A study of the flow in an s shaped duct 1

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Chapter 1
INTRODUCTION AND LITERATURE
REVIEW


1.1 Introduction
The study of flow in curved ducts has received constant attention from researchers due
to its wide applications in the industry. The layout of any practical piping system necessarily
includes bends and the accurate prediction of pressure losses, flow rate and pumping
requirements demands knowledge of the character of curved duct flows.
Curved duct flows are also very common in aerospace applications. Many military
aircraft have wing root or ventral air intakes and the engine is usually located in the centre of
the aircraft’s fuselage. Air entering these intake ducts must be turned through two curves (of
opposite sign) before reaching the compressor face. Such a configuration results in an S-
shaped air intake duct and therefore the engine performance becomes a strong function of the
uniformity and direction of the inlet flow and these parameters are primarily determined by
duct curvature.
The present introductory chapter intends to provide a review of the flows in curved
ducts and S-shaped ducts. Discussion is focused on the mechanism of vortex formation, the
vortex topology, surface pressure measurements and duct’s exit flow conditions.

1.2 Flow in Curved Ducts
Due to the centre-line curvature, flows in a bend are influenced predominantly by two
related forces, namely, the centrifugal force and the radial pressure gradient that exist
between the outside and inside walls of the curved duct. A helical secondary flow is present
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in the duct bend and Miller (1990) provided a good explanation for the origin of this helical
secondary flow. His figures are reproduced in this thesis as Fig. 1.1 (a) and (b).
As shown in the figures, the faster moving fluid near the axis of the duct travels at the
highest velocity (Fig 1.1(a)) and is therefore subjected to a larger centrifugal force than the
slower moving fluid in the neighbourhood of the duct walls. This results in the superposition
of a transverse (or radial) motion onto the primary axial flow, in which the fluid in the central
region of the duct moves away from the centre of curvature and towards the outer wall of the
bend. As this core fluid approaches the outside wall of the bend, it encounters an adverse
pressure gradient as shown in Fig. 1.1(b) and begins to slow down. This energy deficient
fluid approaching the outside wall is unable to overcome the adverse pressure gradient, and
instead moves around the walls towards the low static pressure region on the inside of the
bend. The movement of low energy fluid towards the inside of the bend, combined with the
deflection of the high velocity core region towards the outside of the bend, sets up two cells
of counter rotating secondary flow as shown in Fig. 1.1(a) at the end of the first bend. Thus,
for ducts of symmetrical cross section with respect to the plane of the curvature, a secondary
flow exists which consists of a pair of helical vortices.
The flow structure described above is generally true for curved duct flows and is
termed the “two vortex secondary flow” structure in literature. However, as the flow velocity
increases, additional vortical flow structures appear which show a strong dependence on
Reynolds number (Re), curvature radius ratio (D/2R
c

where D and R
c
are the hydraulic
diameter and radius of curvature respectively), the cross sectional shape and the angle of turn
(). To account for the effects of the first two parameters, a non-dimensional number, the
Dean number (De), is usually used. It is defined as,
De=
Re.

R
D
c
2
.

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Flows at different De range result in the formation of additional vortical structures.
Besides the swirling helical secondary flow mentioned above, a pair of counter-rotating Dean
vortices appears along the outside wall in the bend of circular and square cross sections. An
interesting feature about these Dean vortices is that they are present for a certain
(intermediate magnitude) range of Dean number. That is, they are absent in flows of low De
and again disappear for higher values of De. In a square cross-sectioned,  = 180
O
curved
duct of curvature ratio 6.45, Hille et al. (1985) found that the Dean vortex pair began to
develop along the outside wall only within a De range of approximately 150 < De < 300.The
vortex pair was found in the region between  = 108
O
and 171
O
. The structure of these Dean
vortices was captured clearly in the experimental flow visualization and LDV measurements
of Bara et al. (1992) who conducted their experiments in a  = 270
O
square cross-sectioned
curved duct of curvature ratio 15.1 and at De = 50 to 150. Fig. 1.2 shows the results at De =
150 and the Dean vortex is noted to form at  = 100

