Investigation of the Characteristics of an Axisymmetric Jet Subjected to Azimuthal Forcing by Arthur Weiner A thesis submitted to the Graduate Faculty of Auburn University in partial ful llment of the requirements for the Degree of Master of Science Auburn, Alabama August 03, 2013 Keywords: Axisymmetric round jet, Azimuthal forcing, Strouhal number, PIV, POD, Hot wire anemometry Copyright 2013 by Arthur Weiner Approved by Anwar Ahmed, Chair, Professor of Aerospace Engineering Roy Hart eld, Walt and Virginia Woltosz Professor of Aerospace Engineering Jay Khodadadi, Alumni Professor of Mechanical Engineering Abstract Characteristics of an axisymmetric jet subjected to azimuthal forcing were investigated. A circular variable diameter iris was positioned near the nozzle exit to impart azimuthal excitation to the jet at desired Strouhal numbers. The experiments were conducted at the Reynolds number of 5;500. Two excitation frequencies corresponding to the Strouhal number of 0:12, and 0:09 were used. It was found that both excitation frequencies attenuated the large scale structures in the near- eld of the jet, however, the harmonic forcing introduced low frequency instabilities within the rst two diameters of the nozzle exit plane. The harmonic forcing also introduced more energy into the ow than the sub-harmonic forcing and was evident from the distribution of the turbulent kinetic energy, power spectral density, and visualization of the instabilities. The forcing also had an e ect on the streamwise vortex laments located between successive large-scale structures of the jet. The diameter of the streamwise vortex laments and meandering increased for both forcing cases. The laments played a pivotal role in the entrainment of ambient uid and the distortion of the vortices due to additional strain. ii Acknowledgments The author would like to thank Dr. Anwar Ahmed and the committee members, their guidance and expertise has been invaluable to me. I would also like to thank Mr. Andy Weldon for his machining expertise, willingness to help at every stage of the construction phase and Mr. Brian Davis, Hamza Ahmed, Hayden Moore, Abhishek Bichal, and Aleem Ahmed for their encouragement and giving their time to assist so willingly. The author would especially like to thank his family for their emotional support and patience through this process. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Coherent Structures in Jet Mixing . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Modes and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Characteristics of an Axisymmetric Round Jet . . . . . . . . . . . . . . . . . 3 1.4 Methods of Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.1 Tabs and Blowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.2 Acoustic Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.3 Synthetic Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.4 Passive Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1 Turbulent Jet Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Probe Traversing System . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Forcing Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Hot Wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 iv 2.4 X-Wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5.1 Proper Orthogonal Decomposition . . . . . . . . . . . . . . . . . . . . 18 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1 Baseline Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.1 Power Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.2 Proper Orthogonal Decomposition . . . . . . . . . . . . . . . . . . . . 25 3.2.3 Symmetry Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.4 Reynolds Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.5 Turbulent Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . 36 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 A Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 B Forcing Mechanism Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 C Velocity Contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 D Cross-Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 E Mode Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 F Shear layer PSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 G POD Contour Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 H Turbulent Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 v List of Figures 1.1 Physical structure of a transitional jet [1] . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Vortices coalescing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Isometric view of the iris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Experimental setup with probe traverse and data acquisition system . . . . . . 12 2.3 Isometric view of the forcing mechanism . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The circuit for the CTA bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5 Overview of the IFA300 set-up[2] . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 Unforced Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 Velocity contour from PIV data, Re = 5500 . . . . . . . . . . . . . . . . . . . . 22 3.4 Characteristics for unforced jet at x=D = 0 . . . . . . . . . . . . . . . . . . . . 24 3.5 Velocity spectra, forced cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.6 Turbulent Intensity, forced cases . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.7 Comparison of velocity pro les for the forced an unforced cases . . . . . . . . . 27 3.8 Mode energy, unforced case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 vi 3.9 POD modes - forced jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.10 POD of transverse plane at y=D = 4 . . . . . . . . . . . . . . . . . . . . . . . . 31 3.11 PIV single image with azimuthal cuts at y=D = 4D;6D; and 8D . . . . . . . . 33 3.12 POD of transverse plane at y=D = 4 (St = 0:12) . . . . . . . . . . . . . . . . . 37 3.13 POD of transverse plane at y=D = 4 (St = 0:09) . . . . . . . . . . . . . . . . . 38 3.14 25th POD mode at y=D = 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.15 Location of two probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.16 Flow structure behaviour, probes are located at ( 0:75D;2D) . . . . . . . . . . 41 3.17 Reynolds shear stress ( xy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.18 Reynolds shear stress for forced cases . . . . . . . . . . . . . . . . . . . . . . . . 43 3.19 Turbulent Kinetic Energy for non-forcing . . . . . . . . . . . . . . . . . . . . . . 44 3.20 Turbulent Kinetic Energy for forced cases . . . . . . . . . . . . . . . . . . . . . 45 B.1 H2W Limited Angle Torque Motor . . . . . . . . . . . . . . . . . . . . . . . . . 53 B.2 US Digital Optical Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 B.3 AMC Servo Motor Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 55 B.4 AMC Mounting Card Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . 56 C.1 Velocity Contour, St = 0:12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 C.2 Velocity Contour, St = 0:09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 vii D.1 Cross-Spectra, Unforced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 D.2 Cross-Spectra, St = 0:12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 D.3 Cross-Spectra, St = 0:09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 E.1 Energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 E.2 Energy distribution at y=D = 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 F.1 Shear layer PSD, no forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 F.2 Shear layer PSD, St = 0:12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 F.3 Shear layer PSD, St = 0:09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 G.1 Modal energy for azimuthal cuts at y=D = 4 with streamtracers superimposed (St = 0:12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 G.2 Modal energy for azimuthal cuts at y=D = 4 with streamtracers superimposed (St = 0:09) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 G.3 No forcing, 25th mode at y=D = 6 with streamtracers superimposed . . . . . . . 