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On the flow characteristics behind a backward-facing step and thedesign of a new axisymmetric model for their study
by
Jagannath Rajasekaran
A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science
Graduate Department of Aerospace EngineeringUniversity of Toronto
Copyright © 2011 by Jagannath Rajasekaran
Abstract
On the flow characteristics behind a backward-facing step and the design of a new
axisymmetric model for their study
Jagannath Rajasekaran
Master of Applied Science
Graduate Department of Aerospace Engineering
University of Toronto
2011
An extensive review was made to study the wake characteristics of a backward-facing step.
Experimental and numerical studies of the backward-facing step suggest that the wake of a
separated shear layer to be dependent on parameters such as: expansion ratio, aspect ratio, free
stream turbulence intensity, boundary layer state and thickness at separation. The individual
and combined effects of these parameters on the reattachment length are investigated and
discussed in detail in this thesis. A new scaling parameter, sum of step height and boundary
layer thickness at separation is proposed, which yields significant collapse of the available data.
Based on the literature review, an axisymmetric model is designed for further investigating the
dynamics of the flow independent of aforementioned parameters. Additionally, porous suction
strips are incorporated to study the step wake characteristics independent of Reynolds number.
This model has been built and will be tested extensively at UTIAS.
ii
Dedication
To my parents and sister, for their love and support.
iii
Acknowledgements
I have had help from many people during the course of my masters degree. First, I would like
to start by thanking my supervisor Dr. Philippe Lavoie, for his calm guidance, tremendous pa-
tience and constant encouragement in finishing my thesis. I owe him a debt of gratitude for the
financial support that I have had throughout the program and for being willing to countenance
a delay of nearly a year beyond my original deadline. I would also like to thank the Professors
from my research assessment committee, Dr. Zingg, Dr. Martins and Dr. Ekmekci, for their
invaluable feedback and suggestions for improvement.
I would also like to thank Ronald Hanson for his timely help on countless number of occa-
sions and for being a very good friend. If not for him, I might have had a hard time coping
with the education system in Canada. Special thanks to Arash Lahouti for his time to discuss
regarding the project and for proof reading my thesis. Also, many thanks to Heather Clark
for tolerating and helping with my questions regarding the project. I would also like to ex-
tend thanks to my colleagues Denis Palmeiro, Jason Hearst, Zhou Yuan, Mike Kociolek, Luke
Osmokrovic and Leticia Gimeno for taking interest in my topic and also for sharing knowledge
about theirs during the group meetings.
The research lab at University of Toronto has provided me with several opportunities to
involve both physically and mentally. This was possible because of the regular funding from
the Canadian government, the University and the private firms to our lab. I am very thankful
for that and would like to encourage them to keep funding our lab for many more years to come.
I also am thankful to all the University office staff for their help throughout the course of my
degree. Also special thanks to Mrs. Joan Dacosta and Mrs. Nora Burnett for their assistance
and sincerity.
Last but not the least I would like to thank my parents and my sister for their moral support
and inspiration throughout my degree.
iv
Contents
Abstract iii
Dedication iii
Acknowledgements iv
Contents vi
List of Tables vii
List of Figures ix
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature Review 5
2.1 Common Features of the Backward-Facing Step Flow . . . . . . . . . . . . . . . 5
2.2 Shear Layer Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Vortex Rolling and Pairing Mechanism . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Coherent Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Vortex Shedding Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Reattachment Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Recirculation Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Important Flow Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.1 Effect of the Expansion Ratio . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.2 Effect of Aspect Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.3 Effect of Free Stream Turbulence Intensity . . . . . . . . . . . . . . . . . . 20
2.5.4 Effect of Boundary Layer State at Separation . . . . . . . . . . . . . . . . 20
2.5.5 Effect of Boundary Layer Thickness at Separation . . . . . . . . . . . . . 21
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
v
3 Novel Scaling Analysis 25
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 New Normalization Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Model Design 30
4.1 Model Design Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Wind Tunnel Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Model Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4 Porous Suction Strip Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.1 Evolution of the Turbulent Boundary Layer Thickness . . . . . . . . . . . 33
4.4.2 Effects of Suction on Turbulent Boundary Layers . . . . . . . . . . . . . . 39
4.5 Suction System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.6 Model Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.7 Nose and Trailing Cone Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7.1 Axisymmetric Nose Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7.2 Trailing Edge Cone Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 Conclusions and Recommendations 53
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Future Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
vi
List of Tables
3.1 Important parametric data acquired from different experiments on backward-
facing step flows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
vii
List of Figures
1.1 Backward-facing step flow features. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Flow characteristics behind a BFS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Initial instability of the shear layer, and the roll-up into discrete vortices. . . . . 7
2.3 Streamlines over a bluff plate with splitter plate configuration. . . . . . . . . . . 8
2.4 Acoustic forcing in backward-facing step flows. . . . . . . . . . . . . . . . . . . . . 11
2.5 Convective and absolute instabilities in the shear layer. . . . . . . . . . . . . . . . 13
2.6 Mean flow structure of one half of the secondary vortex. . . . . . . . . . . . . . . 16
2.7 Planar backward-facing step geometry. . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.8 Sketches of oil film pattern on the floor for the region behind the step. . . . . . 19
2.9 Axisymmetric backward-facing step geometry. . . . . . . . . . . . . . . . . . . . . 20
2.10 Effect of boundary layer state at separation. . . . . . . . . . . . . . . . . . . . . . 21
2.11 Effect of boundary layer state and thickness at separation at ReH = 26,000. . . 22
2.12 Effect of Reynolds number and boundary layer thickness at separation. . . . . . 23
3.1 Combined effect of parameters on the reattachment length. . . . . . . . . . . . . 26
3.2 Boundary layer thickness at separation vs. rescaled reattachment length. . . . . 27
4.1 Closed return tunnel schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Schematic of control volume used for momentum integral analysis. . . . . . . . . 34
4.3 Evolution of displacement thickness over a flat plate, with and without suction
at the wall.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Axisymmetric backward-facing step model. . . . . . . . . . . . . . . . . . . . . . . 42
4.5 Evolution of boundary layer thickness for different suction velocity. . . . . . . . 43
4.6 Plenum chamber design within the suction strip system. . . . . . . . . . . . . . . 44
4.7 Cross sectional view of a plenum chamber. . . . . . . . . . . . . . . . . . . . . . . 44
4.8 Experimental set up to measure pressure drop across a porous plate. . . . . . . . 45
4.9 Velocity profile of a fully developed turbulent pipe flow. . . . . . . . . . . . . . . 46
4.10 Schematic of the axisymmetric model with dimensions. . . . . . . . . . . . . . . . 48
viii
4.11 Pressure distribution over a cylinder and a sphere. . . . . . . . . . . . . . . . . . . 49
4.12 Coefficient of pressure versus the normalized streamwise distance for different
nose models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.13 Pressure gradient versus the normalized streamwise distance for different nose
models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
ix
Chapter 1
Introduction
1.1 Background
The discovery of boundary layer theory by Ludwig Prandtl in the early twentieth century was
the beginning to the extensive research on separated flows. Separated flows are common in sev-
eral engineering applications such as aircraft wings, turbine and compressor blades, diffusers,
buildings, suddenly expanding pipes, combustors, etc. The characteristics of a separated flow
has been studied for decades by experimentalists to understand the physics of the separated
shear layers and their instability mechanisms. The instabilities in the free shear layers are the
source to distinctly visible large coherent structures. The existence of coherent structures in
almost every turbulent flows has been well documented [1] and this makes it even more inter-
esting to study such separated shear flows.
Besides the academic interests, knowledge of separated flows can also be applied to many
practical applications. Two of their main applications include the automobile and aircraft in-
dustries, who are developing fuel efficient designs to reduce consumption of the rapidly-depleting
non-renewable resource and minimize green house gas emission. In an aerodynamic perspec-
tive, drag is considered as one of the major reason for inefficient fuel consumption. There are
several types of drag, but in this thesis, the focus will be on the pressure drag created by the
separated flows and the ways to minimize it. Studies by Roos and Keegelman [2] demonstrated
that by actively controlling the flow at separation, characteristics of the coherent structures
can be modified and consequently alter the drag characteristics. These aspects of the flow
make it important to understand the instabilities and characteristics of coherent structures for
controlling flow dynamics to achieve significant drag reduction or lift enhancement. Apart from
drag reduction, understanding the fluid-structure interactions of these separated shear layer
instabilities can be very useful in controlling the noise and vibration characteristics of such
1
Chapter 1. Introduction 2
flows [3].
The physics of separated flows, due to their instabilities, are very complex. In an attempt
to simplify these flow characteristics, researchers conducted experiments on various geometries,
which include rib, fence, bluff body with a splitter plate, suddenly expanding pipes, forward and
backward-facing steps, cavities, and bluff bodies with blunt leading edges. These geometries
simplify the flow characteristics to a certain extent by fixing the separation or the reattachment
point or both, which are otherwise unsteady. The backward-facing step is considered by most
as the ideal canonical separated flow geometry because of its single fixed separation point and
the wake dynamics unperturbed by the downstream disturbances. An illustration of the wake
characteristics behind a backward-facing step is shown in Figure 1.1.
Recirculation bubble!
Shear layer! vortices!
Coherent Structure!
Figure 1.1: Backward-facing step flow features.
In this thesis, an extensive review on the characteristics of the flow features behind the
backward-facing step are discussed. The wake of a backward-facing step has unique features
mainly in two regions: the free shear layer and the low velocity re-circulating bubble. Due to
instabilities, the vortices in the shear layer roll up and pair with the adjacent vortices to form
larger coherent structure [4]. These vortices entrain fluid from the region below and trigger
the recirculation. Due to the adverse pressure gradient in the wake of the step the free shear
layer reattaches at the bottom wall. A more detailed description of the separated shear layer
behind the backward-facing step and the instability mechanisms will be discussed in Section 2.2.
Besides the omnipresent nature of coherent structures in turbulent flows, recent studies
[2, 3, 5, 6] suggest that coherent structures play an important role in altering the flow dynam-
ics to achieve desirable characteristics such as reduced drag, subdued noise, enhanced mixing
and suppressed vibration. Several different passive and active control techniques have been
Chapter 1. Introduction 3
implemented to date mainly to alter the wake characteristics of the step. The active control
experiment on a backward-facing step by Roos and Kegelman [2], was one of the first experi-
ments to indicate that the coherent structures can be modified to achieve desired results. Since
then, in most of the recent studies the emphasis has been to determine the characteristics of
the coherent structures and explore the external means of modifying their dynamics.
There have been several experiments conducted over a backward-facing step geometry and
yet the results obtained from different experiments are not comparable due to their depen-
dency on flow and geometric parameters. Some of these significant parameters were noted in
the review paper by Eaton and Johnston [7]. These parameters include, the expansion ra-
tio, aspect ratio, free stream turbulence intensity, Reynolds number and the boundary layer
state and thickness at separation. The independent effects of each of these parameters on the
reattachment length were extensively studied by different experimentalists [7–11], which are
discussed in detail in Chapter 2. However, a distinct relationship for a combined effect of all
these parameters at various conditions has not been established yet. It is shown in this thesis
that a unique relationship for the combined parametric effect on reattachment length can be
achieved by rescaling the normalizing parameter for the reattachment length.
Owing to the parametric differences between each experiments the reattachment length at
step wake differs accordingly. The long term goals for our lab are to study and actively control
the wake dynamics behind the step. This requires a state of the art model that is independent
of aforementioned parametric effects. Hence, for the current study a unique model is designed
that can either minimize or control the effects of those parameters. The two key features of
this model are the axisymmetry and the porous suction strip design. Experiments on the ax-
isymmetric backward-facing step (the one where the flow is external) has been conducted by
very few researchers [12–14]. This provides an opportunity to investigate more about the effects
of axisymmetry on the backward-facing step flow. Moreover, the axisymmetric step is useful
in achieving a better case of two-dimensional wake behind the step, since the planar models
require large aspect ratios to achieve two-dimensional characteristics at the center. Porous
suction strips are incorporated in the current model to control the boundary layer thickness
at separation independent of the Reynolds number and consequently study their effects on the
step wake characteristics.
