vicinity of the

separation point ......................................................................................................... 66
Figure 4.4 Geometry of Greenblatt’s hump model and PIV measurement locations ....... 67

Figure 4.5 Phase-averaged <q2> contours: comparison of present results with those

calculated from Greenblatt’s data at selected phases .............................................. 69

Figure 4.6 Comparison of <U|U|>and <q2> contours at (p = 0° calculated from

Greenblatt’s data ....................................................................................................... 71

xii

Figure 4.7 Contours of the phase-averaged vorticity, and energy of the streamwise
turbulent velocity component, computed from Greenblatt’s data for selected phases

of the forcing cycle ................................................................................................... 74
Figure 4.8 <q2> contours for selected phases of the forcing cycle ................................... 77

Figure 4.9 Streamwise location of the peak of <q2> at different phases of the forcing
cycle. Straight lines represent least-squares ﬁts used to calculate the convection

velocity ...................................................................................................................... 79
Figure 4.10 a contour plots for selected phases of the forcing cycle ................................ 82

Figure 4.11 rms of the turbulent (top) and the organized (bottom) velocity components.

Broken white line identiﬁes the center of the shear layer based on peak q'rms ......... 84

(Images in this thesis are presented in color.)

xiii

Symbol

F(t)

NOMENCLATURE

Deﬁnition

empirical hotwire calibration constant

amplitude setting of function generator one

amplitude setting of function generator two

amplitude of amplitude-modulated signal

peak amplitude of modulation envelope

empirical hotwire calibration constant

chord length

oscillatory-control momentum-based forcing coefﬁcient

mean-pressure coefﬁcient

slot width of resonator

hotwire voltage

frequency

reduced excitation frequency

amplitude modulated signal

xiv

MI

“5|

£1

.0)

Rec

carrier frequency

modulation frequency

step height

amplitude of modulation frequency

number of forcing cycles in a time series

modulation index

total number of data points in a time series

time shift or delay

mean reference pressure

mean surface pressure

velocity magnitude

time-averaged velocity magnitude

ﬂuctuating component of velocity magnitude

organized-motion velocity magnitude

turbulent-motion velocity magnitude

Reynolds number based on chord length

XV

Reh

Ret

III!

C)

uj,rms

Reynolds number based on step height

Reynolds number based on model height

I'OOt mean square

time

time variable for phase averaging

freestream velocity

streamwise velocity component

absolute value of streamwise velocity component

turbulent-motion streamwise velocity component

rrns jet velocity

wall-normal velocity component

streamwise coordinate

mean reattachment length

wall-normal coordinate

density of air

phase of forcing signal

xvi

(pq' q! power spectrum of q'

1: period of forcing signal
a) spanwise vorticity
( ) denotes phase averaging

xvii

1 Introduction

1.1 Background

Within the ﬁeld of ﬂuid dynamics, there are many areas that are still not completely
understood, one such area is separated ﬂows. Separated ﬂows naturally occur in many
situations: over airfoils at high angle of attack, in turbines, in dump combustors, and in
many other applications. Therefore, there have been many studies of the physics of
separated ﬂows. Some have investigated the unsteady wall-pressure signature generated
by the turbulent ﬂow structures; others have utilized velocity ﬁeld measurements to gain
an understanding of the ﬂow features. A simpliﬁed (canonical) version of a separated
ﬂow is that over a backward-facing step; a generic sketch of the geometry and some ﬂow
features can be seen in Figure 1.1. For this geometry, the ﬂow separates at the step and
creates a shear layer that reattaches at some location farther downstream (on average),
denoted as x,. A mean separation streamline can be drawn from the point of separation at
the edge of the step to the point of reattachment at x,. Beneath the separation streamline,

there is a primary and secondary recirculation zones (see Figure 1.1).

Um Secondary recirculation

—-> region

 

Primary recirculation
region

    
 
 

 

Separation
streamline

  

 

Figure 1.1 A Schematic drawing illustrating the geometry and some ﬂow features of the separated
flow over a backward-facing step

Over the years, a large number of researchers have tried to control the size of the
separation region or eliminate it all together when possible. Many methods have been
tried to control the separation region, the most prominent of which are: steady suction,
steady blowing, and unsteady excitation. Steady suction is a technique that is employed
through either a slot at the point of separation or through a series of slots and/or holes in
the separation region. Through these oriﬁces, ﬂuid is removed from the low-speed
region just above the surface to deﬂect higher-speed ﬂuid from farther above closer to the
surface. The mass removal was believed to be the mechanism that causes the size of the
separation bubble to decrease. This idea was ﬁrst advanced by Prandtl (As cited by
Greenblatt and Wygnanski') and later tested by many individuals, which can be seen
from the extensive research presented in the text book edited by Lachmannz, and is still
being investigated today. These studies have resulted in the realization that momentum,
rather than mass, transfer as suggested earlier, was the mechanism that caused the ﬂow
control. This led to separation control via steady blowing whereby momentum is added
to the low-speed ﬂuid near the surface by steady blowing through a slot at the point of

separation. This idea was vastly studied and was even put into production on a few

aircrafts; however, the cost and weight of the necessary plumbing and compressors to

implement the technique greatly limited its effectiveness.

The importance of unsteady (also termed periodic, or oscillatory) excitation was ﬁrst
realized by Schubauer and Skramstad3 who introduced periodic excitation to trigger a
known instability in a laminar boundary layer. This instability was theorized as a means
to control transition from laminar to turbulent regimes. Since the early work of
Schubauer and Skramstad, there has been extensive work on periodic excitation of
different types of ﬂows. Of particular interest to the present study are investigations
relating to the control of separated ﬂows. In this area, there has been leading work by
Wygnanski and his former students/co-workers (e.g, see references listed in Greenblatt
and Wygnanski') as well as other researchers. However, here only few studies are

described to highlight certain essential features of periodic control of separated ﬂows.

It was thought that periodic excitation would not be effective if applied to turbulent ﬂows
because of the inherent randomness of turbulence. However, experiments by Winant and
Browand4 showed the existence of large coherent structures in a turbulent mixing layer.
By using harmonic excitation, Katz et. al.5 was able to trigger the development of these
large structures and was ultimately successful in attaching a turbulent mixing layer to a

deﬂected ﬂap.

Some recent investigations employed “synthetic jets” as the means of unsteady
excitation. The jets are produced by internal actuators that are embedded in a cavity
behind a slot that is located near or at the point of separation. Periodic oscillation of

these actuators (typically a piezoelectric membrane, speaker, or compression driver)

produces a strong, unsteady jet through the slot at the oscillation frequency. Sigurdson6
conducted an investigation that implemented periodic forcing at the point of separation
over a ﬂat-faced cylinder that was aligned with its axis parallel to the freestream
direction. Sigurdson surmised that the mechanism causing the ﬂow control was the
generation of large-scale vortex structures that produced a higher rate of entrainment and
enhanced momentum transfer towards the separated ﬂow region. This idea of the
periodic forcing producing regular, downstream-convecting vortical structures is widely

accepted at present.

Greenblatt et. al.7 conducted an investigation of the ﬂow over a wall-mounted “hump”
that simulated a deﬂected ﬂap portion of an airfoil, and employed periodic forcing.
Through particle image velocimetry (PIV) measurements they were able to verify the
existence of the large, downstream-convecting vortical structures and determine an

optimal forcing frequency for the geometry.

Amitay and Glezer8 and Glezer et. (11.9 performed research on a stalled, symmetric airfoil
that employed periodic forcing at the leading edge. They found that for the traditional
selection of control frequency, what they termed “order 1” forcing frequency (F+ z 0(1);
where F is deﬁned below), that a wake mode instability is triggered in the shear layer

which generates the large-scale vortex shedding seen in previous studies, where
. fl
F = 1.1
U 00 ( )

f is the forcing frequency, L is a characteristic length of the separation region and U... is

the freestream velocity. However, it was found that if the forcing frequency is increased

by an order of magnitude, F 2 0(10), then the wake instability is no longer triggered.
Surprisingly, the ﬂow stayed fully attached to the surface of the airfoil under the high-
frequency forcing. The exact ﬂow mechanism that caused the ﬂow to remain attached in
this case is still unknown. Interestingly, Amitay and Glezer8 and Glezer et. al.9 suggest
that for the high-frequency control, the control is insensitive to the particular choice of

forcing frequency, as long as at it is above a certain threshold.

An alternative method of forcing was presented by Wiltse and Glezerl0 who used
piezoelectric actuators at the downstream end of a square tube to excite the shear layer of
an air jet issuing from the tube. The piezoelectric actuators were driven with an
amplitude-modulated signal rather than the traditional periodic signal used in most ﬂow-
control investigations. Using this new actuation method they were able to modify the
shear ﬂow. Wiltse and Glezer10 attributed their success to a ﬂow non-linearity that
generates line vortices that affect the ﬂow. The approach of Wiltse and Glezer10 requires
high-level of forcing for the ﬂow-nonlinearity to “kick in” and demodulate the excitation
disturbance. As will become clear, this is different than the approach used here, where
non-linearity of the excitation device, rather than the ﬂow, renders the approach feasible.

In the present case it is possible to excite the ﬂow with low-level disturbance.

1.2 Motivation

The current study follows a sequence of investigations performed on an axisymmetric,
backward-facing-step geometry at Michigan State University in the Flow Physics and
Control laboratory. Lill developed a new, oscillating hotwire technique for measuring

the magnitude and direction of the streamwise, wall-shear stress. Li employed this

technique to obtain single- and two-point wall-shear measurements beneath the
axisymmetric separation bubble. Hudy12 performed simultaneous wall-pressure and PIV
measurements on the model under natural conditions. Hudy found that vortex structures
with a scale of the order of the step height were intermittently generated by the roll-up of
the separating shear layer at a location approximately half way to the mean reattachment
point, then accelerated to a terminal convection velocity farther downstream. This
offered a different view than the classical one of the vortex structures growing in size as
they convect downstream. Later, experiments were conduced by Aditjandral3 who
developed a forcing system to produce an unsteady jet at the point of separation to
control the ﬂow. The jet was created by externally driving a Helmholtz resonator using a
speaker upstream of the wind tunnel that is operating at the resonator’s resonant
frequency. To excite the ﬂow at the desired frequency, which was much lower then the
device’s resonance frequency, the resonator was driven by an amplitude-modulated
signal to generate the lower-frequency disturbance. Details of this forcing system, along
with forcing parameters are described in chapter 2. Using the amplitude-modulated
forcing, Aditjandra was able to successfully reduce the size of the separation region.
Aditjandra also investigated the space-time character of the wall-pressure signature using
a 15-microphone array. However, Aditjandra’s study did not provide information
concerning the velocity ﬁeld. Therefore, it is not clear whether the amplitude-modulated
forcing produces the same changes in the ﬂow ﬁeld as conventional, periodic forcing, or

a totally different ﬂow-control mechanism is at play.

1.3 Objectives

Characterize the ﬂow ﬁeld downstream of the point of separation on the
axisymmetric, backward-facing-step model used by Li, Hudy and Aditjandra,
using a single hotwire. The characterization is to be done for forced and
unforced-ﬂow conditions, where the former is achieved utilizing the amplitude-

modulated forcing approach developed by Aditjandra.

Compare the velocity ﬁeld under forced and unforced conditions, using
conventional and phase-averaged statistics to investigate the mechanism leading

to ﬂow control.

Compare amplitude-modulated excitation to traditional periodic forcing.

1.4 References

 

l Greenblatt, D., Wygnanski, I., “The Control of Flow Separation by Periodic Excitation”
Progress in Aerospace, Vol. 36, 2000, pp. 487-545.

2 Lachmann, G. V., “Boundary Layer Control. Its Principles and Applications” Vol. 1
New York Pergamon Press 196].

3 Schubauer, G. B., and Skramstad, H. K., “Laminar Boundary Layer Oscillations and
Transitions on a Flat Plate” NACA Report 909, 1948.

4 Winant, CD, and Browand, F. K., “Vortex Pairing: the Mechanism of Turbulent
Mixing-layer Growth at Moderate Reynolds Number” Journal of Fluid Mechanics, Vol.
63, 1974, pp. 237-255.

5 Katz, Y., Nishn', B., Wygnanski, 1., “The Delay of Turbulent Boundary Layer
Separation by Oscillatory Active Control” Physics of Fluids, Vol. 1, 1989, pp. 179-181.