O
and continues to develop until =180
O

(as labelled). Beyond  = 180
O
, the Dean vortex seems to attain a fully developed state. At
the lower De = 137, Bara et al. (1992) noted that the Dean vortex, though present, does not
attain fully developed state for the entire axial length of the curve duct. They stated that for
De in the range of 50 to 175, the development axial length decreases with increasing De. The
presence of the Dean vortex is commonly termed the “four vortex or four cell flow”
configuration in the literature.
The critical Dean number for the onset of Dean vortices seems to vary widely among
researchers. Bara et al. (1992), Ghia and Sokhey (1977) and Hille et al. (1985) have tried to
detect the critical Dean number for square cross section ducts, finding it to be respectively
137, 143 and 150. These discrepancies seem to arise from the different curvature ratio of the
curved duct. Thangam and Hur (1990) showed that this hypothesis is true and demonstrated
that the critical Dean number increases with an increase in curvature ratio (that is, a sharper
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bend). The result is reproduced in Fig. 1.3 which shows the variation of critical Dean number
with curvature ratio for square curved duct flows.
The discussion thus far has highlighted that Dean vortices are present in curved duct
flow. To explain its physical mechanism, Winters (1987) showed that the transition from a
two-vortex flow to a four-vortex flow within a critical Dean number range is a symmetry
breaking bifurcation process. Both the two-vortex flow and four-vortex flow are stable to
symmetric disturbances while the four-vortex flow is unstable to asymmetric perturbations.
Experiments by Bara et al. (1992) and stability analysis by Daskopoulos and Lenhoff (1989)
suggested that when perturbed asymmetrically, the four-vortex flow might evolve to flows

with sustained spatial oscillations further downstream. These oscillations in the Dean vortices
are shown to exist in the flow visualisation of Mees et al. (1996a) and Wang and Yang (2005)
and these are reproduced in Fig. 1.4 and 1.5 respectively. In Fig. 1.4, the time series flow
visualisation shows the unsteady oscillation of Dean vortex at De = 220 and  = 200
O
in the
curved bend. Mees et al. (1996a) commented that a characteristic feature of the wavy flow is
the oscillating in-flow region between two Dean vortices. The upper or lower Dean vortex
alternate in size and during a cycle, they can be mirror image of each other (e.g. compare
image 2 and 5 in Fig. 1.4). Also the stagnation point near the center of the outer wall does not
move. In Fig. 1.5, Wang and Yang (2005) noted that between Dean numbers of 192 and
375, the flow in a square cross-sectioned 270
O
curved duct develops a steady spatial and
temporal oscillation that switches between symmetric/asymmetric 2-vortex flows and
symmetric/asymmetric 4-vortex flows as shown. They also found that for De < 192 or De >
375, the flow pattern attains a symmetric 2-vortex solution only, without the presence of
Dean vortex.
The discussion on Dean vortex development shows that it occurs at a relatively low
Re (or De) and at slightly higher De, the flow returns to a two-cell flow. Humphrey et al.
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(1977) and Taylor et al. (1982b) investigated flow in a 90
O
square cross-sectioned curved
duct in this regime and did not detect the presence of Dean vortices. Using LDA and flow
visualisation, they noted that at De = 368, the location of maximum axial velocity (or
commonly called the “fluid core”) moves from the centre of the duct towards the outer wall
as the flow negotiates around the 90