71 G.4 St = 0:12;25th mode at y=D = 6 with streamtracers superimposed . . . . . . . . 72 G.5 St = 0:09;25th mode at y=D = 6 with streamtracers superimposed . . . . . . . . 73 H.1 Turbulent Kinetic Energy for non-forcing . . . . . . . . . . . . . . . . . . . . . . 74 H.2 Turbulent Kinetic Energy for forced cases . . . . . . . . . . . . . . . . . . . . . 75 viii List of Tables A.1 Uncertainties for velocity sample for single probe . . . . . . . . . . . . . . . . . 52 ix Nomenclature A; B Experimental constants C Correlation Matrix Co:::C4 Experimental constants D Nozzle Diameter EAD A/D board input range U Velocity Uc Centerline Velocity Umax Maximum velocity at nozzle exit f Frequency fcut off Cut o frequency m Resolution in bits n Number of snapshots trecord Data record length u0; v0 Velocity uctuation x Eigenvector Re Reynolds number based on jet diameter St Strouhal number x TKE Turbulent kinetic Energy d Displacement thickness m Momentum thickness @U @E Slope or sensitivity factor Eigenvalue Dynamic Viscosity Density Standard deviation, in percent xy Reynolds shear stress xi Chapter 1 Introduction Mixing enhancement has been a subject of research for the last several years as it involves the entrainment of surrounding uid and rapid spreading of a jet. Combustor e ciency, ejectors, noise attenuation etc. are a few applications where mixing enhancement is desirable. Controlling the mixing characteristics of a jet is essential to maximizing the performance of a nozzle for the given application [3]. Fuel and air mixing at the molecular level is important for combustion e ciency and actuators o ering signi cant mixing in the small scale [4]. Excited laminar jets were rst described by Leconte and Tyndall in 1867, they noted the gas ames responded to the music in a synchronized manner. Tyndall studied this phenomenon by using a series of ame tubes with di erent apertures and concluded that the sound led the ame to transition to turbulence [5]. In 1933, Schlichting developed a model for a high Re laminar jet. Realistically, a high Re laminar jet cannot exist because instabilities result in the appearance of turbulence. He, however, concluded that the momentum of the jet remained constant with downstream distance and that the mass ow continually increased [6]. Crow and Champagne were the rst to quantify the patterns of a round turbulent jet and attempted to control the jet through periodic forcing. They studied a round axisymmetric jet using a water and air facility. They visualized jet instabilities as the ow evolved from a sinusoid, to a helix, and nally a train of axisymmetric waves as Re increased from 102 to 103 [7]. 1 1.1 Coherent Structures in Jet Mixing Several early studies focused on the mixing layer [1] [8] [9]. It was originally thought that the measured uctuations of the ow were random and could only be addressed sta- tistically. By the 1960?s some researchers began to postulate that the uctuations were not entirely random. In 1971, Lau et al proposed a model to explain the phase relationships and uctuating velocity in the mixing layer. They believed that underlying structures in the mixing layer could a ect other regions of the jet and conducted hot wire and microphone measurements in the potential core and entrainment regions. Their analysis showed that there was a semi-regular array of vortices. Lau veri ed and concluded by changing the jet velocity that spectral peaks should be located at the fundamental frequency [10] [11]. The work by Crow and Champagne is considered as fundamental in the study of tur- bulent mixing and the frequency spectra within a jet. Using ow visualization methods to study jets at the Reynolds number range of 102 to 105, they noticed that as Re increased the ow transitioned to turbulent and a series of large-scale vortex \pu s" formed downstream with an average Strouhal number of 0.3. They also discovered that acoustic excitation of the jet at the average Strouhal number (0.3) resulted in the largest ampli cation downstream of the vortex pu s ("rings") [7]. Due to their work, orderly structures became known as \coherent structures." Fiedler clari ed the de nition of coherent structures as dominant patterns that can usually be recognised in a ow [9]. Subsequent researchers studied coherent structures based on qualitative data in the form of ow visualizations rather than quantitative data [7] [12] [13]. While advances were made from the qualitative interpretations there was an inherent level of bias, predominately on the viewer. The availability of newer optical diagnostic techniques and data analysis techniques, such as POD, have become more suitable to obtaining quantitative data of coherent structures [14] [15] [16] [17] [18]. 2 1.2 Modes and Stability In an axisymmetric round jet, the initial wave at the nozzle exit is similar to a Kelvin- Helmholtz instability that occurs when a perturbation is introduced between two inviscid ows. As these structures move downstream they grow rapidly, coalesce, and become chaotic [19]. Downstream, the instabilities amplify and non-linear e ects become more pronounced. In axisymmetric ows there are three common modes of symmetry: the ring, helix, and double helix [9] and they correspond to the 0th, 1st, and 2nd modes. The initially most unstable mode is the axisymmetric (ring) mode and this is usually due to the geometric symmetry of the jet. As the distance downstream increases, the antisymmetric (helix) mode becomes more prominent [20]. A dimensionless parameter (Strouhal number), which describes the ow mechanisms, is commonly used to express the preferred mode or most ampli ed frequency and typically the Strouhal number increases with the Reynolds number. According to Crow and Champagne, the preferred mode occurred at a St = 0:3 [7]. 1.3 Characteristics of an Axisymmetric Round Jet Unlike the plane jet that can be statistically considered two-dimensional [21] , a round jet is not completely two-dimensional this is due to the large eddies that contain a majority of the turbulent energy [1] . The jet is borne out of the nozzle exit plane and it entrains the quiescent uid creating a velocity shear between the quiescent and entering uid. The ow spreads in the lateral direction with increasing downstream distance until the initial momentum is spread out in the fully developed far eld or the jet reaches a state of self-similarity. The initial region of a round jet is characterized by a laminar shear layer shown just downstream the nozzle exit plane in Figure 1.1. The initial instability modes are dependent on the nozzle exit conditions and produce the ow structure in the shear layer. A good 3 example of this was studied by Reynolds who produced bifurcating and blooming jets [22]. The instabilities typically grow rapidly due to the unstable nature of the shear layer and form ring vortices that carry the turbulent uid into the ambient uid. The viscosity also helps to initialize the roll-up in the mixing layer and creates a three-dimensional instability [8]. The intensity of the vortex pairing is also dependent on initial conditions. Vortex pairing is a naturally occurring event where the trailing vortex is pulled through the leading ring similar to a \leap frog" motion. This motion increases the radius and decreases the strength of the vortex which in turn makes it more susceptible to instabilities in the azimuthal direction. Vortex pairing is indicated by the arrows in Figure 1.2. The velocity pro le is determined by nozzle geometry. A smooth contraction