PHD THESIS STUDY OF LARGE SCALE COHERENT STRUCTURES IN MECHANICALLY OSCILLATED PLANAR JET THE NEAR FIELD AND TRANSITION REGIONS OF A.

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1 PHD THESIS STUDY OF LARGE SCALE COHERENT STRUCTURES IN THE NEAR FIELD AND TRANSITION REGIONS OF A MECHANICALLY OSCILLATED PLANAR JET Michael Riese School of Mechanical Engineering The University of Adelaide Adelaide, SA 5005 November 2008

2 Chapter 1 Introduction Take Pride in Everything You Do. Origin Unknown 1.1 Flow visualisation and coherent structures For more than a century, the investigation of fluid mechanics has drawn on the use of flow visualisation techniques to identify flow streak-lines and coherent structures in pipe flows, free surface flows and mixing of fluids. One of the most fundamental and famous cases of flow visualisation was published by Reynolds (1883), who used sketches from his pipe flow experiments to define effects of the Reynolds number, classifying the flow to be in either the laminar, transient or turbulent regimes (Figure 1.1). Just 21 years later, Ludwig Prandtl, then professor of mechanics in Hannover, published his ground-breaking findings on the flow of fluids with very low viscosity (Prandtl, 1904), which were the beginning of the boundary layer theory. He used a hand-actuated water tunnel (Figure 1.2) and aluminium flakes to visualise flow streak lines and flow structures (Figure 1.3). Later work by Prandtl, while at the Kaiser-Wilhelm-Institut in Göttingen, clearly established the technique first presented at Heidelberg in 1904 and used them to derive sketches of flow pat- 1

3 CHAPTER 1. INTRODUCTION 2 Figure 1.1: Sketches published by Reynolds (1883) illustrating his findings in regards to flow regimes within a pipe. Figure 1.2: Reproduction of a sketch showing Prandtl s water tunnel apparatus used for his initial investigation into the flow of very low viscosity fluids [from the original conference proceedings where he first presented his findings (Prandtl, 1904).]

4 CHAPTER 1. INTRODUCTION 3 Figure 1.3: Reproduction of some sketches presented by Prandtl (1904). Panels labelled Fig. 3 & 4 showing the starting vortex from a wall protruding into the flow and panels labelled Fig. 5 & 6 showing the vortex growth behind a cylinder. terns and streak lines, later published in works such as Prandtl and Tietjens (1934b). In 1925 Prandtl explained the use of cinematography to visualise and record flow streak lines on celluloid by using a small exposure time delay to convert the movement of aluminium flakes from single points to thin streak lines (Prandtl and Tietjens, 1925). The right hand side of Figure 1.4 shows the effect of extending the film exposure time. The flow around a cylinder is shown in Figure 1.5 as an example of results from the same publication. The continuous use of the technique for decades to follow, resulted in a number of new findings and discoveries such as the separation of flow from an aerofoil. A compilation of streak line images can be found as part of Prandtl and Tietjens (1934a). The decades following these early beginnings resulted in the development and increased uptake of further visualisation techniques. One example of many from the 1960s is Bradshaw et al. (1964), who used shadowgraphs to depict the evolution of vortex rings and transition into turbulence, or Dimotakis et al. (1983) and Mi et al. (2001a) who used Laser Induced Fluorescence (LIF) to visualise vortex structures in jet mixing (Figure 1.6), while Schraub et al. (1965) used the

5 CHAPTER 1. INTRODUCTION 4 Figure 1.4: Fig. 3 & 4 show the same flow of a vortex pair separating behind a cylinder with different film exposure times. (Prandtl and Tietjens, 1925)

6 CHAPTER 1. INTRODUCTION 5 Figure 1.5: Two figures from Prandtl and Tietjens (1925) showing the flow around a stationary cylinder recorded using the then new cinematography technique.

7 CHAPTER 1. INTRODUCTION 6 NOTE: This figure is included on page 6 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.6: Structures in a turbulent water jet at Re 2300, visualised by using LIF and photographed by Dimotakis et al. (1983) from Van Dyke (2005). hydrogen-bubble wire technique for their study. A collection of famous examples of flow visualisation techniques can be found in Werlé (1973) and Van Dyke (2005) and an in-depth description of flow visualisation techniques themselves can be found in Smits and Lim (2000) and Goldstein (1983). From its early beginnings, flow visualisation has been used to acquire a qualitative understanding of flows and orderly structures, such as shown by Prandtl and Tietjens (1934b,a) or Roshko (1961) who investigated the orderly shedding of vortices from a cylinder. However, attention soon also focused onto coherent small-scale as well as transient structures, such as the work shown by Bradshaw et al. (1964) and Brown and Roshko (1974) in Figure 1.7. Crow and Champange (1971) investigated the large-scale structure of axisymmetric jets and especially the influence of frequency excitation on jet behaviour, while Perry and his co-investigators (Perry and Lim, 1978; Perry et al., 1980, 1981) used periodic excitations and stroboscope lighting to enhance and subsequently optically freeze flow structures. 1.2 Basic Types of Jets While flow visualisation has been used in a large number of different areas, a large body of research has been devoted to determine the coherent flow structures in jet mixing, e.g. Dimotakis et al.

8 CHAPTER 1. INTRODUCTION 7 NOTE: This figure is included on page 7 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.7: Brown and Roshko (1974) used spark shadow photography to visualise the coherent structures in a mixing shear layer. (Van Dyke, 2005) (1983); Bradshaw et al. (1964); Roshko (1961); Brown and Roshko (1974); Mi et al. (2001a). Generally, for reasons of simplicity, fundamental research of jets has concentrated on two basic types of symmetric jets: Axisymmetric jets, which have a round exit plane and hence are symmetric in all axial directions within that plane. These type of jets are generally characterised by their nozzle diameter (d). Planar jets, which have a very large nozzle width to nozzle height ratio (w/h) that results in mainly two-dimensional, large-scale motions across the centreline and perpendicular to the nozzle width. These nozzles are generally characterised by the exit height of the nozzle (h). Both types of jets have been investigated to a greater or lesser extent with two different initial boundary conditions in relation to the nozzle exit condition that can be classified as follows: Jets with quasi-steady initial conditions, which are generally discharged from a straight pipe, an orifice plate or a smooth contraction (Mi et al., 2001b). Jets with unsteady or forced initial conditions, which have a continuing disturbance imparted onto them in one or more ways by a number of different forcing mechanisms (Crow and Champange, 1971; Nathan and Luxton, 1991a; Schneider et al., 1997). This combination of different nozzle geometries and initial conditions results in a total of four major different classes, comprising axisymmetric and planar combined with steady and unsteady

9 CHAPTER 1. INTRODUCTION 8 jets. While the present study is concerned with an oscillating planar jet, i.e. with unsteady initial conditions, for comparison and better understanding a short review of round and planar jets with steady initial conditions is first presented. 1.3 Axisymmetric & Planar Jets with Steady Initial Conditions Steady Jet Field Flow Characteristics A jet with steady initial conditions, both round and planar and a smooth contraction leading into the nozzle 1 can be divided into three separate regions (Figures 1.8 & 1.9). Immediately downstream from the nozzle exit is the potential core region. In this region the centreline velocity is nearly constant. As the shear layer thickness increases, it penetrates further and further into the jet core until it reaches the centre line. For a planar jet this distance is approximately 4 to 6 times the nozzle height (h or d depending on the cited investigation). This is followed by the interaction region which reaches from around 6h to 20 h for a planar jet (Browne et al., 1984). Hinze (1959) investigated the centreline velocity decay in turbulent round jets downstream from the end of the potential core region and found that it can be described as ( ) U CL d = k v U 0 x x o1 (1.1) where U CL = Local axial jet centreline velocity, (m.s 1 ); U 0 = Nozzle velocity, (m.s 1 ); k v x o1 d = Velocity decay coefficient; = Location of virtual origin of the jet centreline velocity, (m); = Nozzle diameter, (m). 1 Nozzles with different inlet conditions such as a straight pipe or an orifice plate exhbibit different flow behaviour close to the nozzle exit. This is documented in more detail by Mi et al. (2001c).

10 CHAPTER 1. INTRODUCTION 9 The value of k v depends on initial or boundary conditions. For example Rajaratnam (1976) found a value of k v = 6.3, while other studies such as Hussein et al. (1994) suggest values between 5.8 and 6.0. The self-similar far-field is the third region, which starts at a distance of 15 to 20 d from the nozzle exit depending on initial conditions. In this region, both the jet spreading rate as defined by the jet halfwidth (b) 2 and the centreline velocity decay, amongst other quantities, approach a constant value. For a planar jet, George (1995) empirically found the velocity decay to follow the formula ( U0 U CL ) 2 [ ] x xo1 = k v h (1.2) where h is the nozzle height and all other variables are as in Equation 1.1. This validates the theoretical derivation of this theorem previously undertaken by Rajaratnam (1976) using similarity analysis. The jet halfwidth was found to adhere to ( ) [ ] b x xo2 = k b h h (1.3) in the self-similar jet far-field, where k b is the jet halfwidth coefficient and x o2 is the virtual origin of jet halfwidth, both of which also depend on initial conditions Reynolds Number To be able to compare flows with different underlying configurations, the dimensionless Reynolds number is generally used. To first order, the Reynolds number characterises whether a flow is laminar, transient or turbulent (Reynolds, 1883) as shown in Figure This describes the ratio of inertia to viscous forces in the flow and is defined for pipe and jet flows as Re = U d ν (1.4) 2 The jet halfwidth (b) is defined as the local height of the jet in the transverse direction at which the local mean velocity is half that of the local centreline velocity (b U 0.5, refer to Figure I for more detail).