O
bend. At its exit plane, the fluid core is located around
85% of the duct width from the inner wall and the flow attains its distinctive two-cell
secondary flow with velocities at 65% of the bulk axial velocity. The generation of stream-
wise vorticity (or secondary flow) along the curve duct is responsible for the convection of
the fluid from the outer wall along the sidewall towards the inner wall of the duct. Low
momentum boundary layer fluid accumulates along the inner wall and hence near that wall, a
much thicker boundary layer exists as compared to the outer wall. As an example, Fig. 1.6
shows the flow structure at the duct exit plane by Miller (1990) for 90
O
duct of circular and
rectangular cross sectional shape. The flow near the inner wall of the bend has a thicker
boundary layer while the opposite occurs near the outer wall. The “core fluid” is displaced
towards the outer wall of the bend.
If one is to further increase the Dean number (or Reynolds number) and to compare
the flow structure in the laminar flow case with that in the turbulent flow case in 90
O
bend,
one finds that the flow structure at the duct exit stays relatively invariant as that described
above. That is a thicker boundary layer exists along the inside wall and a thinner boundary
layer at the outside wall of the bend, coupled with secondary flow for both flow regimes. But
minor differences exist upon comparison and Taylor et al. (1982b) and Enayet et al. (1982b)
performed such studies on a square and circular cross sectioned 90
O
bend respectively. The
former made comparisons at De = 368 and 18700 while the latter at about 211, 462 and
18170. Similar comparative work was also done by Humphrey et al. (1977 and 1981). Their
results show the development of secondary flow in the form of a pair of counter rotating
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vortices in the stream wise direction in both the laminar and turbulent regime. But the
differences lie in the magnitude of the swirling flow velocities which were found to depend
strongly on the inlet boundary layer thickness, since the laminar flow case has a thicker inlet
boundary layer than the turbulent one. Taylor et al. (1982b) reported the secondary velocities
attained in these two flow regimes as 0.6U
m
and 0.4U
m
for the thick boundary layer (laminar)
and thin boundary layer (turbulent) case respectively.
In addition to the stated differences, the presence of a bend affects the upstream inlet
flow differently for these two flow regimes, and this determines the subsequent secondary
flow development in the bend downstream. A side-by-side comparison taken from the work
of Taylor et al. (1982b) helps to clarify this. In Fig. 1.7(a) in the laminar flow case, the flow
at the inlet of the bend shows little variation with distance and a fully developed velocity
profile is maintained at the inlet. At the bend inlet, the velocity profile shows a velocity
maximum that is closer to the outer wall of the bend. The opposite occurs for the turbulent
flow case where upstream effects due to the presence of the bend can be felt. As the flow
approaches the bend, the “core flow” migrates towards the inner wall of the bend. At the bend
inlet, the velocity profile thus shows a velocity maximum that is closer to the inner wall (see
Fig. 1.7(a)). In Fig. 1.7(b) to 1.7(e) which shows the velocity contours within the bend, the
“core fluid” for the laminar case is found to migrate progressively to the outer wall, and with
a corresponding low velocity region adjacent to the inner wall. Contrast that for the turbulent
case, and within the first 60
O
of the bend, the velocity maximum stays relatively close to the
inner wall of the bend with little evidence of the accumulation of low velocity fluid along the
inner wall. Thereafter, there is a rapid creation of a region of low momentum fluid along the
inner wall and the flow continues to exit the bend with a corresponding migration of “core

fluid” towards the outer wall. The boundary layer thickness at the inner wall is thicker for the
laminar flow case than the turbulent flow case as noted in Fig. 1.7(e).
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As stated previously, the accumulation of low momentum fluid along the inner wall
was due to secondary flow which transports fluid from the outer wall of the bend towards the
inner wall. Sudo et al. (1998 and 2001) shows this clearly in their work in 90
O
circular and
square cross-sectioned duct at high Re = 6x10
4
and 4x10
4
respectively. The three component
velocity and Reynolds stresses were measured at several stations along the pipe. Fig. 1.8
shows the measured cross flow velocities and axial mean velocity contours at different
stations for a square cross sectioned 90
O
duct. At the inlet of the bend, the fluid is slightly
accelerated towards the inner wall and decelerated near the outer wall which induces a cross
stream towards the inner wall in the central part of the cross section. At the  = 30
O
station,
secondary swirling flow appears in the cross section and it forms two counter-rotating
vortices which circulate outwards (away from the center of curvature) in the central part of
the duct and inwards (towards the center of curvature) near the upper and lower walls. At
stations  = 30
O
to 60

O
, the secondary flow grows and the fast fluid near the inner wall is
convected by the secondary flow to the outer wall through the central portion of the duct. At
the same time, the slow moving fluid near the upper and lower walls is transported towards
the inner wall by the secondary flow. Due to fluid transportation to the inner wall, low
momentum fluid begins to accumulate and decelerate along the inner wall. The boundary
layer along the inner wall thus thickens considerably when the fluid exits at  = 90
O
and at the
same time, the core fluid moves further towards the outer wall.
The above discussion on curved duct flow attempted to provide a broad overview of
the various vortical structures and their formation mechanism that are present in different
Dean number regimes. In the next section, a discussion of the flow development in S-shaped
ducts will be presented.