nozzle produces a top hat velocity pro le and a sharp-edge nozzle produces a saddle-backed initial velocity pro le. Figure 1.1: Physical structure of a transitional jet [1] There are three regions located within a round turbulent jet. The near eld, far eld, and transitional region. The near eld is de ned as the area where the ow characteristics match the nozzle exit and encompasses the potential core. The near eld usually extends 4 Figure 1.2: Vortices coalescing to six to seven diameters downstream. This can be seen in Figure 1.1 before the vorticity- containing uid region engulfs the jet ow. The far eld is located roughly y=D> 70 where the ow is fully-developed and consid- ered to be in equilibrium. The classical self-similarity view is that this state depends only on the rate of momentum addition and is independent of other initial conditions [23]. In other words, the in uence on the ow due to the initial conditions decays rapidly with down- stream distance and is eventually eliminated. Recently, there has been confusion to whether the scalar elds are universal. Pitts and Richards found that there is a 15% variation in spreading rate [24]. Typically the variations have been attributed to experimental error or di erences in experimental conditions or apparatus [25]. George conjectured that there are multiple self-similar states for a particular ow and the initial conditions will uniquely de ne the states [26]. Thus, the entire ow is in uenced by the initial conditions. The work by George was con rmed by Mi who concluded that the turbulent properties throughout the ow do depend upon the initial conditions [23]. Also within this region, the energy spectrum is found to exhibit a 5=3 exponent [27], similar to Kolmogorov?s 5=3 law. The transitional region is located between the two. Here, the vortex rings that were created near the nozzle exit due to the shear layer become three-dimensional. In addition to 5 the vortex rings, streamwise structures have been found between successive vortex cores in the shear layer (known as \braids") [8]. 1.4 Methods of Mixing There are two distinctive methods of jet excitation, active and passive. Both active and passive have been employed to modify the spreading and turbulence characteristics of jet ows. Active techniques add energy at an appropriate frequency and amplitude. Some active methods studied were uidic actuators, blowing, acoustic actuators, and synthetic jets. Passive techniques work by modifying the critical conditions such as nozzle exit conditions or the introduction of objects into the ow to alter the development. Passive techniques include tabs mounted to the jet exit, non-circular shaped nozzle, adding a ring or mesh to the nozzle exit or a speci c distance downstream from the nozzle. 1.4.1 Tabs and Blowing Use of tabs and blowing are passive and active mechanisms, respectively. However, the two forcing designs typically go hand-in-hand therefore they are combined in this section. Tabs e ectively increase the spread rate by obstructing the ow via streamwise vorticity. Samimy et al studied the e ect of tabs and blowing on jets ranging from mach number M = 0:3 1:81. They acknowledged that for subsonic jets the e ects of tabs was more pronounced than that produced by other mixing enhancement techniques. Through schlieren photography they visualized the formation of a pair of counter-rotating streamwise vortices that shed from the tabs[28] and speculated that the tabs act more similar to wing tip vortices and that the streamwise vorticity was pressure driven and inviscid phenomenon [28]. 6 1.4.2 Acoustic Drivers For many years, acoustic drivers were the preferred method of exciting jets because of the availability and the highly controllable nature of the drivers at a wide range of fre- quencies. Acoustics drivers are ideal for laboratory experimentation where the fundamental understanding of the ow is principal. However, they are not well suited for exciting high Re ows as the low amplitude perturbations are drawn out due to the turbulent uctuations within the ow. Therefore, high amplitude uidic actuators became popular for jet mixing applications. Recently Aydemir et al used speakers located in the plenum chamber to acoustically excite a round jet. The design provided large-amplitude acoustic forcing with sinusoidal oscillations that resulted in the high-amplitude forcing initiated the shear layers of the jet to break-up into a series of large scale vortex rings [29]. The size and spacing between consecutive vortex rings remained dependent on the amplitude and frequency of the forcing conditions. 1.4.3 Synthetic Jets Over the last decade synthetic jets have been gaining popularity for the purpose of jet mixing. Synthetic jets use a power and recovery stroke to suck in and blow out equal amounts of ambient uid resulting in a zero mass ow. Synthetic jets tested to date either use a piston cylinder device or piezoelectric ceramics. Piezoelectric ceramics were initially used to detect structural deformation [30], however, due to their properties when an electric eld is applied a proportional deformation is achieved [31]. These ceramics are mounted on exible plates and serve as diaphragms are typically located in the plenum chamber, in a cavity near the jet exit [32] [33]. Typically, ceramics produce lower amplitudes when excited. The amplitude is also restricted to the high frequencies (mostly resonant) that the ceramics are driven at. An advantage of high frequency actuators is that small scale uctuations can more easily be excited [4] [34]. 7 Pothos and Longmire studied rectangular jets excited with a synthetic jet actuator located on one wall. The jet was run at Re = 4240 and excited at St = 0:25; 0:42; and 1:46. They found that forcing at the lowest frequency increased the centerline velocity decay as well as spreading rates in the far eld. They concluded that the e ects of forcing at St = 1:46 were nominal and the disturbances were quickly attenuated [33]. 1.4.4 Passive Techniques Unlike active methods, passive techniques depend on modifying critical conditions. These conditions are typically exit conditions or introducing an obstruction into the ow. An advantage of passive techniques are that they do not require an external energy source. Mi et al [3] designed a self-exciting nozzle to analyse the mixing characteristics of a low-frequency apping jet. Here the \ apping" is described as the two-dimensional ip- op motion of the entire jet with respect to the major plane of symmetry of the inner nozzle . This form of excitation enhances the large-scale mixing and suppresses ne scale turbulence generation. However, the large-scale oscillations decayed rapidly and were not captured in the far eld. They also found that the large scale turbulence suppressed the small scale mixing downstream of the nozzle. Parker and Rajagopalan used a thin wire ring to alter the ow and placed a 0:5 mm wire at x=D = 0:15 and found that adding a thin ring axisymmetrically in the mixing layer im- proved the similarity throughout the mixing layer [35]. They also found signi cant reductions in both, the RMS axial and radial velocity uctuations (22% and 15%, respectively) 1.5 Objectives Previous studies on the excitation of jets have focused on discrete locations for the forcing, however even for the unforced jet, secondary ows in the form of jet blooming ([22]) have been reported. The location of blooming and preferred location of the onset of instabilities, although attributed to imperfections in the nozzle, remains to be investigated. 