6 Sigurdson, L. W., “The Structure and Control of a Turbulent Reattaching Flow”,
Journal of Fluid Mechanics. Vol. 298, 1999, pp. 139-165.

7 Greenblatt, D., Paschal, K., Yao, C., Harris, J ., “A Separation Control CFD Validation
Test Case Part 2. Zero Efﬂux Oscillatory Blowing”, AIAA-2005-0485 43rd AIAA
Aerospace Sciences Meeting and Exhibit, Reno, NV 2005.

8 Amitay M., Glezer, A., “Role of Actuation Frequency in Controlled Flow Reattachment
Over a Stalled Airfoil” AIAA Journal Vol. 40, No. 2. February 2002, pp. 209 — 216.

9 Glezer, A., Amitay, M., Honohan, A., “Aspects of Low- and High-frequency Actuation
for Aerodynamic Flow Control” AIAA Journal Vol. 43, No. 7. July 2005, pp. 1501 —
1511.

 

'0 Wiltse, J. M., and Glezer, A., “Manipulation of Free Shear Flows Using Piezoelectric

Actuators” Journal of Fluid Mechanics. Vol. 249, 1993, pp. 261-285.

H Li, Y. and Naguib, A.M., “High-Frequency Oscillating-Hot-Wire Sensor for near- Wall
Diagnostics in Separated Flows,” American Institute of Aeronautics and Astronautics

Aerospace Journal, Vol. 43, No. 3, 2005, pp. 520.

'2 Hudy, L. M., “Simultaneous Wall-Pressure and Velocity Measurements in the Flow
Field Downstream of an Axisymmetric Backward Facing Step”, PhD. Dissertation,
Michigan State University, 2005.

l3Aditjandra, A., “Amplitude-modulated Excitation of a Separated Flow Using an
Externally Driven Helmholtz Resonator” Masters Thesis, Michigan State University,
2006.

2 Experimental Setup

This chapter outlines the experimental setup and methods used in this investigation. Two
main techniques were used to characterize the ﬂow: single-hotwire velocity
measurements, and static wall-pressure measurements. A detailed description of the

setup, methods, and hardware is provided in the following sections.

2.1 Wind Tunnel and Facility

The experiment was conducted in the Flow Physics and Control Laboratory at Michigan
State University, in a low-speed, wind tunnel. The tunnel is an open-retum, low-
turbulence-intensity, suction-driven facility. It measures approximately 9 meters long
from end to end and its centerline is 1.35 meters above the ﬂoor. As seen in Figure 2.1,
the tunnel consists of 6 sections: inlet, contraction, test section, pre-diffuser, diffuser, and

fan sections.

Contraction Adjustable

. . . Diffuser Fan
cellrng Test Pre-drffuser
section

Flow T
I l I 1.346
|"-— 8096 1.889 1.005 1.829 *‘ﬁl-P 1.486 —.i J-

.\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\‘

       
 
  

 

Figure 2.1 Schematic of wind tunnel (demission in meters)

The inlet consists of a square section of aluminum honeycomb with each side measuring

1.549 meters. The honeycomb is followed by three layers of high-porosity screens that

10

reduce the turbulence intensity of the inlet air. Downstream of the screens, a contraction
section is attached. The contraction is constructed from a laminate of ﬁberglass-

reinforced, molded plastic and has an area contraction ratio of 6.25: 1.

Immediately downstream of the contraction is the test section that is constructed from
sealed plywood mounted in an aluminum frame. The test section is 1.83 meters long and
has a square, cross section at the inlet, with each side measuring 610 mm. Four, hinged,
acrylic windows, two on each side of the test section, allow access to the test model for
inserting and positioning test devices and instruments. Additionally, the test section has
an adjustable false ceiling that was set in order to establish a nominally zero-pressure-
gradient condition along most of the length of the test section. The ceiling has 16.5 mm-
wide slots running the length of the test section to allow introduction of instrumentation

into the ﬂow.

Adaptation of the test section’s ﬂow area to that of the driving fan is done through a
combination of a pre-ditfuser and diffuser. The pre-diffuser, which follows the test
section, measures 1.005 m long and has a ﬂoor that diverges from the centerline by 6°. A
movable ceiling in the pre-diffuser is adjusted to match the ceiling position at the end of
the test section while providing smooth transition to the diffuser at the downstream end.
The connection between the pre-diffuser and diffuser is not rigid. Instead the two units
are aligned and separated by a layer of foam rubber; this is done in an attempt to
eliminate the inﬂuence of any vibrations that are produced by the fan and motor on the
test section. The diffuser is 1.83 meters long and has a divergence angle of 59°. It

serves to connect the pre-diffuser to the fan section, and recover the ﬂow pressure. An

11

adaptor between the diffuser and fan is used to transition from the square, cross-sectional
area of the diffuser to the circular, cross section of the fan shroud. Finally, the fan section
houses the motor and fan that draws air through the tunnel. The axial-ﬂow fan is driven

by a GE 15 HP DC motor that is controlled via an adjustable speed controller.

2.2 Axisymmetric Backward Facing Step Model

This investigation is conduced on an existing axisymmetric, backward-facing-step model.
The model was designed, and the associated ﬂow ﬁeld around it was characterized by
Hudyl and Liz. For excitation of the separated ﬂow, the model was equipped with an
extemally-driven, Helmholtz resonator located at the point of separation that was
developed and characterized by Aditjandra3. In the following, a brief description of the
model and resonator is provided. For more detailed information the reader is referred to

the aforementioned studies.

2.2.1 Model Dimensions

A schematic of the model can be seen in Figure 2.2. As labeled in the ﬁgure, the
model is composed of several sections; which include the nose, 2D section, rotator

section, Helmholtz resonator, step, support, and tail.

12

Helmholtz

Flow
[::> Sand paper Rotator resonator Steel support
R 0.0635 F0 0124 [*— o 0.100

jlfi—————$-~j— :— i;-

—#- 0.3505 *— 0.7493 —'- 0.5438 ‘40. 8604”.—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~I 8.3885 *-

Figure 2.2 Schematic of the axisymmetric backward-facing-step model (dimensions in m)

The nose of the model is a hemisphere with a diameter of 124 mm. Following the nose is
a segment created from a cylinder with an outer diameter of 124 m that is 350.5 mm
long. This section is intended for the initial development of a “two-dimensional” (i.e.,
azimuthally-uniform) boundary layer and is therefore referred to as the 2D section.
Wrapped around the upstream end of the 2D section are three strips of 120-grit sandpaper
that help to accelerate the development of the boundary layer towards a turbulent state.
Downstream of the 2D section, a 749 mm-long cylinder of the same diameter as the 2D
section composes the rotator section. This cylinder is capable of rotation about the
centerline of the model in order to produce a three-dimensional boundary layer at

separation; however, in the present experiments, this capability was not utilized.

Just downstream of the rotator section, there is a hollow cavity that acts as an externally
driven, Helmholtz resonator. This resonator, which is described further in 2.2.3, is the
mechanism that was used to force the ﬂow at the point of separation. At the downstream

end of the resonator, the back step is created by an abrupt decrease in the outer diameter

13

of the resonator to 100 mm, producing a step of 12.2 mm. The region downstream of the
step is the separation/reattachment ﬂow region, which is the main focus of the present
investigation. Beneath this ﬂow region, the top surface of the model is ﬁtted with a
removable insert containing 32 pressure taps and 32 microphones, side by side, which
may be used for mean- and unsteady-pressure data acquisition respectively which can be

clearly seen in Figure 2.3.

Slit o enin
p g Hotwire probe

V .553?

 

  
  
  

 

 

    
     

, Helmholtz l

t
resenator

L
, _,‘,— -l‘ -'— x- — ,— _ "a .-— _
- . ..v . ,‘ If .. . . . . . l, 1- s ,. . .‘ ,v . . _, '.v ',

 

 

 

H 32 static pressure __ Reattachment
taps in surface point (Xr)

Figure 2.3 Close up of the measurement region

Farther downstream of the reattachment region, resides the model support module;
which, with the assistance of four 1mm-diameter piano wires at the upstream end of the
model, holds the model ﬁrmly in place and allows for adjustment to align the model
parallel to the freestream. The last model component is the tail, which is a 260 mm-long
cone that is used to reduce the strength of any separation at the end of the model. For

more detailed speciﬁcations of the model construction, see Hudy'.

14

2.2.2 Measurement Region

The data-acquisition region downstream of the step contains four primary measurement
locations in a plane perpendicular to the mean ﬂow that are denoted as north, east, south,

and west, as seen in Figure 2.4

North is the main
measurement region North

East

 

Figure 2.4 Cross section of the measurement region downstream of the back step (flow is out of the
Paper)

The majority of the measurements were conducted on top of the model (north side)
because at this location the model contains a wall-sensor insert (or I-plate) with 32 static
pressure taps that were used to obtain details of the mean-pressure distribution beneath
the separation bubble under forced and unforced conditions. Furthermore, the studies of
Hudyl and Aditjandra3 were both conducted at this location. To stay consistent with
these studies, particularly the latter, which is directly related to this one, the north

position was selected for the present measurements. The east, south, and west locations

15

contain additional wall inserts ﬁtted with static-pressure taps (8 at each location) that are

used for model alignment.

The static pressure taps are offset 1mm from the center of the I-plate and are spaced at
4.76 mm center to center. It is important to note that the streamwise location of the taps
was selected for earlier studies not employing a ﬂow excitation device. Subsequent
assembly of the resonator on the model resulted in covering the ﬁve upstream most
pressure taps. Thus, the ﬁrst usable pressure tap immediately downstream of the step is
the 6th tap, which is located 11.7 mm downstream of the separation point. This reduced
the number of taps used in the acquisition to 18. The resulting streamwise range for the
mean-pressure data extended from 0.96 to 7.99 step heights with inter-sensor spacing of

0.39 step heights.

2.2.3 Resonator

For this investigation, the unsteady disturbance that “controls” the ﬂow was generated by
an externally driven, Helmholtz resonator located at the point of separation. The
resonator was composed of three pieces: the outer shell, the shell supports, and the cover.

A cross-section drawing of the resonator and step region can be seen in Figure 2.5

16

Outer shell

 
  

  

\\\

.‘

     
  

 

////,.

 

 
 
 

 

 

Figure 2.5. Cross section drawing of the resonator and step region (note drawing is not to scale;
dimensions in mm)

The outer shell is made of a ring of acrylic that has a 124 mm outer diameter; a 117.5
mm, inner diameter; and is 68.8 mm long. The outer shell is supported by four small
brackets (see Figure 2.6). These supports are necessary to maintain proper positioning of
the outer shell. The cover is a machined ring of acrylic that is placed just downstream of
the outer shell to create a 0.5 mm gap forming the neck, or slit, of the Helmholtz
resonator. The end cap has a tapered tip that allows the disturbance to be generated as
close to the point of separation as possible while still retaining structural integrity of the
end cap. When assembled, the resonator has an internal volume of 202.3 cm3 and the

resonant frequency was determined by Aditjandra to be 657 Hz.

17

Resonator shell

 

 

 

 

 

Axisymmetric model

Figure 2.6 Geometry of the resonator’s outer shell supports (dimensions in mm)

2.2.4 Forcing System

The resonator is externally driven by a speaker that is located upstream of the wind
tunnel, as seen in Figure 2.7. The speaker used was a 0.385 m-diameter, 450-Watts
Eminence LLC subwoofer (model Kappa 15) that was located on the centerline of the

tunnel, approximately 2.3 meters upstream of the entrance of the wind tunnel.

   

Contraction
Subwoofer intake

 

 

\\\\\\\\\\\\\\\\\\\\\ \ \\\\‘

Figure 2.7 Location of the speaker used to drive the resonator relative to the wind tunnel (dimensions
in meters)

The speaker was powered by a two-channel, Haﬂer (Transana P 1000), power ampliﬁer.
The ampliﬁer was used in strapped single-channel mode to boost the output power from
110 to 220 watts. The input signal to the ampliﬁer was generated from two Hewlett

Packard (model 33120A) function generators (model 33120A).