This document including the introduction is divided into five chapters. An extensive lit-
erature review on the flow characteristics behind the backward-facing step and the effect of
parameters on their characteristics are discussed in the Chapter 2. The combined effect of
Chapter 1. Introduction 4
parameters on the reattachment length with the inclusion of new scaling length are discussed
in Chapter 3. The Chapter 4 focuses on the design of the axisymmetric backward-facing step
model to be used in future studies at the Flow Control and Experimental Turbulence lab at
UTIAS. A brief conclusion, followed by a future scope is given in Chapter 5. The major findings
of this thesis has been published in a conference [15].
Chapter 2
Literature Review
2.1 Common Features of the Backward-Facing Step Flow
The flow behind the backward-facing step (BFS) is complex and involves various instability
mechanisms. Some of the most common features behind the step recognized in the literature
are illustrated in the Figure 2.1.
!
H
U"
Secondary vortices Separation bubble
Shear layer
Time averaged
dividing streamline Vortex merging
Coherent
structure
Vortex shedding Reattachment
zone
Figure 2.1: Flow characteristics behind a BFS (adapted from Driver et al. [16]).
Based on the important flow features studied by previous researchers in a planar BFS geom-
etry, the flow wake can be distinguished into three main regions namely, the shear layer region,
separation bubble or recirculation zone and the reattachment zone. The general characteris-
tics of a BFS flow begins with an upstream boundary layer separating at the step edge due
to the adverse pressure gradient that develops into a thin shear layer. As the flow progresses
5
Chapter 2. Literature Review 6
downstream, the shear layer grows in size with the amalgamation of the turbulent structures
contained within. This region where the shear layer develops and grows is referred to as the
shear layer region and is shown in Figure 2.1. The turbulent structures in the shear layer
entrain irrotational fluid from the non-turbulent region outside the shear layer. This flow en-
trainment causes the formation of a low velocity recirculation in the region, which is located
between the shear layer and the adjacent wall. The recirculation zone is mainly comprised of
a primary vortex in the center and a secondary vortex adjacent to the corner of the step as
shown in Figure 2.1. Due to the favorable pressure gradient created by the fluid entrained,
the shear layer eventually curves down towards the wall and impinges at a location known
as the reattachment point. The horizontal distance between the step and the reattachment
point is defined as the reattachment length. The reattachment length is unsteady due to the
inherent oscillatory motion of the shear layer known as the flapping. As a result, the reattach-
ment point spreads within a certain span along the streamwise distance, which is referred to
as the reattachment zone. These three regions in a whole comprise the important features of
a BFS flow that can be altered or controlled to achieve desirable outcome such as, enhanced
mixing characteristics and reduced drag, noise and vibrations. Hence it is essential to under-
stand these flow features to control the flow dynamics. In most earlier studies [7, 9–11, 17],
the reattachment length has usually been the primary parameter of interest to study the wake
characteristics of a BFS flow. With the advancement in technology and the recent discovery
of the coherent structures in the shear layers, more researchers have shifted their interests to
studying these turbulent structures. The fact that these coherent structures can be altered
to get desired characteristics highlights the importance of understanding their dynamics. In
the following sections, a detail description of the flow characteristics in the wake of a step with
more emphasis on the evolution and the significance of the coherent structures will be discussed.
2.2 Shear Layer Region
The layer of fluid with a velocity gradient subjected to viscous shearing is known as the shear
layer. The shear layers are of two types, wall-bounded and free shear flows; the latter is the
one of interest in BFS flows. The free shear layer in the BFS originates at the separation point
and eventually curves down towards the wall to impinge at the reattachment point. This layer
is created due to the fast moving fluid (free stream velocity) on the top and the low momentum
fluid in the wake of the step. The separated free shear layer behind the BFS involves numerous
instabilities. In the following section, a description of the free shear layer features behind the
BFS and related instabilities are discussed.
Chapter 2. Literature Review 7
2.2.1 Vortex Rolling and Pairing Mechanism
The rolling and amalgamation of vortices are characteristics of every free shear layer flows such
as, the wakes, mixing layers and the jets. Browand [18] was one of the earlier researchers to
have noted the existence of vortex pairing mechanism in the shear layer of a BFS flow. How-
ever, a better description of the vortex pairing mechanism was available only when Winant and
Browand [19] observed them in a mixing layer using flow visualization. In their experiments,
they observed a periodic train of vortical structures, also known as vortices, in the turbulent
mixing layer. The vortices in the shear layer are formed by the rolling and pairing of the ad-
jacent turbulent structures. This pairing process was seen to continue until the mixing layer
thickness increased to the channel height. In the case of a BFS, the experiments suggested that
these vortices grew at most to the height of the step [20].
A model to describe the physics behind the roll up process of the vortices in a mixing
layer was developed by Winant and Browand [19]. Since the initial growth of the separated
shear layer behind the step resembles the mixing layer flows, this model can also be used to
describe the roll up of vortices in BFS flows. The model is described through an illustration
shown in Figure 2.2. To describe this phenomenon they considered the inviscid instability of
a constant-vorticity layer between two parallel streams. According to their theory, the initial
distortion in the boundary of the region containing the vorticity requires an initiation from a
small amplitude wave, as shown in Figure 2.2(a). It is known that the vorticity region induces
vertical velocity thus resulting in the growth of these perturbations. Due to these perturba-
tions the region containing the vorticity becomes periodically flatter and thinner as shown in
Figure 2.2(b) and 2.2(c). As the instability grows the vortical areas between the two streams
get to the verge of pinching off. Finally they break into discrete vorticity lumps as shown in
Figure 2.2(d). This process of forming vortical lumps is known as the roll-up process.
(a) (b)
(c) (d)
Figure 2.2: Initial instability in the shear layer, and the roll-up into discrete vortices [19].
Chapter 2. Literature Review 8
The next and the most dominant stage in this interaction is the merging mechanism of adja-
cent vortices commonly known as the vortex pairing. Winant and Browand [19] suggested that
the pairing process in a turbulent free shear layer is a result of a mutual interaction between
adjoining vortices due to slight imperfections in the vortex spacing and strength. In the pairing
process, neighboring pairs of vortices roll around each other and due to viscous diffusion their
identities are smeared out leaving a single large vortex. It has been noted in several BFS flows
[2, 13, 21], like in the mixing layer flows, most vortices double, triple and quadruple, as shown in
Figure 2.3, before the reattachment of the shear layer. Nevertheless, it is not always necessary
for two adjacent vortices to merge in a shear layer. There are some odd ones referred to as
the ‘drop outs’ that do not merge initially but do further downstream with a larger adjacent
vortical structure. This instability mechanism involving vortex rolling and pairing observed in
the mixing layer is related to the Kelvin-Helmholtz Instability.
Figure 2.3: Streamlines over a bluff plate with splitter plate configuration [4].
The amalgamation of vortices plays an important role in the growth of separated free shear
layers. The growth of a shear layer is mainly caused by the increase in size of vortices due to
the vortex pairing mechanism. However, there are other mechanisms, like the fluid entrainment
process that contribute to the growth of a shear layer. As the flow progresses downstream the
shear layer grows larger in size, due to the incessant pairing of adjacent vortices that advect
downstream with the shear layer. The vortex pairing continues as long as it is not inhibited
by a wall or other boundaries. The resulting large scale turbulent structure, which is phase
correlated over its spatial extent, is commonly termed as a coherent structure. The features
and significance of coherent structures are discussed in section 2.2.2.
The process of vortex roll up and the pairing mechanism in the separated shear layer of a
BFS flow was investigated by Troutt et al. [20]. During their study, they detected the presence of
Chapter 2. Literature Review 9
large scale structures in the separated shear layer close to reattachment. These structures were
formed by vortex pairing interactions in the separated shear layer similar to the mechanism
observed in mixing layer flows. Unlike mixing layer flows, the vortex pairing in BFS flows
cease to occur close to reattachment of the shear layer. They believed that the pairing process
stopped due to the proximity of the bottom wall in a BFS. Thus suggesting that the length
scale of coherent structures formed by vortex pairing close to reattachment is at most one step
height. The vortex pairing mechanism in BFS shear layers was also noted by Lee and Sung [22],
when they measured the wall pressure fluctuations at various streamwise and spanwise location
downstream to the step. Their results suggested that the flow behind the step were organized
and coherent along the spanwise direction. The non-dimensional frequency (St) for the vortex
pairing process in a BFS flow was noted by Liu et al. [23] to be approximately equal to 0.13. It
was later confirmed that similar non-dimensional frequency were also observed in several other
BFS flow experiments. The Strouhal number for these experiments is given by St = fH/U∞,
where f is the vortex pairing frequency, H is the step height and U∞ is the free stream velocity.
2.2.2 Coherent Structures
A coherent structure is a connected turbulent fluid mass with instantaneously phase-correlated
vorticity over its spatial extent, and the vorticity is termed as the coherent vorticity [1]. Coher-
ent structures are spatially non-overlapping and have their own boundaries. It has been noted
in many BFS flows that the vortices in the unstable shear layer roll-up and pair to form a single
large coherent structure. Hence a turbulent shear layer can be decomposed into coherent and
incoherent turbulence. Although the turbulence at Kolmogorov scale are the most coherent
[1], the large-scale structure are the ones that are often referred to as the coherent structures
because of their dynamical significance. The existence of a coherent vorticity is the primary
indicator of a coherent structure and hence is important to be able to identify them in a flow
amidst the incoherent turbulence. Winant and Browand [19] described that the property of a
coherent structure can be determined by obtaining the ensemble average of sufficiently large
number of structures. The ensemble averaging is critical to identify a coherent structure be-
cause it filters the effects of incoherent turbulence. This process of measuring the properties of
a coherent structure over its spatial extent is commonly known as eduction.
Significance of Coherent Structures
Coherent structures have been a hot topic for research in the past few decades. These structures
are almost omnipresent in flows involving turbulence such as, boundary layer flows, mixing lay-
ers, jets and wakes. Hussain [1] describes coherent structure as a tool to find order in apparent
Chapter 2. Literature Review 10
disorder in turbulent flows. Several studies have been conducted to understand the proper-
ties of a coherent structure because of its significant influence on the flow. It is known from
literature that the coherent structures play an important role in heat, mass and momentum
transfer, and hence can be useful in controlling drag. Some of the other benefits of these struc-
tures as described by Hussain [1] are understanding of entrainment phenomena, explanations
for excitation-induced enhanced mixing, turbulence and noise suppression. There are instances
where knowledge of coherent structures have been used for controlling BFS flows.
There have been several active control studies conducted on BFS flows in which the char-
acteristics of the coherent structures are altered to achieve desired results. In active control
studies the forcing on the separated shear layer is usually applied through two methods: flaps
or by acoustic forcing [24], the latter being the most common. The flap was implemented by
Roos and Kegelman [2] in a backward-facing step flow at the step edge. They investigated the
effects of active flow control on coherent structures and the wake of the BFS by oscillating the
flap periodically at a certain frequency. They observed remarkable change in the reattachment
length when the flap was activated at a non dimensional frequency (St) 0.29. Their spectral
map results of shear layer velocity fluctuations showed that the strong concentration of energy
at the excitation frequency evolved into a peak at half the excited frequency farther down-
stream. This suggests enhanced amalgamation process within the shear layer due to forcing.
They attributed the reduction in reattachment length to the enhanced vortex pairing mecha-
nism and formation of coherent structures slightly upstream in comparison to the unforced case.
Similar observations were made when Bhattacharjee et al. [5] tried to modify the vortex
interaction mechanism in a reattaching separated shear layer behind the BFS. They succeeded
in altering the flow characteristics behind the wake of a step by applying forcing through a
single acoustic speaker located on the top of the step edge as shown in Figure 2.4(a). When the
acoustic speaker was forced at St = 0.2 they observed high turbulent activity within the shear
layer including enhanced merging of vortices and organization of turbulent structures along the
spanwise width. The reattachment length reduced by at most 15% from the unforced case.
The wake characteristics, however, remained nearly unchanged when the speaker was forced at
St = 1.2.
In some other BFS flow control studies, the acoustic speaker was installed close to the step
edge functioning like a synthetic jet [3, 23]. Chun and Sung [3] investigated the most effective
forcing frequency for influencing the reattachment length by varying the forcing frequency from
0 to 5. Their results suggested that the reattachment length reached its minimum at St ≈ 0.27
Chapter 2. Literature Review 11
and a maximum at St ≈ 1.5. They believed that the reduction in reattachment length is
caused due to the increased entrainment in the recirculation region. Furthermore, it can be
seen that in most of these flow control experiments the ideal forcing frequency for reducing the
reattachment length is determined to be St ≈ 0.27 and this frequency is the first harmonics
of the amalgamation process in the separated shear layer [23]. It is evident from the above
studies that the knowledge on coherent structures is key to controlling BFS flows and hence is
important to study the characteristics of coherent structures further.