8 The primary objective of the present work was to perturb the jet in a novel manner that ensured continuous forcing along the outer periphery of the jet near the origin of the shear layer and to study the spatial growth of instabilities along the axis of the jet. 9 Chapter 2 Experimental Set-up Experiments were performed in the Vortex Dynamics Lab at Auburn University. A ow conditioner consisting of honeycomb and serveral screens was designed for low turbulence ow at the exit of a smooth contoured nozzle. A mechanical forcing mechanism was designed to azimuthally force the ow at 360 . Due to the design of the mechanism (Figure 2.1) there was a slight rotation in the leaves as the aperture diameter changes. The mechanism also needed to provide uidic motion at the nozzle exit in the form of a square wave. Figure 2.1: Isometric view of the iris 2.1 Turbulent Jet Facility The jet facility consists of a vertical, cylindrical plenum chamber with an internal diam- eter of ?5 in and a length of 18 in. A Dayton Electric Company DC blower supplied air to 10 the chamber. A series of ne mesh and 2 in thick honeycomb are located in the ow condi- tioning chamber to eliminate swirl and achieve uniformity. The nozzle with an exit diameter of 0:5512 in was machined from aluminium with a smoothly contoured inner pro le to give a top-hat exit velocity pro le. The jet exit velocity was varied by varying the pressure in the plenum chamber. A total pressure probe was machined in the wall of the plenum chamber for calibration purposes. 2.1.1 Probe Traversing System A two axis traverse was designed to vary the location for single point measurements and allowed measurements to be taken up to 20D downstream. The traverse was a xed to an optical table that was aligned with the jet. Figure 2.2 shows the set-up used for single point measurements. The two stepper motors at the end of the traverse are controlled by a Velmex NF90 stepper motor controller that was connected to a PC. A customized LabVIEW program was written to control the streamwise and lateral traversing distance and resolution with a high level of spatial accuracy for velocity measurements. 2.2 Forcing Mechanism A limited angle high torque brushed motor from H2W Technologies, Inc., model TMR- 060-005-2H, was used for forcing mechanism as the air jet was pressed through an optical iris consisting of 16 leaves. A schematic of the forcing mechanism is seen in Figure 2.3. The brushed motor was driven by an AMC DigiFlex Servo drive, DZRALTE-020L080 and mounted on an MC1XDZR02-QD mounting card. Block diagrams for the set-ups are found in Appendix B.3 and B.4, respectively. The digital servo drive was selected as it o ered optimal performance for brushed motor, and included encoder feedback, and ran smoothly with DriveWare software. A rotary encoded purchased from US Digital and used to send feedback information of the motor shaft. Software developed by AMC, DriveWare 7.0.2, was 11 used to control the motor. Within the software, the current, position, and velocity loops were tuned to minimize the residual in the target and measured waveform. x y Stepper9motor Dantec9CTA Probe9support Dantec Bridge Velmex9Controller NI960099 DAQ Oscilloscope Figure 2.2: Experimental setup with probe traverse and data acquisition system Figure 2.3: Isometric view of the forcing mechanism 12 2.3 Hot Wire The technique of constant temperature anemometry (CTA) works through the heat transfer from a wire to the surrounding uid. By using thin wire sensors and a closed loop system it is possible to measure ne velocity uctuations within a ow. Hot wire anemometry can measure ow velocities in up to three separate directions. This is accomplished by a single, dual, triple wire sensor. Single wire sensors measure one component (U), dual and triple measure two (U and V) and three (U;V;W) components. Each sensor o ers its advantages and disadvantages based on application. While CTAs have been around for many years and they still compete with non-intrusive optical diagnostic techniques such as particle Image Velocimetry (PIV). Also, no information is lost while collecting data because output data is a continuous analogue voltage. This also allows anlysis of the data for turbulence statistics and spectral analysis. CTA also has a very high frequency response ( 100 kHz ). While dual and triple wire sensors can collect data in multiple directions they also increase experimental error due to the disturbances induced by additional wires [21]. This error is small and usually accounted for within the in situ calibration. This method, however, is an intrusive technique and can modify the local ow eld. There can also be errors in the calibration due to neglecting higher order terms and the wires can be insensitive to reversal in the ow direction [36]. The sensors are also fragile and prone to breaking and burn out. 2.3.1 Circuit The CTA utilizes a Wheatstone bridge, servo ampli er, and voltage source as seen in Figure 2.4. The probe that is exposed to the ow is added to one arm of the Wheatstone bridge and opposite to a variable resistor (R3). This resistor de nes the operating resistance and temperature of the circuit. While the bridge is balanced, there is not a voltage potential across the circuit. As the ow velocity increases, the wire resistance will decrease. The servo 13 ampli er within the closed loop will increase the current within the probe. This will continue until the balance is restored within the bridge. Servo Amplifier R1 R2 R3 Probe E Figure 2.4: The circuit for the CTA bridge The setup of the anemometer is crucial to ensuring accuracy of the data collected and minimizing erroneous frequencies. The set-up consists of a signal conditional. It is important to apply a high and/or low pass lters to "clean" the signal. A low pass lter is used to remove noise and to prevent higher frequencies from folding back (aliasing). If a low pass lter is not utilized, the energy at frequencies 2 > 3 >:::> n 0 (2.5) Commonly a singular value decomposition is used, C = U VT (2.6) where U is an nxn orthogonal matrix, V is an mxm orthogonal matrix, and is an nxm matrix with only values on the diagonal non-negative and are in the same form as equation 2.5. The rank of this matrix is n and length(n) 0. From equation 2.5 and since the sum of all the eigenvalues gives the total turbulent kinetic energy in the ow, the rst eigenvalue contains the largest amount of kinetic energy and each subsequent mode will contain a decreasing amount [14]. POD is commonly used be- cause it is e cient at capturing the dominant components (modes) of an in nite-dimensional process with only a few functions [15]. 19 Chapter 3 Results Measurement were made at several streamwise and cross-stream locations measuring instantaneous velocity and consisted of turbulence statistics and spectral content. The fol- lowing section contains the velocities and turbulence eld characteristics due to the forcing mechanism. It is also important to note that for nondimensionalizing purposes a capital letter in the denominator corresponds to a global quantity and lower case is local. x y Figure 3.1: Coordinate System The coordinate system for the jet were de ned in Figure 3.1. Typically polar coordinates would characterize a round jet. However, for this research, a Cartesian coordinate system was used since the jet is axisymmetric. Therefore, the round jet has the dominant motion in the streamwise (y) direction and jet growth in the lateral or azimuthal (x) and (z) directions. It has been established that at high Re the mean velocity pro les and spreading rates of a round jet are nearly independent of Re and at su ciently low Re (Re< 10;000), both the mean and turbulence eld are dependent on Re [21] . Therefore, test were conducted at Re = 5;500 where Reynolds number was calculated from, Re = VD (3.1) 20 x/D u / U m a x -2 -1 0 1 2 0 0.2 0.4 0.6 0.8 1 y/D = 10 y/D = 6 y/D = 4 y/D = 2 y/D = 1 (a) Velocity Pro le (b) Turbulent Intensity Figure 3.2: Unforced Jet 3.1 Baseline Jet Velocity pro les were measured at several streamwise locations and are