11 CHAPTER 1. INTRODUCTION 10 Figure 1.8: A schematic diagram of a steady round jet. d = Nozzle diameter; X o1 = Virtual Velocity Origin; X PC =Potential Core Length; U 0 = Nozzle Exit Velocity; U CL = Jet Centreline Velocity; U (r,x) =Local Jet velocity. Figure 1.9: Schematic diagram of a planar jet with simplified vortex structures. (Browne et al., 1984)

12 CHAPTER 1. INTRODUCTION 11 where Re = Reynolds number; U = Fluid mean velocity (m.s 1 ); d = Characteristic dimension, h in planar jets (m); ν = Kinematic viscosity (m 2.s 1 ). The characterisitc length scale for circular jets and pipe flows is the diameter of the pipe or the nozzle diameter of the jet, as it represents the characteristic dimension of the flow. For rectangular cross sections, the hydraulic diameter is commonly used for calculations (Massey and Ward-Smith, 1998) in the form of d hydraulic = 4 Area Circum f erence (1.5) Massey and Ward-Smith (1998) state that the equivalent hydraulic diameter should only be used for w/h 8, as the distribution of shear stresses in a rectangular pipe or nozzle varies significantly from that in a circular pipe and sufficiently accurate results are not obtained for larger aspect ratios of w/h > 8. In the case of the Oscillating Planar Jet (OPJ), the nozzle height h is used to calculate the jet s Reynolds number Re h as the investigation intentionally is only interested in the downstream region of the jet flow where aspect ratio effects are negligible. In pipe and jet flows with Re 2300, the jet is generally found to be laminar flow. Flows with a Re 4000 are generally found to be turbulent. A transition region from laminar to turbulent flow lies in between these two values (Gerhart et al., 1993). As the kinematic viscosity is generally a constant for a single fluid in an isothermal flow, increasing Re for a given configuration necessitates an increase in inertia forces, i.e. the influence of the Reynolds number on an experiment diminishes from being very significant for Re < 10 4 to minor importance at Re > 10 5.In other words, for constant viscosity, increasing the Reynolds number by one order of magnitude decreases the effect of the viscous forces by one order of magnitude.

13 CHAPTER 1. INTRODUCTION 12 NOTE: This figure is included on page 12 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.10: Reynolds Experiment [from Van Dyke (2005)] Coherent structures A considerable effort has been made to investigate and visualise coherent large-scale structures in planar and round jets. Studies by Dimotakis et al. (1983) showed the development and growth of vortex structures in a round turbulent jet (Figure 1.6) likewise images by Drubka and Nagib (Van Dyke, 2005), as shown in Figure 1.11, have been used to further the understanding of flow development and mixing and to supplement quantitative studies. Studies of coherent structures in turbulent planar jets such as Oler and Goldschmidt (1981, 1982, 1984) or Goldschmidt and Bradshaw (1973) have shown that the vortex roll-up from a planar nozzle predominantly takes place alternately on each side of the nozzle for a smooth contracting nozzle geometry as shown simplified in Figures 1.9 & This is similar to the shedding of vortices in a Karman vortex street behind a cylinder. To understand the effect of mechanical excitation on planar jets it will be necessary to also identify any qualitative changes to large-scale structures in the flow.

14 CHAPTER 1. INTRODUCTION 13 NOTE: This figure is included on page 13 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.11: A laminar round jet flowing from a tube at Re = The jet displays axisymmetric oscillations that roll up into vortex rings and become suddenly turbulent. (Van Dyke, 2005) Vortex Shedding Frequencies Also to be able to compare the vortex shedding frequency of different fluidic systems, a dimensionless frequency in the form of the Strouhal number is used. This parameter was originally developed to represent the dimensionless vortex shedding frequency behind an object in a flow (Figure 1.12) and is defined as where St = f h U (1.6) St = Strouhal number; f = Characteristic oscillation frequency (Hz); h = Characteristic system length scale (Nozzle height in planar jets; m); U = Characteristic mean fluid velocity (m.s 1 ). It is named after its originator Vincenz Strouhal ( ), who first investigated resonant excitation of wires by vortex shedding at the end of the 1870s (Massey and Ward-Smith, 1998). Preferred Strouhal numbers have been identified for a wide range of systems, some of which have very different characteristic dimensions, each chosen to best represent the given system or facility. Examples include vortex shedding after a sudden expansion in a duct (Eaton and Johnston, 1982) or the preferred Strouhal number ranges in combustion systems (Putnam, 1971). It

15 CHAPTER 1. INTRODUCTION 14 NOTE: This figure is included on page 14 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.12: Vortex shedding behind a round cylinder. The cylinder diameter represents the characteristic length-scale in this system (Van Dyke, 2005). is also possible to define a Strouhal number in different ways for the same system, with neither of them being wrong, but one being more relevant than the other for a given purpose or application (e.g. Nathan et al. (1997)). The Strouhal number is sometimes also interpreted as the ratio of two characteristic velocities in a system (Gerhart et al., 1993), making it very relevant to jet applications. Natural Strouhal numbers for planar jets defined on the mean exit velocity and the nozzle height have been found to be generally in the range of St h = for the majority of published studies, as is described further below and also shown for two examples in Table 1.1. However, it is important to note that there are also studies in the public domain that have St h that are certainly higher and lower, with Everitt and Robins (1978) and Goldschmidt and Bradshaw (1973) being two examples, respectively. 1.4 Jet Excitation Free jets can be excited in different ways and at different places in relation to the jet nozzle. Generally though, excitation is provided by one of three basic methods: Acoustic A small amplitude but often high frequency oscillation is imparted to the jet in the axial or lateral direction using the sound pressure generated by one or more loudspeakers. The amplitude of oscillation can be changed by increasing the speaker volume, hence the movement of the speakers membrane and so the volume of air moved by the speaker. It is

16 CHAPTER 1. INTRODUCTION 15 possible to individually control the oscillation frequency and amplitude but this is limited by the loudspeaker s operating envelope. Fluidic The oscillation is triggered and dependent on the nozzle geometry and the jet velocity. No moving parts are necessary. As a result, the oscillation amplitude and frequency are dependent on the jet velocity and cannot be easily changed independently. Mechanical Mechanical components change the direction or mass flux of a jet in a repeatable transient fashion. It is possible to achieve large-amplitude oscillations which can be independent of the jet velocity and excitation frequency. However, the frequency and amplitude are generally limited by the physical properties of the facility, in most cases allowing only for an oscillation frequency far smaller than the ones achievable using acoustic methods. While it is certainly possible to combine these methods, this is rarely done in fundamental scientific investigations due to the need for precisely defined boundary conditions Excitation of Axisymetric Jets Axisymmetric jets are generally excited using one of three different methods, whereby axial and radial excitation are the easiest and jet precession is the hardest to implement. Crow and Champange (1971), for example, used a loudspeaker to introduce an axial perturbation to investigate preferred modes of turbulent jets. On the other hand, Hill and Greene (1977) is an example of a nozzle designed to radially oscillate an axisymmetric jet-flow using a fluidic mechanism, resulting in an increased mixing rate as inferred from a higher entrainment rate and higher velocity decay in comparison with a steady round jet. One investigation worth noting with respect to the present study is Perry and Lim (1978). By using a loudspeaker physically connected to a circular glass tube in combination with strobe lighting, they were able to amplify the dominant coherent structures and optically freeze the eddy structures. The experiments undertaken were in a Reynolds number range from 300 to Perry and Lim documented a range of different eddy structures that varied as a function of oscillation

17 CHAPTER 1. INTRODUCTION 16 frequency and amplitude as well as the buoyancy of the smoke used for visualisation. Three key findings from this study are that only very small oscillation amplitudes are necessary to enhance dominant structures; the structures once amplified were coherent over a range of up to 30 to 40 wavelengths; and all eddy structures were also observed in unforced jets, but were of a more transient nature. During the early 1990s, jet precession was established as an additional form of jet instability. A precessing jet describes a mode of instability whereby the jet rotates around an axis of symmetry that is not the jet centre line. The two most common nozzles are the fluidic precessing jet (FPJ) as shown in Nathan and Luxton (1991b,a) and the mechanically precessing jet (MPJ) as shown in Schneider (1996); Schneider et al. (1997). FPJ nozzles have been shown to have a number of beneficial attributes associated with them, such as increased efficiency and a reduction in NO X emissions when used in relevant combustion scenarios (Nathan et al., 1997). The MPJ nozzle can be seen as the mechanical analogue of the FPJ nozzle which allows for the independent variation of jet velocity, precession angle and oscillation frequency, making it more suitable to rigourous scientific investigations Planar Excited Jets A large number of studies on mechanically oscillating planar jets were undertaken and published during the 1970s and 80s. However, as the forcing of coherent jet structures was found to increase the entrainment of ambient fluid by early research, nearly all research during this time concentrated on the aim of thrust augmentation for V/STOL propulsion nozzles and other applications. Hence, different objectives from those in this study were pursued and past research has to be seen in this light.

18 CHAPTER 1. INTRODUCTION 17 Figure 1.13: Nomenclature relating to the physical aspects of oscillating planar jets used in the present study: r 0 = Nozzle contraction radius; h= Nozzle exit height; S= Oscillation stroke; w= Nozzle width in the spanwise direction (not shown); CL= Oscillation centreline; TDC= Top dead centre of oscillation; BDC= Bottom dead centre of oscillation. Oscillating Planar Jet Nomenclature To allow for an accurate description of oscillating planar flows, a concrete and precise nomenclature is needed. The nomenclature in relation to oscillating planar jets (OPJs) used in the present study is shown Figure 1.13, whereby the centreline corresponds to the phase angles of 0 and 180 and TDC corresponds to +90 displacement together with BDC equal to either 270 or 90 displacement. All nomenclatures of references cited within the present study have been transformed into the above nomenclature from their original to ensure consistency. Axisymmetric, Antisymmetric & Asymmetric Planar Jet Excitation A number of different methods have been used to excite planar jets in the lateral direction, but only 3 pure modes are possible. Fiedler and Korschelt (1979) investigated the influence of axisymmetrical and antisymmetrical lateral excitation of planar jets. Axisymmetric oscillation in this case refers to an excitation that occurs symmetrically at both sides of the jet at the same time, while antisymmetric oscillation refers to excitation that still occurs on both sides of the jet but is out of phase with respect to each other. Fiedler and Korschelt (1979) found that axisymmetric excitation