As known from the literature (e.g., Greenblatt and Wygnanski4), a separated ﬂow
responds best to periodic excitation at an optimum non-dimensional, forcing frequency
(normalized with the freestream velocity and a length-scale characteristic of the
streamwise size of the separation bubble) on the order of l; i.e., 0(1). Therefore, for
effective forcing of the ﬂow, the resonator’s should have a non-dimensional, resonant
frequency of 0(1) as well. However, one issue that arises when forcing the ﬂow directly
at the optimum forcing frequency is that the forcing system would produce acoustic noise
(originating from the speaker in the current study) at the same frequency as that of the
forced ﬂow structures. This acoustic noise would be difﬁcult to separate from the wall-
pressure ﬂuctuations produced by the forced ﬂow structures when using surface-mounted
microphones to investigate the wall-pressure characteristics beneath the forced ﬂow.
Although such wall-pressure measurements are not the concern of this study, they are
part of the overall research goal of studying the axisymmetric, back-step ﬂow under
natural and force ﬂow conditions, which has been studied by Liz, Hudy], and Aditjandra3.
In fact, the last study developed the driven-resonator device with the speciﬁc objective of
producing periodic excitation of the separation bubble without contaminating wall-

pressure sensors by sound resulting from the actuation device.

19

To eliminate the aforementioned problem as well as to generate a forcing effect at
frequencies substantially below the resonant frequency of the resonator, amplitude-
modulated excitation was employed through multiplication of two sine waves as given in

equation (2.1).

F (t) 2 Am sin(274fmt)sin(27gfct) (2,1)

where F(t) is the amplitude-modulated signal, Am is the amplitude of the signal, fm is the
modulation (low) frequency, and fc is the carrier (high) frequency. When forcing the
ﬂow, fc was set equal to the resonant frequency of the resonator and fm was set to half the
frequency at which the ﬂow is to be excited. This method proved effective in exciting
the ﬂow at 2fm because of the non-linearity of the Helmholtz resonator when driven by
high-intensity sound. For further explanation of the coupling mechanism the reader is

referred to Aditjandra3 .

Although, it is possible to generate an amplitude-modulated forcing signal from a single
function generator, this proved to be problematic in the present work. To clarify, it is
helpful to recall that the amplitude-modulated signal given by equation (2.1) consists of
the sum of two equal-amplitude sinusoidal signals with frequencies of fc-fm and fc+fm.
Thus, when using a single function generator to drive the speaker, one feeds two, equal-
amplitude, acoustic sine waves at these two frequencies into the wind tunnel. However,
due to acoustic resonance of the wind tunnel, and acoustic wave reﬂections produced by
components downstream of the test section, (i.e., fan, motor, walls etc.), standing wave
patterns are established along the test section. The relative strength of these patterns is

generally a function of frequency and they cause the sound amplitude of each of the two

20

waves to change at different streamwise locations within the tunnel. Therefore, at the
location where the resonator’s “neck” exists, the sound amplitude at fc-fm and fc+fm was
found to become different, and the modulation quality was generally poor. More
speciﬁcally, referring to Figure 2.8, the modulation quality may be quantiﬁed using a

“modulation index” (MI), deﬁned as

M1 = — (2.2)

me
where Ame is the peak of the modulation envelope and m is as deﬁned in Figure 2.8. To
maximize the amplitude of the disturbance induced in the ﬂow at 2fm, an M1 of l is
desired. With the use of a single function generator it was not possible to guarantee that

this is the case for all choices of fm, as describe above.

21

 

[ Envelope of modulation

3L\\/ ///’ ‘\\\ T ///

 

 

 

 

 

3
N

 

 

 

 

 

 

Amplitude
O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/
/ \\ // \\\

 

 

 

 

 

3 774' 5 H 6 7 8
Time(ms)

 

Figure 2.8 Example of an amplitude-modulated sine wave with MI = 2/3
To counteract the poor modulation effects, the amplitude modulation signal was
generated utilizing two function generators. In particular, one of the function generators
was used to provide a sine wave at frequency of fc+fm, while the other generator produced

a second wave at frequency of fc-fm. This allowed independent control of the amplitude

of each wave, to produce a signal of the form
F(t) = A1 C05(27r(f;. — fm ))+ A2 COS(27t(f;. + fm )t) (23)

A1 and A2 were then adjusted independently to produce an acoustic signal with M1 = l at

the neck of the resonator. The procedure to reach this condition is outlined later in 2.4.2

22

2.3 Data Acquisition Systems

For this investigation, different types of information are recorded. These are mean static
pressure on the surface of the model, freestream velocity, air temperature, ﬂow velocity
downstream of the step, speaker forcing signal, hotwire position, and images for probe
positioning. In order to acquire this information, two independent data acquisition
systems controlled by a number of custom LabView software programs were utilized.
The primary system was an analog-to-digital (A/D) converter employed for acquisition of
the velocity, pressure, temperature, and forcing signal data. A PC-based National
Instrument A/D board (model NI 6024 E) with 16 single-ended, analog-input channels
and a maximum sampling rate of 200,000 Hz at 12 bit resolution was used to capture
these ﬁve signals. This board has an adjustable input-voltage range for each channel; by
using the smallest possible range that still captures the entire signal, the voltage
resolution for each signal can be maximized. The available voltage ranges for the board
are: 110 V, 15 V, $0.5 V, and $20.05 V that correspond to resolutions of 4880 uV/div,
2440 uV/div, 244 uV/div, and 24 uV/div respectively. Due to the channels being
sampled sequentially there is an inter-channel time delay of 5 us. This time delay, when

accumulated over all ﬁve channels, is equal to 0.09% of the period of one forcing cycle.

The second system was used for acquiring images for hotwire positioning. To this end,
an NI-IMAQ PC1 -1411 single-channel, image-acquisition board (frame grabber) was
used to capture the output of a standard-video CCD camera that is described later in
2.3.5. The IMAQ card is capable of acquiring both black and white and color RS-170,
CCIR, NTSC, and PAL standard video images; RS-170 mode is utilized in this

investigation.

23

2.3.1 Mean Static Pressure

Mean static-pressure data were sampled in the region downstream of the step via static-
pressure taps embedded in the surface of the model’s I-plate, as described previously.
These pressure taps are connected to a 48-p0rt Scanivalve Corporation (48D9-1/2)
pressure scanner using long urethane tubing. The scanner was driven by a rotary solenoid
(48D9M-1/2), which was controlled by a homemade circuit. The latter is designed to
step the scanner from one port to the next either manually by depressing a button, or
through a connection to one of two digital to analog channels of the NI 6024 E board

described above.

The output of the Scanivalve was connected to the negative port of a Setra model 239
pressure transducer with a range of 0 -125 Pa and a sensitivity of 0.04 V/Pa. The positive
port of the Setra was connected to the static-pressure port of a pitot tube placed a short
distance upstream of the step to provide a reference pressure for the measurements. The
static pressure taps at which data were acquired covered a streamwise distance extending
from x/h = 0.96 to x/h = 7.99 in increments of 0.39 step heights. The output of the Setra
transducer was connected to the data acquisition system with the input range set to 3:

0.5V.

2.3.2 Pitot Tube

The Pitot tube in this experiment has two purposes: to measure the freestream velocity
and to provide a reference, freestream, static pressure for the surface mean-pressure
measurements. An 8 mm-diameter, pitot tube was placed in the freestream through a slot

in the ceiling of the test section. The tube was located 0.55 meters upstream of the step

24

and 63.5 mm below the ceiling of the test section. With a ceiling’s boundary layer
thickness of approximately 38 mm at this location, the tube was in the freestream. The
total and static pressure ports of the pitot tube were connected to opposite ports of a 0-
ltorr Baratron (model 223 BD) pressure transducer using urethane tubing. The transducer
outputs a 0-1V signal that was connected to the data acquisition system with the input

range set to d: 0.5V.

2.3 .3 Temperature

Temperature data were needed to calculate the density of air for pitot-tube velocity
measurements, and were also employed for hotwire-velocity-measurement correction.
An Omega (DP-25-TH) thermistor was used to measure the temperature of the freestream
ﬂuid downstream of the model. The thermistor used has an analog output signal with a
sensitivity of 0.1V per °C and a range of 0-50 °C. The output of the thermistor was

connected to the data acquisition system with the input range set to i 5V.

2.3 .4 Hotwire Velocity

A single, hotwire probe was used to measure the velocity in the investigated ﬂow. The
single wire can measure the velocity magnitude, but it is incapable of measuring the
velocity direction. Therefore, it cannot resolve the measurement into different
components. In comparison, an x-wire probe may be used to obtain two components of
the velocity. However, the x-wire could introduce spatial averaging errors that are
particularly signiﬁcant for measurements immediately downstream of the step where the
shear layer is very thin. Therefore, for this ﬁrst study of the velocity ﬁeld of the forced

ﬂow it was decided not to employ an x probe.

25

The hotwire used in this investigation was constructed from 3.75 tum-diameter tungsten
wire with 0.97 mm sensing length, yielding a cold resistance of 6.4 ohms. The hotwire
was controlled with a TSI, Flowpoint, constant temperature anemometer (CTA) with the
overheat ratio set to 1.7. The hotwire was attached to a dual-axis traversing mechanism

as seen in Figure 2.9.

  
 
  

Stepper Motor

Horizontal Traverse

_"‘r‘unnel ceiling

Figure 2.9 Picture of Hotwire Traverse System

The vertical traversing unit was a 15" Velmex A25 series unislide screw drive traversing
unit with a pitch of 40 turns per inch of travel. It is driven by a TMG Model 56183-01
hybrid stepper motor that has an angular resolution of 800 steps per revolution, which
provides 0.823 um of vertical motion per step when calibrated. The stepper motor is
computer controlled using a custom-developed LabView program that controls the

stepper motor’s power/controller box. Orthogonally mounted to the vertical traverse

26

carriage is a 6" Velmex A15 series unislide screw drive traversing unit to allow
streamwise translation of the hotwire probe. The horizontal traversing unit has a lead
screw with 40-tums-per-inch pitch and is turned manually using a knob that is graduated
at increments of 0.01mm. The traversing accuracy of the unit is speciﬁed by the

manufacturer to be within 0.033 mm per 20 cm of travel.

The hotwire is mounted to the end of a long of 6 mm by 12 mm steel support rod that is
connected to the horizontal traversing unit’s carriage via an aluminum support bar (see
Figure 2.9) and fed through the slot in the ceiling of the test section. The steel support
rod is covered by an aluminum airfoil tubing to reduce drag. The entire traversing
assembly is mounted on a large aluminum plate positioned on top of the test section and

is supported by vibration isolation material.

For this investigation the constant temperature anemometer output falls in the range of l-
2 Volts. To capture the hotwire signal, an A/D input range of :t 5V was used. However,
to optimize the digitization resolution of the ﬂuctuating component of the signal, the
hotwire output was also routed through a Larson-Davis preampliﬁer/power supply
(model 2200c) that functioned as a high-pass ﬁlter with a cut off frequency of 1.6 Hz and
20db (i.e., factor of 10) gain. This generated an ampliﬁed mean-removed signal that was
recorded at higher resolution than the full signal by utilizing d: 0.5V A/D input range.
During post-processing of data, the mean-removed signal was added to the mean voltage
from the full hotwire signal to recover the full signal with a more accurately captured

ﬂuctuating component.

27

2.3.5 Positioning Camera System

A camera system mounted outside the test section was utilized for positioning the hotwire
above the surface of the model. The camera used for this operation was a standard video
Sony (model XC-75) Charge Couple Device (CCD) camera. The camera was connected
to a National Instruments IMAQ board model PC1—1411 frame grabber. For positioning
the hotwire, the camera was ﬁtted with a Nikkor 500 mm (model NH - 27) lens. The area
where the probe was to be positioned was illuminated with a high-intensity, ﬂorescent
light from Stocker & Yale, Inc. (model 13 Plus Lite Mite Series). A sample of the

hotwire-positioning images can be seen in Figure 2.10.

Hotwire Prong

 

Figure 2.10 Sample image of the hotwire above model wall during positioning procedure

2.4 Experimental Procedure

This subsection gives a summary of the experimental procedure and methodology that

was used in the collection of data.

28

2.4.1 Testing Parameters

Two different sets of data acquisition parameters were used: one set for the velocity data
and the other for the mean-pressure proﬁles. For the velocity data, the acquisition rate
was set to 8000 Hz, acquiring a total of 2'8 (262,144) samples. This sampling rate was
determined to be sufﬁciently above twice the highest-frequency velocity ﬂuctuations
produced by the ﬂow structures (approximately 1 kHz for the current ﬂow), therefore
eliminating the possibility for aliasing. The duration was selected to be long enough to
capture multiple cycles of the velocity produced by the lowest-frequency structures.
More speciﬁcally, with this selection of data sampling parameters, frequency spectra

could be obtained with a resolution of 4 Hz and random uncertainty of 8.8%.