presented in Figure 3.2a. The potential core appeared to exist for approximately 2D, the turbulent intensity at the nozzle exit is fairly low (< %3). However, at x=D > 3 the turbulent intensity increased throughout the lateral direction of the jet. The shear layer displayed the highest levels of turbulence as expected. Distribution of velocity for the unforced case was extracted from the PIV measurements and shown in Figure 3.3. The momentum thickness and displacement thickness of the initial boundary layer were calculated from, m = Z D 2 0 u Uc 1 uU c dy (3.2) 21 Figure 3.3: Velocity contour from PIV data, Re = 5500 d = Z D 2 0 1 uU c dy (3.3) respectively. The values were calculated from the hot-wire traverse data at y=D = 0:1 are, m = 0:0019 and d = 0:00860D. These values found at the nozzle exit are congruent with the values found by Mi ( d = 0:004d; m = 0:0018d [23]) with the di erence being attributed to Reynolds number. Figure 3.4a shows the decay of centerline velocity for the unforced case up to 20D. The data was tted with a third degree polynomial. The curve is typical for round turbulent jets. 22 Figure 3.4b is the power spectral density of the round jet at the centerline of the nozzle exit at various y=D locations. The power spectrum was calculated using a Fourier transform of the velocity measurements made with the CTA. There is a clear dominant frequency located at the preferred instability (150Hz). As the probe was moved downstream to a more turbulent region the total energy increased. 3.2 Forcing In the past both the preferred and sub-harmonic frequencies have been used. In the present work, an approximate harmonic of 50Hz was used for the forcing that resulted in a Strouhal number (St) of 0.12. The tests were also conducted and compared with a St = 0:09. The Strouhal number was calculated from, St = fDU max (3.4) In addition to the frequency, the amplitude of the oscillation was also controlled through the DriveWare software. A peak-to-peak amplitude of 400 counts was set for St = 0:12 and 480 counts for St = 0:09. After taking into account losses in the transfer of energy from the arm to the iris and the tuning of the loops, the peak-to-peak amplitude was calculated to be 0:02D. 3.2.1 Power Spectra The power spectra of the forcing are displayed in Figure 3.5. At each downstream location, there is a visible peak at the forcing frequency. At y=D = 1 there is a sharp drop-o in amplitude after the forcing frequency. This is attributed to the forcing frequency attenuating the initial instabilities. However, as the distance downstream increased the drop-o decreased. Comparing the non-forcing to forcing conditions, it appeared that the 23 (a) Centerline Decay (b) Velocity Spectra Figure 3.4: Characteristics for unforced jet at x=D = 0 forcing introduced an instability earlier than expected. There are also a myriad of peaks from approximately 75 450Hz. These double-peaks (fa and fb) appear to form at frequencies near the fundamental such that the average of fa and fb is the fundamental frequency and the range of fa to fb is the forcing frequency. Previous researchers have coined similar peaks \parametric resonance" which are typically induced by the fundamental and sub-harmonic frequencies [20]. However, in the current research the peaks appear attributed to harmonics of the forcing frequency. Figure 3.6 shows turbulent intensity for the two forcing cases. It appears that the instability introduced by the forcing is making the jet more stable. This could be due to the introduction of a series of vortex rings near the exit plane. Figure 3.7 compares the velocity pro le from the hot-wire data. It is apparent in each image that the maximum velocity decay is only 5 10% for the forcing cases as the location downstream approaches 20D. Initial analysis hints that harmonic, low frequency excitation increases entrainment until approximately 10D downstream. It can conjectured that the excitation only attenuates the instabilities until 10D. 24 (a) St = 0:12 (b) St = 0:09 Figure 3.5: Velocity spectra, forced cases Additional velocity contours of the forcing cases are located in Appendix C. Mini- mal information can be gathered by comparing the velocity contours of the forced cases to the unforced (Figure 3.3). Therefore a statistical method is incorporated to quantify the modi cations and evolution of the energy distribution within the ow. 3.2.2 Proper Orthogonal Decomposition The POD contour plots were created by reconstructing the velocity eld with the eigen- functions. The eigenfunctions are similar to the modes and represents a behaviour of the ow as mentioned in section 2.5.1. Each contour plot was then non-dimensionalized by the maximum value found from the non-forcing case to adequately compare di erent cases. The modal numbers were chosen because there was a change in the slope from the subsequent mode to the desired mode. The slope indicated an evolution in the energy. The modal distribution are located in Appendix E. For the analysis on the streamwise cuts, the rst and sixth eigenvalues are plotted. These eigenvalues were chosen because they are two of the principal modes for representing the dynamics of the large-scale structures and typically the rst mode represents the \large 25 (a) St = 0:12 (b) St = 0:09 Figure 3.6: Turbulent Intensity, forced cases 26 (a) y=D = 10 (b) y=D = 15 (c) y=D = 20 Figure 3.7: Comparison of velocity pro les for the forced an unforced cases 27 (a) First mode (b) Sixth mode Figure 3.8: Mode energy, unforced case eddies" in the ow [14]. In Figure 3.8a the large scale vortex rings are clearly visible with alternating positive and negative uid advection patterns. They appear to rst become visible at approximately 2D and exist up to 6D. The absence of clean indication of vortex rings after 6D is attributed to the coalescesing of rings similar to Figure 1.2 which leads to the formation of unstable vortices. The unsteadiness of vortex pairing increases the likelihood of vortex breakdown Figure 3.8b represents the energy content of the sixth mode. Two distinct structures are visible in this mode. The structures with positive velocity-direction appear to be located on the zenith of the individual vortex rings and maintain symmetry about the axis of the jet and are likely due to the streamwise vortex laments wrapping around the large-scale structure. As the vortex laments stretch, the axial strain results in an increase in vorticity that in turn increases the entrainment. The asymmetric structure with a negative velocity direction in Figure 3.8b is similar in geometry and strength to the large-scale structures seen in the previous image, however the energy content is substantially less. The structure is most similar to the structure at y=D 2:75 in Figure 3.8a. 28 (a) First mode, St = 0:12 (b) Sixth mode, St = 0:12 (c) First mode, St = 0:09 (d) Sixth mode, St = 0:09 Figure 3.9: POD modes - forced jet With the loss of symmetry on the right hand side of the structure and similar velocity to the aforementioned structure it is conjectured that the modal content at y=D 6:75 in Figure 3.8b depicts the decay of vortex rings into smaller structures. This would be due to the \leap frog" e ect or vortex roll-up of subsequent vortices which in turn increase the susceptibility of vortex breakdown. 