19 CHAPTER 1. INTRODUCTION 18 had little or no effect on jet amplification and on changes in jet structures beyond the jet core region relative to a steady jet. This was later verified during separate studies by Lai and Simmons (1980, 1983) and Lai (1984) inducing axisymmetric oscillation utilising a pulsating jet set-up. Galea and Simmons (1983) and Galea (1983) later excited a planar jet in an asymmetric fashion, i.e. only excited one side of the flow and found that this had comparable effects on the jet flow to the antisymmetric excitation methods reported by other investigators Natural Self-Oscillation By the beginning of the 1970 s extensive work had been undertaken to examine velocities and turbulence in planar jets. Starting with the work of Wygnanski and Gutmark (1971) investigations were undertaken to study the instantaneous lateral movement of the jet flow and in later years the large-scale coherent structures in steady planar jets. Wygnanski and Gutmark (1971) used two parallel hot-wire probes to investigate the correlation between the shear layer motions on both sides of the jet and their relative correlation to each other. While the findings reported were deemed to be inconclusive, Goldschmidt and Bradshaw (1973) conducted a range of initial experiments of their own and concluded that a lateral flapping movement was present. Independently, Gutmark and Wygnanski (1976) undertook a number of investigations to characterise the far-field of a turbulent jet and, by correlating some of their data, came to the same conclusion as Goldschmidt and Bradshaw (1973). At the start of the 1980s, Oler and Goldschmidt (1980) and Cervantes de Gortari and Goldschmidt (1981) published further studies, and, by extending the sampling time and moving the probes to a number of different locations, confirmed an opposing movement of the jet boundaries, deducing that natural flapping motion of jet was an extremely likely possibility. However, during this decade a gradual shift in perception from purely random jet turbulence to orderly large-scale structures had developed (Brown and Roshko, 1974; Perry and Lim, 1978; Everitt and Robins, 1978). In this light, new investigations by Oler and Goldschmidt (1981, 1984) moved away from the terminology of a flapping jet and, with the aid of iso-correlation measurements and contours,

20 CHAPTER 1. INTRODUCTION 19 NOTE: This figure is included on page 19 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.14: Reproduction a sketch presented in Oler and Goldschmidt (1981, 1984) showing the organised structures in two-dimensional free shear flows in a planar jet. argued that the antisymmetrical shedding of large, coherent tubular vortex structures, similar to a vortex street structure, (Figure 1.14) are a more accurate description of the jet oscillation. However, throughout all studies no definite definition of a flapping jet has been established. A summary of the aforementioned studies have been compiled in Table Acoustic Excitation Acoustic excitation of jets for research purposes has been used throughout the 1970s starting with Crow and Champange (1971), but has been mostly applied to axisymmetric jets. In the area of acoustically oscillated planar jets, Fiedler and Korschelt (1979) performed a noteworthy study, that had considerable impact on MOPJ investigations by other researchers in years to follow. Their investigation is split into a large qualitative flow visualisation study and a quantitative part. The experimental facility used by Fiedler and Korschelt (1979) is shown in Figure 1.15.a. As mentioned above, a key part of the study was to establish the influence of anti- and axisymmetric excitation on jet amplification and behaviour. Using antisymmetric excitation, Fiedler and Korschelt (1979) established that a minimum excitation amplitude is necessary to achieve amplification, but no quantitative results are reported in relation to this finding. They further established that, once amplification is evident, there are three

21 CHAPTER 1. INTRODUCTION 20 Table 1.1: Summary of relevant publications investigating the natural large-scale oscillations within unexcited planar jets. Oscillation Reh/ f Stn/ Range Authors w/h S/h Key Motivitation Method [10 3 ] (Hz) [10 3 ] (x/h) Natural Oscillations Wygnanski and Gutmark (1971) Goldschmidt and Bradshaw (1973) Gutmark and Wygnanski (1976) Oler and Goldschmidt (1980) Cervantes de Gortari and Goldschmidt (1981) Oler and Goldschmidt (1981) Notes: n/a = Not Available; N/A = Not Applicable. Natural N/A n/a n/a Lateral Jet Movement Natural N/A Lateral Jet Movement Natural N/A n/a n/a Planar Jet Characterisation Natural N/A n/a n/a Jet Flapping, Coherent Structures Natural N/A n/a Jet Flapping Natural N/A n/a Jet Flapping, Coherent Structures

22 CHAPTER 1. INTRODUCTION 21 distinct flow phases present in the time-averaged flow. The jet initially spreads like a quasi-steady jet, but at a distinct location downstream from the nozzle exit (x f, Figure 1.16) the spreading rate increases considerably. After a further distance to a location downstream from where the local height of the excited jet is approximately twice the height of the steady jet, the spreading rate reduces to approximately the undisturbed jet case again (Figure 1.16b). This location has been termed the amplification distance (x a ). Overall, Fiedler and Korschelt do not provide any detailed data, but refer to a systematic study that was underway at the time of publication. A review of literature published by the authors shows no further published data in the public domain concerning the described experimental program. On a further note, Fiedler and Korschelt observed, that for each frequency tested, once the minimum excitation threshold was surpassed to achieve amplification, a constant downstream distance corresponding to the onset of increased spreading exists, which moves upstream with an increase of excitation amplitude. However, again, no quantitative values are reported. In contrast to a minimum excitation amplitude threshold, they also state that an upper limit exists, beyond which no further increase in jet amplification is evident. Additionally, they report that no vortex pairing is observed in the flow, while the jet exhibits flapping structures that roll in fluid similar to the motions in a two-dimensional shear layer. From their quantitative data, Fiedler and Korschelt establish that three different configurations of mixing are present in the amplified flow (Figure 1.17): 1. At low forcing frequencies, the jet exhibits a strong flapping motion. Strong velocity fluctuation has been observed but no increase in entrainment is present. 2. At medium forcing frequencies, the jet exhibits enhanced entrainment and strong fluid engulfment through a roll-in motion. 3. At high frequencies, the flow exhibits strong entrainment, but no change in coherent structures relative to a non-amplified jet. Although the three configurations have distinctly different inferred mixing capabilities, they all

23 CHAPTER 1. INTRODUCTION 22 NOTE: This figure is included on page 22 of the print copy of the thesis held in the University of Adelaide Library. NOTE: This figure is included on page 22 of the print copy of the thesis held in the University of Adelaide Library. NOTE: This figure is included on page 22 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.15: Selection of relevant oscillating planar jet nozzles: a) Acoustic nozzle with two side speaker (Fiedler and Korschelt, 1979); b) Acoustic nozzle with single side speaker (Fiedler and Mensing, 1985); c) Coanda-effect fluidic flip-flop nozzle (Viets, 1975); d) Fluidic flip-flop nozzle (Mi et al., 1995).

24 CHAPTER 1. INTRODUCTION 23 Figure 1.16: Schematic diagram of time-averaged jet flow: a) Steady jet; b) Oscillating jet with excitation above minimum threshold: x f = Formation distance; x a = Amplification Distance. (Fiedler and Korschelt, 1979) exhibit a distinct widening of the jet and a strong change in the transverse velocity fluctuation variance. Once again no quantitative data are given in relation to the change-over between individual excitation regimes. Chambers and Goldschmidt (1982) used a single speaker to acoustically excite a planar jet that was confined by two side walls. In general they confirmed that excitation leads to an increased spreading rate accompanied by an increased velocity decay rate. Using Pitot tubes to acquire jet velocities, they further found that the excitation, combined with the increased jet spread, led to a movement in the virtual origin of the jet flow in the axial direction. In contrast, Fiedler and Mensing (1985) investigated the effect of acoustic excitation on a single planar shear layer (Figure 1.15.b). They established three different types of flow conditions in the shear layer: Neutral: The flow is completely natural and no external excitation is present. The shear layer is completely turbulent and no regular peaks are visible in the frequency spectrum.

25 CHAPTER 1. INTRODUCTION 24 Figure 1.17: Three different configurations of forced jet flow identified by Fiedler and Korschelt (1979). Disturbed: The shear layer turbulence does not show any initial periodic structures but some isolated spectral peaks evolve at a constant frequency that is independent of location. Excited: The shear layer exhibits periodic structures of defined frequencies and amplitudes initiated by the external excitation downstream from the nozzle exit. Fiedler and Mensing (1985) generally report that, within the excited flow condition, the strongly coherent vortex structures travel without general pairing. This is then followed by sudden diffusion and vortex break-up. As this point of vortex dissipation is at a fixed location downstream from the nozzle for each given excitation frequency and amplitude, the authors define the point as the amplification saturation point. Recently, a study by Iio et al. (2008) using an experimental facility with two side speaker found coherent structures similar to those reported by Fiedler and Korschelt (1979) (Figure 1.18), as well as higher fluid entrainment and increased jet spread than a steady planar jet. Further details of the experimental conditions of these previous studies can be found in Table Fluidic Excitation Hermann Viets first presented a fluidic nozzle (Figure 1.15.c) using the Coanda effect in 1975 (Viets, 1975). This work was mostly concerned with the suitability of a fluidic nozzle to increase

26 CHAPTER 1. INTRODUCTION 25 Table 1.2: Summary of relevant previous studies of acoustically and fluidically oscillated planar jets. Oscillation Reh/ f Sth/ Range Authors w/h S/h Key Motivitation Method [10 3 ] (Hz) [10 3 ] (x/h) Acoustic excitation Fiedler and Korschelt (1979) Chambers and Goldschmidt (1982) Fiedler and Mensing (1985) Iio et al. (2008) Symmetrical Side Speakers Single Side Speaker Single Side Speaker Symmetrical Side Speakers Mixing features n/a 700 & 1400 n/a Mean flow field interaction N/A n/a Shearlayer structures n/a Coherent Structures and Motion Fluidic excitation Viets (1975) Coanda Effect n/a 13.3 N/A N/A n/a Thrust augmentation Piatt and Viets (1979) Coanda Effect n/a n/a N/A 4 18 n/a 0 40 Conditional sampling Mi et al. (1995) Flip-flop Phase-locked measurements Mi et al. (2001a) Flip-flop Velocity measurements Notes: n/a = Not Available; N/A = Not Applicable.