The second set of testing parameters, which were used to sample the mean surface-
pressure, corresponded to a sampling rate of 1500 Hz and 15,000 samples. These
parameters produced a 10-second sampling duration for the acquired time series, which
was determined to be sufﬁcient to accurately calculate the average pressure. The rationale

for this determination will be further discussed in 2.4.3.

2.4.2 Forcing-Signal Parameters

As explained earlier, the ﬂow forcing in this investigation was achieved by externally
driving a Helmholtz resonator with a speaker located upstream of the wind tunnel
entrance. The carrier frequency of the forcing signal was set to a nominal frequency of
630 Hz, which was slightly different from the resonator’s resonance frequency of 657 Hz.
This was done to obtain the strongest possible ﬂuidic disturbance by the resonator for a

given driving-sound level. As explained by Aditjandra3, the shift in the frequency of the

29

strongest disturbance from the resonator’s resonance frequency is caused by wind

tunnel’s resonance.

The carrier frequency value of 630 Hz was ﬁne tuned from day to day within a few Hz
due to the effect of changes in the ambient temperature on the speed of sound (and hence
on the resonance frequency of both the forcing device and wind tunnel). To account for
these temperature variations in the resonance frequency, the carrier frequency was always
determined empirically prior to data acquisition on different days. The procedure
involved utilization of a hotwire that was placed 0.02 mm above the resonator’s slot
while the speaker was driven by a sine wave produced from a single function generator.
A sketch of the hotwire location relative to the resonator can be seen in Figure 2.11. The
output of the hotwire was displayed on an oscillosc0pe and the frequency of the input
sine wave was adjusted within a few Hz around 630 Hz until the ﬂuctuation of the
hotwire trace reached a maximum. The frequency setting of the function generator at this

condition was then used as the carrier frequency in equation (2.3).

%

 

 

 

Figure 2.11 Location of hotwire for carrier frequency determination

After the determination of the carrier frequency, it was also important to set the values of

A1 and A2 to achieve a modulation index of 1, as discussed in section 2.2.4. Two

30

function generators were used to create the frequencies required by equation 2.3: (fc+fm)
and (fc-fm). The signals were combined using a homemade, operational-ampliﬁer,
summation circuit, the output of which was routed to the ampliﬁer that drives the
speaker. The resulting velocity of the jet at the exist of the resonator’s slot was
monitored using the hotwire signal, which was observed on the oscilloscope while the
amplitude of each function generator is adjusted independently until the modulation

index is determined visually to be 1.

Figure 2.12 is a hotwire trace of the jet velocity showing what is considered to be good
modulation. As seen from the ﬁgure, the amplitude of high-frequency sinusoidal
oscillations (at the carrier frequency) is made to modulate in time. The modulation
corresponds to an M1 of 1 since the oscillations are completely turned off when the
amplitude is minimum (for example, when the jet velocity approaches zero at t = 0.0153
in Figure 2.12). It is noted here that the rectiﬁed-wave appearance of the trace in Figure
2.12 is due to the existence of a streaming ﬂow component of the jet velocity (see
Aditjandra3) and rectiﬁcation effects due to direction insensitivity of the hotwire. For the
velocity data presented in this document, the modulation settings used may be seen in
Table 2.1. Note that these values correspond to fc = 632 Hz and fm = 18 Hz, where the

selection of fm is described in the following paragraph.

31

 

 

 

 

l

 

 

LILL\. 7 l‘L—_l¥.

5 6
time (ms)

 

Figure 2.12 Amplitude modulated resonator’s jet velocity

Table 2.] Function generator settings for the forcing signal

 

Function
Generator 1

Function
Generator 2

 

Amplitude

1020 mV

980 mV

 

Frequency

 

 

650 Hz

 

614 Hz

 

 

The amplitude-modulated signal produces an unsteady jet that grows and decays at a rate
of twice the modulation frequency. This may be seen from the hotwire trace of the
velocity of the jet shown in Figure 2.13. The red trace shown in the ﬁgure is corresponds
to one full cycle of the modulation frequency. When this trace is low-pass ﬁltered to

obtain the low-frequency disturbance that actually excites the ﬂow, it is evident that the

32

frequency of the ﬁltered signal (shown using black line in Figure 2.12) is twice as high as
the modulation frequency. Note that the amplitude and frequency (2fm) of the low-pass

ﬁltered signal is what is employed here to obtain the non-dimensional, forcing amplitude
and frequency values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 7' 7 T" V I if 7 71 l
. — Jet velocity j
— Low-pass ﬁltered jet velocity >
1.5 ’
E 1
5‘2 z'H-‘~
;/ \\\
0 5 I U U M U U
0F 2 7 3 ’4 7

 

time (ms)

Figure 2.13 Hotwire trace of the ﬂow velocity above the resonator's slit
A non-dimensional forcing frequency of F+ 2 0.541 was determined to be the optimal

forcing frequency from the investigation by Aditj andra3, where

F+ = 2fmxr

U (2.4)

with xr being the mean reattachment length. As discussed by, for example, Greenblatt and

Wygnanski“, F+ is the proper non-dimensional forcing frequency to use for unsteady

33

separation control. The length scale used in normalizing the frequency should be
descriptive of the size of the separation bubble in the streamwise direction. For the back-

step ﬂow, the mean reattachment length is typically used.

Finally, the forcing level was also selected based on the study of Aditjandra3 who found
that increasing the forcing amplitude of the resonator within the limits of the audio
ampliﬁer results in a larger effect on the ﬂow. Therefore, to study the forced ﬂow with
the biggest modiﬁcation relative to the natural case, it was desirable to force the ﬂow at
the largest amplitude attainable by the ﬂow excitation system. However, to maintain the
same forcing level from day to day, one needs the ability to ﬁne tune the ampliﬁer gain to
offset the small ﬂuctuation in resonator response caused by changes in the ambient
temperature (as discussed earlier). Hence, an amplitude lower than the maximum
allowed by the system was used to allow for this correction. The non-dimensional,

forcing level used for this investigation was C“ = 0.0434%, where

C .1 = ——hU2 (2.5)
d is the slot width, h is the step height, and um“, is the rrns velocity measured
immediately above the resonator’s exit. It is important to note that ujms is calculated
based on the sinusoidal component of Uj at the forcing frequency of the ﬂow; i.e., 2fm.
This is done by low-pass ﬁltering the hotwire signal to remove the signal components at

fm+fc and fm-fc before calculating the rms as seen in Figure 2.13.

34

2.4.3 Mean-Pressure Proﬁles

Mean-pressure proﬁles were measured in the separating/reattaching ﬂow region
downstream of reattachment to quantitatively examine the extent to which the forcing
system was affecting the ﬂow. The information was obtained from the static-pressure
taps located downstream of the separation point as described in section 2.3.1. Data
acquisition settings were determined based on the study of Hudys. Tests conducted by
Hudys showed that 10 seconds of data is the minimum average duration required to
calculate the mean pressure with acceptable accuracy. Moreover, the system requires at
least one second to stabilize after switching ports on the Scanivalve before data sampling

can begin.

Figure 2.14 shows the mean-pressure coefﬁcient (Cp) plotted vs. downstream position

normalized by step height, where

C _ P.—P,
p—l 2 (2.6)
/2pU..

P5 is the mean surface pressure at a given x location, Pr is the reference pressure from the

pitot tube (see section 2.3.2), p is the air density, and U00 is the freestream velocity.

35

 

0.150
0.100
0.050 7

0.000 » . . . l . . .. L ,.

Cp

-0.050

-0.100 7 new» ‘ 1. . ,, . .+ ,,

  

-o.150 . l . . , ,
i + Unforced ‘

l
+Forced 7 ‘
I

 

 

 

-0.200 .
0 l 2 3 4 5 6 7 8

Figure 2.14 Forced- and unforced-ﬂow mean-pressure proﬁles downstream of the step

The curve corresponding to the unforced-ﬂow case in Figure 2.14 is consistent with a
typical, backward-facing-step, wall-pressure proﬁle. The proﬁle clearly shows the broad
negative Cp peak associated with the low-pressure recirculation bubble in the region of 0
S x/h 5 2.5. Farther downstream, there is a pressure recovery region that extends to
approximately x/h = 5. For x/h > 5, the ﬂow is completely reattached and the pressure

gradually approaches the freestream, static pressure.

The forced-ﬂow, wall-pressure distribution exhibits the same general characteristics,
however there are important differences. The negative Cp peak associated with the
recirculation bubble has a lower negative pressure coefﬁcient, and the extent of this peak

does not extend as far downstream as under the unforced condition. This suggests that

36

the average recirculation ﬂow is stronger and it occupies a smaller space. Additionally,
the pressure recovery begins farther upstream, at approximately x/h = 2, relative to the
unforced case. All of these features are consistent with data seen in the literature for

periodically-excited separation bubbles; e.g., Greenblatt etal".

2.4.4 Velocity Acquisition Procedure

This section outlines the testing procedures and methodology for acquiring the hotwire

velocity proﬁles at various locations within the measurement domain of interest.

2.4.4.1 Hotwire Calibration

Hotwire calibration was needed for two purposes: ﬁrst, to obtain the required constants to
relate the voltage output from the CTA to the velocity and second, to ensure that this
relationship between voltage and velocity does not drift during testing. The voltage to

velocity relationship used here is that suggested by Collis and Williams7
E2 = A + Bq"45 (2.7)

where A and B are empirical constants obtained though calibration, E is the voltage
output from the CTA, and q is the velocity magnitude. A and B are obtained by placing
both the hotwire and a Pitot tube in the freestream inside the test section and exposing
them both to the same velocity. By acquiring E and q data for a range of different
freestream velocities, a least-squares curve ﬁt to equation (2.7) provides the constants A

and B. Typical calibration data and associated curve ﬁts are shown in Figure 2.15.

37

 

voltage (V)

 

 

 

 

 

 

 

i
0.9 '
0'8“ I —-; Precalibration ﬁt
, g — Post calibration ﬁt
0'7 l 0 Pre calibration data
[I] post calibration data
0,6 —— *7 x ,_ 1 - .:;:' l 7 L ,_ g
0 l 2 3 4 5 6 7

velocity (m/s)

Figure 2.15 Sample Hotwire calibration curves

The maximum deviation of the data from the calibration curve is less than 1%.
Furthermore, very little change is found between the calibrations obtained pre and post
the experiment. More speciﬁcally, the maximum pre- to post-calibration difference is

less than 1.5%.

2.4.4.2 Velocity Measuring Positions

In order to study the velocity ﬁeld, single-hotwire measurements were conducted at
several locations downstream of the separation point. Three main parameters were taken
into account when deciding on these locations. x resolution, y resolution, and the ﬂow

region within which strong reverse ﬂow from the recirculation bubble would make it

38

difficult to interpret the single-wire measurements. Based on examination of PIV data
taken by Hudy1 on the same test mode], a region with signiﬁcant probability of upstream
velocity was identiﬁed from the forward ﬂow probability seen in Figure 2.16 and
excluded from the present, measurement domain. The hotwire sampling points (shown
using black dots in Figure 2.15) that encroach to low, forward-ﬂow-probability areas
were deemed necessary to avoid missing relevant data under the forced-ﬂow condition,

where the recirculation bubble shrinks.

 

Figure 2.16 Forward flow probability from PIV measurements of Hudy (color map); and hotwire
measurement locations for the present investigation (black dots)

Data were taken at every half-step height downstream of the step from 0 S x/h S 5 and
every step height from 5 < x/h S 8. This covers a range that is approximately twice the
mean reattachment distance (xrlh r“: 4) for the unforced case. This xr value is an

approximate estimate given by Aditjandra3 from surface-pressure measurements.

Data were taken in the y direction at increments of 0.4 mm starting from 1 mm above the
surface of the model downstream of the step up to 1.5 step heights, excluding the region
determined to be in high-reverse-ﬂow areas. This resulted in approximately 10 y

measurement locations within the thin shear layer downstream of separation. The black

39

dots in Figure 2.16 show the full measurement grid, which consists of 14 different x

locations and a total of 513 grid points.

2.4.4.3 Testing Procedure

The process to acquire the hotwire velocity information was automated through the use of
a LabView program that was designed to capture velocity data at a number of y locations
for a given x position. First, the probe was positioned at the desired x/h location and the
lowest y/h position. This was done with the assistance of the CCD camera described in
2.3.5. However, the CC D camera needed to be calibrated to determine the imaging scale;

i.e., distance in the object plane per pixel in the image plane.

