Chapter 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 Sshaped 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 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/2Rc where D and Rc 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= D Re 2Rc 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, = 180O 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 = 108O and 171O 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 = 270O 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 (as labelled) Beyond = 100O and continues to develop until =180O = 180O, 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 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 = 200O 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 and 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 270O 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 (1977) and Taylor et al (1982b) investigated flow in a 90O 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 90O 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 streamwise 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 90O 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 90O 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 90O 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 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 0.6Um and 0.4Um 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 60O 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) 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 90O circular and square cross-sectioned duct at high Re = 6x104 and 4x104 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 90O 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 = 30O 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 = 30O to 60O, 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 = 90O 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 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, twocell swirl configuration at the S-duct exit Secondly, core flow (or fluid with high flow 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 lowmomentum 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 crosssectioned 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 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 90O 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 0.22Um and 0.15Um for the thick and thin boundary cases noted by Anderson et al (1982) Rojas et al (1983) and Whitelaw and Yu (1993a) quoted respectively 0.4Um versus 0.15Um and 0.16Um versus 0.12Um 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- 10 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 crosssectioned S-duct bend has curvature ratio (Rc/D) of 2.5, with turning angle of 225O for both bends Their results show that Dean vortices formed at De = 101, 151, 201 and 252 and at a turning angle of about 180O in the first bend These vortices continue to grow until 225O 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 225O 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 45O 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 135O 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 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 11 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) 12 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 RC/D = 7, duct turning angle of = 22.5O , and their investigation was conducted at Re = 750 and 4.0x104 The present work was conducted at higher Re = 4.73x104 and 1.47x105 and with three square cross-sectioned, Sshaped 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 13 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 Cp, 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 to In Chapter four, swirl development and the flow structures within S-duct is investigated in greater detail Side wall pressure coefficient Cp, 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 Sduct 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 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 14 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 15 ... 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... exist in the flow visualisation of Mees et al (19 9 6a) 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. .. known data from Taylor et al (19 8 2a) and Sugiyama et al (19 97) and an analysis of the experimental errors is discussed 13 Radial pressure gradient and centrifugal force play important roles in flow