27 CHAPTER 1. INTRODUCTION 26 Figure 1.18: Coherent flow structures observed by Iio et al. (2008). mixing and thrust efficiency by exciting the jet flow. While the study mainly reports on the effect of variations of the nozzle geometry, it finds that the nozzle is suited to enhance either thrust or mixing but not simultaneously. Piatt and Viets (1979) then used those findings to investigate the phase-resolved jet flow. They show a widening of both the time-averaged and phase-locked flow. A double hump can be found in the time-averaged velocity profile close to the nozzle up to a distance of x/h 14 which disappears downstream from this axial location. The study s main purpose was to develop a system to conditionally sample a velocity field depending on the instantaneous velocity field at the nozzle exit. Sixteen years later, Mi et al. (1995) present a new planar fluidic nozzle (Figure 1.15.d) that does not rely on an external feedback system like the Viets-nozzle to achieve jet oscillation. By using a conditional sampling method in combination with hot-wire probes, the authors equally show that a flapping jet exists that exhibits a faster velocity decay than a steady jet combined with an increased spread in the jet near field. One further key finding is that beyond a distance of only x/h = 5 (where h is the larger nozzle exit in Figure 1.15.c oscillation is no longer evident. Further

28 CHAPTER 1. INTRODUCTION 27 investigation by Mi et al. (2001a) also establish that the flow exhibits an increase in Reynolds stresses and a redistribution of the energy spectrum with a higher content in the low frequency spectrum in comparison with a steady jet, which may be related to the fact that the jet acts like a bi-stable coanda-effect reattaching jet. A summary of the key motivations for and experimental conditions employed in the above studies can also be found in Table Literature Review Mechanically Oscillated Planar Jets Mechanically oscillated planar jets (MOPJ) can generally be classified into four different regimes, depending on the location of excitation and the the excitation method: Indirect mechanical (Acoustic): The flow is excited using a method that is external to the nozzle area in the transverse direction, but which can be altered independently of the other flow variables. Mass-flow variation: The mass flow is varied in a regular fashion, creating a puffing jet with time-varying nozzle exit velocity. Potential core excitation: Flow excitation is undertaken downstream from the nozzle exit but still within the potential core region of the jet. Nozzle excitation: The nozzle is varied in a mechanical fashion to excite the jet flow. Both the potential core and nozzle excitation can be undertaken by either using a linear transverse movement method or by imparting an angular excitation into the jet flow. Excitation by indirect mechanical means and mass-flow variation have little relevance to the present investigation, but are discussed for completeness and because some of the mentioned work was undertaken concurrently with some of the other investigations referred to in the following sections.

29 CHAPTER 1. INTRODUCTION Indirect Mechanical Excitation Rockwell (1972) excited a jet by using a flap located 8h above the nozzle exit area in the transverse direction to push a volume of fluid onto the jet across its entire width as shown in Figure 1.19.a. The authors used flow visualisation in the potential core region (x/h 3.0) to identify five different vortex regimes in the jet shear layer. While different excitation frequencies in relation to the natural vortex shedding frequency ( f n ) have different impacts on the vortex formation and behaviour in the shear layer, the authors established that when the forced excitation frequency ( f o ) is approximately f n, the flow exhibits strongly increased vortex growth and formation. In Rockwell s opinion, this finding may be used to enhance large-scale mixing in planar jets Puffing Jets A sliding valve apparatus (Figure 1.19b) was used by Lai and Simmons (1980, 1983) and Lai (1984) to create a puffing jet by mass-flow variation. The sliding valve opened in a sinusoidal fashion releasing air from the side of the facility. The studies were mainly concerned with the influence of the excitation on the fluid entrainment and decay rates. All studies found that, for the mean velocity profiles and decay rates, the flow only differs insignificantly from that of a steady jet. The authors postulated that this might be due to the fact that the pulsation is insufficient in amplitude to excite the coherent shear layer structures. In regards to instantaneous quantities, all studies describe a change of peak-to-peak amplitude oscillation of the instantaneous centreline velocity from the exit velocity and the maximum peak moves downstream from 10h to 40h for pulsation frequencies of 1 to 10 and 20 Hertz, respectively Potential Core Excitation Potential core excitation studies refer to configurations where the oscillation mechanism is placed downstream from the nozzle exit and hence not all jet fluid exiting the nozzle is directly attenuated by the excitation.

30 CHAPTER 1. INTRODUCTION 29 Angular Excitation Methods A number of studies have been performed using facilities that place an aerofoil in the centreline of the nozzle exit (Figure 1.19c). The aerofoil is then rotated up and down around an axis placed at approximately 1/3rd of the cord length from the leading edge of the aerofoil. Collins et al. (1981, 1982) first undertook a study of the effects of a small excitation amplitude on the mean velocity decay, the jet spreading rate and the flow entrainment. In comparison with a steady jet, the excited flow was found to have an increased velocity decay and jet spreading rate, both of which were related to an increase in oscillation frequency as well as an increase of flow entrainment ranging from 10% to 175% depending on the combination of excitation angle, oscillation frequency and jet velocity. Noteworthy from this study is also the fact that some of the experiments showed a bifurcation of the velocity profile in measurements taken at x/h = 60. This may be a direct result of the angular deflection imparted onto the jet flow by the rotation of the aerofoil. It is not reported which individual conditions showed this phenomenon, but it can be surmised that this feature is related to the conditions that induce large deflections. When using a slightly different experimental setup, Simmons et al. (1981) found similar tendencies in regards to jet spread, centreline velocity decay and flow entrainment. Lai and Simmons (1983) and Lai (1984) used the same arrangement as the previous authors and, with some further measurements combined with the results of the two previous studies, generated a numerical model with a thin shear layer approximation and constant eddy viscosity for both the single oscillating vane and puffing jet cases. The authors conclude that the model predicts the general trends of the mean flows, but fails to predict any of the unsteady influences of the jet excitation. The latter study further refines the initial model by including new terms for momentum conservation, but still fails to predict the influence of instantaneous unsteady effects on the flow. Lai and Simmons (1985) reported further measurements of instantaneous velocities as well as mean-flow data for the same set-up as used beforehand. Again, they find an increase in centreline velocity decay, jet spread and entrainment, which are tied to inceases in oscillation frequency and amplitude.

31 CHAPTER 1. INTRODUCTION 30 Transverse Excitation Methods Concurrent with the above studies, Badri Narayanan and Raghu (1982, 1983, 1984) investigated the excitation of planar jets by moving an aerofoil through the nozzle centreline in the transverse direction. As this airofoil is located outside the nozzle, it will deflect the overall jet stream and impart a transverse momentum that is directly proportional to the product of oscillation amplitude and frequency. The authors showed that this method is also suitable to increase the spreading rate and entrainment ratio of the jet together with an increase in the decay rate of the mean centreline velocity. For the reported set-up, it was also shown that a higher jet spread occurred at lower jet exit velocities, which might be explained by the momentum ratio between the jet fluid and the transverse motion of the aerofoil. A further system investigated is the push-pull twin vane oscillator shown in Figure 1.19e. In this system two vanes were solidly linked together and placed on each side of the nozzle in the lateral direction and then oscillated in unison. The first study to investigate this set-up was conducted by Badri Narayanan (1987). However, this study is no longer available in the public domain and the author has since passed away. Badri Narayanan (1988) reviewed the system without giving specific details about the experimental conditions but states a number of key discoveries. One key point is the formation of large-scale vortices on each side of the jet that result in the sudden blooming of the jet at a certain distance downstream from the vanes, which moves upstream with an increase in excitation frequency. This formation distance is limited to a minimum distance that seems to coincide with the end of the potential core region for the jet. A summary of the experimental conditions for the semi-mechanical, the puffing and potential core excited jet studies can be found in Table Nozzle Excitation The main difference between this type of nozzle and those in the previous section is the fact that all jet fluid is directly subjected to the excitation at the nozzle exit. A summary of the experimental envelopes of the discussed studies can be found in Table 1.4.

32 CHAPTER 1. INTRODUCTION 31 NOTE: This figure is included on page 31 of the print copy of the thesis held in the University of Adelaide Library. NOTE: This figure is included on page 31 of the print copy of the thesis held in the University of Adelaide Library. NOTE: This figure is included on page 31 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.19: Different methods of mechanical excitation of planar jets: a) Indirect mechanical oscillation using a side flap (Rockwell, 1972); b) Puffing jet flow from mass flow variation (Lai and Simmons, 1980); c) Oscillating wing in potential core region (Collins et al., 1981); d) Pitching twin-vane oscillator (Badri Narayanan, 1988); e) Push-pull twin-vane oscillator (Badri Narayanan, 1988); f) Reciprocating lip oscillator (Badri Narayanan et al., 1985).

33 CHAPTER 1. INTRODUCTION 32 Table 1.3: Different MOPJ excitation methods including potential core excitation. Oscillation Reh/ f Sth/ Range Authors w/h S/h Key Motivitation Method [10 3 ] (Hz) [10 3 ] (x/h) Semi-Mechanical Excitation Rockwell (1972) Side Flap n/a Vortex structure breakdown Puffing jets Lai and Simmons (1980) N/A 1 20 n/a 0 80 Fluid entrainment Lai and Simmons (1983) N/A 1 20 n/a 0 80 Fluid entrainment Lai (1984) N/A Fluid entrainment Angular Excitation Methods Collins et al. (1981) n/a Mass flow entrainment Simmons et al. (1981) n/a Mixing enhancement Lai and Simmons (1983) n/a 1 20 n/a 0 80 Theoretical Modelling Lai (1984) n/a 20 n/a 0 60 Fluid entrainment Single Oscillating Vane Sliding valve pulsed jet Lai and Simmons (1985) Transverse Excitation Methods Badri Narayanan and Push-pull Raghu (1982) oscillating vane Badri Narayanan and Raghu (1983) Badri Narayanan (1988) Push-pull twin vane Notes: n/a = Not Available; N/A = Not Applicable. 0.11, Instantaneous jet behaviour n/a 0 50 Jet spreading n/a 0 50 Jet spreading n/a n/a n/a n/a 5.0, 6.7 n/a Jet excitation