29 Azimuthal contour plots of the ow were also taken at this vertical location to analyze the modal distribution and to gain insight into these instabilities (Figure 3.10) at y=D = 4. The results are presented in Figures 3.10, 3.12, and 3.14. Vectors were superimposed on the image, to add clarity on the direction of the ow within the speci c mode. To extrapolate the ow in the y-direction continuity must be used, i.e., if the x and z radial components are small the y velocity component must be large. In Figure 3.10a, the regions of high contrast are evident of symmetric large-scale struc- tures. Figure 3.10b represents the 25th POD mode, this mode was chosen because it corre- sponded to the highest mode calculated and these modes can be related to the ner scale of turbulence. Even though this mode contains the smallest percentage of energy at the azimuthal location it is ample relative to other locations and the non-forcing case. This is con rmed by interpolating the lines in Figure 3.5. In Figure 3.10b, there appear to be two counter rotating streamwise laments or \braids" within this mode from the vectors. The centroids of the braids are approximately at: (0:25; 0:3); ( 0:35; 0:4);and (0:05; 0:1). This is in contrast to the contour plot which indicates four pairs of vertical ow. This is pos- sibly due to the top-half of the image, which appears to be dependent on two saddle points. A saddle point is a type of critical point that commonly represents a two-dimensional sur- face where one direction curves up and the other curves down. The surface curvature more closely represents a line than parabolic curve but still indicates a two-dimensional structure within the 25th mode. There appears to be two saddle points symmetric about the x-axis at x=D = 0:5. The ow travels at approximately an 45 deg angle with respect to negative z. The ow then bifurcates at the critical point and either travels towards the center or away from the centerline. For St = 0:12 and 0:09 (Figure 3.12a and 3.13a) there are similarities in the energy content of the rst mode. Both images shown lack of large-scale structures and parallel, non-obstructed ow. 30 (a) Mode 1 (b) Mode 25 Figure 3.10: POD of transverse plane at y=D = 4 31 The harmonic forcing frequency (St = 0:12) attenuated large-scale structures at y=D = 4 and it appears from Figure 3.9a that the forcing introduced low frequency instabilities at this location. These instabilities can be in the form of large-scale structures but it is not conclusive from the POD. For sub-harmonic (St = 0:09) the forcing attenuated the low frequency instabilities at all vertical locations, not only the speci c location. In the 25th POD mode the sub-harmonic forcing appears to skew the radial advection pattern. In Figure 3.12b, the streamwise vortices have meandered through the ow and appear to form an isosceles triangle. This could be due to the laments beginning to di use and weakening or an imposed oscillation of the laments due to the forcing. The ability of the streamwise laments to entrain uid is evident on the right-hand-side of the contour. The center of one of the vortices is approximately at, (0:4; 0:1). This lament ejects and then quickly entrains the ejected uid as well as surrounding uid. This shows that the streamwise vortices do increase the entrainment of ambient uid. For St = 0:09 (Figure 3.13b) only one streamwise lament but is weaker than in the previous forcing condition. This mode also appears to be dominated by nodal critical points. This is depicted by the uid travelling away from the node. Higher levels of turbulence were noted in this mode. In addition to the time average snapshots (Figure 3.10, 3.12, and 3.14), instantaneous images were examined that showed the vortex breakdown and asymmetry as the distance downstream increased and is shown in Figure 3.11. At y=D = 4, there is a saddle that spans approximately 225 , it is also outlined in red. This was determined due to the expected ow direction at the azimuth of the structure. The e ect that large-scale structures have on entrainment is also depicted by the streamtracers. The ow outside of the jet is directed to the origin and being pulled underneath the \mushroom" shape of the structures into the core. The black arrows in the center image depict the location of the entrainment. There is also an asymmetric vortex breakdown partially due to visible streamwise counter rotating vortex laments indicated by large black arrows. Coalescing of vortex 32 4D 6D 8D 4D 6D 8D Figure 3.11: PIV single image with azimuthal cuts at y=D = 4D;6D; and 8D rings also makes them more susceptible to vortex breakdown due to decreasing the strength and convection. This, however, was not be visualized in the azimuthal instantaneous im- ages. These vortical structures are important in the entrainment process, they advect the quiescent uid into the jet ow. As the distance downstream increases, the vortex breakdown engulfs nearly the entire structures. The streamwise vortices meander within the ow indicating either a swirling motion of the jet or a natural oscillating motion of the vortices. Figure 3.9 shows the e ect of azimuthally forcing of the jet at the desired Strouhal number. For the rst case (St = 0:12) the forcing energizes the initial instability and hastens 33 the growth of the instability into large scale structures. There is also a loss of symmetry within the apparent vortex rings. From these images it is di cult to conclude whether the asymmetry is due to the forcing mechanism or addition of a asymmetry mode. Mcllwain and Pollard used an LES to investigate the near eld of round jets. They noted a vortex ring located at x=D 2 and despite the perfectly symmetry forcing the ring was slightly distorted which they attributed to the presence of a negative helical mode, m = 1 [40]. In the sixth POD mode there is complete loss of symmetry or organized structures near the nozzle exit plane. What is left are aperiodic markers or turbulence. In Figure 3.9c it is evident that forcing at a frequency other than the harmonic attenuates the formation of any large scale structures. In jets, uid entrainment is mainly due to large scale structures and vortex pairing and since the structures are attenuated at the exit, entrainment and velocity decay should be minimal. According to Figure 3.7a, the centerline decay and uid entrainment as a function of the velocity pro le are similar for the non-forcing, St = 0:12 and St = 0:09 conditions. A possibility, is that the streamwise vortices increase the entrainment of ambient uid. This can occur due to the high strain eld formed by the vortices, increases the velocity in the azimuthal direction. 3.2.3 Symmetry Analysis Two probes were placed in the shear layer (0:75D; 2D) to give additional insight into the asymmetry of the jet (Figure 3.15). Figure E.2 show the streamwise velocity uctuations, u01 and u02. There is evidence of a asymmetry in the non-forcing condition that was otherwise undistinguished. This is evident from the slight phase shift at various time intervals. How- ever, from t = 20 ms to approximately 37 ms there is commonality within the uctuations indicated a varicose or symmetric mode. Both forcing cases increase the asymmetry of the instabilities. The forcing also intro- duces a large velocity increase. These outlying uctuations have multiple peaks which could indicate that there are multiple instabilities attributing to the rapid increase. In Figure 3.16c 34 there are a myriad of peaks at the base of the outlying uctuation. This can be indicative of the parametric resonance originally seen in the PSD plots of Figure 3.5. Cross-spectra analysis was also conducted on the signals. The spectra is located in Appendix D. In Figure 3.16a the average of the curve is zero, indicating that the magnitudes of the structures measured by the two probes are similar. In Figures D.2 and D.3 there is a non-zero average indicating a variation in the structure magnitude. It can also be extrapolated that the variation of structure magnitude would indicate an asymmetry or helical mode. 3.2.4 Reynolds Shear Stress Reynolds shear stresses ( xy) were calculated from, xy = %u 0v0 U2max (3.5) where the overbar corresponds to the averaged quantity. Reynolds shear stress are in Figures 3.17 and 3.18. In the no forcing case, there is a small region near the nozzle exit plane due to the shear and growth of the initial instability. After that, xy is not visible until y=D 4, and then there is a lateral and streamwise growth. For the forcing cases, xy is visible and grows near the nozzle exit plane. This is due to the earlier formation and growth of the large scale structures seen in Figure 3.9a. In Figure 3.18a the color contour plot has a higher level than both the non-forcing and forcing at St = 0:09. This is due to the combination of the forcing mechanism adding energy into the ow and the formation of large scale structures closer to the nozzle exit plane. It would be expected to see the same results at St = 0:09, except the sub-harmonic attenuated all large scale structures. 