The imaging scale was determined by positioning the hotwire probe at an arbitrary
distance above the model, but within the view of the camera, and acquiring an image.
Following this, the probe was moved vertically a known distance by the stepper motor,
which was further veriﬁed by a dial indicator with an accuracy of 0.0127 mm. A second
image was then acquired, and the number of pixels per mm could be calculated by
locating the pixel location of the probe tip in the ﬁrst and second image and dividing the
difference between these pixels by the probe translation distance. This procedure was
repeated 5 times to obtain an average and reduce random errors that may be present such
as that associated with accuracy of locating the probe tip. A typical imaging scale factor

was 52 um/pixel.

After the hotwire was calibrated and properly positioned, the wind tunnel was set to
operate at a freestream velocity of 3.25 m/s via the adjustable speed controller of the

fan’s motor which corresponds to a Reynolds number based on step height of Reh =

40

2,630. As described in section 2.3, the hotwire voltage, high-passed-ﬁltered and
ampliﬁed hotwire voltage, forcing signal, freestream velocity and temperature were all
sampled simultaneously. A block diagram showing the complete experimental setup may
be seen in Figure 2.17. During post processing, the temperature measurements were used
to correct the hotwire output for any temperature change between the calibration and
main experiments. Additionally, any freestream velocity ﬂuctuations (which were limited
to less than 2.5%) were taken into account when normalizing the long-time and phase-
averaged statistics presented in later chapters. It is to be noted that the selected velocity
of 3.25 m/s is the lowest stable velocity that can be established in the tunnel. The
selection of such a low speed was motivated by the desire to maximize the non-

dimensional strength of the ﬂow control.

 

 

 

Pressure
[— transducer 1” CTA —'

J Pitot tube

 

 

 

 

 

 

 

 

 

Hotwire Thennistor

l_,
Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature
r
A to D High pass
ﬁj board :1] fillﬁl J
l- ? i . . I Function
To speaker Afkhf‘on generator 1
crrcurt *1 F .
unctron
generator 2

 

 

 

Figure 2.17 Block diagram of experimental setup

41

2.5 References

 

' Hudy, L. M., “Simultaneous Wall-Pressure and Velocity Measurements in the Flow
Field Downstream of an Axisymmetric Backward Facing Step”, PhD. Dissertation,
Michigan State University, 2005.

2 Li, Y. and Naguib, A.M., “High-Frequency Oscillating-Hot-Wire Sensor for near— Wall
Diagnostics in Separated Flows,” American Institute of Aeronautics and Astronautics

Aerospace Journal, Vol. 43, No. 3, 2005, pp. 520.

3 Aditjandra, A., “Amplitude-modulated Excitation of a Separated Flow Using an
Externally Driven Helmholtz Resonator” Masters Thesis, Michigan State University,
2006.

4 Greenblatt, D and Wignanski, 1., “Control of Separation by Periodic Excitation”,
Progress in Aerospace Sciences, Vol. 37, Issue 7, 2000, pp. 487 - 545.

5 Hudy, L. M., “Simultaneous Wall-Pressure Array and PIV Measurements in a

Separating/Reattaching Flow Region”, MS. Thesis Michigan State University 2001.

6 Greenblatt, D., Paschal, K., Yao, C., Harris, J., “A Separation Control CFD Validation
Test Case Part 2. Zero Efflux Oscillatory Blowing”, AIAA-2005-0485 43rd AIAA
Aerospace Sciences Meeting and Exhibit, Reno, NV 2005.

7 Collis, D. C. and Williams, M. J ., “Two-Dimensional Convection from Heated Wires at

Low Reynolds Numbers” Journal of Fluid Mechanics, Vol. 6, 1959, pp. 357 — 389.

42

3 Conventional-statistics Results and Discussion

This chapter contains a discussion of the velocity-ﬁeld data, focusing on conventional
statistics. Conventional statistics convey information concerning the long-time-average
characteristics of the ﬂow ﬁeld, which helps to identify any major changes that occur in

the ﬂow under the forcing conditions.

Hereafter, reference will be made to “unforced” and “forced” cases extensively. The
“unforced” case refers to the natural ﬂow over the test geometry without any externally
applied perturbations; this will act as the base line against which to compare the forced
results. The “forced” case refers to the condition when the resonator is being externally
driven by the speaker producing an unsteady jet that perturbs the ﬂow, changing its
structure. In this and the following chapter, results are provided to examine how the

resonator’s disturbance affects the ﬂow ﬁeld.

3.1 Mean Velocity

Figure 3.1 shows normalized mean-velocity contours plotted with the y/h position shown
on the vertical axis and x/h position given on the horizontal axis. These plots were
generated by averaging the hotwire, time-series data at every location and dividing by the
freestream velocity obtained using the pitot tube. Normalizing the data should remove
any errors that result from the small deviations in free-stream velocity between sampling

locations.

43

Unforced

 

 

 

 

Figure 3.1 Normalized mean-velocity plots

Although the mean-velocity contours for the unforced case look similar to the forced
case, there are a few subtle differences. By comparing the velocities at separation, x/h =
0, the y location of the same-color contours (i.e., the same velocity magnitude) for the
forced case are located at higher y locations than the unforced case. This may be seen
more clearly in Figure 3.2 where line plots are made of the mean-velocity proﬁle at
selected x/h locations. It is believed that the upward shift in the velocity proﬁle in the
forced case is associated with enhancement in the momentum transport in the y direction,
caused by the streaming motion introduced by the control jet. Another interesting point is
that in both cases, high-velocity ﬂuid at the top of the measurement domain seems to

“dip” into the test region. This may be visualized with the aid of the dark red contour at

44

the top of the plots in Figure 3.1, in the region of 0.5 S x/h S 4. For the forced case this

dip happens closer to the point of separation.

Another difference may be found in the region: 1 S x/h S 5. In this region, it appears that
the shear layer is spreading faster in the forced ease. The spreading of the shear layer can
be seen more clearly from the proﬁle line plots in Figure 3.2. For example, if one locates

the outer edge of the shear layer, say, at ﬁ/U,o = 0.8, it is evident from the plots in

Figure 3.2 that this would be at a higher y location for the forced in comparison to the
unforced case. Alternatively, the width of the shear layer may be linked to the slope of
the velocity proﬁle at the inﬂection point ( maximum velocity gradient); i.e., the vorticity
thickness. The steeper this slope, the wider the shear layer. It can be seen that for x/h =
1, both the forced and unforced cases seem to have the same peak velocity gradient,
therefore they have the same vorticity thickness near separation. However, at x/h = 3, the
forced case has a steeper slope at the inﬂection point, corresponding to a thicker shear
layer. Far downstream of reattachment, x/h = 7, both proﬁles have the same inﬂection-
point slope, suggesting that the biggest difference between the time average velocity ﬁeld
of forced and unforced cases is mostly conﬁned to the ﬂow region upstream of

reattachment (x/h z 4).

45

1.5; :v » LL, 15' :. , .
1- m j . 1. Km 1 j

 

 

 

0'5» — Unforced 05‘
— Forced _ l .
00 0.2 0.4 0.6 0.8 1 00 02 0.4 i 0.6 0.8 ' 1
1 5 - . - - 1.5 -
x/h =3 x/h =4
1 1-
E 1
>5
0.5» 0 5
l
O - . . . O ._. _,_ . . .77,7L, . l
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
1.5- » a,
i
1 l
S f
3. I l
0.5: i l
| l .
0 - - . 5 , ,
0 0.2 0.4 0.6 0.8 1 1

 

a/Uw

Figure 3.2 Normalized mean-velocity profiles at selected x/h locations

The above suggests that forcing leads to faster development of the shear layer, ultimately
leading to shortening of the separation bubble (as reﬂected in the mean-pressure
measurements in Figure 2.14). This is consistent with well-established physics of
oscillatory control of separated ﬂows (e.g., Kiya et. al. 1, Bhattacharjee et. al.2, and many

others).

3.2 Fluctuating Velocity

The strength of the ﬂuctuating (mean-removed) component of velocity (q') is represented

by its normalized, root-mean square, or rms, value plotted in Figure 3.3, with the y/h

46

position given on the vertical axis and the x/h position shown on the horizontal axis. The
rrns plots reveal information about the energy of the turbulent motion in the ﬂow. The
results obtained here, for the unforced case, agree well qualitatively with Hudy3 who
measured the velocity using PIV on the same test model under unforced conditions. In
Figure 3.3, high rrns values are indicated by red and orange contours, while low values

correspond to green and blue shades.

Unforced

 

Forced

 

 

 

 

 

 

 

Figure 3.3 Normalized turbulent-velocity rms contour plots

Comparing the unforced and forced rrns contour plots, the most noticeable difference is
the emergence of a second peak (the ﬁrst peak being that found near reattachment, x/h z

4) in the forced case in the region 0.5 S x/h S 2 and approximately y/h = 1. It will be

47

shown in chapter 4 that the most likely cause of this peak is enhancement of the vertical
“ﬂapping” of the shear layer near the point of separation. As previously seen in the mean-
velocity contours, both the unforced and forced rms contour plots seem to be very similar
downstream of reattachment. This is interesting because the forcing presumably creates
periodic, organized ﬂow structures in the ﬂow. However, the structures apparently
dissipate quickly within the separation bubble; thus, they do not affect the ﬂow ﬁeld

downstream of reattachment.

Figure 3.4 shows line proﬁles of the normalized rrns values for the forced and unforced
cases at selected x/h locations. The higher rms value near separation (x/h = l) in the
forced case is evident from the ﬁgure. Additionally, consistent with the mean-velocity
results, the rms data spread over a larger y extent for the forced case, reﬂecting a larger
shear-layer width. Downstream of reattachment, at x/h = 7, the results for both forced

and unforced cases are very similar.

48

 

0.2

0.2

0.2

.1:
\>. .r p , ________L
0'5' 7 Unforced ’
1 — Forced," '
00 0.05 0.1 50.15 F
1.55 ’ |
x/h=3
1' l
.C
3.
0.5'
0 . ; .
0 0.05 0.1 0.15
1.5 *
x/h =5
l.
'5 .
>‘ I
0.5'
0}. t , . L 1 .
0 0.05 0.1 0.15
q'm/UO0

 

 

 

 

 

0.5
O , :
0 0.05 0 l 0.15 0.2
1.5 * '
x/h =4
1 r J
l
0.5 l
l
0: , , . __ .1 _ _ 1
0 0.05 0.1 0.15 0.2
1.5 7 7*
x/h =7
1 1
i 1
0} _ .. . 7 ___.-
0 0.05 0.1 0.15 0.2
q'nns/Uoo

Figure 3.4 Normalized turbulent-velocity rms proﬁles at selected x/h locations

In many shear-layer studies, such as Castro and Haque4 as well as Ruderich and

Femholzs, the lateral (y) location of the maximum rrns value at any particular x location is

used to mark the center of the shear layer. Using this criterion, the center of the shear

layer for both the unforced and forced cases is plotted in Figure 3.5. There appears to be

very little difference in the location of the center of the shear layer between the forced

and unforced case.

49

-;-_Unforcedﬂ :

 

—Oj Forced
IN
'5
- - - Jig-7
0.5 ~- ~ - 57 =‘
O _ . _ _ 1 —
O l 2 3 4 5 6 7 8

x/h
Figure 3.5 Peak q’m, location at different streamwise positions
In addition to inspection of the rms proﬁles at selected x locations, it is instructive to
examine streamwise evolution of the maximum q' rrns values. These results are shown in
Figure 3.6. For the unforced case, the peak-rms magnitude increases from the point of
separation to approximately reattachment (x/h 7: 4) where it peaks, then decays farther
downstream. The forced case does not follow this pattern; instead, the peak-rms value
peaks just after separation at x/h = 1, then rapidly decays to a local minimum.
Downstream of this minimum, the curve follows the same trend as the unforced case,
slowly building to a local peak around reattachment and then decaying. The initial peak
in the forced case, found just downstream of separation, is believed to be a product of
enhancement in the shear layer ﬂapping and not increase in the energy content of the
ﬂow structures. This hypothesis, which originated based on comparison with other
studies of oscillatory separation control (to be discussed in Chapter 4), is supported by
probability-density-function (PDF) data given later in this chapter and other analyses
presented in chapter 4. Another interesting point is that the local maximum that the rms

value in the forced case reaches near reattachment is lower than in the unforced case.