34 CHAPTER 1. INTRODUCTION 33 Angular Excitation Methods Badri Narayanan et al. (1985) and Badri Narayanan and Platzer (1987a) used the reciprocating lip apparatus shown in Figure 1.19.f. The facility is classified here as angular excitation method, as the lips change the jet ejection angle during different phases of the throw. Hence a horizontal jet is only generated when the two lips are in the neutral position. Aside from the previously described faster velocity decay and increased jet spreading rate, they found three different flow regions to exist for S/h > 1. In the first region the jet flow exhibits a flapping motion in sync with the throw of the reciprocating lips of the facility. Towards the downstream end of the region, the flow starts to roll up into large-scale vortices marking the start of the second region. This vortex roll-up is coupled with increased entrainment compared to a steady jet. At the end of the second region the large-scale structures break up and become fully turbulent, beginning the third region. The description given by Badri Narayanan and Platzer (1987a) is consistent with the findings made of Fiedler and Korschelt (1979). The distance to the start of the second region or vortex formation distance, was found to be directly related to a constant Strouhal number as is discussed separately below. Badri Narayanan and Platzer (1987b) reported the same results together with some measurements on thrust augmentation, but also suggested a flow structure as shown in Figure 1.20, which is generated for throws above S/h = 0.5 for the oscillating lip apparatus. Badri Narayanan (1988) further developed the study into a twin vane pitching facility as shown in Figure 1.19.d, which was later also used by Badri Narayanan and Platzer (1989). Due to the proximity of the vanes to the nozzle exit, the entire jet flow is forced through the excitation mechanism. Badri Narayanan (1988) confirms the findings of the reciprocating lip facility in regards to Strouhal number dependence of the vortex formation distance and the general flow regions that exist within the excited flow. However, in addition, the authors argue that the oscillation stroke has no influence on the vortex formation distance but only controls the size of the amplified vortex structures. Badri Narayanan and Platzer (1989) focused their study to mainly assess thrust augmentation in relation to excitation Strouhal number as well as the visualisation of the large-scale flow structures as shown in Figure 1.21, again confirming the findings of earlier studies.

35 CHAPTER 1. INTRODUCTION 34 Figure 1.20: Flow pattern reported by Badri Narayanan and Platzer (1987b) for the reciprocating lips apparatus. Transverse Excitation Methods Only two investigative campaigns have been undertaken with mechanisms that oscillated a nozzle in a purely transverse motion. Galea (1983) and Galea and Simmons (1983) used an asymmetric excitation in the apparatus shown in Figure This successfully generated vortex structures on both sides of the jet. Furthermore, as described in section 1.4.2, the authors found this to be a successful method to increase the jet entrainment and increase the spreading angle in comparison with a steady jet using a small S/h = While an extensive campaign was undertaken, only mean values are reported for spreading rate and fluid entrainment. However Galea (1983) again describes the concept of a vortex formation distance. This is covered in more detail in the next section. He also reports that the generation of large-scale coherent structures did not undergo vortex pairing in a range of 10 x/h 40 for the flow conditions investigated. Finally, the author of the present study undertook a preliminary visualisation study in a small simple harmonic motion oscillating facility which transversed the nozzle vertically using a crank mechanism as part of the present investigation to determine the boundary envelope for a new

36 CHAPTER 1. INTRODUCTION 35 NOTE: This figure is included on page 35 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.21: Formation of large-scale vortex structures generated by the twin vane pitching facility as documented by Badri Narayanan and Platzer (1989).

37 CHAPTER 1. INTRODUCTION 36 Figure 1.22: Asymmetric excitation apparatus used by Galea (1983); Galea and Simmons (1983). large-scale facility (Riese et al., 2004). That study concentrated on the generation of large-scale structures in the flow for large S/h (Table 1.4) but since then has been found to be too inaccurate to be useful for further analysis Vortex Formation Distance and Strouhal Number Dependency To further understand the Strouhal number dependence of excited planar jets, a large study was performed by Korst (1982) for the US Navy. However, even though extensive efforts were made to acquire a copy of the report, it is no longer available in the public domain. The studies listed in Table 1.5, which investigated the excitation of planar jets, formulated two key concepts that are fundamental to the creation of large-scale structures in planar excited jets. These are: 1. When excited above a minimum threshold in the lateral direction as a product of f o and S, a planar jet exhibits a flapping motion downstream from the nozzle exit. This is then

38 CHAPTER 1. INTRODUCTION 37 Table 1.4: Summary of relevant studies of nozzle excitations of mechanically oscillated planar jets. Oscillation Reh/ f Sth/ Range Authors w/h S/h Key Motivitation Method [10 3 ] (Hz) [10 3 ] (x/h) Angular Excitation Methods Badri Narayanan et al. (1985) ± Thrust augmentation Reciprocating Lip Badri Narayanan and Platzer (1987a) Badri Narayanan and Platzer (1987b) Badri Narayanan (1988) Badri Narayanan and Platzer (1989) Thrust augmentation & jet mixing Thrust augmentation Various n/a n/a n/a n/a 50, 67 n/a Jet excitation Pitching twin vane oscillator n/a Vortex structure definition Transverse Excitation Methods Galea (1983) , , 51, Mean flow excitation Galea and Simmons Asymmetric (1983) excitation , , 51, Jet entrainment Riese et al. (2004) SHM Sliding 0.25 Plate n/a N/A Flow structures Notes: n/a = Not Available; N/A = Not Applicable.

39 CHAPTER 1. INTRODUCTION 38 followed by the sudden roll up of large-scale vortices. This point of vortex creation marks the start of a second distinct region in the flow, which shows little or no jet spreading and large-scale coherent vortices which do not undergo any pairing. This region ends at an axial location where the coherent structures break up and fully dissipate into small-scale incoherent turbulent structures marking the beginning of a third region in the flow. 2. The vortex formation distance (x f, Figure 1.16.b) is associated with a distinct dimensionless frequency and a distinct formation distance in the axial direction appears to exist for each flow case. As discussed previously, Fiedler and Korschelt (1979) defined x f as the downstream point in the averaged flow where the jet starts to exhibit increased spreading due to the onset of vortex roll-up. Results of their investigation, reproduced in Figure 1.23, show that for a given h and U 0, the variation of f o results in a linear variation of x f. Approximately parallel to this function for x f, a second linear function is visible that represents x a as a function of f o. In neither case do the authors report how many different flow cases were collated to define these functions for x f and x a. It is important to note that the findings presented by Fiedler and Korschelt (1979) were obtained for a constant oscillation amplitude and that it does not play any role in the formulation of proposed governing equations for x f. While these authors also establish the existence of three distinct phases shown in Figure 1.17, no data are given on how these phases apply to different flow conditions or on what constitutes the minimum excitation threshold discussed earlier. Galea (1983) in his thesis work also indicated the existence of a minimum excitation amplitude, but no information in regards to the relationship of the amplitude to other flow variables is given. Badri Narayanan and Platzer (1987a) reported the influence of various flow conditions and oscillation stroke lengths on changes in x f. They found that only for excitation strokes of S/h 1 does a noticeable flow structure amplification exist in the vicinity of the nozzle exit. However, for S/h = 0.5 vortex roll-up was found to exist from a distance of x/h 100. To investigate x f in the aforementioned study, a hot wire probe was placed laterally away from

40 CHAPTER 1. INTRODUCTION 39 NOTE: This figure is included on page 39 of the print copy of the thesis held in the University of Adelaide Library. Figure 1.23: Reproduction of Figure 13 from Fiedler and Korschelt (1979) with rotated axes, showing the onset of strong amplification (x f ) and the saturation distance (x a ) as a linear function of f o for constant h and U 0. the centreline (y p, Figure 1.24) at a distance of a few centimetre (Badri Narayanan, 1988), i.e. at least 4h. This hotwire probe was then traversed in the streamwise direction and the instantaneous velocity output was observed. At streamwise locations upstream from x f, where the jet was considered to exhibit a flapping motion, the instantaneous velocity profile showed discrete periods of time of zero velocity as shown in Excerpt (a) in Figure At points located at or downstream from x f the voltage signal from the hotwire probe took on distinctly different characteristics (Excerpt (b) in Figure 1.25). At these points, the instantaneous velocity profile would remain above zero for the entire time of the oscillation cycle. Badri Narayanan and Platzer (1987a) used their results to calculate a Strouhal number that coincides with the measured location of x f and found that, for a Strouhal number defined as St b = f o b U CL, where f o is the oscillation frequency, b is the jet halfwidth in the steady jet at x f and U CL is the mean centreline velocity of the steady jet at x f, St b = over nearly all examined flow cases (Figure 1.25). The same results are also reported by Badri Narayanan and Platzer (1987b). It is noteworthy that their definition of a St b again does not include any reference to the oscillation stroke length.

41 CHAPTER 1. INTRODUCTION 40 Figure 1.24: Set-up of the hotwire probe to find x f by traversing the probe downstream and recording the instantaneous voltage signal for Badri Narayanan and Platzer (1987b,a); Badri Narayanan (1988); Badri Narayanan and Platzer (1989). Figure 1.25: Instantaneous hotwire signals over 2 oscillation cycles: a) Voltage signal at a location upstream from x f ; b) Voltage signal at x f and further downstream. (Badri Narayanan, 1988) Also, the flow variables relate to a steady state jet and hence still necessitate the measurement of these variables in the steady jet flow to compare the claims made by authors with other flow cases. Furthermore, the distance of y p from the oscillation centreline will certainly have an influence on the measured distance of x f, i.e. changing the lateral distance will translate x f up- or downstream by an unknown distance as can be seen from Figure Importantly, this issue has not been quantified in any of the studies shown in Table 1.5. Badri Narayanan (1988) reviewed the work undertaken by himself and his collaborators to that date and again stated that St b = at x f. However, he also reported that, for small nozzle exit velocities, St b = at x f, but gave no details on the flow cases for which he makes this

42 CHAPTER 1. INTRODUCTION 41 claim. Once again the author also claims that x f is independent of the oscillation amplitude, but does not present any substantial data to verify this. Badri Narayanan and Platzer (1989) undertook a further study using the twin vane pitching facility (Figure 1.19.d) and found that x f 6h for this particular facility. Any efforts to reduce x f to below 6h by reducing U 0 or increasing f o were unsuccessful and only led to a merging of the vortices, negating any excitation effect on the lateral spread of the jet. For this facility though, x f was found to occur at a streamwise location at which St b = The slightly lower value of St b in this study than the St b = reported in the majority of the investigations by the same authors, is most probably due to difference in experimental facility and excitation method when compared with the studies previously discussed. 1.6 Motivation for the Present Work The current study was stimulated by the change of large-scale mixing behaviour that was found to occur downstream from the the FPJ nozzle exit plane (Manias and Nathan, 1993) and the quasiplanar flip-flop nozzle exit plane (Mi et al., 1995). Both nozzle types exhibit fluidic instabilities and do not readily lend themselves to a rigourous investigation using independently varied flow parameters. Much of the previous work was undertaken on planar mechanically oscillating jets and it has been shown that the results presented in published documents lack in three key areas: 1. Very little effort was spent on describing large-scale flow structures and the influence of different St h on the jet flow in investigations undertaken during the 1970s and 1980s as these were stimulated by the interest in loss-less thrust augmentation for the use in V/STOL aircrafts. 2. Only the study undertaken by Galea (1983) utilised a system that linearly translated the excitation mechanism in the transverse direction by exciting the jet nozzle. This provided well defined jet boundary conditions. This investigation is limited because excitation was only applied to one side of the flow, making the device asymmetrical.