(a) Acoustic forcing from the top wall [5].
(b) Acoustic forcing from the step edge [3].
Figure 2.4: Acoustic forcing in backward-facing step flows.
2.2.3 Vortex Shedding Mechanism
The shear layer characteristics on reattachment and after were studied extensively by Brad-
shaw and Wong [25]. Their results suggested that the shear layer after reattachment continues
to spread downstream into a new shear layer with a sub-boundary layer underneath. The
key behavior they observed in the relaxing boundary layer was the region of rapid distortion
which depended on the amount of mass flow deflected upstream upon shear layer reattach-
ment. In another experimental study, Farabee and Casarella [26] measured the wall pressure
fluctuations using static pressure taps downstream of the step at various streamwise locations
to understand the wake characteristics. Their results indicated the presence of coherent, highly
energized, velocity fluctuations within the shear layer. They also noted that these coherent
structures after attaining the maximum length scale, which in their case was the step height,
shed and convected downstream due to the momentum of the free stream velocity. These co-
Chapter 2. Literature Review 12
herent structures were still identifiable as far as 72 step heights downstream of the step location.
In a comparative study, Sigurdson [6] noted that the shedding instability were a common
phenomenon in free shear layer flows. He suggested that the shedding instability resembled
the von Karman vortex shedding that is commonly seen in the wake of bluff bodies. This
vortex shedding characteristics of separated shear layers were noted in most of the recently
conducted BFS experiments. In an experiment by Roos and Kegelman [2] they analysed their
hot-wire data acquired from within the shear layer at different streamwise locations. Their re-
sults suggested that the size of the vortex increased due to amalgamation as the flow progressed
downstream. These results were also observed by Liu and Sung [23], however they also noted
those structures to shed after attaining maximum size. The non-dimensional vortex shedding
frequency in the wake of a BFS was measured by Lee and Sung [22] to be approximately equal
to 0.07. Similar non-dimensional frequency for vortex shedding phenomenon in BFS flows were
also observed by many other researchers [13, 23, 27].
Based on the above-mentioned evidence, it was commonly believed that small scale vortices
in the shear layer grew in size due to the Kelvin-Helmholtz instability as it advected down-
stream. In other words, it was believed that the growth of the shear layer structures occurred
spatially and then shed downstream after attaining their maximum possible length scale, the
step height. Contrary to this view, Hudy et al. [13] observed the temporal growth of stationary
coherent structures to occur intermittently along with the spatially growing coherent structures.
They noted similar shedding mechanism for temporally growing coherent structures once they
attained the size of the order of step height. They drew similarities between the temporally
growing coherent structure with the development of the vortex structure in the wake of bluff
bodies. To distinguish between these two shedding modes, they referred to the temporally grow-
ing coherent structure as the wake mode, while the other as the shear-layer mode. Sketches
illustrating both these modes are shown in Figure 2.5.
The important behavior to note is that regardless of which mode is prevalent, the flow
structures eventually grow to a length scale of the order of the step height and then shed down-
stream with a certain advection velocity. Hence, Hudy et al. [13] believed that the distinction
between the two modes is likely to affect flow characteristics within the separation bubble.
Similar observations were also noted in a numerical study conducted by Wee et al. [27]. In
their study, they noted that the large-scale structures formed periodically in the middle of the
recirculation zone before shedding downstream. They attributed the temporal growth of the
structures to the existence of an absolute instability in the flow. Wee et al. [27] stated that
Chapter 2. Literature Review 13
xr
H
x
y
Free stream
velocity (U!)
Vortical structures in
shear layer Edge of
shear layer
(a) Shear mode.
xr
H
x
y
Free stream
velocity (U!)
Vortical structures
developing in place Coherent structures
accelerating downstream
(b) Wake mode.
Figure 2.5: Convective and absolute instabilities in the shear layer (referred from Hudy [28]).
absolute modes are most likely to originate in the region with strongest back flow. It was also
suggested by Huerre and Monkewitz [29] that absolute modes were likely to appear when the
velocity ratio, R is greater than 1.315, where R is the ratio of the difference and the sum of
velocities of the two co-flowing streams. Based on those results, Hudy et al. [13] suggested that
the absolute modes most likely existed around two to three step heights downstream of the step.
Although they were able to identify the possible cause for the intermittently appearing
temporally growing structures, the question still remains as to why this shift between modes
occurred intermittently. The switching behavior between the shear-layer mode and the wake
mode was also seen in numerical computations in cavities by Rowley et al. [30].
2.3 Reattachment Zone
The reattachment point of an uncontrolled separating and reattaching shear layer in a BFS is sel-
dom fixed at a single point. This unsteadiness in the point of reattachment is associated with the
low-frequency oscillations detected in the shear layer [31]. This unsteadiness in the shear layer
trajectory is referred to as the flapping of the shear layer. Several researchers [2, 5, 23, 26, 31],
Chapter 2. Literature Review 14
who have experimented on BFS flows, have observed highly energized low-frequency peaks in
the power spectrum obtained near the separation point. The non-dimensional frequency (St)
of the flapping phenomenon were noted to be of the order of 0.02 in many experiments [21–
23, 32]. Eaton and Johnston [31] were among the first to associate low frequency oscillations to
the flapping of the shear layer. Although many researchers have proposed several hypothesis
(based on their observations), the source of the flapping phenomenon is not clearly understood
yet. In this section, some of these theories are discussed briefly.
Eaton and Johnston [31] studied the source of the low frequency disturbances in a flow
behind a BFS using hot-wires and thermal tuft probes. Their results suggested that these dis-
turbances could be caused due to the non-periodic, vertical fluctuation of the reattaching free
shear layer. In other words this can be realized as the flapping of the shear layer resulting in
the fluctuation of reattachment point. They suspected that this low-frequency motion could be
caused due to the imbalance in the flow injection and entrainment rate within the recirculation
region. This theory is the most widely accepted for the likely cause of the flapping phenomenon
in the separated shear layer. The occurrence of flapping in the shear layer was also confirmed
by Durst and Tropea [33], while measuring the probability density function of the velocity at
various streamwise locations behind the step.
A different theory was proposed by Troutt et al. [20] based on the coherence of data ob-
tained from hot-wires placed at several streamwise locations. Their results suggested that the
coherence at lower frequencies were the unsteadiness involved within the recirculation region.
They also believed that the unsteadiness could be caused due to the passage of large-scale vor-
tices through the reattachment region, which was later supported by Simpson [34]. According
to Driver et al. [16], flapping is caused by a particularly high-momentum structure moving far
downstream before reattachment. They noticed the abnormal contraction and elongation of
the separation bubble as a result of the shortening and lengthening of the reattachment length.
They suggested that the moving structures in the shear layer intermittently creates greater
pressure gradient within the recirculation region resulting in the higher recirculation rate and
shorter reattachment length. More recently, Spazzini et al. [35] studied the characteristics of a
BFS flow using Particle Image Velocimetry (PIV). Their analysis on the low frequency motion
using a wavelet transform suggested that a frequency comparable to the flapping phenomenon
was also observed within the secondary vortices. Similar to their results Hall et al. [36] also
observed activities in the secondary vortices that were closely related to the low-frequency shear
layer flapping.
Chapter 2. Literature Review 15
Although many theories have been proposed based on the experimental observations, they
are difficult to verify. One of the reason being the lack of more detailed information regarding
the flow-field behind the step especially in the recirculation region. It is known from various
experiments that the separation bubble intermittently changes shape and size with the flapping
of the shear layer. Hence measuring data from the recirculation region to determine the entrain-
ment rate and the injection rate is complex and difficult. With the advent of technology, new
instruments, such as time-resolved PIV, are capable of acquiring the velocity information from
the wake of the BFS flow for different instances of time separated by a small duration. This
will be helpful in tracking the transfer of fluid between the shear layer and the recirculation
zone through entrainment and injection and thus serve to advance our understanding of these
flow.
2.4 Recirculation Zone
The region behind the step, which is bounded by the separating and reattaching shear layer on
the top and by the wall on the bottom is the recirculation zone. Due to the presence of vortices
in the separated shear layer fluid from the recirculation zone is entrained and thus creates a
low pressure triggering recirculation. This region also referred to as the separation bubble is
dominated primarily by a large two-dimensional vortex (or primary vortex) that possesses a
low circulation velocity. The other significant turbulent structure commonly seen in the recir-
culation region is the secondary vortex located at the corner of the step. A sketch illustrating
the recirculation region in a BFS wake can be seen in Figure 2.1.
The literature describing the recirculation region and its prominent features were very few
in the past [17, 25, 37] mainly because of difficulties in measuring recirculating flows. Hot-wires
and pitot tubes were amongst the common instruments used to measure flow properties in early
experiments. These instruments are insensitive to the direction of the flow and hence inaccurate
in highly turbulent regions. Later, with the introduction of new instrumentation techniques
such as the Laser Doppler Anemometer and the PIV, more measurements were acquired from
the recirculation region. Some of the recent studies on the characteristics of the recirculation
region are discussed below.
The characteristics of the recirculation region behind the BFS were studied by Scarano
and Reithmuller [32] using a Digital Particle Image Velocimetry. Their flow streamline results
behind the step suggested that the primary vortex extends from the step edge to the reattach-
ment point while the counter-rotating secondary vortex remains in the corner of the step wall.
Chapter 2. Literature Review 16
Figure 2.6: Mean flow structure of one half of the secondary vortex [36].
Similar results were also noted by other researchers [13, 21, 35, 36]. According to Hudy et al.
[13], the primary vortex is driven by the mass and momentum of the fluid moving upstream
from the shear layer on reattachment, while the secondary vortex is driven by the fluid from the
primary vortex. Due to the frequent oscillation of the reattachment point the size and shape
of the separation bubble is subjected to change. In a flow visualization experiment conducted
by Spazzini et al. [35], they observed the secondary vortex in the recirculation region of a BFS
wake undergoing changes in shape and size in a quasi-periodic cycle. During this cycle, the
secondary vortex was seen to increase in size as large as the step height and then break down to
its smaller size. They believed that the cycle of change in the size and shape of the secondary
vortices and the flapping motion of the shear layer to be two different aspects of a same motion.
Another important property of these vortices were noted by Hall et al. [36], while studying
the characteristics of a BFS wake using PIV. Based on their velocity streamline results, they
suggested that in both primary and secondary vortices the mass flow spiraled towards the center.
This fluid inflow by conservation of mass produces a spanwise directional motion leading to the
transport of the fluid from the core to the step edge as shown in the Figure 2.6. They also
believed that a significant spiral inflow for the primary vortex can have pronounced effect, like
the flapping, on the shear layer and the reattachment length.
2.5 Important Flow Parameters
The most commonly observed characteristics of the flow behind a BFS were discussed in the
previous sections. Apart from the complexity involved due to the instabilities in the flow, the
Chapter 2. Literature Review 17
flow characteristics behind the step were also found to be dependent on certain flow and geomet-
ric parameters. The parameters that significantly affect this flow are the aspect ratio (w/H),
expansion ratio (Y1/Y0), free stream turbulence intensity (√u′2 + v′2 +w′2/U∞), Reynolds num-
ber (U∞H/ν), and the boundary layer state and thickness (δ) at separation [7]. It is essential to
understand the effects of these parameters mainly to be able to compare the results from various
BFS experiments conducted under different conditions. Moreover, in the current research the
knowledge of these effects are used in designing a unique BFS model with wake characteristics
less dependent on such governing parameters. An illustration of the planar BFS geometry and
the aforementioned parameters are shown in Figure 2.7
U!
H
w
Y0 Y1
"
y
z
x
Top wall
Bottom wall
xr
Separation
streamline
Figure 2.7: Planar backward-facing step geometry.
In the following section, the effect of each individual parameter on the reattachment length
are studied extensively. The choice of a reattachment length as an indicator of the step wake
characteristics was preferred in the earlier literature [25, 37–39] mainly because it is easy to
measure and also useful in predicting the base drag. Technological advancements in the in-
strumentation field and analytical schemes have make it possible to measure readily more
information such as the coefficient of pressure, the turbulent structure characteristics in the
shear layer, power spectral data, to name only a few. Nonetheless, the reattachment length is
used in the following discussion as the primary parameter of comparison since it is the most
commonly reported parameter in previous studies. This section serves as an extension to the
study conducted by Eaton and Johnston [7] and includes several more recent results.