50

0.27 : ' 7 771777 7 -1-.- ~ - ' , _ I ;:__._,,,,,i_

l + Unforced l;
0.19» 55-13““!

|

0.18' l

0.17-~~

0.16'

/U

 

0.15: ..

rrns

0.14;
0.13:
0.12; ;

0.11 —

,7

0.1 7 5 ~ ~ 1., ,, -- ,, -7. 7. A i. __ ,

Figure 3.6 Streamwise evolution of the maximum q'm. values

3.2.1 .1 Power Spectral Density

The power spectral density (PSD) is a mathematical technique that is used to compute the
frequency content of a time series of data. The ability to obtain PSD information is a
major advantage of using hotwire over typical Particle Image Velocimetry (PIV)
measurements. The hotwire signal captures time-resolved information at a particular,
spatial location; whereas PIV yields spatially resolved data at a particular point in time.
Figure 3.7 and Figure 3.8 display PSD plots at selected x/h locations for the unforced and
forced-ﬂow cases respectively. The PSD values are normalized by the freestream

velocity and the step height and plotted on the vertical axis versus the normalized

51

frequency (Fh/Um), on the horizontal axis. The different color lines in each plot represent

the 44 different y/h locations where velocity data were taken.

 

Figure 3.7 Power spectral density of q' for the unforced flow at selected x/h locations

52

 

 

 

 

Figure 3.8 Power spectral density of q' for the forced flow at selected x/h locations

The large harmonic peak in Figure 3.8 at x/h = 1 corresponds to the forcing frequency
(Fh/U.0 = 0.1385 or F = 36 Hz). Close to the forcing location (i.e., near separation) q' is
dominated by the ﬂuctuations at the forcing frequency. The farther downstream from the
forcing location, the less dominant are the velocity ﬂuctuations at the forcing frequency.
Upstream of reattachment (x/h z 4), the frequency content of the unforced ﬂow exhibits a
broadband character, with no signiﬁcant peaks. However, downstream of reattachment a
broad peak begins to emerge in the frequency range Fh/U... = 0.02 — 0.1, which
corresponds to 5 - 25 Hz. By x/h = 7, the peak is very noticeable and is believed to
correspond to the ‘natural’, or preferred, frequency of the ﬂow (i.e., the frequency

corresponding to the passage of the shear-layer vortices in the absence of forcing). This

53

is interesting because a broad peak in the same frequency range is also found for the
forced ﬂow. In this case, the peak is better deﬁned and is found to correspond to the lSt
sub-harmonic (i.e., half) of the forcing frequency. This harmonic link to the natural
frequency of the ﬂow is possibly tied to why 36Hz was found to be the optimum forcing
frequency of the ﬂow. This result agrees with Chun and Sungé, who used sinusoidal
forcing at the point of separation over a backward facing step. They also found the

optimal forcing to be twice that of the natural frequency of the ﬂow.

To identify the y location where the velocity ﬂuctuations at the forcing and natural
frequencies are dominant, normalized PSD results are plotted verses y/h for selected x/h
locations using ﬂooded, color, contour maps in Figure 3.9 and Figure 3.10 for the
unforced and forced ﬂow respectively. The PSD contours show that a broad spectrum
peak is found in both the forced and unforced cases downstream of reattachment. As
discussed earlier, the frequency of the peak is more well deﬁned for the forced ﬂow, and
is found centered around a y/h location just above 0.5 for x/h = 5 and 7. Referring to
Figure 3.5, it is seen that this location corresponds to the center of the shear layer at the

given streamwise positions.

The PSD contour maps for the excited ﬂow show the harmonic peak at the excitation
frequency (as seen earlier in the PSD proﬁles). The y location at which the peak is
strongest appears to be near the center of the shear layer at x/h =1. Farther downstream
this location is closer to the surface of the model: at x/h = 3 the peak has migrated to y/h
= 0.5. After reattachment, x/h = 7, the peak is found near the wall, well below the shear-

layer center.

54

      

0.05 I 0.1 0.15 0.2 0.25 0.3 0.35 0.4

 

 

£ 1
>05 , -;;
0.05. 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Fh/U ¢.,
' I Knew _qq
o 0.1 0.2 0.3 0.4 0.5 0.6 Ugh

Figure 3.9 Power spectral density of q' for the unforced ﬂow at Selected x/h Locations (broken line
shows sub-harmonic of the forcing frequency)

55

 

 

      

 

 

0. 5 I 0.1 0.15 0.2 0.25 0.3 0.35 0.4
F h / U 1 ,
m . 1 esteem-n— qq
0 0.1 0.2 0.3 0.4 0.5 0.6 Ugh

Figure 3.10 Power spectral density for the forced flow at selected x/h locations (broken line shows
sub-harmonic of the forcing frequency)

3.3 Velocity Probability Density Function

Velocity probability density functions, or PDF’s, are used to determine the probability
that the velocity would assume a value in a particular range at a given location in the
ﬂow. Figure 3.11 shows PDF results obtained from data acquired at x/h = 1.5. This
streamwise location is chosen because it falls in the region where the near-separation

peak is found in the q' rrns results of the forced ﬂow (see Figure 3.3 and Figure 3.6).

56

Figure 3.11 contains (a) a partial time-series trace of the velocity time series for the
unforced case, (b) a partial time-series trace of the velocity for the forced case, and (c) the
PDF’s for both forced and unforced cases. Figure 3.11 shows data for y/h z 0.68 (which
is near the low-speed edge of the shear layer). Both velocity traces are plotted with
velocity magnitude on the vertical axis and time on the horizontal axis. The PDF is
plotted with probability on the vertical axis and velocity magnitude on the horizontal

axis.

(a) Unforced

l

 

Velocity (m/s)

    

 

 

 

O 0.15 0.2 0.25 0.3 0.35 7 K4 *7 $15 0.5
time(s)
2", I "7 '7‘ ’7 V __—'—
3 1 b Forced
é ( )
£1
.8
O
>
0 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
time(s)

f 7 if 7 I" T 7 ' 7 ' 7* if k I V 77’ 7V— 7'
>‘41 — Unforced 4
.3 —— Forced
L; 1 (c)PDF J
.o 21
9
Q- 1

0 l 1 I; 41* 1

0 0.5 1 1 3 3.5 4 4.5

2 2.5
Velocity (m/s)

Figure 3.1] Velocity properties at y/h = 0.6833 and x/h = 1.5: (a) sample velocity trace for unforced
case, (b) sample velocity trace for forced case, (c) PDF’s

Inspection of the hotwire trace for the unforced case in Figure 3.11, shows that the
velocity magnitude is low most of the time but spikes to high-magnitude velocity

occasionally. It is hypothesized that these spikes are produced when the shear layer

57

“dips” downward (as a result of ﬂapping at separation) and brings higher-velocity ﬂuid in
contact with the hotwire sensor. Under forcing conditions, the hotwire trace is seen to
exhibit these spikes more frequently (middle plot in Figure 3.11), suggesting that the
ﬂapping of the shear layer is more energetic, bringing the higher-speed ﬂuid in contact
with the hotwire more frequently. This results in an increase in the skewness of the PDF
in the positive direction, with the PDF for the forced case showing a longer tail at large
values of the velocity in comparison to the unforced case. These observations support the
idea that the q' rms peak found near separation when forcing the ﬂow is likely associated

with enhanced vertical ﬂapping of the shear layer.

58

3.4 References

 

' Kiya, M., Shimizu, M., Mochizuki, O., “Sinusoidal Forcing of a Turbulent Separation
Bubble”, Journal of Fluid Mechanics, Vol. 342, 1997, pp. 119-139.

2 Bhattacharjee, S., Scheelke, B., Troutt, T., “Modiﬁcation of Vortex Interactions in a
Reattaching Separated Flow”, American Institute of Aeronautics and Astronautics
Journal, Vol. 24, No. 4, July 1986, pp. 623 — 629.

3 Hudy, L. M., “Simultaneous Wall-Pressure and Velocity Measurements in the Flow
Field Downstream of an Axisymmetric Backward Facing Step”, PhD. Dissertation,
Michigan State University, 2005.

4 Castro, 1. P., and Haque, A., “The Structure of a Turbulent Shear Layer Bounding a
Separation Region”, Journal of Fluid Mechanics, Vol. 179, 1987, pp. 439-468.

5 Ruderich, R., and Femholz, H. H., “An Experimental Investigation of a Turbulent Shear
Flow with Separation, Reverse Flow, and Reattachment”, Journal of Fluid Mechanics,

V01. 163, 1986, pp. 283-322.

6 Chung, K., and Sung, J. “Control of Turbulent Separated Flow Over a Backward-Facing
Step by Local Forcing”, Experiments in Fluids, Vol. 21, 1996, pp. 417-426.

59

4 Phase-average Results and Discussion

This chapter contains a discussion of the velocity-ﬁeld results obtained from phase-
averaged statistics. Phase-averaged statistics are employed in this investigation to
decompose the hotwire signal according to the triple decomposition introduced by
Hussain and Reynolds”. It is hoped that this will provide further insight into the
structure of the ﬂow and shed some light on the mechanism that causes the decrease in
size of the separation bubble and reduction in the reattachment length of the forced ﬂow.
The phase-averaged analysis was performed on the forced-ﬂow case based on the phase
of the forcing cycle. Since a similar phase reference did not exist for the natural-ﬂow

case, the analysis was not applied to the unforced ﬂow.

4.1 Phase averaging

Phase averaging is used here to compute an average of q at any particular phase of the

forcing cycle and is deﬁned by

<q(x,t0)> =Lim—Zq(x, to +nr) (4.1)

M—900M

where t is the period of the forcing signal (half the modulation period in this study),
shown in the top plot of Figure 4.1, M is the number of forcing cycles in a time series,
and to is a time variable corresponding to a particular phase of the forcing cycle; i.e., 0 S
t0 5 t. Thus, the average may be computed at any particular phase (p (0° 5 (p 5 360°) of

the forcing cycle by changing to.

60

1 111; ”ii” "1:1 1 ”it

  

 

Voltage (V)

Forcing signal
Demodulated signal '

'1 <r>= 90° .
o=1so° I
"-5: 3A o=270° }
2 1* a>=36o° .1
0 1 2 3 4 5 6
' I

 

<1 mm

 

 

 

I
‘ |
1.2} 1
L- 1, ”.1 ’-
10

1 2 3 4 5 6
Time (ms)

Figure 4.1 Sample time series illustrating different forcing-cycle phases for phase averaging: (a)
forcing signal; (b) flow velocity

61

Figure 4.1 demonstrates graphically how the phase average was computed. First, the
forcing signal, shown in blue was demodulated, which produced the curve shown by the
red line. One cycle of the demodulated signal has a period of 1: (which is also the period
of the disturbance induced in the ﬂow, corresponding to a frequency of 36 Hz) that can
be divided into any number of phases, (p. For the current sampling rate of 8000 Hz, one
36 Hz cycle contains approximately 222 data points. Therefore, it was possible to

calculate pahse averages for every 1.62° of the ﬂow-excitation cycle.

To select the data point corresponding to a speciﬁc phase in different forcing cycles, the
start of the cycle (or (b = 0°) was ﬁrst identiﬁed by marking the minimum point in the
demodulated signal (blue squares in Figure 4.1). Knowing that points succeeding the
zero-phase point are separated by 1.62°, it was then possible to pick the point that is
closest to the desired phase. It should be evident that the maximum resolution error in

locating the desired phase is 1.62°, or 0.45% of the forcing cycle period.

After determining the data points in the velocity time series corresponding to a particular
forcing-cycle phase as seen in (b), an average of the velocity signal at the selected phase
can be computed. For example, black triangle makers are used in Figure 4.1 to identify
the forcing cycle phase of 270°. The measured velocities corresponding to this phase
occur at time instants that are marked with vertical dashed grey lines in Figure 4.1. By
averaging the velocity values for all such time instants, a velocity phase average for 270°
is generated for one location in the flow ﬁeld. This process was repeated for different
phases of the forcing cycle and every location where velocity data were gathered to

generate the phase-averaged information.

62

Normalized, phase-average velocity contours are plotted with y/h on the vertical axis and
x/h on the horizontal axis in Figure 4.2. Note that (p = 0° corresponds to the phase where
the unsteady jet flow (produced by the resonator) exhibits peak blowing. There are a
number of observations that can be made from the phase-average plots. First, vertical
“compressions” and “expansions” of the contours seems to occur successively along the
streamwise direction. By examining Figure 4.2 for (p = 0°, at x/h = 0.5 - 1, the contours
are densely packed in the y direction, whereas farther downstream at x/h = 1.5 - 2.5 the
contours are widely separated in comparison. This pattern seems to repeat farther

downstream, forming a wave-like pattern.