43 CHAPTER 1. INTRODUCTION 42 Authors Table 1.5: Relevant studies exploring the relationship of the vortex formation distance and local jet Strouhal number. Fiedler and Korschelt (1979) Galea (1983) Badri Narayanan and Platzer (1987a) Badri Narayanan and Platzer (1987b) Oscillation Reh/ St/ S/h f (Hz) Method [10 3 ] [10 3 ] Def + Vortex Formation Distance Symmetrical Side Sth = f o h Speakers U0 Linear St x f relationship shown Asymmetric excitation , n/a n/a No St x f relationship reported Reciprocating Stb = f o b Lip UCL b & UCL from steady jet Reciprocating Stb = f o b Lip UCL b & UCL from steady jet b & UCL from steady jet; lower St for smaller fo & U0 Badri Narayanan (1988) n/a n/a n/a 50, 67 = f o b Various Stb UCL Badri Narayanan and Platzer (1989) Pitching twin vane oscillator Notes: + Def= Definition; n/a= Not Available n/a = f o b Stb UCL Min. x f = 6h for this facility; St slightly lower than previous studies

44 CHAPTER 1. INTRODUCTION No systematic effort has been made to relate the large-scale flow structures to the initial conditions of a MOPJ. Only a few studies examined the change in flow features over a discrete Strouhal number range and reported on coherent large-scale structures that were found in the jet flow. In addition, no studies of systematic variation of S/h and St h have been reported for a single well-defined nozzle configuration. The large variety of different nozzle types and facilities and the absence of a welldefined fundamental study make it impossible to assess the variation of flow features and coherent structures with changes in flow conditions from the available literature. 1.7 Thesis Aim & Scope The aim of this study is to classify the types of flow structures and identify regimes in which they are present over a wide range of defining parameters of the MOPJ. Furthermore this study investigates the vortex formation distance in the current facility for a number of different flow cases and relates them to the previous findings. 1.8 Thesis outline This thesis is divided into five individual chapters structured in a logical sequence. The current chapter gives an introduction to the history and use of flow visualisation in prominent cases such as Osborne Reynolds famous pipe flow experiment and Prandtl s water tunnel observations. This is followed by an introduction to steady, unsteady, planar and axisymmetric jets. The majority of the chapter, though, is dedicated to a review of MOPJs and establishes the gaps in knowledge with regards to oscillating planar jets that are excited in a linear transverse fashion. This establishes the need to investigate the subject further with an emphasis on the development of large-scale coherent structures and the behaviour of the jet in the near field. The following chapter reviews the specific methods, concepts and the experimental apparatus devised to meet the aims of the present study. This reaches from the use of flow visualisation

45 CHAPTER 1. INTRODUCTION 44 techniques, including a novel method to capture phase-locked images, to the principles of Particle Image Velocimetry (PIV) and the set-up of the measurement system. The facility used in this study was purpose-built and a review of the actual facility as well as the upstream flow behaviour is also given. The third chapter showcases the findings of this study and compares the results in the wider context with those of previous studies. The chapter is split into its separate parts of flow visualisation and PIV. The first part of the chapter investigates the formation and near-field behaviour of the MOPJs using phase-locked imaging and flow visualisation. Three individual flow regimes and the associated coherent structures in each are described. The next part shows that these flow regimes are generally independent of any Strouhal number classification and proposes instead a new criterion incorporating the stroke to nozzle height ratio and a relationship between the oscillating frequency and the natural shedding frequency. Data acquired using PIV is then used to demonstrate the congruence of the coherent structures and flow regimes found from flow visualisation experiments. This is further expanded to report how time-averaged vorticity data can be used to undertake flow regime classifications. Returning to the flow visualisation results, this section shows cycle-averaged flow cases and determines that indeed three different flow regions exist for two of the three flow regimes identified, which largely agree with observations documented in previous studies. The vortex formation distance for the flow cases for which quantitative data have been acquired, is then considered and compared with that from previous investigations. A number of differences are identified and the suitability of the definition of x f proposed by Fiedler and Korschelt (1979) is discussed. A new definition of the vortex formation distance is subsequently provided and the results of the present study re-examined. This leads to the proposal of a relationship between the vortex formation distance and other relevant flow variables. The final part of the chapter using quantitative data investigates the centreline velocity decay of the jet in relation to changes of the jet velocity and stroke length. The results show an increase in velocity decay rate with increasing stroke length as well as higher velocity decay rates than

46 CHAPTER 1. INTRODUCTION 45 those of steady planar jets, as is to be expected from the findings of earlier studies. In addition, the centreline velocity decay rates in the mean jet far-field appear to be constant for each stroke length in the cases examined. It is further demonstrated that the mean exit velocity of the steady jet cases is not necessarily the correct parameter to normalise the centreline velocity in MOPJ applications. Following the PIV results, a small section of Chapter 3 is dedicated to the observation of large-scale low frequency oscillations in the flow that came to light during the data analysis and, although not part of the scope of this study, warrant a mention for completeness. The fourth chapter is dedicated to a case study of one example from each flow regime. The purpose of these examples is to tie together the findings of this study. The fifth and final chapter summarises the findings of this study and relates them to each other. It also gives recommendation for future work.

47 Chapter 2 Experimental Set-up and Methods Jack of all trades, Master of none, PhD of one! 2.1 Fundamental Fluid Dynamics Turbulence Although mixing does occur in laminar flows (and is undertaken in laboratories under closely controlled conditions), jet mixing in industrial processes is generally performed using turbulent flow conditions. Turbulence is defined as a quantity associated with velocity, which varies from a mean in an irregular pattern and the instantaneous velocity in a given flow can be expressed as u = ū + u (2.1) where u = instantaneous velocity (m.s 1 ); ū = mean, time-averaged velocity component (m.s 1 ); 46

48 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 47 u = fluctuating velocity component (m.s 1 ). While there is a random velocity component to turbulent flows, Hinze (1959) shows that the distribution of the velocities at a given point in a flow, if sampled long enough, takes on a periodic or pseudo-periodic pattern and hence statistical methods can be applied to the flows. From the definition of Eq. 2.1 it can also be deduced that ū = 0 resulting in the definition of the fluctuating flow quantity as the root mean square u rms = (u ) 2 (2.2) Using this definition it is then common to describe the turbulence intensity as u rms ū (2.3) when describing turbulent flows. The actual flows can be seen as a superposition of scales of different characteristic sizes reaching from macroscales of the order of the nozzle height or diameter in the case of a jet, down to microscales in the energy dissipation range of micrometer size. Hinze (1959) also reports that, while the macroscales or large-scale eddies are dependent on the apparatus, the micro scales are mainly determined by the viscosity of the flow and hence the smallest eddies in the flow are not turbulent but viscous and the molecular effects dominate. As the flow is a superposition of eddies of different sizes, certain kinetic energy values are linked to individual eddy sizes and determined by vorticity and the intensity of velocity fluctuations at the corresponding frequencies (Hinze, 1959). Figure 2.1 shows a typical energy spectrum for an unforced turbulent flow, indicating that most energy is dissipated in the smaller eddies due to high velocity gradients and increased viscous effects.

49 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 48 NOTE: This figure is included on page 48 of the print copy of the thesis held in the University of Adelaide Library. Figure 2.1: Energy Spectrum of a turbulent flow. (Hinze, 1959)

50 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS Simple Harmonic Motion The transverse oscillation of the present nozzle opening is undertaken in a close to sinusoidal simple harmonic fashion with the actual mechanism and errors described further below. As a result, for this study the angular velocity, vertical displacement, instantaneous velocity and acceleration are defined as follows: ω = 2π f o (2.4) x(t)=acos(ωt + θ) (2.5) v(t)= aω sin(ωt + θ) (2.6) a(t)= aω 2 cos(ωt + θ) (2.7) where ω = angular velocity (s 1 ); f o a t = oscillation frequency (Hz); = oscillation amplitude (m); = time (s); x(t) = instantaneous displacement (m); v(t) = instantaneous velocity (m.s 1 ); a(t) = instantaneous accelaration (m.s 2 ); θ = Phase offset (rad). As the errors associated with the vertical movement of the nozzle are small for this study, the pure SHM characteristics shall be used throughout.