Chapter 2. Literature Review 18
2.5.1 Effect of the Expansion Ratio
The expansion ratio is defined as the ratio of downstream to upstream height of the channel
at the step location, i.e. Y1/Y0 as shown in Figure 2.7. The effect of the expansion ratio on
separating and reattaching shear flows was reviewed by Eaton and Johnston [7]. In their re-
view, they compared the results from various experiments on backward-facing step operating
at nearly similar conditions. Their comparative study included expansion ratios ranging from
1.1 to 1.67, although other parameters such as the relative boundary layer thickness at sepa-
ration (δ/H), free stream turbulence intensity and the Reynolds number (ReH) varied slightly
between each experiments. The boundary layers for all the experiments used in this comparison
were fully developed turbulent at separation. Based on those results, Eaton and Johnston [7]
observed a trend that the reattachment length increased with the increase in expansion ratio.
The effect of expansion ratio on the reattachment length was also investigated by Kuehn [40]
by increasing the angle of upper wall divergence at the step location and by changing the step
height. Their results were similar to Eaton and Johnston’s findings, i.e. reattachment length
increased with the increase in expansion ratio. Kuehn [40] attributed the effect on reattachment
length by expansion ratio to the change in adverse pressure gradient. He further confirmed the
role of adverse pressure gradient by observing similar results that were obtained by changing
expansion ratio, while rotating the channel wall.
Later, Otugen [11] studied the effects of expansion ratio on the reattachment length by
changing the step heights between each experiment. The expansion ratios for his experiments
were 1.5, 2 and 3.13, which is higher than most of the previously obtained results. While the
expansion ratio was altered, other flow parameters such as the boundary layer thickness (δ)
and state at separation, Reynolds number (ReH), and the free stream turbulence intensity were
all maintained constant. Their results suggested that the reattachment length decreased with
increasing expansion ratio. They attributed this reduction in the reattachment length for higher
expansion ratios to the increase in turbulence levels in the separated shear layer. Although
Otugen’s [11] results appear to contradict the results observed by Eaton and Johnton [7], the
higher expansion ratios and the different relative boundary layer thickness at separation(δ/H)
in their experiments makes a direct comparison impossible.
2.5.2 Effect of Aspect Ratio
In the case of a planar BFS geometry, like the one shown in Figure 2.7, the wake adjacent to
the step is two-dimensional. This however is not the case for a BFS with finite span. The
two-dimensionality of the flow behind the step with finite span is usually affected by vortices
Chapter 2. Literature Review 19
developing from the side corners of the step or the boundary layers developing from the side
walls. Extensive study was conducted by Brederode and Bradshaw [8] to understand the effect
of aspect ratio (the ratio of width to height of the BFS) on the two-dimensionality of the step
wake. They traced the oil-film patterns on the floor of the turbulent region downstream of
the step for different aspect ratios. Here, the oil-film patterns obtained for aspect ratios 15
and 7.5 are shown in Figure 2.8 for reference. Their results suggested that the flow remained
two-dimensional but not uniform along the width, when the aspect ratio was greater than or
equal to 10:1. They, however, observed improvements in spanwise uniformity with increasing
aspect ratio.
(a) Aspect ratio = 15. (b) Aspect ratio = 7.5.
Figure 2.8: Sketches of oil film pattern on the floor for the region behind the step [8].
Alternative to the above approach, there has also been several studies on the separating
and reattaching shear layer characterisitics behind an axisymmetric BFS geometry. Most have
been on suddenly expanding pipes [41–44] (Figure 2.9(a)) while only a few recent experiments
were conducted on concentric cylinders that are aligned axially to the flow [12–14], as shown
in Figure 2.9(b). The mean flow characteristics surrounding the axisymmetric geometry is
the same as in any finite width planar BFS geometry except the mean flow characteristics are
similar around all azimuthal plane for the axisymmetric geometry [28]. Recently, Li and Naguib
[12] studied the flow characteristics of a separating and reattaching flow over an axially aligned
concentric cylinder. In their experiments, they observed smaller reattachment lengths compared
to the flow over a finite width planar BFS geometry. They hypothesized that the reduction in
reattachment length were caused due to the change in circumferential lengths upstream and
downstream at the step location of the axisymmetric geometry, which was referred to as the
curvature effect [12]. A similar effect was also observed by Hudy and Naguib [13]. In order to
Chapter 2. Literature Review 20
U!
r R
(a) Expanding pipe.
U!
R r
(b) Concentric cylinder.
Figure 2.9: Axisymmetric backward-facing step geometries.
avoid confusion of this effect with the “transverse curvature effect” mentioned in Willmarth et
al. [45] (which will be discussed later in section 4.4.1), the curvature effect suggested by Li et
al. [12] will be referred to as the “circumferential effect” for the remainder of this thesis.
2.5.3 Effect of Free Stream Turbulence Intensity
The free stream turbulence intensity, which is the ratio of the turbulent fluctuation to the
free stream velocity (√u′2 + v′2 +w′2/U∞), has a significant effect on the reattachment of the
shear layer behind the BFS. In a review by Eaton and Johnston [7], while comparing different
experimental results they suspected that the increase in free stream turbulence intensity caused
reduction in the reattachment length. Later, a more systematic and comprehensive study was
conducted by Isomoto and Honami [10] to investigate the effects of free stream turbulence
intensity on the reattachment length. In their work, they changed the free stream turbulence
by using different turbulent grids upstream of the step while maintaining other significant
parameters nearly constant. They observed results similar to Eaton and Johnston’s [7], where
the reattachment length decreased monotonically with the increasing free stream turbulence
intensity. They attributed the reduction in reattachment length to the increase in turbulence
levels within the separated shear layer immediately downstream of the step.
2.5.4 Effect of Boundary Layer State at Separation
The boundary layer state at separation plays an important role in characterizing the flow behind
the step. The effect of boundary layer state on BFS flows is highly nonlinear and difficult to
Chapter 2. Literature Review 21
isolate due to its dependency on Reynolds number and boundary layer thickness at separation.
Hence the combined effect of boundary layer state and thickness on the reattachment length
was studied by Eaton and Johnston [7]. Their results are shown in Figure 2.10. It can be seen
from the figure that the reattachment length increases sharply to a peak value with the change
in boundary layer state from laminar to transitional and then decreases gradually to a steady
value as the boundary layer becomes turbulent.
!"
#"
$"
%" &%%%" '%%%" (%%%"
)*+" ,-*./0,01.*)" ,2-32)4.,"-567689:5;<"=5;><9"?@ ABCD"
+E:5;<F:"<9G8H;5II"-5J;E=KI";F:L5A""?-5MD"
Figure 2.10: Effect of boundary layer state at separation [7].
Similar results (shown in Figure 2.11) were also obtained by Adams and Johnston [46]
when they studied the effect of boundary layer state and thickness on the reattachment length
for different Reynolds number (ReH). In Figure 2.11, it can be seen that the reattachment
length increases to a peak as the boundary layer state changes from laminar to turbulent and
then remains nearly constant. Based on the above results, it can be seen that the effect of
turbulent boundary layer thickness on the reattachment length is negligible. This suggests that
the effects of boundary layer state on reattachment length can be minimized by maintaining a
fully developed turbulent boundary layer at separation.
2.5.5 Effect of Boundary Layer Thickness at Separation
The effect of boundary layer thickness at separation on the reattachment length is not evident
because of its dependence on the boundary layer state and Reynolds number (ReH). Adams
and Johnston [46] attempted to study the effect of boundary layer thickness independent of
the Reynolds number on the reattachment length by applying suction through porous plates
installed upstream of the step. Their BFS model consisted of 24 porous plates which were
Chapter 2. Literature Review 22
0 0.5 1 1.5 24.5
5
5.5
6
6.5
7
Boundary layer thickness at separation (δ/H)
Rea
ttach
men
t len
gth
(Xr/H
)
laminarturbulent
Figure 2.11: Effect of boundary layer state and thickness at separation; ReH = 26,000 [46].
installed approximately 5.98H to 0.01H upstream of the step. When all the plates were in use
they were able to achieve a boundary layer thickness less than 0.005H at the step edge. With
the application of suction Adams and Johnston [46] were able to study the effect of boundary
layer thickness at separation on the reattachment length for different Reynolds number (ReH).
Their results for different Reynolds number and turbulent boundary layer at separation are
shown in Figure 2.12. It can be seen from the figure that the Reynolds number, has significant
impact on the reattachment length. The other key feature to note is that the boundary layer
thickness appears to have a limited effect on the reattachment length due to its turbulent state.
However, the application of suction very close to the step edge is not advisable because
of the change in boundary layer properties immediately after suction thus altering the flow
characteristics behind the step [47]. Experiments conducted by Antonia et al. [47] suggested
that the application of suction to remove the boundary layer resulted in a significant alteration
of the boundary layer properties downstream of the suction. The parabolic variation observed
in the reattachment length with increasing boundary layer thickness could be due to change in
boundary layer turbulence intensity caused by suction. More details on the effects of suction
on the boundary layer will be discussed later in this thesis. Based on the above discussion, it
is clear that further experimentation is required to verify the effect of boundary layer thickness
Chapter 2. Literature Review 23
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.85.2
5.4
5.6
5.8
6
6.2
6.4
6.6
6.8
7
Boundary layer thickness at separation (δ/H)
Rea
ttach
men
t len
gth
(Xr/H
)
ReH = 8,000
ReH = 13,000
ReH = 20,000
ReH = 26,000
Figure 2.12: Effect of Reynolds number and boundary layer thickness at separation [46].
independent of Reynolds number on the reattachment length.
2.6 Summary
In this chapter, the flow characteristics in the wake of a BFS were reviewed and discussed in
detail. From earlier studies, it is understood that the free shear layer behind the step involves
several instability mechanisms such as, vortex rolling and pairing, shedding and flapping. The
rolling and pairing of vortices in the shear layer results in the formation of large coherent struc-
tures. Coherent structures are significant features observed in flow over a step. It has been
demonstrated in several studies that by altering the coherent structures desired characteristics
such as enhanced mixing, reduced drag and subdued noise can be achieved. Hence it is nec-
essary to understand the characteristics of the coherent structures in order to control the flow
actively. The wake characteristics behind a step differs between experiments due to different
operating conditions. Consequently, the individual effects of each significant parameters on the
Chapter 2. Literature Review 24
reattachment length were reviewed. Studies suggests that a number of parameters such as free
stream turbulence intensity, aspect ratio and boundary layer state at separation have a promi-
nent effect on the reattachment length. In Chapter 3, the combined effect of these parameters
with a novel scaling length for reattachment length are discussed.
Chapter 3
Novel Scaling Analysis
3.1 Introduction
In the previous sections, the effect of each significant BFS flow-affecting parameter was re-
viewed. For some parameters such as the free stream turbulence intensity, boundary layer state
at separation and the Reynolds number, their independent effect on the reattachment length
were observed to have a unique relationship. This, however, does not exist while studying
the combined effects of the aforementioned parameters on the reattachment length. In other
words, it has been difficult to predict the reattachment length for a combination of wide range
of BFS flow-affecting parameters. As an example, the effect of the boundary layer thickness at
separation on the reattachment length is studied here with sets of data acquired from several
experiments conducted under different parametric conditions. The results thus obtained are
shown in Figure 3.1 and the data sets used for the current study are included in Table 3.1.
The data set considered for the current analysis is limited to the experimental results with
fully developed turbulent boundary layers at separation and aspect ratios greater than 10. In
Figure 3.1, the experimental uncertainty associated with each measurement is illustrated us-
ing error bars for the few cases where this information is available. The larger error bars are
associated with the changes in the reattachment length due to the flapping of the shear layer,
while the smaller ones represent the uncertainty on the time averaged reattachment length.
The data presented in the figure exhibit a significant amount of scatter due to variations in the
Reynolds number, free stream turbulence intensity, boundary layer thickness at separation and
expansion ratio between each data set. This was to be expected given the discussion of the
previous sections.