63

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.2 Phase-average-velocity contour plots at selected phases of the forcing cycle

64

The wavy pattern seems to convect downstream. This may be seen by tracking the center
of the ﬁrst contour compression that starts at x/h = 0.5 for (p = 0. At (p = 120 the
compression is found at x/h = 1.5, and ﬁnally at (p = 300 it has progressed to x/h = 3. The
wave-like disturbance and associated downstream convection implies that the ﬂow
control is generating a quasi-periodic coherent structure. These wave-like disturbances
have been seen in other experimental and numerical studies by Greenblatt eta].3 and

Rumsey4 when examining separation control over a wall-mounted hump.

Finally, the <q> results provide additional support to ﬁndings in Chapter 3 that suggest
the existence of vertical ﬂapping of the shear layer near separation. This becomes clear
by following the phase-progression of the contour line that originates from x/h = 0 and
y/h z 1.3, marked with a white line in Figure 4.3 that shows a close up of the shear layer
in the vicinity of the separation point for the two phases corresponding to the down most
and up most excursions of the <q> contours, (p = 0° and (p = 180° respectively. Initially,
at (p = 0°, the contour line highlighted with white line in Figure 4.3 has a slope of
approximately -0.39. Later in the cycle, at (p = 180°, this contour line is almost horizontal
with a slope of approximately -0.1. The implied ﬂapping of the shear layer is believed to

be the cause for the q' rms peak seen near separation for the forced flow (see Figure 3.3).

65

 

 

Figure 4.3 Close up of the phase-average-velocity contour plots in the vicinity of the separation point

A key objective of the present study is to examine whether the nature of the ﬂow
structures produced by amplitude-modulated forcing are any different from those found
in periodically-excited ﬂows. To this end, it is important to compare the present results
with those from an appropriate study involving periodic excitation of a separated ﬂow.
The study of Greenblatt et al.3 was selected for this comparison for two reasons: ﬁrst, the
study provided carefully documented, extensive PIV measurements of the ﬂow ﬁeld; and,
second, the data compiled in the investigation are available for public access at

http://cfdv312004.larc.nasa.gov/index.html.

The geometry used in the Greenblatt investigation is a wall-mounted, hump model, as
seen in Figure 4.4 in black. The oscillatory forcing was generated by an internally
driven, zero-mass-ﬂux jet through a slot located at 65% chord length (c = 0.42 m) of the
model. The velocity ﬁeld was captured via two-component PIV in three regions (shown
in Figure 4.4) downstream of the forcing location, at 36 different phases of the forcing
cycle. Here, results from only 4 phases will be used for comparison purposes. Also, the
Greenblatt study was conducted at a much higher Reynolds number than the present

investigation (Rec = 1,114,800 based on chord length and Re! =142,670 based on

66

maximum thickness of the humI:>), and the forcing conditions corresponded to F: 0.77

and c,=0.110%.

0.4 ' * * ,, * , " W * , *‘
Measurement Measurement Measurement

Point of region 1 region 2 region 3
excitation \ 1

l l
' 1.2 7717.4

Figure 4.4 Geometry of Greenblatt’s hump model and PIV measurement locations

Flow

 
      

y/c

0.2

x/c

Figure 4.5 provides a comparison between the Greenblatt data and the data obtained in
this investigation for the phase-average of the square of the velocity magnitude (<q2>).
Because only certain computed statistics, rather than the raw data, were available from
the Greenblatt investigation, <q> could not be obtained. It was possible however to
compute <q2>, which is used as the basis for comparison between results obtained from
the present and Greenblatt’s data (details relating to <q2> calculation from Greentblatt’s
data are provided in Appendix A). Note that in Figure 4.5, (p = 0° corresponds to peak
blowing of the control jet in both studies. Also, it is helpful to point out that the mean
reattachment location for the Greenblatt data is at x/c = 0.94, while in the present study it
is roughly estimated to be in the range 3.5 — 4 h based on the mean-pressure

measurements.

67

Greenblatt 4) =00

 

 

Greenblatt .1: =900

 

/\

.D
N

V

~l

©9539—-
mug
LII U!

Iii-ﬂ a:

 

/\

.D
N

V

Ci

Greenblatt ¢ = l 800

3.
i061

1‘

z!

0.8

09
&

 

/\

.D
N

V

‘11

6.0.0.0—
Nlllﬂ
M M

 

Greenblatt 4) =2700

 

Figure 4.5 Phase-averaged <qz> contours: comparison of present results with those calculated from
Greenblatt’s’ data at selected phases

In Figure 4.5, <q2> contour maps are plotted above Greenblatt’s <q2> contours for four

selected phases of the forcing cycle, q) = 0, 90, 180, and 270. Both contour maps are

69

plotted as function of the position in the ﬂow, normalized by the step height and chord

length for the present and Greenblatt’s results respectively.

Inspection of Figure 4.5 shows close, qualitative similarity between the present and
Greenblatt’s results. In particular, Greenblatt’s results also depict the convective, wavy-
like disturbance found here. The ﬂapping of the shear layer near the point of separation
is also noticeable in the Greenblatt data. This is evident from the movement of the <q2>
contours of the latter case just downstream of separation, as explained earlier in
connection with Figure 4.3 (the ﬂapping motion will be observed more clearly based on
vorticity results of the Greenblatt data). Finally, it is also interesting to note that the
spatial wavy structures from the Greenblatt data, and the current study, seem to be in
phase with each other for similar phases of the forcing cycle. Collectively, the
observations derived from Figure 4.5 provide evidence that the ﬂow structures produced
by the amplitude-modulated forcing employed here are inherently similar to those
produced via the conventional periodic excitation. This is quite useful in the sense that it
shows that periodic control of ﬂows could be achieved by low-frequency modulation of
actuators that have operating frequency that is substantially higher than the desired
control frequency. In other words, the selection and design of an actuator operating
frequency may be decoupled and hence becomes unconstrained by the required excitation

frequency of the ﬂow.

The Greenblatt data are also helpful in demonstrating that q information is dominated by
the streamwise component of the velocity. This is relevant in showing that, for all

practical purposes, the present single-wire measurements may be interpreted as a

70

measurement of U, with V having a negligible inﬂuence on the outcome. To demonstrate
this, Figure 4.6 (top) shows contours of <U|Ul> normalized by U...2 while the bottom plot
in the ﬁgure provides <q2> contours. <U[U|> is plotted instead of <U2> to preserve the
direction of the reverse ﬂow region near the surface upstream of reattachment. Both
contours were obtained from Greenblatt’s data. By comparing the two plots, it is evident

that q 3 U is a reasonable assumption for all regions except near reattachment (x/c = 1).

<U |U|>
Uj
no

 

Figure 4.6 Comparison of <U|U|>and <q2> contours at (p = 0° calculated from Greenblatt’s data

4.2 Triple decomposition

By using a method known as triple decomposition, introduced by Hussain and
Reynolds”, it is possible to decompose the velocity time-series into three, distinct

quantities as given by

71

q(x,t) = 6(x)+ 5(x,t)+ (20,!) (4.5)

where q is the organized-motion, disturbance velocity that is computed form the phase

average velocity using

21“ = (q) —21‘ (4.6)

and 6; corresponds to the turbulent (random) motion velocity that is obtained from

c} = q(t)- (4) (4.7)

For the purposes of the present study, one advantage of the triple decomposition is that it
provides a means for tracking the evolution of the forcing-induced, coherent structures.
To demonstrate this, consider the comparison between the phase-averaged vorticity and
<ﬁz> obtained from the Greenblatt data for different phases of the forcing cycle (given in

Figure 4.7).

72

 

¢ =90°

   

73

¢ =l80°

 

1.3

Figure 4.7 Contours of the phase-averaged vorticity, and energy of the streamwise turbulent velocity
component, computed from Greenblatt’s data for selected phases of the forcing cycle

74

In Figure 4.7, the normalized vorticity contour maps are plotted above the normalized
<ﬁz> contours for four selected phases of the forcing cycle: (p = 0°, 90°, 180°, 270°; the
coordinates for both contour maps are normalized by the chord length. Examination of
the vorticity plots reveals the periodic roll-up and subsequent downstream convection of
large-scale coherent structures from the initially thin separating shear layer (as identiﬁed
from the concentration of vorticity. The structures will be referred to as vortex structures
with the understanding that, more generally, regions of high vorticity do not necessarily
correspond to vortices; Blausius boundary layer is a good example). The streamwise
location of the center of the vortex structures is marked with vertical, black, dashed lines
based on the vorticity contours. By extending these lines down into the <ﬁz> plot, it is
seen that the center of a vortex structure is associated with high <ﬁz> regions. In turn,
high <ﬁz> values should result in correspondingly high <q2>. Consequently, regions of

large <q2> values should be helpﬁil in “tagging” the vortex structures produced by the

forcing. This is valuable for the present study, given the lack of vorticity data.

Normalized <q2> velocity contours are plotted in Figure 4.8 for excitation-cycle phases of
(p = 0°, 60°,120°, 180°, 240°, and 300°. As explained above, regions of high <q2> will be
used to track the evolution of the implied vortex structures that are generated by the
forcing. Examination of the results suggests that these structures remain quite small near
separation as they convect downstream. Once they reach approximately x/h = 2, they
appear to grow in the wall-normal direction to approximately the height of the step and
continue to travel downstream, this is very similar to what Hudy5 saw in the unforced

case. Beyond reattachment (x/h I: 4) the <q2> signature weakens. This weakening could

75

be caused by loss of phase locking between the forcing and the induced structures at

distances that are far from the point of actuation.

76

 

 

 

 

Figure 4.8 <ff> contours for selected phases of the forcing cycle

77

An estimate of the convection velocity of the ﬂow structures was found by tracking the
streamwise location of the peak <q2> value at different phases of the forcing cycle. The
results are plotted on an “x-t” diagram using red circles in Figure 4.9. Note that the data
have a “staircase” appearance that is caused by the limited streamwise spatial resolution
of the measurement grid. A straight line ﬁt to the data was employed to determine the
convection velocity. Speciﬁcally, the inverse SIOpe of this line is equal to the convection
velocity. Note that two different line ﬁts were utilized. First, a line that ﬁts all data
points (shown in blue in Figure 4.9) provided an estimate for the convection velocity
averaged over the entire measurement domain. However, although this line provides a
good description of the data trend for x/h > 2, the results for x/h < 2 seem to follow a
trend with steeper slope than given by the blue line. Therefore, a second line (the green

dashed line in Figure 4.9) is used to ﬁt the data in the region x/h < 2.

Considering the linear ﬁt to the entire data set, a convection velocity of 1.521 m/s or
0.47U,o was found. This value agrees closely with the results of Hudy5 who found the
convection velocity at the end of the separation bubble for the unforced ﬂow to be
0.45Um. Note that Hudy, who conducted her measurements on the same test model as the
present one, found this velocity value from tracking the surface-pressure signature.
Greenblatt3 found a slower convection velocity of 0.324Uoo. The difference may be

related to the difference in test-model geometry.

78

   

1; Fit f0? adeat;
‘--- Fit for x/h < 2 H
7. ,, ,_,,, ,,. 7 la. ,__, .7K2;:;; L;:: :a:;4ﬁ;l

2 3 4 5 6 7 8

 

Figure 4.9 Streamwise location of the peak of <q’> at different phases of the forcing cycle. Straight
lines represent least-squares ﬁts used to calculate the convection velocity

Near separation (x/h < 2), the convection velocity computed from the green-line ﬁt in
Figure 4.7 was 0.75 m/s or 0.233Um. This suggests that the ﬂow structures have a slower
convection velocity up to x/h = 2, then they accelerate to 0.47U..0 farther downstream. It
is interesting to note, however, that this change in the velocity takes place in the region 2
< x/h < 4, where Hudy5 found the shear layer to roll-up into large-scale vortical
structures. Thus, it seems that the slower convection velocity is found in a zone upstream
of the location of formation of the vortex structures. This is also consistent with the
results in Figure 4.8, where there is an abrupt change in the scale of the implied, coherent

structure downstream of x/h = 2.