51 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS Triple Decomposition Scheme The vertical motion of the nozzle is periodic and the present study utilises a triple decomposition scheme proposed by Reynolds and Hussain (1972) to investigate the oscillating flow. Reynolds and Hussain (1972) state that u = ū + ũ + u (2.8) where u = instantaneous velocity (m.s 1 ); ū = mean, flow-averaged contribution (m.s 1 ); ũ = averaged periodic velocity contribution (m.s 1 ); u = uncorrelated fluctuating velocity component (m.s 1 ). It follows then that the phase average is hence defined as u = ū + ũ (2.9) and for large sample sizes and low sampling times, Reynolds and Hussain (1972) have shown that u = 0, ũ = 0, u = 0, ūv = ū v, ũv = ũ v, ūv = ū v, u = ū, ū = ū, ũv = ũv. (2.10) This decomposition scheme has been successfully used by a number of authors such as Kelso (1991) and Iio et al. (2008). 2.4 Experimental Facility A new experimental facility was designed and fabricated for the present study (Figures 2.2 & 2.3) using water as the working medium. Water gives an advantage over air as the working medium

52 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 51 because for equivalent Re h, the jet exit velocity (U 0 ) of water is two orders of magnitude lower when compared with the velocity of air and hence is more suitable to undertake flow visualisation studies. Also, lower U 0 requires lower f o to achieve the same St h relative to the use of air. However, the use of water brought with it the disadvantage of a limited facility size that needs a dedicated working section, which is shorter than the measurement areas in a lot of other studies discussed in the previous chapter. Also, the floor and ceiling of the working section, respectively, were closer (50h) than a lot of those other studies. This has significance for the results obtained as discussed further below. The facility was designed to achieve a maximum flow velocity of U 0 = 2.22m.s 1 (Re h = ) and a maximum oscillation frequency of 10 Hertz at a maximum stroke length of 0.09 metres (S/h = 10). A crankshaft was used to oscillate the plate in simple harmonic motion (SHM). The connection rod had a length of 1.0 metre resulting in a maximum displacement error from SHM of ε SHM = ±2.5% (Appendix G). A number of different crankshafts were used in this study ranging from a throw of 2.25mm (S/h = 0.5) to 45mm (S/h = 10). The working section was constructed from Acrylic (PMMA) to allow optical access from the bottom and the sides. A submerged false ceiling was used to achieve symmetrical boundary conditions on the top and the bottom of the working section (Figures 2.4 & 2.5). The working section has a length of 2.0m (x/h > 220). The facility is a closed-loop system utilising a Venturi meter for flow metering and an electric pump connected to a variable frequency drive to control volumetric flow. During the commissioning phase the system was calibrated to provide repeatable results (Appendix F). The flow conditioning section contained a number of screens made from polyethelene mesh (22GG950) as well as a flow straightening section made from 5mm diameter drinking straws and a perforated stainless steel plate to ensure uniform distribution of flow upstream from the oscillating plate as shown in Figure 2.6. A larger version of this Figure is presented in Appendix E. To reduce the ambient light and the reflection of diffuse light during the study, the facility was enclosed in a darkened window-less room and the supporting frame as well as the false ceil-

53 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 52 Table 2.1: Experimental Envelope for MOPJ Facility Variable SI Unit Values h mm 9 w mm 900 S/h w/s Re h f Hz ε SHM (max) % ±2.5 Tank Height mm 900 Tank Width mm 960 Working Section Length mm 2000 ing were painted matt black. To further achieve a reduction in diffuse laser light during PIV experiments and compliance with current OH&S laws in Australia, the laser beam terminated on a non-reflecting black surface and the optics as well as the laser head were covered with black skirting as shown in Figures 2.4 & 2.5. The experimental conditions did not approach the limits of the facility and the actual conditions used in the present study are shown in Table Upstream Flow Investigation During the commissioning process, an investigation of the upstream flow was undertaken as part of a final year undergraduate honours project (Paice, 2005a,b). The objectives of this investigation were to identify the flow structures upstream from the oscillating nozzle and downstream from the flow conditioning section as well as the entrainment of flow into the nozzle from various positions. Flow visualisation was undertaken using dye nozzles placed across the spanwise and lateral centrelines (Figures 2.7 & 2.8), as well as at the vertical walls to investigate the behaviour of the wall boundary layer. Experiments were performed upstream from the nozzle held stationary at various vertical po-

54 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 53 Figure 2.2: MOPJ research facility showing flow conditioning section and oscillating plate together with a cutaway view of the working section. Notes: 1 = Thin, knife-edge, cover-plate in front of oscillating plate (top & bottom); 2 = Oscillating plate; 3 = Perforated metal plate, mesh screens and flow-straightening element for flow conditioning.

55 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 54 Figure 2.3: MOPJ facility after assembly without protective curtains and walls. The flow diffuser and conditioning section are on the left hand side.

56 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 55 Figure 2.4: View of the MOPJ facility looking towards the oscillating plate showing the protective skirting attached to the frame. sitions as well as behind the nozzle oscillating at frequencies up to 5 Hertz. Still images and video recordings were taken of all experiments, such as shown in Figure 2.9. For all cases investigated, it was shown that the fluid and dye entrainment into the nozzle is continuous, smooth and symmetrical, and flow near to the walls is entrained continuously. 2.5 Dye Flow Visualisation While a number of quantitative experiments were undertaken in the present study using Particle Image Velocimetry (PIV), the majority of experiments were of a qualitative nature and performed utilising dye visualisation. Non-toxic food dye mixed with water was used as the flow marker. For best contrast, brilliant blue and red were used as marker colours. This raw marker mixture was found to have a specific density of greater than unity. If used in this negatively buoyant state, it was shown to have an impact on the visualised flow structures as described by Perry and Lim

57 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 56 Figure 2.5: MOPJ facility with view towards the flow outlet and protective skirting attached to the frame. The visual access port to the upstream section of the facility can be seen through the blackened motor frame.

58 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS A A 300 Add flanges for attachement to connection plate, including seal Perforated Plate Flow Screen B Hole to fit Ø80 mm upvc pipe Flow Straightener B Note: 1 off Flow box made out of Perspex Perforated Plate: at least 50 % open area, Stainless Steel Flow Screen: 22GG950, Polyethylen Box inside dimensions: 300 x960 x DESIGNED BY UNLESS OTHERWISE SPECIFIED M Riese DIMENSIONS ARE IN MILLIMETERS DRAWN BY T OLERANCE ON ANGLE ± 0.5 _ M Riese 0 PL ± 0.21PL ±0.05 CHECKED BY INTERPRET DIM AND TOL PER ASME Y14.5M-1994 APPROVED BY G. Nathan THIRD ANGLE PROJECTION OTHER APPROVALS 2 TITLE SIZE A3 CAD FILE NAME FlowStraighteningBox.vwf SCALE 1: 5 Perspex Flow Straightening Box OPJ Water Tunnel Design CAGE CODE EST. DRAWING NO. WGT N/A SHEET 1 OF REV 1 Figure 2.6: Schematic diagram of the flow conditioning section in the MOPJ rig (reduced scale). Figure 2.7: Vertical flow visualisation from a central aerofoil shaped nozzle upstream from the stationary plate at Re h = 1000 (Paice, 2005a).

59 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 58 Figure 2.8: Horizontal flow visualisation upstream from stationary plate showing uniform flow distribution (Paice, 2005a). Figure 2.9: Vertical flow visualisation behind the oscillating plate showing smooth and continuous flow through the nozzle (Paice, 2005a).

60 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 59 NOTE: This figure is included on page 59 of the print copy of the thesis held in the University of Adelaide Library. Figure 2.10: Changes in visualised flow structures in a jet depending on dye buoyancy as shown in Perry and Lim (1978). (1978). Figure 2.10 shows how the visualised jet structures change depending on buoyancy effect of the dye. To achieve neutral buoyancy of the dye in water, the solution was mixed with small quantities of alcohol. In the present study, Methanol was used and with the help of a hydrometer, the solution density was matched to the working fluid in the experimental facility (Figure 2.11). It was found during experimentation that the deviation of density of the dye of only 1 kg per cubic-metre from the working fluid was sufficient to alter the visualised structures in the way described by Perry and Lim (1978). As a result, great care was taken during the preparation of the dye solution to match the densities as closely as possible. If required, further details on the work with dyes for flow visualisation purposes can be found in a number of books such as Smits and Lim (2000). The dye was injected approximately 0.15m upstream from the oscillating plate through one, two or three small-diameter stainless steel tubes that were placed along the vertical centreline. One tube was aligned with the oscillation centreline and one each with the nozzle centre at both TDC and BDC of the oscillation stroke (Figure 2.12). The position of the nozzle outlets was changed during experiments to accommodate different stroke heights. Although the three tubes were in line with the flow, vortex shedding from the tubes had to be considered. Paice (2005a) found this not to have any tangible influence on the flow downstream from the nozzle orifice.

61 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 60 Figure 2.11: Density matching of dye solution for flow visualisation experiments: a) Hydrometer; b) Density of working fluid; c) Density of pure dye solution; d) Dye solution with correct density after addition of methanol (Paice, 2005a). 2.6 Phase Locked Imaging & Pseudo-Video Flow visualisation experiments were recorded using a custom-designed and -built control mechanism connected to a Hall effect sensor and a digital SLR camera (Figure 2.13). In the present study a 8.0 Megapixel Canon EOS 20D with a 50 mm wide-angle lens was used. Signals from the Hall effect sensor connected to the oscillation crankshaft were fed into the CamTrigger II control box, which acts as a remote trigger for the still camera. As shown in Figure 2.14, the control mechanism advances the trigger point by a number of predetermined steps upon each rotation. The resultant images, while independent from each other, when applied to a cyclic system, result in a movie showing pseudo-continuous motion. The CamTrigger II mechanism can be set to take either 25, 30, 50 or 60 images per cycle to conform with PAL and NTSC standards. As the present system is cyclical in nature it is hence possible to conduct high-definition, high-speed imaging with a low-cost commercial digital SLR camera.

62 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 61 Figure 2.12: Configuration of dye ports in MOPJ facility for flow visualisation experiments shown for the example of S/h = 10.

63 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 62 Figure 2.13: The phase-locked image capturing system used for recording of flow visualisation data utilising a commercial digital SLR, Hall effect sensor and custom made control system.

64 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 63 Figure 2.14: Sequential advance of the camera trigger mechanism and image splicing to achieve a pseudo-video movie.