25
Chapter 3. Novel Scaling Analysis 26
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
5
5.5
6
6.5
7
7.5
8
Boundary layer thickness (δ/H)
Rea
ttach
men
t len
gth
(xr/H
)
Figure 3.1: Combined effect of parameters on the reattachment length. The legends of thefigure are, + Driver et al. [16]; ● Adams and Johnston [46]; ○ Kim [17]; ◻ Tani et al. [48]; ×Otugen [11]; ◇ Jovic and Driver [49]; △ Lee and Sung [22] ; ▽ Scarano and Reithmuller [32];▷ Scarano and Reithmuller [50]; ◁ Schram et al. [51]; ⊙ Le et al. [52]; ⊡ Heenan and Morrison[53]; � Jovic and Driver[54]; � Roos and Kegelman [2]; ⧫ Chun and Sung [3]; ∎ Troutt et al.[20]; ◂ Adams and Eaton [55]; ▸ Kang and Choi [56]; ⟐ Hudy [28].
3.2 New Normalization Scheme
For the present analysis, a novel normalization scheme is proposed, which includes the bound-
ary layer thickness as part of the characteristics length scale of the flow. The new length scale
parameter is stated as the sum of step height, a geometric parameter, and the boundary layer
thickness at separation, a flow parameter. This contrasts from the common approach, where the
step height is the only length scale considered. The results obtained with the new normalizing
factor are shown in Figure 3.2. It can be seen from the figure that the collapse of the data on
this normalization is greatly improved.
The collapsed data shown in Figure 3.2 is fitted with second-order polynomial, included in
the figure for reference. The curve is given by,
xrH + δ
=
xr
H
1 + δH
≈ −5.73⎛
⎝
δH
1 + δH
⎞
⎠
2
− 2.59⎛
⎝
δH
1 + δH
⎞
⎠+ 6.04 (3.1)
Chapter 3. Novel Scaling Analysis 27
which has a root mean square error of approximately 0.89% with the plotted data and a maxi-
mum error percentage of ≈ 17%. This suggests that there is an excellent collapse of data. This
curve fit serves as a good visual guide and may be a potential model for predicting the reattach-
ment length with only knowledge of the boundary layer thickness and step height at separation.
0.1 0.2 0.3 0.4 0.5 0.6 0.71.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
Boundary layer thickness (δ/H)/(1 + δ/H)
Rea
ttach
men
t len
gth
(xr/H
)/(1
+δ/H
)
Figure 3.2: Boundary layer thickness at separation vs. rescaled reattachment length. Thelegends of the figure are, + Driver et al. [16]; ● Adams and Johnston [46]; ○ Kim [17]; ◻ Taniet al. [48]; × Otugen [11]; ◇ Jovic and Driver [49]; △ Lee and Sung [22] ; ▽ Scarano andReithmuller [32]; ▷ Scarano and Reithmuller [50]; ◁ Schram et al. [51]; ⊙ Le et al. [52]; ⊡Heenan and Morrison [53]; � Jovic and Driverl [54]; � Roos and Kegelman [2]; ⧫ Chun andSung [3]; ∎ Troutt et al. [20]; ◂ Adams and Eaton [55]; ▸ Kang and Choi [56]; ⟐ Hudy [28]; - -- −5.73((δ/H)/(1 + δ/H))2 − 2.59((δ/H)/(1 + δ/H)) + 6.04.
The addition of step height and the boundary layer thickness as a scaling parameter phys-
ically represents the dimension of a geometric and viscous boundary. It is possible that the
momentum or displacement thickness would be more appropriate length scales to add to the
step height since they are the length scales governing the coherent structures in the separated
shear layer. In the current analysis, the boundary layer thickness is used because it is more
readily found in the cited literature. Besides, knowing that the ratios of displacement and
boundary layer thickness (δ∗/δ), and momentum and boundary layer thickness (θ/δ) are nearly
constant, the changes to the existing curve will be small when either one is used. The bound-
ary layer thickness is known to be affected by the Reynolds number (Rex) based on streamwise
Chapter 3. Novel Scaling Analysis 28
Table 3.1: Important parametric data acquired from different experiments on backward-facingstep flowsAuthors Symbols ReH × 10−4 Y1/Y0 δs/H u′/U∞(%) xr/H
Tani et al. [48] ◻ 6 1.07 0.28 na 6.7 ± 0.2Kim [17] ○ 3.00 1.33 0.45 0.60 7 ± 1
4.50 1.5 0.30 0.60 7 ± 1Troutt et al. [20] ∎ 4.5 1.1 0.18 0.6 7Roos and Kegelman [2] � 3.9 1.31 0.38 < 0.05 6.8Driver et al. [16] + 3.7 1.125 1.5 na 6.11 ± 1Adams and Johnston [46] ● 0.8 1.25 0.7 0.3 - 0.4 6.15 ± 0.1
0.8 1.25 1.3 0.3 - 0.4 6 ± 0.10.8 1.25 1.62 0.3 - 0.4 5.85 ± 0.11.3 1.25 0.72 0.3 - 0.4 6.45 ± 0.11.3 1.25 1.16 0.3 - 0.4 6.55 ± 0.11.3 1.25 1.78 0.3 - 0.4 6.25 ± 0.12 1.25 0.14 0.3 - 0.4 6.2 ± 0.12 1.25 0.18 0.3 - 0.4 6.35 ± 0.12 1.25 0.7 0.3 - 0.4 6.6 ± 0.12 1.25 1.1 0.3 - 0.4 6.8 ± 0.12 1.25 1.62 0.3 - 0.4 6.45 ± 0.1
2.6 1.25 0.14 0.3 - 0.4 6.4 ± 0.12.6 1.25 0.2 0.3 - 0.4 6.55 ± 0.12.6 1.25 0.54 0.3 - 0.4 6.8 ± 0.12.6 1.25 1.1 0.3 - 0.4 6.7 ± 0.12.6 1.25 1.62 0.3 - 0.4 6.45 ± 0.1
Adams and Eaton [55] ◂ 3.6 1.25 1 0.2 - 0.4 6.6Otugen et al. [11] × 1.66 1.50 0.72 0.70 6.90
1.66 2.50 0.36 0.70 6.651.66 3.13 0.17 0.70 6.35
Jovic and Driver [54] � 0.5 1.2 1.17 1 6 ± 0.15Jovic and Driver [49] ◇ 0.68 1.09 2 1 5.35
1.04 1.14 1.27 1 6.352.55 1.14 1.2 1 6.92.55 1.2 0.82 1 6.73.72 1.2 0.82 1 6.84
Chun and Sung [3] ⧫ 2.3 1.5 0.38 < 0.6 7.2Le et al. [52] ⊙ 0.51 1.2 1.2 na 6.28Heenan and Morrison [53] ⊡ 19 1.1 0.21 < 0.05 5.88 ± 0.3Scarano and Reithmuller [32] ▽ 0.5 1.2 1.2 0.8 5.9Scarano and Reithmuller [50] ▷ 0.5 1.2 1.5 0.3 6Lee and Sung [22] △ 3.3 1.5 0.41 < 0.8 7.4Kang and Choi [56] ▸ 0.51 na 1.34 na 6.2Schram et al. [51] ◁ 0.51 1.25 1.3 2 5.24Hudy et al. [28] ⟐ 0.6 1.07 ≈1.49 < 1 4.29
0.8 1.07 ≈1.53 < 1 4.481.5 1.07 ≈1.22 < 1 4.791.9 1.07 ≈1.07 < 1 4.94
Chapter 3. Novel Scaling Analysis 29
distance and free stream turbulence, and hence its inclusion in the scaling appears to account
for the effect of these two parameters on the reattachment length. This suggest that these two
parameters are more important in as much as they affect the state of the flow at separation,
rather than play an important role in the separated shear layer evolution. Nonetheless, more
targeted experiments are necessary to evaluate the validity of this scaling unambiguously due
to the limited information available from the studies listed in the Table 3.1.
Chapter 4
Model Design
4.1 Model Design Objective
The wake flow characteristics behind the backward-facing step are dependent on several geomet-
ric and flow parameters such as, the expansion ratio (Y1/Y0), aspect ratio (w/H), free stream
turbulence intensity (u′/U∞), and the boundary layer state and thickness at separation (δ/H).
The effects of each aforementioned parameters on the reattachment length were discussed in
section 2.5. With this knowledge it will be possible to design a BFS model such that the effect
of these parameters are either controllable or eliminated.
4.2 Wind Tunnel Facility
The experiment will be conducted in a subsonic wind tunnel at Flow Control and Experimental
Turbulence (FCET) Lab, University of Toronto Institute for Aerospace Studies. The exper-
imental model was designed taking into account the wind tunnel specifications. The FCET
facility is a closed return wind tunnel with a contraction ratio of 9 ∶ 1 and a test section 5
m long, 1.2 m wide and 0.8 m high. The test section has adjustable corner plates installed
to minimize the disturbance due to the corner vortices. The tunnel is also designed with a
heat exchanger unit to maintain the temperature constant within the test section. A schematic
drawing of the wind tunnel is shown in Figure 4.1. The fan is powered by a 60 hp motor and
can generate wind speeds up to 30 m/s in the test section. The free stream turbulence intensity
within the test section is measured to be approximately 0.05% of the free stream velocity.
30
Chapter 4. Model Design 31
Primary diffuser
Secondary diffuser
Test section
Motor housing
Contraction
Fine mesh
Honeycomb chamber
Heat exchanger
Figure 4.1: Closed return tunnel schematic.
4.3 Model Design
In this section, the key features of the model and rational for their selection are briefly stated
before discussing the details of the model design. Choosing the right geometry is the crucial
decision while designing a backward-facing step model. One of the primary objective while
designing the geometry is to ensure minimal disturbance in the wake due to the boundary
layers from the test section walls and the vortices from the side edges of the step. In other
words, the wake of the step must remain uniform and two-dimensional throughout the span-
wise width. It was discussed earlier in section 2.5.2 that the above criterion can be satisfied if
the geometry were to be axisymmetric. Based on that requirement, two concentric cylinders
forming an axisymmetric backward-facing step is the geometry selected for the current research.
Experiments on an axisymmetric backward-facing step geometry were previously conducted
by Hudy et al. [13]. Their results suggested that the reattachment length was shorter for the
Chapter 4. Model Design 32
axisymmetric geometry than for those measured for the planar case. They believed that the
reduction in reattachment length was caused by the circumference effect. This effect due to
the cylinder curvature can be minimized by choosing big radius for both the cylinders while
maintaining a small step height. However, the maximum size of the model is also limited by
the test section dimensions to maintain an appropriate blockage ratio and an expansion ratio
close to unity.
The bigger radii and step height for the current model were chosen as 125mm (twice as
large as the radii of Hudy’s [28] model) and 12.5mm (equal to Hudy’s [28] model) respectively,
to minimise possible circumference effects. For the above mentioned dimensions, the blockage
ratio is approximately equal to 5.57 %, while the blockage ratio was 3.6 % for Hudy’s [28]
model. Nevertheless, the blockage ratio for the current model is less than 6 %, which according
to West and Apelt [57] is the minimal limit to determine an approximate blockage correction.
The expansion ratios for this model are 1.039 along the Y-axis and 1.024 along the Z-axis.
Although the expansion ratios are not symmetric circumferentially, the values are expected to
be small enough not to have a significant impact on the flow characteristics.
The state and thickness of the boundary layer at separation are the other parameters known
to have significant effect on the characteristics of the step wake. Based on the discussion in
section 2.5.4 it is understood that a fully developed turbulent boundary layer profile at separa-
tion has little impact on the reattachment length. Hence the effects of boundary layer state can
be eliminated by either choosing a longer upstream model length or by tripping the boundary
layer near the leading edge to obain a self similar turbulent boundary layer profile at the sepa-
ration point. For a fixed upstream model length, the boundary layer thickness still varies with
the change in Reynolds number (Rex) and hence will continue to affect the step wake unless
controlled.