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1.3 Flow in S-shaped Ducts
As stated in the previous section, the internal flows in curved S-shaped ducts are often
found in various aerodynamics and fluid mechanics applications, where a combination of
bends is employed to re-direct the flow. A good example is an aircraft jet engine intake (Guo
and Seddon (1983)). Similar to the flow in a simple curved duct, flows in S-ducts are
influenced predominately by two related forces, namely, the centrifugal forces and the radial
pressure gradients that exist between the outside and inside walls of the curved duct resulting
in the formation of secondary flow. The description in the previous sections for swirling flow
in a single bend also occurs in the first bend of an S-duct. Hence, a pair of helical vortical
flow exists in the first bend of the S-duct. Additional complex flow structures form when the
flow enters the second bend of opposite curvature. In the second bend, the swirl that

developed initially in the first bend of an S-duct is attenuated and reversed in the second bend
due to the opposite curvature and the reversed radial pressure gradient. Since an S-duct
consists of bends of opposite curvature and the radial pressure gradient changes sign along
the S-duct, the side wall pressure distribution is sinusoidal-like in shape. An example of such
a distribution is shown in Fig. 1.9 from Kitchen and Bowyer (1989) where at the inlet of the
duct, the high and low pressure side walls are respectively at the outer wall and inner wall of
the first bend. The high and low pressure side changes in the second bend to reflect the
change in duct curvature.
The observation on swirl development in S-duct is generally true for both circular and
non-circular geometry. Previous work by Bansod and Bradshaw (1972) and Taylor et al.
(1984) (both for circular cross-sectioned S-duct) and Sugiyama et al. (1997) and Taylor et al.
(1982a) (both for square cross sectioned S-duct) drew similarities between them. Firstly, it
was noted that the swirl flow in the second bend still retains a distinctive symmetrical, two-
cell swirl configuration at the S-duct exit. Secondly, core flow (or fluid with high flow
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velocity) in the S-duct migrates towards the outside wall of the first bend and exits near the
inside wall of the second bend. Lastly, large scale, vortical structures exist along the outside
wall of the second bend in both the circular and square cross-sectioned S-ducts. This finding
is consistent with many other works, for example Anderson et al. (1982) and Cheng and Shi
(1991) (for square cross-sectioned S-ducts). In particular, the development of these
longitudinal vortices near the wall is accompanied by the rapid thickening of the boundary
layer at the outside wall of the second bend. Fig. 1.10, taken from Bansod and Bradshaw
(1972) on circular S-shaped duct, shows the total pressure distribution on the S-duct exit and
the thickened boundary layer along the outside wall of the second bend. The core flow exists
close to the inside wall of the second bend. Bansod and Bradshaw (1972) pointed out that
since a favourable longitudinal pressure gradient exists on the outside wall of the second
bend, the flow near this wall is accelerating and hence these longitudinal vortices could
undergo “ vortex stretching” , thus intensifying vorticity. This causes the boundary layer near

that wall to thicken rapidly due to enhanced entrainment and accumulate into a region of low-
momentum fluid.
Another variant in S-duct flows is the S-shaped diffuser which can be found in many
applications. In addition to the combined effects of centrifugal forces and radial pressure
gradient in S-duct flows, flow separation is another important factor that influences the flow
structure in an S-duct diffuser. Due to the increasing cross sectional area, a stream-wise
adverse pressure gradient is also present. The combined effects may result in increased flow
non-uniformity and total pressure loss at the duct exit as compared to a uniformed cross-
sectioned S-duct. In a circular cross sectioned S-duct diffuser, flow separation results in a
comparatively large pair of contra-rotating stream-wise vortices, which occupy about a third
to a half of the S-duct exit area. Such problems were investigated by Whitelaw and Yu
(1993a, b) and Yu and Goldsmith (1994), Anderson et al. (1994) for circular cross sectioned
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diffusers. The flow in S-duct diffusers of rectangular or square cross section was studied by
Rojas et al. (1983), Sullerey and Pradeep (2003), and Pradeep and Sullerey

(2004).
Among these works on constant cross sectioned S-duct or diffusers, the effects of inlet
boundary layer play an important role in the swirl development. Anderson et al. (1982) (for
constant square S-duct), Rojas et al. (1983) (for square S-duct diffuser) and Whitelaw and Yu
(1993a) (for circular S-duct diffuser), investigated the effects of boundary layer thicknesses
in their respective studies. Similar to the case of a single 90
O
bend, flows with a thicker inlet
boundary layer result in a larger magnitude swirl generated in the first bend. The difference in
swirl magnitude can be 0.22U
m
and 0.15U