79

To further examine the change in the magnitude of the convection velocity, the reader is
referred to Figure 4.7 of the phase-averaged-vorticity results computed from Greenblatt’s
data. Inspection of the vorticity at different phases of the forcing cycle shows the
formation of the large-scale vortices to commence at x/c z 0.77. Upstream of this
location, there is no evidence of existence of any vortices. Instead, the region is
dominated by the thin, separating shear layer, which exhibits up/down ﬂapping motion

throughout the forcing cycle.

The above suggests that the slower convection velocity near separation is more likely an
artifact of the velocity signature caused by the ﬂapping of the shear layer. That is, the
ﬂapping of the shear layer could create a signature that is commensurate with that of a
convecting disturbance. In particular, given two sensors positioned at the same y location
in a separating shear layer, one downstream of the other, as the shear layer begins to ﬂap
(say moving from its downward most position in the upward direction), the upstream
probe will detect the disturbance caused by the shear layer ﬁrst, followed by the
downstream probe at some later time. This time delay would appear to be that of a

convecting disturbance.

Another useful result to examine is that concerning the organized component of the triple
decomposition (i.e., (‘1'). This velocity component is displayed for various phases of the
forcing cycle in Figure 4.10 with y/h on the vertical axis and x/h shown on the horizontal
axis. Note that these results could be obtained from <q> data displayed earlier in Figure
4.2 after subtraction of the mean of q. That is, 61 is essentially the phase average of the

mean-removed velocity. Generally speaking, it is difﬁcult to deduce the nature of the

80

flow structures in a frame of reference where the local mean is removed (because
different parts of the structures appear distorted after removal of the velocity associated
with the mean shear). However, q results allow isolation of the organized disturbance
that is directly related to the forcing which could shed some light on certain

characteristics of the associated ﬂow features.

81

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.16 -0.08 0 0.08 0.16 U.”

Figure 4.10 q contour plots for selected phases of the forcing cycle

82

Not surprisingly, examination of Figure 4.8 reveals the evolution of an organized
disturbance. The nature of the disturbance is different for x/h < 2 in comparison to
farther downstream. Within the former domain, the disturbance appears to be
concentrated within the thin, separating shearlayer. Farther downstream, the disturbance
spreads substantially in the wall normal direction with the strongest disturbance found in
two localized regions: One near the wall, and the other near the top edge of the
measurement domain. The sign of the disturbance within these two regions alternates
from positive to negative in the streamwise direction, which causes the wave-like
appearance discussed earlier in connection with Figure 4.2. It is also notable that the
magnitude of q is stronger near the wall than it is close to the top of the measurement

domain.

Comparison of the evolution of the random and organized disturbance (in Figure 4.8 and
Figure 4.10, respectively) reveals that, for x/h > 2, the former is strongest along the center
of the shear layer, while the latter makes the most energetic contribution near the edges.
This may be seen more clearly by calculating the rms of q and q, the results of which are

displayed in Figure 4.11.

The stronger values of 61 near the edges of the shear layer is consistent with the idea that
the forcing introduces organized, vortex structures, as discussed earlier in connection
with the vorticity results based on Greenblatt’s data. More speciﬁcally, a streamwise-
traveling vortex is likely to contribute to the ﬂuctuations of the streamwise velocity (and

hence q) strongest towards the edges of the vortex, rather than at the core.

83

Another interesting observation from Figure 4.11 relates to the ms of the organized
disturbance near the separation point. It is evident that the contours extend over a
considerably wider distance in the y direction in comparison to the rrns of the random
velocity. This is likely a reﬂection of the enhanced lateral motion of the shear layer (i.e.,

ﬂapping) in synchronization with the forcing, as discussed previously.

 

Figure 4.11 rms of the turbulent (top) and the organized (bottom) velocity components. Broken
white line identiﬁes the center of the shear layer based on peak q',,.,,

84

4.3 Reference

 

I Hussain, A.K.M.F., and Reynolds, W.C. “The Mechanics of an Organized Wave in
Turbulent Shear Flow”, Journal of Fluid Mechanics, Vol. 41, part 2, 1970, pp. 241-258.

2 Reynolds, W.C., Hussain, A.K.M.F. “The Mechanics of an Organized Wave in
Turbulent Shear Flow Part 3. Theoretical Models and Comparisons with Experiments”,
Journal of Fluid Mechanics, Vol. 54, part 2, 1972, pp. 263-288.

3 Greenblatt, D., Paschal, K., Yao, C., Harris, J ., “A Separation Control CFD Validation
Test Case Part 2. Zero Efﬂux Oscillatory Blowing”, AIAA-2005-0485 43rd American
Institute of Aeronautics and Astronautics Aerospace Sciences Meeting and Exhibit, Reno,

NV 2005.

4 Rumsey, C., “Reynolds-Averaged Navier-Stokes Analysis of Zero Efﬂux Control over a
Hump Model” AIAA-2006-11 14 44th American Institute of Aeronautics and Astronautics
Aerospace Sciences Meeting and Exhibit, Reno, NV 2006.

5 Hudy, L. M., “Simultaneous Wall-Pressure and Velocity Measurements in the Flow
Field Downstream of an Axisymmetric Backward Facing Step”, PhD. Dissertation,
Michigan State University, 2005.

85

5 Conclusions and Recommendations for Future Work

This chapter contains a summary of the work presented in previous chapters and an
outline of the major ﬂow-ﬁeld characteristics downstream of an axisymmetric backward
facing step under natural and forced conditions. Also provided here are suggestions for

future work that could further the understanding of the topic investigated here.

5.1 Conclusions

The main goal for this investigation was to characterize the ﬂow ﬁeld downstream of an
axisymmetric, backward-facing-step under unforced- and forced-ﬂow conditions. The
forcing method was based on the use of a Helmholtz resonator that is externally driven
with an acoustic, amplitude-modulated disturbance (which was developed by
Aditjandral). This forcing system is unique in comparison to the typical direct harmonic
forcing seen in the literature, to the best of the authors knowledge. Therefore, the present
study’s primary concern was to address the question of whether amplitude-modulated
excitation affected the ﬂow in a manner that is similar to, or different from, conventional
oscillatory control. To this end, a single-hotwire sensor was employed to gather velocity
information downstream of the axi-symmetric back step. The compiled data were
analyzed using conventional and phase-averaged statistics. The results were found to be

consistent with those found in the literature for harmonic forcing.

The similarity between amplitude-modulated and conventional harmonic forcing was
determined based on detailed comparison of phase-averaged statistics obtained from the
present study to those obtained from a database compiled by Greenbalt et. al.2 in a

periodically-excited separation over a wall-mounted hump. Data from both studies verify

86

that large-scale coherent structures are produced regularly during the forcing cycle.
These structures are initially produced from the thin shear layer at a location
approximately half way to reattachment (x/h = 2 —- 3) where they grow in size to

approximately one-step height and convect downstream.

The contrast in the characteristics of the organized motion produced by the control
upstream of x/h z 2 - 3 and farther downstream is not limited to the scale of the forced
disturbance. Additional differences include the convection velocity, which was found to
be 0.233U,0 in the former region and 0.47U00 in the latter. Moreover, the forcing was
found to produce a localized peak in the rrns of the mean-removed velocity at x/h = 1.0.
Given that this location is upstream of the location of formation of the large-scale
structures, in addition to evidence based on a number of statistical analyses, this peak was

attributed to enhancement of the vertical ﬂapping of the shear layer at separation.

Finally, a power spectral density analysis showed that the ﬂow response to the forcing is
very strong near the point of separation but it quickly dissipates farther downstream. The
analysis also provides insight to the possible reasoning for the selected forcing frequency
being the optimal control frequency (as found by Adjeranda'). More speciﬁcally, the
forcing frequency was found to be twice the natural frequency of the ﬂow at the end of
the separation zone under unforced conditions. This ﬁnding is similar to that found by
Chun and Sung3 who also found the optimal forcing frequency to be twice the natural

frequency of the ﬂow.

5.2 Recommendations for Future Work

A few suggestions for extension/enhancement of the present study follow:

87

Conduct wall-pressure measurements at the same conditions of the forcing
employed here in order to investigate the surface-pressure imprint of the ﬂow
structures produced by the forcing. Results from the present investigation could
be synchronized with the surface-pressure data through the phase reference of the

forcing cycle.

The above would also allow examination of the utility of stochastic estimation in
estimating the ﬂow structures from the unsteady wall-pressure signature under
forced conditions. Such an examination could be useﬁil for implementation of

feedback control of the separation bubble.

Conduct the experiment using particle image velocimetry, or laser Doppler
velocimetry to capture the details of the velocity ﬁeld accurately everywhere,

including within the re-circulation region and in the vicinity of reattachment.

88

5.3 References

 

lAditjandra, A., “Amplitude-modulated Excitation of a Separated Flow Using an
Externally Driven Helmholtz Resonator” Masters Thesis, Michigan State University,
2006.

2 Greenblatt, D., Paschal, K., Yao, C., Harris, J ., “A Separation Control CFD Validation
Test Case Part 2. Zero Efﬂux Oscillatory Blowing”, AIAA-2005-0485 43rd American
Institute of Aeronautics and Astronautics Aerospace Sciences Meeting and Exhibit, Reno,

NV, 2005.

3 Chung, K. and Sung, J. “Control of turbulent separated ﬂow over a backward-facing

step by local forcing” Experiments in Fluids, Vol. 21, 1996, pp 417-426

89

 

A. Appendix

In the following, a derivation is provided to show how <q2> was computed from

Greenblatt’s data
(A. 1)

<q2>=<u2+v2>

since summation and averaging are commutative:

(,2>-<.2>.<.2> o2)
decomposing velocities into mean and ﬂuctuating components
(42> = <67 + “72> + <07 + V') > (A.3)
<q2>=<z72 +2t7u'+u'2>+<t72 +217v'+v'2> (A.4)
because the mean of a and 37 are constant quantities
<17) 2 27
(‘7) = ‘7 (A.S)
substituting (A.5) into (A.4)
(A.6)

<q2> = 7:2 + 25(u') +<u'2> + 172 + 2i7<v'>+<v'2>

the ﬂuctuating component can be further divided into periodic component and turbulent

component

90

OI'

substituting in equation (A.11) into (A.6) results in <q2>

 

 

<q2>=172 +2iiz7+<u'2>+i2'2 +2Vi7+<v'2>

 

 

91

(A7)

(A8)

(A9)

(A10)

(A.11)

(A12)

Beginning with values that are available from Greenblatt’s database, <u> and <v>, and

expanding into mean and ﬂuctuating components
<u>2 +(v)2 = (t7+u'>2 +(t7+v'>2 (A.13)
<u>2 + <v>2 = 52 + 217<u'> + <u')2 + 172 + 2t7<v’) + (v')2 (A.14)
substituting equation (A.11) into (A.14) results in

<u>2+<v>2=§2+227i7+z72+i52+2t73+32 (A.15)

To get the right hand side of equation (A.15) to be the same as the right hand side of

t 2

(A.12) in order to compute <q2>) from <u> and <v>, <u > and <v' 2> are added and

subtracted to the right-hand side of equation (A. 1 5), yielding
<u>2 + M2 = [172 + 2551 + <u'2>]— <u'2> + 172 + [v2 + 297 + <v'2>]—<v'2> + v2 (A.16)
grouping and recognizing terms corresponding to <q2> from equation (A. 1 2) results in
<u>2+<v>2 =<q2>—<u'2>+t72—(v'2>+$2 (A.17)
expanding u' and v' in terms of periodic and random components leads to
<u>2 +(v)2 = <q2> —<172 +2i7ﬁ+ ziz> +272 -<i72 + 236+t32>+iiz (A.18)

using (A9)

92

<u>2 + (v)2 .—. <q2> — 172 — 217<li>—<122> + 172 — 9'2 — 217(9) — (£22) + a? (A.19)
using (A.10) and canceling terms of equal magnitude but opposite sign results in
<u>2 +<v>2 =<q2>-<&2>—<f22> (A.20)

which yields the equation needed to calculate <q2> using the phase-averaged quantities

provided in Greenblatt’s data set

 

<qz>=<u>2 +<V>2 +<132>+<92> (A21)

 

 

 

References

 

l Greenblatt, D., Paschal, K., Yao, C., Harris, J ., “A Separation Control CFD Validation
Test Case Part 2. Zero Efﬂux Oscillatory Blowing”, AIAA-2005-0485 43rd American
Institute of Aeronautics and Astronautics Aerospace Sciences Meeting and Exhibit, Reno,

NV 2005.

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