There have been several control techniques implemented in the past to maintain the bound-
ary layer thickness independent of the Reynolds number. Mass transfer is described as the
most prominently used boundary layer control technique by Schlichting and Gersten [58]. For
the current design, the boundary layer will be controlled through suction. The application of
suction to control the boundary layer thickness independent of the Reynolds number has been
implemented before in a BFS geometry by Adams and Johnston [9]. In their experiments, they
managed to achieve a boundary layer thickness less than 0.005H at the separation point by
extending the porous strips up to the step edge. Similar suction control experiments on the
boundary layer were also conducted by Antonia et al. [47] on a flat plate. According to Antonia
Chapter 4. Model Design 33
et al. [47], the boundary layer profile changes due to suction and requires some distance to
recover to its unperturbed state. More details on the effects of suction on the boundary layer
profile will be discussed in section 4.4.2. Based on the above information, it is understood that
the presence of suction strip close to the separation point could introduce different effects in
the step wake. Hence for the current model, the suction strip must be located carefully to allow
sufficient relaxing distance downstream of the strip for the boundary layer to recover. Therefore
to choose the upstream length of the model the porous strips are to be designed first and their
details are discussed in following section.
4.4 Porous Suction Strip Design
The objective for the porous suction strip design is to be able to control the boundary layer
thickness independent of the Reynolds number, while avoiding the change in boundary layer
profile due to suction affecting the separated shear layer. The first step to suction strip design
is to derive an analytical expression to estimate the evolution of boundary layer thickness along
the streamwise direction with suction. The estimate is essential for locating the porous strips to
achieve a wide range of boundary layer thickness at separation for a constant Reynolds number
(Rex).
4.4.1 Evolution of the Turbulent Boundary Layer Thickness
An approximate relationship between the boundary layer thickness (δ) and the streamwise
distance (x) with suction is derived using the momentum integral method. In the case of
an axisymmetric geometry, for e.g. a cylinder, the boundary layer development is not usu-
ally the same as the one over a flat plate due to the transverse surface curvature [45, 59, 60].
However, this curvature effect can be neglected on two conditions; if the boundary layer thick-
ness is smaller than or equal to the radius of the cylinder, i.e., δ/r ≤ 1 [61], and if the non-
dimensionalized radius of the cylinder (r+ = r/(ν/uτ)) is greater than or equal to 250 [62, 63].
In the subsonic wind tunnel operating at 5 m/s, assuming the boundary layer to be turbulent
from the leading edge, the model will require more than 5 m to grow a boundary layer as
thick as the radius of the cylinder (125 mm). Also, for the same velocity and an estimated
upstream model length of 1 m the Reynolds number based on the streamwise distance (Rex) is
calculated to be of the order of 3.2 × 105. The local coefficient of friction (cf ) for a turbulent
boundary layer (1/7th power law profile) over a flat plate is given as 0.0592Re−1/5x [64]. From
the above information cf can be calculated to be approximately equal to 0.0047. Assuming the
radius of curvature of the axisymmetric model has negligible effect on cf , the friction velocity
Chapter 4. Model Design 34
(uτ =√τw/ρ), where τw is the wall shear stress, can be calculated to be approximately equal
to 0.2421. The non-dimensionalized radius (r+) based on the above information is calculated
to be 1940. This suggests that the transverse curvature effect to be negligible for the current
model as long as the upstream length is less than 5 m.
The evolution of turbulent boundary layer on the axial cylinder can thus be derived assuming
the flat plate conditions. The growth of turbulent boundary layer for an incompressible flow
along a flat plate with suction is derived using momentum integral method [65]. The control
volume under study is illustrated in Figure 4.2.
mda
mbc
mab
x
y
b
a
c
d
mcd
V0
δ + dδ
δ
dx
Figure 4.2: Schematic of control volume used for momentum integral analysis.
Conservation of Mass
The mass flow rate into the system through ‘ab’ surface is given by,
mab = ρ
δ
∫
0
u(y)dy, (4.1)
where ρ is the density of the incompressible fluid and u(y) is the velocity profile within the
boundary layer. The mass flow rate out of the system through ‘cd ’ surface can be derived using
the Taylor series expansion (neglecting the higher order terms) as,
mcd = ρ
δ
∫
0
u(y)dy +d
dx
⎛⎜⎝ρ
δ
∫
0
u(y)dy⎞⎟⎠
dx. (4.2)
The mass flow rate out of the system through ‘da’ surface due to suction can be given as,
mda = ρ (V0dx) , (4.3)
Chapter 4. Model Design 35
where V0 is assumed to be uniform suction velocity along the porous strip. Finally, the mass
flow rate into the system through ‘bc’ surface can be determined using the continuity equation
to be,
mbc =d
dx
⎛⎜⎝ρ
δ
∫
0
u(y)dy⎞⎟⎠
dx + ρ (V0dx) . (4.4)
Conservation of Momentum
The conservation of momentum is established along the x-direction. The momentum along the
x-direction is due to the mass flow through the surfaces ab, bc and cd. The momentum due to
the mass flow into the control volume can be given as,
Fab + Fbc = ρ
δ
∫
0
u2(y)dy +
ddx
⎛⎜⎝ρ
δ
∫
0
u(y)U∞dy⎞⎟⎠
dx + ρ (V0dx)U∞, (4.5)
where U∞ is the free stream velocity along the streamwise direction. The momentum along
x-direction due to the mass flowing out of the control volume can be given as,
Fcd = ρ
δ
∫
0
u2(y)dy +
ddx
⎛⎜⎝ρ
δ
∫
0
u2(y)dy
⎞⎟⎠
dx. (4.6)
Fcd − Fab − Fbc gives the total momentum acting along streamwise direction.
F =d
dx
⎛⎜⎝ρ
δ
∫
0
u2(y)dy
⎞⎟⎠
dx −d
dx
⎛⎜⎝ρ
δ
∫
0
u(y)U∞dy⎞⎟⎠
dx − ρ (V0dx)U∞. (4.7)
Since the pressure gradient is assumed to be zero, the only force acting on the flat plat (i.e. the
axisymmetric model) will be the shear stress acting along the suction strip. Therefore, the F
on the flat plate can be written as
F = −τwdx, (4.8)
−τw = ρd
dx
δ
∫
0
u2(y)dy − ρ
ddx
δ
∫
0
u(y)U∞dy − ρ (V0U∞) . (4.9)
The boundary layer thickness (δ) is defined as the distance normal from the wall to the
point where u(y) = 0.99U∞. The expressions for displacement thickness (δ∗), and momentum
thickness (θ) are given as
Chapter 4. Model Design 36
δ∗ =δ
∫
0
(1 −u(y)
U∞)dy, (4.10)
θ =
δ
∫
0
u(y)
U∞(1 −
u(y)
U∞)dy. (4.11)
Using the above definitions, the following equations can be derived
δ
∫
0
u (y)dy = U∞ (δ − δ∗) , (4.12)
δ
∫
0
u2(y)dy = U∞
δ
∫
0
u (y)dy −U2∞θ = U
2∞ (δ − δ∗ − θ) . (4.13)
With the above two relationships (4.12),(4.13), (4.9) can be simplified to,
τwρ
= U2∞
dθdx
+U∞V0. (4.14)
This can be represented in terms of δ by replacing θ with the relation in (4.13) as
τwρ
= U2∞
ddx
⎡⎢⎢⎢⎢⎣
δ
∫
0
u (y)
U∞(1 −
u (y)
U∞)dy
⎤⎥⎥⎥⎥⎦
+U∞V0. (4.15)
The turbulent boundary layer profile is assumed to remain self-similar along the length
of the suction strip and is approximated by u(y)/U∞ = (y/δ)1/7. Assuming the power-law
approximation, an empirical expression for the coefficient of friction of a turbulent boundary
layer over a flat plate without suction can be given as cf ≈ 0.02Re−1/6δ [64]. Based on the above
expression the wall shear stress can be written as,
τw = 0.01ρU2∞ (
ν
U∞δ)
16
. (4.16)
Substituting (4.16) in (4.15) and rewriting in terms of η, where η = y/δ, we get
0.01ρU2∞ (
ν
U∞δ)
16
= ρU2∞
dδdx
1
∫
0
η17 (1 − η
17 )dη + ρU∞V0, (4.17)
0.01(U5∞νδ
)
16
=772U∞
dδdx
+ V0. (4.18)
Chapter 4. Model Design 37
Let A = 0.01 (U5∞ν)16 , B = 7
72U∞ and h = δ16 , such that (4.18) can be expressed as,
dx = B6h6dhA − V0h
. (4.19)
The evolution of the boundary layer thickness can be calculated from (4.19) by numerically
integrating using a fourth-order Runge-Kutta method. However, to get more insight on the
expression, the above equation is further simplified by assuming s = A − V0h. The modified
equation is given as,
dx = −6BV 7
0
[A6dss
− 6A5ds + 15A4sds − 20A3s2ds + 15A2s3ds − 6As4ds + s5ds] . (4.20)
The above assumption is only valid for V0 /= 0. Choosing V0 = 0 makes s = A (a constant),
and thus ‘dh’ cannot be replaced by ‘ds’. Hence for the case where V0 = 0, the following
derivation is not applicable. For further simplification, (4.20) is then integrated on both sides
to get,
x = −6BV 7
0
[A6 ln ∣s∣ − 6A5s +152A4s2 −
203A3s3 +
154A2s4 −
65As5 +
s6
6] +C, (4.21)
where C is the integral constant. Substituting and expanding s and h in (4.21) gives,
x = −6BV 7
0
[A6 ln ∣A − V0δ16 ∣ −
14760
A6+A5V0δ
16 +
12A4V 2
0 δ13 +
13A3V 3
0 δ12 ]
−6BV 7
0
[14A2V 4
0 δ23 +
15AV 5
0 δ56 +
16V 6
0 δ] +C.
(4.22)
The constant ‘C’ in (4.22) can be determined by substituting the appropriate boundary
conditions. For instance, at x = 0 let the initial boundary layer thickness before the suction
strip δ = δ1, therefore the constant can be calculated as,
C =6BV 7
0
[A6 ln ∣A − V0δ161 ∣ −
14760
A6+A5V0δ
161 +
12A4V 2
0 δ131 +
13A3V 3
0 δ121 ]
+6BV 7
0
[14A2V 4
0 δ231 +
15AV 5
0 δ561 +
16V 6
0 δ1]
(4.23)
On substituting (4.23) in (4.22) the equation is simplified to,
Chapter 4. Model Design 38
x = −6BV 7
0
⎡⎢⎢⎢⎢⎢⎣
A6 lnRRRRRRRRRRRRR
A − V0δ16
A − V0δ161
RRRRRRRRRRRRR
+A5V0(δ16 − δ
161 ) +
12A4V 2
0 (δ13 − δ
131 ) +
13A3V 3
0 (δ12 − δ
121 )
⎤⎥⎥⎥⎥⎥⎦
−6BV 7
0
[+14A2V 4
0 (δ23 − δ
231 ) +
15AV 5
0 (δ56 − δ
561 ) +
16V 6
0 (δ − δ1)] .
(4.24)
It is interesting to note that in (4.24) when V0 → 0.01U∞Re−1/6δ , the streamwise distance
x →∞. This implies that, δ will asymptote to a value equal to (0.01 (U5∞ν)16 /V0)
6
as x →∞.
The asymptotic state of the boundary layer on suction is physically reasonable because it is
the condition when a balance exists between the free stream mass flow entering the boundary
layer due to entrainment and the mass flow leaving due to suction. This also suggests that
theoretically complete suction of the boundary layer is not possible, since it implies infinite
shear stress at the wall.
In the following, the validity of (4.24) is tested by comparing analytical predictions to ex-
perimental measurements. The experimental measurements on the evolution of boundary layer
with streamwise distance can be obtained from the suction control study conducted by Yoshioka
et al. [66] on a flat plate. Due to the complexity involved in measuring the turbulent boundary
layer thickness with suction, they measured the velocity profile at several streamwise distance
to calculate the displacement thickness.
The analytical expression given in equation (4.24) is based on a major assumption that the
turbulent boundary layer with suction follows a power law profile, i.e., u(y)/U∞ = (y/δ)1/7.
Hence the analytical and the experimental results can be comparable only if both have similar
velocity profiles. This can be verified by comparing the boundary layer evolution obtained
from analytical and experimental methods for the no suction case. The results are shown in
Figure 4.3.
For the cases when suction was applied the results suggest that the theory slightly over
predicts the effect of suction on displacement thickness in comparison to the experiments. The
percentage of error between the experimental and analytical results are maximum when the
suction velocity is large. The highest error recorded was approximately 27%. The displacement
thickness were measured at various streamwise locations (x/δ∗0 ) along the suction strip, where δ∗0is the displacement thickness at the leading edge of the strip. The analytical results are mostly
within 10% of the experimental value and therefore suggesting acceptable match between them.