m
for the thick and thin boundary cases noted by
Anderson et al. (1982). Rojas et al. (1983) and Whitelaw and Yu (1993a) quoted respectively
0.4U
m
versus 0.15U
m
and 0.16U
m
versus 0.12U
m
for the corresponding thick and thin
boundary layer cases. However, the details in flow topology within the second bend are
dependent on whether flow separation is present. For the work of Anderson et al. (1982) and
Rojas et al. (1983) where flow separation is not present, increasing the inlet boundary layer
thickness led to a corresponding increase in boundary layer development along the outer wall
of the second bend. However, for Whitelaw and Yu (1993a) where flow separation is present,
they found that an increase in inlet boundary layer thickness led to a corresponding decrease
in boundary layer thickness along the outer wall of the second bend. Whitelaw and Yu
(1993a) also found that increasing inlet boundary layer led to a reduction in separation region
in their S-duct study and argued that the earlier reattachment of separated flow for the thick
inlet boundary layer case led to a corresponding decrease in outlet boundary layer along the
outer wall of the second bend. Their LDA measurements show this very clearly.
The above review has concentrated mainly on S-duct with limited turning angle at
relatively high Re (or De) where Dean vortices are not present. It is of interest to study flows
within the critical Dean number range and where the turning angle in the first bend of the S-
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duct is large enough to initiate the formation of Dean vortex and investigate the flow

structure in the second bend of opposite curvature. Cheng and Shi (1991) studied such flows
using flow visualization only and in a Dean number range of 25 to 350. The square cross-
sectioned S-duct bend has curvature ratio (R
c
/D) of 2.5, with turning angle of 225
O
for both
bends. Their results show that Dean vortices formed at De = 101, 151, 201 and 252 and at a
turning angle of about 180
O
in the first bend. These vortices continue to grow until 225
O

within the first bend and with increasing asymmetric structure for the higher De  201, while
the vortices stay relatively symmetric for lower De of 101 and 151. Fig. 1.11(a) shows the
formation of a pair of Dean vortices on the outer wall of the first bend at De = 151 at 225
O
.
Upon entering the second bend, the curvature of the outer and inner wall changes and the
direction of the centrifugal force also changes accordingly. At 45
O
into the second bend,
Cheng and Shi (1991) noted that there still exist some remnants of the Dean vortices on the
inner wall of the second bend that was generated on the outer wall of the first bend. These
occur at low De = 151 and 200 and a picture is reproduced here in Fig. 1.11(b). These
decaying Dean vortices disappear as they are suppressed by secondary flow generated in the
second bend. A new set of Dean vortices starts to appear on the outer wall of the second bend
at about 135
O
into the second bend and they continue to grow downstream. Some results are

shown in Fig. 1.12 for De = 151. Flows at higher De > 200 seem to display complex and
asymmetrical structures in the second bend. Cheng and Shi (1991) can identify 6 vortices
including the dominating Dean vortex at De = 354.
Another facet of the study of flow in S-duct is flow control because these ducts find
practical application as aircraft air-intake ducts. The trend in modern fighter aircraft is to
have a short and highly curved S-shaped intake duct. The short length reduces the structural
weight of the aircraft and increases the internal space packaging efficiency. However, the
shortening of the duct results in a highly curved duct profile while still maintaining the
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correct offset of the engine fan face (housed in the fuselage) and the intake entrance face (at
the exterior of the fuselage). Although the short intake duct is highly desirable for its
compactness and weight reduction, it is aerodynamically inefficient, as it is highly susceptible
to massive flow separation. In addition, the flow is coupled with bulk swirl with the presence
of stream-wise vortices. These flow features lead to total pressure losses in the duct, flow
distortion at the duct exit and hence flow non-uniformity at the engine fan face.
The improvements in performance of S-shaped ducts are thus a reduction in flow
distortion at the duct exits, maximizing the flow rate and hence minimising the total pressure
losses and elimination of flow separation if it is present. These requirements involve flow
control devices like vortex generators, blowing techniques and vortex generator jets to
suppress flow separation, and fences to attenuate swirl. Separation flow control is discussed
in a review by Gad-el Hak and Bushnell (1991) and Lin (2002). These flow control devices
are placed on the side walls of the S-duct and slightly upstream of the separation point.
Vortex generators “ locally” mix the high momentum fluid in the free stream with the low
momentum fluid near the wall and thus energise the boundary layer to suppress flow
separation. Vakili et al. (1985), Reichert and Wendt(1996) and Anderson and Gibb (1998)
used vortex generators for separation control in circular cross-sectioned S-shaped diffuser
while Sullerey and Pradeep (2002) and Sullerey et al. (2002) used vortex generators in a
rectangular cross sectioned S-shaped diffuser. Blowing and vortex generator jets use mass