65 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS Particle Image Velocimetry For many years fluid dynamicists had to rely on intrusive measurement techniques such as the Pitot-static tube or hot-wires for their investigations. With the advent of lasers during the 1960s, so called non-intrusive techniques, such as Laser Doppler Anemometry (Bates, 1977, LDA), Particle Dynamics Analysis (Durst et al., 1997, PDA), Laser Induced Fluorescence (LIF) and Particle Image Velocimetry (PIV) became readily available. Since then, PIV has become a well established technique. The theoretical background will only be touched on briefly, together with an overview of the experimental equipment and set-up used in the present study. For in-depth information on the theory and applications of PIV, the reader should refer to the works of Adrian (1986, 1991); Willert and Gharib (1991); Keane and Adrian (1992) and texts such as Smits and Lim (2000); Raffel et al. (1998); Westerweel (1993). A more detailed explanation of the PIV arrangement for the present study can be found in Appendix A Theoretical Background The technique used for the present investigation is termed single exposure, multi frame PIV, where two laser pulses image the movement of particles onto two separate image frames with a known time separation. For this case it is beneficial to use the fundamental definition of velocity (Kalt, 1998) to estimate the local instantaneous velocity u u(x, t)= lim Δt 0 Δx(x,t) Δt (2.11) where Δx is the particle displacement and Δt is the time separation between image recordings. Consider an image frame with 3 tracer particles at locations x1, x2 & x3, illuminated by the first laser pulse (Figure 2.15) at time t followed by a second image frame at time t with a known temporal separation of Δt. In the second frame the pixels have moved from their original to new positions at x1,x2 & x3. Assuming it is possible to clearly identify where each respective tracer

66 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 65 Figure 2.15: Schematic representation of 3 particles at locations (x1, x2, x3) at time t moving a distance during a known time Δt to their respective new positions at (x1,x2,x3 ) at time t. The resultant velocity vectors (V,V 2,V 3) can hence be found. particle has moved, one is now able to determine the displacements in x and y direction, respectively. Together with Δy, this allows for the following expression in two geometrical dimensions V 1x V 1y V 2x V 2y V 3x V 3y = 1 Δt Δ1x Δ1y Δ2x Δ2y Δ3x Δ3y (2.12) where V ix & V iy are velocity components in the x and y direction, respectively and Δix = X i X i Δiy = Y i Y i i = 1,2,3 (2.13) If one was to use a seeding density where the distance between particles is larger than the individual particle movement between images, it would be very easy to extract the relevant information. However, this would translate into a very low information density that can be extracted from any given image pair. In practice the seeding density is much higher, i.e. the particle spacing is smaller than the particle movement. Hence it is not possible to track individual particles in an image pair and one has to revert to correlations to identify the most likely corresponding particles in each

67 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 66 Figure 2.16: Conceptual arrangement of frame-to-frame image sampling. (Raffel et al., 1998) image Cross-Correlation of Image Pairs The system used in this investigation is a fully digital system from the image acquisition to the data analysis. As a result, only the relevant image correlation technique utilising Fast Fourier Transforms (FFT) is described here in detail. If one considers a pair of images (Figure 2.16), where Image 1 is the input and Image 2 the output with corresponding sample regions I(m,n) and I (m,n) it is possible to find the displacement d(m,n) as described in previous section. In this case, d(m,n) is the spatial transfer function for samples I and I. Expressed in mathematical terms, this equates to I(t)= D(t)= I (t) (2.14) where I(t) is the input function, I (t) is the output function and D(t) is the linear transfer function,

68 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 67 Figure 2.17: Idealised linear signal processing model relating the input (I(m, n)) to the output (I (m,n)) via the transfer function under the addition of random noise. (Raffel et al., 1998) all of which are dependent on time. While this is an ideal situation, in reality the image samples as well as the transfer functions will contain an amount of random noise as shown in Figure By cross-correlating samples I and I in the spatial dimension, it is possible to find the relevant transfer function. This requires large amounts of calculations as shown in Raffel et al. (1998) and hence it is easier, and nowadays common practice, to convert the image samples into the frequency domain using FFT to undertake the cross-correlation followed by re-conversion into the time domain. This holds as I Î I Î (2.15) where Î and Î are the Fourier transforms of I(m,n) and I (m,n), respectively, whereby the transformations are reversibly and hence hold true in both directions. In this case, the linear transfer function can be found by the complex conjugate multiplaction of the Fourier transforms as R II Î Î (2.16) where R II is the cross-correlation in the frequency domain. This is equivalent to the FFT of the linear transfer function (D( f )). By taking the inverse Fourier transform of D( f ), the transfer function is replaced into the time domain (D(t)) and the displacement can hence be estimated. This is also shown graphically in Figure 2.18.

69 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 68 Figure 2.18: Implementation of cross-correlation in the frequency domain using FFTs. (Raffel et al., 1998) To achieve optimum data correlation it is desirable to follow a number of guidelines such as those describing the correct seeding density, particle movement during the recording interval, particle size as well as out of plane particle movement as described in detail in Keane et al. (1995) Experimental PIV Set-up Overview The PIV system used for data acquisition in the present study consisted of a Qantel Brilliant B Twin Nd:YAG laser, frequency doubled to a wavelength of 532nm. The system was pulsed at a frequency of 10 Hertz and the power output was measured to be 400mJ per pulse. The laser was fed though a series of lenses and a mirror from underneath the working section and culminated in a laser sheet of approximately 1 mm thickness that ran spanwise across the centreline of the facility as shown in Figure A more detailed description of the physical arrangement of the PIV set-up is given in Appendix A. Hollow glass spheres with a mean diameter 20μm were used as reflective seeding particles and deemed to be following the flow in a satisfactory manner from information given by Raffel et al.

70 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 69 Figure 2.19: PIV set-up used in present investigation.

71 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 70 Figure 2.20: PIV target image with resolution pattern included. (1998). The data sheet for the seeding particles can be found in Appendix J. PIV Images were recorded using a Kodak 1.0 Megapixel CCD camera with a resolution of pixels mounted onto a three-axis traverse. The physical size of the image recorded had a size of 108 mm square, with a region of interest of 100 mm square. This resulted in an overlap of 8 mm (0.9h) on each side of the image. The actual grid for the PIV experiments conducted can be found in Appendix H. From target images such as Figure 2.20, the resulting image and pixel size was found to be 94 pixels per 10 mm, which equals a resolution of 106.4μm per pixel. For a pixel correlation window this equates to a physical size of 3.4mm 3.4mm. PIV image acquisition was synchronised with the position of the oscillating plate by using a custom designed control system. The control system again takes an input from plate crankshaft similar to the CamTrigger II system to drive the laser system and camera. To allow for identification of images in relation to the crank position, the control system drives a set of LEDs, which are blended into PIV image representing the crankshaft angle in binary code, which can be examined during the data analysis stage. The system set-up and an example of an image containing the LED binary coding are shown in Figures 2.21 & Due to the fact that a mirror was used to blend the LEDs into the images, it is important to note that while the highest bit is on the left hand side and the lowest bit is on the right hand side, that actual HIGH-LOW-bit LEDS are mirror images. This means that the LOW -set LEDS are on the top and the HIGH -set LEDs are on the bottom.

72 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 71 Figure 2.21: The trigger control box synchronises the Laser pulses with the camshaft and displays the phase angle in correspondence to the camshaft sensor on a LED display in binary form. Figure 2.22: The LED display array is recorded as part of the PIV image on the CCD camera to allow phase by phase identification. The array can be seen in the bottom right hand corner.

73 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS PIV Image Errors & Data Analysis From previous experimental campaigns using the same image acquisition components, it was known that 2 pixels on the camera s CCD are permanently damaged and record a binary value of 255 resulting in bright white pixels in the digital image. These pixels get mistakenly treated as seeding particles during the cross-correlation process if left untreated. An automated method to interpolate and replace the faulty pixel value from surrounding pixels in each instant has been developed by England (2009) and was applied to all raw PIV images prior to data analysis. The correction method is described in detail in Appendix B. The actual PIV analysis was undertaken using the PIVview 2.4 software package (PivTec GmbH, Göttingen, Germany). The software contains a number of methods for outlier or spurious vector detection for the PIV post-processing phase. Except for the application of a global histogram filter algorithm 1 to the data, no further image correction was undertaken. Phase-locked and flow averaged PIV images were analysed using a pixel grid with a grid overlap of 75%. The measurement uncertainty in the PIV data was calculated using the methods documented by Raffel et al. (1998). The measurement uncertainty was found to be a maximum of 15% in one case of Re h = 1800 with U x,y 0.25U 0. For all other cases investigated, the maximum measurement uncertainty was found to be less than 10% for U x,y 0.25U 0. During the analysis of the PIV data it was noted that a constant overestimation of the jet velocities was obtained along the facility centreline in the streamwise direction at a distance of x/h = 3.3 ± 0.2 and at x/h = 5 ± 0.5, as shown in Figure Upon inspection of acquired target images used for the system set-up some optical distortion was discovered in those locations. It was hence concluded that the distortions are most probably either an artefact of the experimental facility, as non-optical grade PMMA was used for the walls of the working section, or dried water droplets on the outside of the facility. 1 For more details on Global Histogram Filters and other outlier detection methods refer to Raffel et al. (1998).

74 CHAPTER 2. EXPERIMENTAL SET-UP AND METHODS 73 Figure 2.23: Normalised velocity magnitude for the mean flow of a sample MOPJ case (Re h =2700, S/h = 0.5, f = 2Hz) close to the nozzle exit. The blue circled area highlights the area where velocities were found to be overestimated due to an optical distortion Steady Jet Velocity Profiles The PIV set-up was used to acquire velocity data of steady planar jets of the three cases earmarked for further experiments and to verify the exit velocity profiles and centreline velocities close to the nozzle for a further three Reynolds numbers that were investigated as part of the flow visualisation study. For all steady jet cases a minimum of of 440 image pairs were used in each case to obtain the velocity profiles. Figures 2.24 & 2.25 show the normalised streamwise velocity profiles of the steady jets cases from the nozzle exit to a distance of x/h = 8. All cases show an initial top-hat velocity profile that gradually transforms into a smooth bell-curve profile as the jet shear layer expands. Inspection of the individual velocity profiles in the two figures show the overestimation of the velocities at x/h = 3 & 5, especially for the higher Reynolds number cases as discussed in the previous section (Figure 2.23), presenting further evidence to the claim that the velocity errors are inherent to the experimental facility and not a result of faulty data analysis. The normalised centreline velocities for six Reynolds numbers (Re = 1000, 1800, 2700, 3420,