Chapter 4. Model Design 39
0 0.5 1 1.5 2 2.54
5
6
7
8
9
10
11
12
Suction Strip Width (m)
Dis
plac
emen
t Thi
ckne
ss (
mm
)
V0 = 0.024 (m/s)
V0 = 0.016 (m/s)
V0 = 0.008 (m/s)
V0 = 0 (m/s)
V0 = 0.024 (m/s)
V0 = 0.016 (m/s)
V0 = 0.008 (m/s)
V0 = 0 (m/s)
Figure 4.3: Evolution of displacement thickness over a flat plate, with and without suction atthe wall. Symbols denote the experimental results and the lines denote the analytical resultscomputed from 4.19.
The slight mismatch between these results can be attributed to the several assumptions made to
arrive at 4.24. One of the major assumptions in the analytical method is that the velocity profile
of the boundary layer would remain similar with or without suction. The changes in boundary
layer properties and the velocity profile, however, has been well documented by Antonia et al.
[47]. Despite these assumptions, the analytical model predicts the evolution of boundary layer
within certain level of accuracy and hence is adequate for designing the porous strip for the
model.
4.4.2 Effects of Suction on Turbulent Boundary Layers
The method of controlling the boundary layer thickness through mass transfer is a commonly
used technique. The application of suction to control the boundary layer has its pros and cons
and hence it is important to understand the limitations of suction control for the current study.
The effect of suction can be understood by observing the characteristics of the boundary layer
evolving downstream of the suction strip. There have been several studies both experimental
Chapter 4. Model Design 40
[67], [47] and numerical [68] on the evolution of the boundary layer after suction. It can be
realized from these studies that the effect of suction causes suppression in turbulence level by
removing the near-wall eddies from the turbulent boundary layer, which causes a significant
change in the boundary layer characteristics. For higher suction rates, the turbulent boundary
layer has been observed to undergo relaminarization close to the wall. Nevertheless, the changes
that occur in the boundary layer due to suction fades away downstream as the boundary layer
recovers to its original velocity profile, however, with a smaller boundary layer thickness than
it would have had without suction. If those changes in the turbulence intensity within the
boundary layer were to happen near the separation point of the model it will alter the shear
layer and consequently the flow characteristics behind the step [10]. Hence it is necessary to
locate the suction strip such that the boundary layer recovers to a full-developed state before
separation.
The evolution of boundary layer properties at various streamwise locations downstream of
suction strip were extensively studied by Antonia et al. [47]. Their experiments were limited to
the application of suction to a flow with self preserved turbulent boundary layer over a flat plate.
Their measurements included variables such as skin friction coefficient (Cf ) and the Reynolds
stresses u′2, v′2 and −u′v′ at different streamwise locations. They conducted the experiments
for various levels of non-dimensionalized suction rate (σ). The suction rate, σ, is given by,
σ =V0w
U∞θ0, (4.25)
where V0 is the suction velocity, w the suction strip width and θ0 the momentum thickness
of the turbulent boundary layer at the leading edge of the suction strip when no suction is
applied. According to Antonia et al. , the suction rate (σ) required for completely removing the
boundary layer can be calculated to be approximately 10. In their experiments, they applied
different suction rates namely, 2.6, 5.2 and 6.5, and observed the changes in the boundary layer
properties immediately downstream of the strip. Based on the Reynolds stress measurements
acquired from different downstream locations, they were able to predict the approximate recov-
ery distance required for the boundary layer to develop back to its original state. For a suction
rate, σ = 2.6, the recovery length for the boundary layer was determined to be approximately
40δ0, where δ0 is the boundary layer thickness at the leading edge of the suction strip for the
no suction case. As for higher suction rates, the boundary layer was observed to be still in the
process of recovery at the farthest measurement location, which was 63δ0 downstream from the
strip.
Chapter 4. Model Design 41
The application of suction to control boundary layer thickness in a BFS flow provides two
benefits. Firstly, it is essential in studying the characteristics of the step wake independent of
the boundary layer thickness effects. Secondly, it provides an opportunity to extend the study
conducted by Adams and Johnston [9] in understanding the effects of boundary layer thickness
independent of Reynolds number on the reattachment length. To be able to perform both, it
must be possible to achieve a wide range of boundary layer thicknesses at the separation point
independent of the Reynolds number. Based on the above discussion, the turbulent boundary
layer thickness achievable after recovery with one suction strip is dependent on δ0 and the
suction velocity. Therefore, the range of boundary layer thickness that can be attained with
one suction strip is limited by those parameters. This range can be increased by incorporating
multiple porous strips. Experiments with double suction strip to delay the transition in bound-
ary layer were performed by Oyewola et al. [69]. They demonstrated that the transition of the
relaminarized boundary layer from the first suction strip can be delayed by introducing a second
suction strip before the transition starts. However, for the current design the objective is to
hasten the recovery process while smaller boundary layer thickness can be achieved. Therefore,
with multiple suction strip in place it must be ensured that strips downstream of the first one
are placed near the location where the boundary layer has nearly fully recovered from the effect
of suction. However, choosing fixed locations for the porous strips is difficult as the boundary
layer recovery process depends on the operating Reynolds number of the flow.
For the current model design, the length of the model from the stagnation point at the nose
to the step was selected to be 1450 mm. The model is designed long so that the boundary layer
will be fully-developed turbulent at separation and also contain multiple porous strips if neces-
sary. To have a large range of boundary layer thickness at the separation point, three porous
strips 40 mm wide each are incorporated in the upstream length. The porous strip width was
chosen based on the model by Antonia et al. [47], which was adequate for complete removal of
the boundary layer. The location for the three porous strips were predicted based on equation
(4.19), but due to the variable Reynolds number range to be used in the experiments, some
flexibility was required. The porous strips were located at 750 mm, 1000 mm and 1200 mm
from the trailing edge of the nose cone. The first suction strip is placed near the center of
the bigger cylinder to ensure the boundary layer is fully developed and turbulent. The porous
strips are designed to be interchangeable so that their widths can be adjusted by placing two or
three strips adjacent to each other. Moreover, the bigger cylinder is made of five interchange-
able parts as shown in Figure 4.4 so that the location of the porous strips can be adjusted if
necessary. Furthermore, the suction velocity through each strip is controlled independently via
individual control valves to provide further flexibility to the suction system.
Chapter 4. Model Design 42
!"#"$%&%'#()%&
*'+)&
&,"-+.&
*$))"#'&
Figure 4.4: Axisymmetric backward-facing step model.
The evolution of boundary layer thickness upstream of the step is calculated using [4.19] for
certain free-stream and suction velocities. The boundary layer thickness at different conditions
are shown in Figure 4.5. The porous strip location were also altered to achieve different bound-
ary layer thickness at separation. The first four cases shown in the legend, are for strip location
placed at 750 mm, 1000 mm and 1200 mm from the trailing edge of the nose cone respectively.
The last two cases shown in the legend are when the strips are located at 450 mm, 750 mm
and 1000 mm from the trailing edge of the nose cone respectively. The option of changing the
porous strip location also provides more distance for the boundary layer to recover to its origi-
nal state. The range of boundary layer thickness that can be achieved by altering the suction
velocity and free stream velocity is between 2.88 δ/H and 0.33 δ/H.
Chapter 4. Model Design 43
Figure 4.5: Evolution of boundary layer thickness for different suction velocity.
4.5 Suction System Design
Apart from choosing the porous strip width and their locations in the axisymmetric model, it
is also essential to ensure that the application of suction is uniform along the surface of the
model. Similar to the experimental set up conducted by Antonia et al. [47], for the current
model plenum chambers are installed between the porous strip and a vacuum pump. An illus-
tration of the suction system design used for the current model is shown in Figure 4.6. Each
Plenum chamber is built with two holes, outer diameter 5/32”, for air tubings to achieve uni-
form suction along its circumference. The metal link between each plenum chamber, as seen
in figure, is required for the structural integrity of the model. Nevertheless, the metal link is
designed concave (curved inwards) on the top surface, as shown in Figure 4.7, to allow air flow
between chambers and thus create a 360○ suction surface without discontinuity.
Furthermore, in order to estimate the approximate power required to activate the suction
strip, a simple experiment was conducted to determine the pressure drop across a porous strip.
A sketch of the experimental set up is shown in Figure 4.8. A square, 4” × 4”, porous sample
Chapter 4. Model Design 44
Figure 4.6: Plenum chamber design within the suction strip system.
Figure 4.7: Cross sectional view of a plenum chamber.
with pore density 40 µm was used for this experiment. The porous strip was installed in front
of a 2 inch inner diameter (D) and 6 feet long acrylic pipe. The dynamic pressure was measured
using a pitot static tube, which was connected to a 223-B MKS Baratron differential pressure
transducer with full scale range up to 1 mbar and accuracy of 5% of full scale reading. The
pitot static tube was installed at about 20D downstream from the porous strip to allow the flow
to achieve developed turbulent state. The static pressure at the same location was separately
monitored using a Betz manometer. During the experiment, each measurement was sampled
thirty times for a time period of one second to minimize the precision uncertainty. The precision
uncertainty for 95% confidence is given by 2σ/N , where σ is the standard deviation and N is
the total number of samples (in this case 30) per data. The total uncertainty for the velocity
measured in this experiment was calculated to be within ±6%
Chapter 4. Model Design 45
Vacuum pump!
Ball valve!
Pressure transducer!
Porous plate!
Pitot static tube!
Figure 4.8: Experimental set up to measure pressure drop across a porous plate.
The velocity profile thus obtained from the measured dynamic pressure is shown in Fig-
ure 4.9. The experimental data is in good agreement with a power law fit of a fully developed
turbulent pipe flow profile. The power law fit is given by U/Umax = (r/R)(1/7), where U is the
instantaneous velocity, Umax is the maximum velocity, r is an instantaneous position in the
radial direction of the pipe and R is the radius of the pipe. From the velocity profile, the mean
velocity is calculated to be 3.73 m/s. Using Bernoulli’s equation the pressure drop (Pd) across
the porous plate can be given as,
Pd = P1 − P2 −12ρV 2
2 − Pl, (4.26)
where P1 is the atmospheric pressure, P2 is the static pressure near the pitot static tube, ρ is the
density of air, V2 is the average flow velocity inside the pipe and Pl is the pressure loss due to
the sudden entrance. The difference between the static pressures, P1−P2 was measured using a
Betz manometer to be approximately 107.91 Pa. The pressure loss due to the sudden entrance
can be calculated using the formula, Pl = KV 22 /2, where K is 0.78 for reentrant type pipe
entrance [70]. Based on the above results, the ratio of pressure drop to dynamic pressure at the
location of measurement per square inch of the porous plate is determined to be approximately
4.13. Therefore the non-dimensionalized pressure drop across three porous strips in the model
for the same suction velocity can be calculated to be approximately 525.5.
4.6 Model Support
The support is essential for centering the model inside the test section. It is also necessary for
holding the model firmly to minimize any deflection due to its own weight and avoid the unde-
Chapter 4. Model Design 46
−0.2 0 0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
1.2
1.4
r/R
U/U
max
experimental datapower law fit
Figure 4.9: Velocity profile of a fully developed turbulent pipe flow.
sirable structural vibration. In the current research, the field of study is at the wake of the step
and hence placing the model support upstream of the step could affect the wake characteristics.
Alternatively, the model support can be located downstream from the step.
In an experimental study conducted on a BFS, Farabee and Casarella [26] observed the
large scale turbulent structures shedding and convecting downstream from the separated shear
layer. These turbulent structures were detected to be steadily decaying and diffusing away as
they progressed downstream and yet were identifiable as far as 72H from the separation point.
Based on these observations, it will be preferable to locate the support at least 72H to minimize
noise due to the support from propagating upstream. Simultaneously, locating the support too
far downstream could lead to large deflections closer to the leading edge of the model due its
own weight. Such deflections can be a major issue for the current study because of their effects
on the flow symmetry over the model.
For the current study, the support is located at 932 mm, i.e., 74.5H, downstream from the
step and the total length of the smaller cylinder is 1.5 m. Based on the finite element analysis
(carried out by the manufacturer), for the aforementioned dimensions the cantilever type model
was ensured minimal deflections, which is approximately 0.36 mm at the leading edge. The
height of the support is chosen as 287.5 mm to center the model inside the test section. The
Chapter 4. Model Design 47
support cross-section was designed using the NACA 0012 profile. The aerodynamic section
provides minimum flow blockage, while being structurally stiff and allowing enough space to
pass the suction system piping.