addition near the separation point to energise the low momentum fluid close to the wall to
overcome the adverse pressure gradient. The former method has the added flexibility of
altering the blowing direction. Blowing jets were implemented by Senseney et al. (1996) and
Sullerey and Pradeep (2003) while vortex generator jets were used by Hamstra et al. (2000)
to improve the flow in S-shaped duct. Other techniques like zero-net-mass-flux jets were used
in S-duct for separation control by Mathis et al. (2008).
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1.4 Objective and Outline of the Thesis
A survey of the current literature reveals that information on the flow in a constant
square cross-sectioned S-shaped duct is lacking, especially flow data for S-ducts of large
curvature (or sharper bend) and at higher Re. This is the main motivation of the present
investigation. The objectives are,
(a) To study the vortical and flow development in such S-ducts.
(b) To investigate the parameters (e.g. radial pressure gradient, centrifugal force and
inlet boundary layer thickness) that influence the flow development.
(c) To propose a flow model for the vortex development.
(d) To assess the flow control methods applicable in such S-ducts.
In the current literature, flow in square cross sectioned S-duct of lower curvature were
reported by Taylor et al. (1982a), Anderson et al.(1982) and Sugiyama et al.(1997) (in
Japanese) and their S-duct geometry had a curvature ratio R
C
/D = 7, duct turning angle of  =
22.5
O
, and their investigation was conducted at Re = 750 and 4.0x10
4
. The present work was
conducted at higher Re = 4.73x10

4
and 1.47x10
5
and with three square cross-sectioned, S-
shaped ducts with sharper bends and larger turning angle.
The organisation of the thesis is as follows:
In chapter two, the experimental set-up is described in detail. This includes a
description on S-duct wind tunnel, the geometry of the S-duct test sections and the
experimental apparatus for measurements of surface pressure, total pressure and flow
velocities. Flow visualisation techniques are described. The apparatus used in flow control
and the different flow control devices are introduced. Lastly, data from the present work is
benchmarked against known data from Taylor et al. (1982a) and Sugiyama et al. (1997) and
an analysis of the experimental errors is discussed.
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Radial pressure gradient and centrifugal force play important roles in flow of curved
and S-duct. In Chapter three, a new non-dimensional quantity, defined as a ratio of these two
forces, is computed using data from literature and the present experiment. A collapsed curve
that shows its variation along the ducts’ axial distance is obtained. Its relation to other more
common non-dimensional numbers e.g. C
p
, Re and De is highlighted. Scatter in the data for
the various cases is noted and attributed to different vortical/swirl development within the
duct and to the influence of inlet boundary layer thickness. These are studied in more detail in
subsequent chapters 4 to 5.
In Chapter four, swirl development and the flow structures within S-duct is
investigated in greater detail. Side wall pressure coefficient C
p
, total pressure and cross flow

velocity are measured. In addition, smoke wire flow visualisation and surface flow
visualisation were also conducted. Based on the above quantitative and qualitative
information, a flow model is proposed to describe the swirl development and formation of
stream-wise vortices within the S-duct. The formation mechanism for the stream-wise
vortices is explained based on the Squire and Winter formula (1951).
In Chapter five, cross flow measurements at multiple interior planes within the S-duct
are presented and discussed for different inlet boundary layer thickness. The focus of this
chapter is to provide further evidence to support the proposed flow model in Chapter four and
to investigate the influence of inlet boundary layer thickness on swirl development within S-
duct. It is shown that an increase in inlet boundary layer thickness will lead to increase in
swirl in the first bend of the S-duct and altered the vortex configuration of the stream-wise
vortices. The vorticity growth rate is higher with increased inlet boundary layer thickness.
Chapter 6 discusses the use of vortex generators, tangential blowing, vortex generator
jets to control flow separation in S-duct. Their effects on flow separation, total pressure loss,
flow uniformity and swirl flow magnitude are investigated. The focus of the chapter is to
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show that competitive aerodynamic requirements exist in S-duct flow where the improvement
of one criterion leads to a deterioration of another.
The thesis concludes with Chapter seven and provides a recommendation for future
work.