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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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R
D
c
2
.

3
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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

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

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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

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. 8
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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

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

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

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

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.