4.7 Nose and Trailing Cone Design
The nose and the trailing cone are integral parts of the axisymmetric model. They are necessary
to keep the flow attached and therefore minimize aerodynamic disturbances. In the following
section, the selection of nose and trailing cone using potential flow theory will be discussed
briefly.
4.7.1 Axisymmetric Nose Design
The objective for the nose design is for the flow to remain attached along the surface at any
given velocity within the operating range. Although the nose model is axisymmetric, a two-
dimensional analysis is used for the current study because it is the most stringent with respect
to separation and is simpler to perform with available tools. For better understanding over
the choice of two-dimensional analysis, as an example the variation of coefficient of pressure
Cp = 2(P−P∞)/(ρU2∞) data over the surface of a cylinder and a sphere, shown in Figure 4.11, are
studied here. It can be seen from the figure that the change in pressure is smoother in the case
of a sphere, implying a less chance of separation in comparison to the cylinder. This suggests
that designing a nose profile based on two-dimensional analysis will only ensure better chances
for the flow to remain attached. Therefore for the current study a 2D analysis is sufficient. The
other requirements for the nose design include short length and light weight to minimize the
deflections at the leading edge of the model. The nose design procedure involves two steps and
they are,
• creating co-ordinates for the nose profile using potential flow theory and
• analysing the flow characteristics over the profile using Xfoil.
Some of the shapes considered for the nose cone design are hemispherical nose, elliptical
nose and the leading edge of the symmetrical NACA airfoil profiles.
Hemispherical Nose Profile
A hemispherical profile for the nose can be designed using potential flow theory by assuming
it as the combination of a uniform flow and a source flow. For the current design, with the
Chapter 4. Model Design 48
! ! !
Fig
ure
4.10
:Sc
hem
atic
ofth
eax
isym
met
ric
mod
elw
ith
dim
ensi
ons.
Chapter 4. Model Design 49
Figure 4.11: Pressure distribution over a cylinder and a sphere [71].
diameter of the model known the hemispherical nose can be easily designed. The co-ordinates
for the nose are obtained using the equation of a circle, which is given by,
x2+ y2
= R2, (4.27)
where x and y are the co-ordinates of the circle and R is the radius of the circle. The flow over the
resulting profile is then analysed using Xfoil and the coefficient of pressure (Cp = 2(P−P∞)ρU2∞ )
along the surface of the nose are obtained, where P is the local static pressure and P∞ is the free
stream static pressure. Since the flow is more likely to stay attached when the flow is turbulent
the analysis is tested for the lowest operational velocity, 5 m/s. A graphical representation of
the change in Cp with normalized streamwise distance x/xn, where xn is the length of the nose
profile, is shown in Figure 4.12. The length for the hemispherical model is equal to the radius
of the hemisphere, i.e., 125 mm.
Rankine Oval
The combination of uniform, source and sink flow creates an elliptical profile, which is also
commonly referred to as the Rankine oval. The co-ordinates for the Rankine oval can be
generated by knowing the major and minor diameters of the ellipse. The minor radius (Ra) of
Chapter 4. Model Design 50
the nose profile is equal to the radius of the cylinder attached to the nose, which is 125 mm.
The major radius (Rb) is dependent on two variables and they are the strength of the source or
sink flow (Λ) and the distance between the source and the sink (2d). For the current case, the
strength of the source and the sink are the same and can be determined based on minor radius
and different values of d. The source or sink strength Λ is given by,
Λ =2πU∞Ra
tan−1 ( 2dRa
R2a−d2 )
. (4.28)
Knowing the source strength and the distance between the source and sink, the major radius
can be determined using the following expression,
Rb =
√
d2 +ΛdπU∞
. (4.29)
Rankine oval profiles were considered for five different d values namely, 0.1, 0.2, 0.3, 0.4 and
0.5. The corresponding major radius or the length of the nose profile for all the above cases
are 169 mm, 254 mm, 349 mm, 447 mm and 0.545 mm respectively. Their equivalent major
to minor radius ratios are 1.352, 2.032, 2.792, 3.576 and 4.36 respectively. The front half of
the ellipse profile is then combined with the profile of a long cylinder and is then inputted into
Xfoil for analysis. The change in Cp with x/xn, for the elliptical leading edge are included in
Figure 4.12.
Symmetrical NACA Airfoil
The symmetrical NACA airfoils chosen for the current study are 0012, 0015, 0018, 0021, 0024,
0027 and 0030. The co-ordinates for the above mentioned symmetrical airfoil profiles can be
obtained from the following equation,
y =t
20(0.2969
√x − 0.126x − 0.3516x2
+ 0.2843x3− 0.1015x4) , (4.30)
where t is the thickness to chord ratio of the airfoil. The lengths of the leading edge in the afore-
mentioned NACA airfoil profiles are 625 mm, 500 mm, 417 mm, 357 mm, 313 mm, 277.8 mm and
250 mm respectively. The results of Cp versus x/xn for these airfoils are included in Figure 4.12.
It can be observed from Figure 4.12 that along the surface of each nose profiles the Cptends to decrease initially to a minimum value, Cpmin , and then increase to a constant value
on the straight section of the model. For the hemispherical model, Cpmin reaches the largest
amplitude in comparison to the rest of the nose model designs. This suggests that the wall
static pressure on the hemispherical nose model varies largely along the curvature and hence is
Chapter 4. Model Design 51
0 0.5 1 1.5 2−2
−1.5
−1
−0.5
0
0.5
1
Normalized streamwise distance (x/xn)
Coe
ffici
ent o
f Pre
ssur
e (C
p)
doubletRankine−0.1Rankine−0.2Rankine−0.3Rankine−0.4Rankine−0.5airfoil−0012airfoil−0015airfoil−0018airfoil−0021airfoil−0024airfoil−0027airfoil−0030
Figure 4.12: Coefficient of pressure versus the normalized streamwise distance for different nosemodels
most likely for the flow to separate. This is also evident from Figure 4.13, which suggests that
the flow experiences adverse pressure gradient close to the junction connecting the nose and
the cylinder, i.e., x/xn = 1.
In the case of the Rankine oval models the Cpmin value increases with the increase in the
length of the nose, i.e., the major axis radius of the ellipse. It can be seen from the Figure 4.13
that the pressure gradient becomes positive for small nose lengths. This suggests that the
probability of the flow separating are higher. For the NACA symmetrical airfoils, with the
decrease in thickness to chord ratio the Cpmin increases gradually. Consequently, the pressure
gradient over the surface changes gradually and reaches positive but small values close to the
nose and cylinder junction for higher t. Although NACA airfoils with smaller thickness performs
better, they have large lengths. Based on the information from the plots, NACA 0027 with a
nose length of 0.2778 m is preferred for the axisymmetric model because of its reactively small
Chapter 4. Model Design 52
0 0.5 1 1.5 2−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
Normalized streamwise distance (x/xn)
Pre
ssur
e gr
adie
nt (
dP/d
x)/1
000
N/m
3
doubletRankine−0.1Rankine−0.2Rankine−0.3Rankine−0.4Rankine−0.5airfoil−0012airfoil−0015airfoil−0018airfoil−0021airfoil−0024airfoil−0027airfoil−0030
Figure 4.13: Pressure gradient versus the normalized streamwise distance for different nosemodels
length and small positive pressure gradient.
4.7.2 Trailing Edge Cone Design
The tail cone forms the trailing edge of the axisymmetric model. In place of a blunt trailing
edge, a tail cone plays an important role in minimizing the aerodynamic disturbances due to
separation. For the current model, the half cone angle of the tail is chosen as 11 degrees,
based on Hudy’s [28] model. The cone angle was appropriate for Hudy’s study and besides the
resulting length, 580 mm, is appropriate for the space available in the tunnel.
Chapter 5
Conclusions and Recommendations
5.1 Conclusions
The characteristics of a separating and reattaching flow on a BFS geometry was reviewed exten-
sively in this thesis. Despite numerous experimental studies on a BFS, definite understanding of
the flow characteristics has not been accomplished because of the different parametric conditions
in each experiments. In a review by Eaton and Johnston [7], they identified few geometrical
and flow parameters such as, expansion ratio, aspect ratio, free stream turbulence intensity,
boundary layer state and thickness at separation to have significant effect on the reattachment
length. The individual effects of each aforementioned parameters were reviewed in this thesis.
The effect of aspect ratio was extensively investigated by Brederode and Bradshaw [8]. They
suggested that three-dimensional effects in the wake can be minimized close to the centerline
by using a planar model with an aspect ratio greater than 10. Even though more larger aspect
ratio in a planar BFS model can produce nearly two-dimensional wake, a better alternative is
to use an axisymmetric geometry with an expansion ratio close to unity. Hudy [28] studied
the flow over an axisymmetric model which not only had minimal three dimensional effects,
but also uniform wake along the circumference. The effects of free stream turbulence intensity
on the reattachment length was studied by Isomoto and Honami [10] by using different grids
upstream of the step. They found that the reattachment length grew shorter with increasing
free stream turbulence intensity and attributed it to the increase in turbulence within the shear
layer. In the case of a boundary layer state, Eaton and Johnston [7] demonstrated that it had a
nonlinear relationship with the reattachment length. However, an interesting observation was
that the reattachment length had little or no effect on the boundary layer thickness when it
was fully developed turbulent.
In the current study, using the data obtained from different experiments, the combined ef-
53
Chapter 5. Conclusions and Recommendations 54
fect of parameters on the reattachment length was investigated. A new scaling factor, the sum
of boundary layer thickness at separation and step height, was proposed for the reattachment
length. The novel scaling parameter physically represents the dimension of a geometric and
viscous boundary. With the new scaling and by studying the effects of boundary layer thick-
ness on the reattachment length, it was observed that the data collapsed with a second order
polynomial. This curve fit acts as a visual guide and can be a potential model for predicting
the reattachment length. The boundary layer thickness is known to be affected by both the
Reynolds number (Rex) and the free stream turbulence, and hence its inclusion in the length
scale appears to account for their effects on the reattachment length. This also suggests that
these two parameters are important as much as they affect the state of the flow at separation.
Since the information of the data used in this analysis was limited, more targeted experiments
will be required to further verify this collapse.
The extensive review on the effects of parameters on separated shear layer can be useful in
designing a model to either eliminate or control the parametric effects. In the current study, an
axisymmetric BFS model is designed. The model dimensions such as the bigger cylinder radii
and the step height were chosen as 125 mm and 12.5 mm respectively. These aforementioned
dimensions were particularly designed based on Hudy’s [28] set up, to further investigate the
circumference effect for a bigger radii ratio. The upstream cylinder is designed 1.45 m long to
accommodate three porous strips and also ensure turbulent boundary layer at separation. The
porous strips were installed to control the boundary layer thickness at separation independent
of the Reynolds number. The nose cone for the axisymmetric geometry is designed from a
NACA 0027 profile based on two-dimensional flow analysis to avoid flow separation.
5.2 Future Experimentation
The literature review study conducted on the flow characteristics in the wake of a BFS provides
a number of interesting topics to investigate in the future.
• The unusually short reattachment length observed in the previously tested axisymmetric
geometries were believed to be due to the circumference effect. The current model specif-
ically designed twice as big as the Hudy’s model [28], while maintaining the same step
height, can provide some insight on the circumference effect.
• In the previously conducted boundary layer thickness control experiment by Adams and
Johnston [46], they did not account for the change in boundary layer properties due to
suction. Hence with the suction control available in the current model, the effects of
Chapter 5. Conclusions and Recommendations 55
boundary layer thickness independent of Reynolds number on the reattachment length
can be conducted to provide more quantitative data. Further more, the effect of Reynolds
number on the reattachment length can also be examined.
• The effect of turbulence intensity on the reattachment length has been previously stud-
ied by Isomoto and Honami [10]. Nonetheless, conducting a similar investigation using
structured grids upstream of the model will not only provide more data to support their
results, it can also be useful to validate the new scaling length proposed in this work.
• The effect of wall suction on the boundary layer properties over a flat plate were studied
by Antonia et al. [47]. In the current model the effect of wall suction on the boundary
layer over a curved surface can be investigated.
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