35 3.2.5 Turbulent Kinetic Energy The turbulent kinetic energy (TKE) was calculated from the following equation, TKE = u 02 +v02 2U2max (3.6) The largest region of kinetic energy is located in the center of the shear layer for the non forcing condition (Figure 3.19). This is due to the predominately large uctuations in the u component from the rotation of the large scale structures. For the forcing conditions (Figure 3.20a and 3.20b) the maximum TKE is substantially less. This is attributed to the forcing that quickly attenuated the large scale structures. For St = 0:12, there is a small region of higher TKE than for St = 0:09 and this is because of the low frequency energy that was introduced by the forcing and evident in Figure 3.9a. Appendix H contains the same gures but with contour lines superimposed to distinguish regions of similar color. 36 (a) First mode, St = 0:12 (b) 25th mode, St = 0:12 Figure 3.12: POD of transverse plane at y=D = 4 (St = 0:12) 37 (a) First mode, St = 0:09 (b) 25th mode, St = 0:09 Figure 3.13: POD of transverse plane at y=D = 4 (St = 0:09) 38 (a) No forcing (b) St = 0:12 (c) St = 0:09 Figure 3.14: 25th POD mode at y=D = 6 39 Figure 3.15: Location of two probes 40 (a) No forcing (b) St = 0:12 (c) St = 0:09 Figure 3.16: Flow structure behaviour, probes are located at ( 0:75D;2D) 41 Figure 3.17: Reynolds shear stress ( xy) 42 (a) St = 0:12 (b) St = 0:09 Figure 3.18: Reynolds shear stress for forced cases 43 Figure 3.19: Turbulent Kinetic Energy for non-forcing 44 (a) St = 0:12 (b) St = 0:09 Figure 3.20: Turbulent Kinetic Energy for forced cases 45 Chapter 4 Conclusions A round axisymmetric turbulent jet was subjected to azimuthal excitation at various forcing frequencies. A forcing mechanism was used to azimuthally excite the ow in 360 . The experiments were conducted at Reynolds number of 5;500 and forcing frequencies with equivalent Strouhal numbers of 0:12 and 0:09. Both forcing frequencies resulted in an in- crease in the entrainment from the streamwise vortex laments and increase the asymmetry of the large scale structures. The harmonic frequency, St = 0:12, attenuated the large scale structures as evident in the PIV and POD analysis. The instabilities appeared to be in the form of large scale vortex rings. The forcing case also appeared to introduce low frequency instabilities near the nozzle exit plane (y=D = 2). There was also a higher level of xy not only within the rst four diameters downstream but also throughout the ow and a slightly higher TKE near the exit plane due to the velocity uctuations of the low frequency inabilities introduced by the forcing. For St = 0:09, all large scale structures were attenuated and unlike the harmonic fre- quency, low frequency instabilities were not introduced into the ow. This forcing frequency also increased the sinuous instability as evident from the u0 comparisons. 46 Bibliography [1] Yule, A., \Investigation of Eddy Coherence in Jet Flows," The Role of Coherent Struc- tures in Modelling Turbulence and Mixing, edited by J. Jimenez, Vol. 136, Springer- Verlag, 1980, pp. 188{207. [2] TSI, IFA 300 Constant Temperature Anemometer System, revision d ed., December 2010. [3] Mi, J., Nathan, G., and Luxton, R., \Mixing Characteristics of a Flapping Jet from a Self-Exiciting Nozzle," Flow, Turbulence, and Combustion, Vol. 67, 2001, pp. 1{23. [4] Ritchie, B., Mujumdar, D., and Seitzman, J., \Mixing in Coaxial Jets Using Synthetic Jet Actuators," American Institute of Aeronautics and Astronautics, 2000. [5] Brown, G., \On Sensitive Flames," Philosophical Magazine, Vol. 13, No. 82, 1932. [6] Panton, R. L., Incompressible Flow, New York: J. Wiley, 1996, 2nd ed. [7] Crow, S. and Champagne, F., \Orderly Structure in Jet Turbulence," Journal of Fluid Mechanics, Vol. 48, No. 03, August 1971, pp. 547{591. [8] Yule, A., \Large-Scale Structure in the Mixing Layer of a Round Jet," Journal of Fluid Mechanics, Vol. 89, No. 3, 1978, pp. 413{432. [9] Fiedler, H., \Coherent Structures in Turbulent Flows," Progress in Aerospace Sciences, Vol. 25, No. 3, 1988, pp. 231{269. [10] Lau, J., Fisher, M., and Fuchs, H., \The Intrinsic Structure of Turbulent Jets," Journal of Sound and Vibration, Vol. 22, No. 4, 1972, pp. 379. [11] A.S. Ginevsky, Y.V. Vlasov, e. a., \Acoustic Control of Turbulent Jets," Foundations of Engineering mechanics. [12] Becker, H. and Massaro, T., \Vortex Evolution in a Round Jet," Journal of Fluid Mechanics, Vol. 31, No. 3, 1968, pp. 435{558. [13] Dimotakis, P. E., MiakeLye, R. C., and Papantoniou, D. A., \Structure and Dynamics of Round Turbulent Jets," Physics of Fluids, Vol. 26, No. 11, November 1983, pp. 3185{ 3192. [14] Citriniti, J. and George, W., \Reconstruction of the Global Velocity Field in the Ax- isymmetric Mixing Layer Utilizing the Proper Orthogonal Decomposition," Journal of Fluid Mechanics, Vol. 418, 2000, pp. 137{166. 47 [15] Patte-Rouland, B., Lalizel, G., Moreau, J., and Rouland, E., \Flow Analysis of an Annular Jet by Particle Image Velocimetry and Proper Orthogonal Decomposition," Measurement Science and Technology, Vol. 12, 2001, pp. 1404{1412. [16] Gordeyev, S. and Thomas, F., \Coherent Structure in the Turbulent Planar Jet. Part 1. Extraction of Proper Orthogonal Decomposition Eigenmodes and Their Self-Similarity," Journal of Fluid Mechanics, Vol. 414, 2000, pp. 145{194. [17] Bernero, S. and Fiedler, H., \Application of Particle Image Velocimetry and Proper Orthogonal Decomposition to the Study of a Jet in a Counter ow," Experiments in Fluids, 2000, pp. S274{S281. [18] Semeraro, O. and Bellani, G., \Analysis of Time-Resolved PIV Measurements of a Con ned Turbulent Jet using POD and Koopman Modes," Vol. 53, 2012, pp. 1203{ 1220. [19] Wickersham, P., Jet Mixing Enhancement By High Amplitude Pulse-FLuidic Actuation, Ph.D. thesis, Georgia Institute of Technology, 2007. [20] Huang, J.-M. and Hsiao, F.-B., \On the Mode Development in the Developing Region of a Plane Jet," Physics of Fluids, Vol. 11, No. 7, July 1999, pp. 1847{1857. [21] Deo, R. C., Experimental Investigation of th In uence of Reynolds Number and Bound- ary Conditions on a Plane Air Jet, Ph.D. thesis, The University of Adelaide, 2005. [22] Reynolds, W., Parekh, D., and Juvet, P., \Bifurcating and Blooming Jets," Annual Review of Fluid Mechanics, Vol. 35, January 2003, pp. 295{315. [23] MI, J., Nobes, S., and Nathan, G., \In uence of Jet Exit Conditions on the Passive Scalar Field of an Axisymmetric Free Jet," Journal of Fluid Mechanics, Vol. 432, 2001, pp. 91{125. [24] Richards, C. and Pitts, W., \Global Density E ects on the Self-Preservation Behaviour of Turbulent Free Jets," Journal of Fluid Mechanics, Vol. 254, 1993, pp. 417{435. [25] Dowling, D. R. and Dimotakis, P. E., \Similarity of the Concentration Field of Gas- Phase Turbulent Jets," Journal of Fluid Mechanics, Vol. 218, 1990, pp. 109{141. [26] George, W. K., \The Self-Preservation of Turbulent Flows and Its Relation to Initial Conditions and Coherent Structures," Advances in Turbulence, Hemisphere, 1989, pp. 39{73. [27] Dimotakis, P. E., \Some Issues on Turbulent Mixing and Turbulence," GALCIT Report FM93-1, March 1993, Updated as FM93-1a. [28] Samimy, M., Reeder, M. F., and Zaman, K. B. M. Q., \E ect of tabs on the ow and noise eld of an axisymmetric jet," AIAA Journal, Vol. 31, April 1993, pp. 609{619. [29] Aydemir, E., Worth, N., and Dawson, J., \The Formation of Vortex Rings in a Strongly Forced Round Jet," Experimental Fluids, Vol. 52, 2012, pp. 729{742. 48 [30] Sirohi, J. and Chopra, I., \Fundamental Understanding of Piezoelectric Strain Sensors," Journal of Intelligent Material Systems and Structures, 2000. [31] \Guide to Modern Piezoelectric Ceramics," Morgan Matroc Inc, March 1993. [32] Koso, T. and Kinoshita, T., \Agitated Turbulent Flow eld of a Circular Jet with an Annular Synthetic Jet Actuator," Journal of Fluid Science and Technology, Vol. 27, No. 2, 2008, pp. 323{333. [33] Pothos, S. and Longmire, E. K., \Asymmetric Forcing of a Turbulent Rectangular Jet with a Piezoelectric Actuator," Physics of Fluids, Vol. 13, No. 5, 2001, pp. 1480{1492. [34] Wiltse, J. M. and Glezer, A., \Direct Excitation of Small-Scale Motions in Free Shear Flows," Physics of Fluids, Vol. 10, No. 8, 1998, pp. 2026{2037. [35] Parker, R., Rajagopalan, S., and Antonia, R., \Control of an axisymmetric jet using a passive ring," Experimental Thermal and Fluid Science, Vol. 27, 2003, pp. 545{552. [36] Chopra, M., \Hot Wire Anemometry and Fluid Flow Measurement," University Lecture, 2008. [37] Jergensen, F. E., How to Measure Turbulence with Hot-Wire Anemometers, Dantec Dynamics, 2002. [38] Perry, A. E., Hot-Wire Anemometry, Clarendon Press, 1982. [39] Lumley, J. L., \The Structure of Inhomogeneous Turbulent Flows," Atmospheric tur- bulence and radio propagation, edited by A. M. Yaglom and V. I. Tatarski, Nauka, Moscow, 1967, pp. 166{178. [40] Mcllwain, S. and Pollard, A., \Large Eddy Simulation of the E ects of Mild Swirl on the Near Field of a Round Free Jet," Physics of Fluids, 2002. [41] Ra el, M., Willert, C. E., and Kompenhans, J., Particle Image Velocimetry: a Practical Guide, Springer-Verlag, 1998. 49 Appendices 50 Appendix A Uncertainty Analysis A statistical analysis was conducted to ensure the accuracy of the hot wire data col- lected according to the method described by Dantec Dynamics ([37]). The Re of 5,500 corresponding to 7:2 m=s was chosen. The sources of uncertainty that were considered are as follows. 1. Pressure transducer error From the manufacturer speci cations, the accuracy of the transducer was found to be 0:5%. 2. Pressure transducer calibration error The uncertainty of the calibration is due to curve tting. A rst order polynomial was applied to the pressure transducer calibration. The residuals at each calibration point was found and from there the standard deviation (in percentage) was calculated. The relative standard uncertainty can be calculated from relativestandarduncertainty = 1100 (%) (A.1) 3. A/D board resolution The A/D board resolution error was calculated from, relativestandarduncertainty = 1p3 1UEAD2m @U@E (A.2) 51 Table A.1: Uncertainties for velocity sample for single probe Error Source Relative Standard Uncertainty Pressure transducer error 0.005 Pressure transducer calibration error 0.005 A/D board resolution 0.0026145 Hot wire calibration error 0.00061 @U @E is the slope of the inverse calibration curve. For the A/D board used (PD2 MFS 4 2M=14); EAD = 10v; @U@E = 53:42 and m = 14. 4. Hot wire calibration error The hot wire calibration error is calculated similar to the calibration error due to the pressure transducer. For the current work, the calibration error is given by the IFA300 system. The relative uncertainties are located in Table A.1. The total uncertainties involved are 2 p0:0052 + 0:0052 + 0:00261452 + 0:000612 = 0:015 = 1:5% The PIV measurements were taken using a 32 x 32 pixel interrogation window. Ac- cording to Ra el et all the RMS uncertainty is roughly 0.01 pixels [41]. When data is acquired perpendicular to the ow direction, the uncertainty typically increases by an order of magnitude. 52 Appendix B Forcing Mechanism Components The following Figures were purchased to control the azimuthal forcing mechanism. .250 .962 24.4 2.0 .080 28.4 1.119 6.4 (2 Pl) 0.000 .515 22.0 0.051 - .866 -.002 +.000 .1875 4.8 .394 on a 1.600 BC) (2 @180 M3 x .5, 5mm Dp Location of flat on shaft with rotor at mid rotation point. 1258 TITLE DWG # MATERIAL FINISH DRAWNREV 80-0001 permission from H2W Technologies, Inc. www.h2wtech.com TMR-060-005-2H MPW APPROVED DATEDATE 10-5-01FGW10-5-01 ECN H2W Technologies, Inc. Tel: (661)-702-9346 Fax: (661)-702-9348 28310-C Ave Crocker Valencia, CA 91355 USA .010 FILLETS AND .020 CORNERS .010 .X Remove All Burrs and Sharp Edges UNLESS SPECIFIED OTHERWISE: All dimensions are in inches Standard Tolerances are as follows .XXX .005 ANGLES ?1? .XX These drawings and specifications are the property of H2W Technologies, Inc. They are issued in confidence and shall not be reproduced, copied, or used without written C (-) Black (+) Red Direction .750 1.772 45.0 .375 Model Number: Constant Torque Angular Displacement:60degrees Resistance:1ohms Total Weight:147grams Continuous Torque:5in-oz Peak Torque:15in-oz Motor Constant:3.3in-oz/sqrt(watts) Rotor Inertia7.26E-03lbs-sq.in. TMR-060-005-2H SPECIFICATIONS Figure B.1: H2W Limited Angle Torque Motor 53 Toll-free: 800.736.0194 www.usdigital.com Vancouver, Washington 98684, USA Local: 360.260.2468 info@usdigital.com 1400 NE 136th Avenue .025 SQUARE PINSMATES TO CON-C5 OR CON-LC5 PIN 1 .69 17.62 .62 15.62 1.41 35.92 .59 15.09 2X .113 .750 19.05 3X .078 [1.98] SPACED EVENLY ON .823 [20.90] BC .438 [11.13] THRU .548 [13.92] .045 [1.14] 1.19 30.18 E2 Optical Kit Encoder Drawing UNITS: INCHES [MM]METRIC DIMENSIONS FOR REFERENCE ONLY RELEASE DATE: 7/2/2012 Figure B.2: US Digital Optical Encoder 54 DigiFlex ? Performance?gServogDrive DZRALTE-020L080 ReleasegDate: 9/7/2012 Revision: 2w02 ADVANCED MotiongControlsg?g3805gCallegTecate-gCamarillo-gCA-g93012 phxg805638961935?gfxxg805638961165?gwwwwa6m6cwcom Pageg2gofg8 BLOCK0DIAGRAM GND GND PDO-q696k MOTEENCEX6B6IE( MOTEENCEX6B6IE? HXLLEX6B6C GND HIGHEVOLTXGE MOTOREX MOTOREB MOTOREC LOGICEPOWER GND Mo torEF eedb ack I)OEI nterfa ce Hk (HV Hk (HV z:Gk z:Gk 9k Hk (HV I/O Interfa ce Power Stage Drive Logic Logic Power HVVk Moto r Fee dbac k PDI-q696kEDCXP-X2 PDI-R6HE(EDPWM(E) XUXEENCEX6BE(E)ESTEP(E) DIR(E)ECXP-B6CE(2 PDI-R6HE?DPWM?) XUXEENCEX6BE?)ESTEP?) DIR?)ECXP-B6CE?2 PXI-qE?DREF?2 PXI-qE(EDREF(2 RSRPHEBXUD6 RSRPHEXDDREV6q RS232/485 Interface SELECT RS9k9ETXE)ERSRPHETX? RS9k9ERXE)ERSRPHERX? RSRPHETX( RSRPHERX( Information0on0Approvals0and0Compliances USEandECanadianEsafetyEcomplianceEwithEULEHVPc6EtheEindustrialEstandardEforEpowerEconversionEelectronics:E UL registeredEunderEfileEnumberE qRVqGk:E NoteEthatEmachineEcomponentsEcompliantEwithEULEareEconsideredEUL registeredEasEopposedEtoEULElistedEasEwouldEbeEtheEcaseEforEcommercialEproducts: CompliantEwithE uropeanECEEforEbothEtheEClassEXE MCEDirectiveE9VVR)qVP)ECEonE lectromagneticECompatibility DspecificallyE NEzqVVV-z-RT9VVGEandE NEzqVVV-z-9T9VVH2EandELVDErequirementsEofEdirectiveE9VVz)OH)EC DspecificallyE NEzV9VR-qT9VVz26EaElowEvoltageEdirectiveEtoEprotectEusersEfromEelectricalEshock: RoHSEDReductionEofEHazardousESubstances2EisEintendedEtoEpreventEhazardousEsubstancesEsuchEasEleadEfromEbeing manufacturedEinEelectricalEandEelectronicEequipment: Figure B.3: AMC Servo Motor Block Diagram 55 MountingfCard MC1XDZR028QD ReleasefDate: 6#22#2-w2 Revision: 26-w ADVANCED MotionfControlsf?f38-5fCallefTecateFfCamarilloFfCAFf93-w2 phdf8-5x389xw935f?ffxdf8-5x389xww65?fwww6axmxc6com Pagef2foff9 BLOCKoDIAGRAMo1oSPECIFICATIONoSUMMARY GND PDOBL8x8W MOTsENCsY8B8Is) MOTsENCsY8B8Is? HYLLsY8B8C) RSWxsRX RSxWxsTX HIGHsVOLTYGE MOTORsY MOTORsB MOTORsC GND Mo to rs F e e d b a ck I VO s In te rf a ce Gk )GV Gk )GV N?Dk N?Dk xk Gk )GV I/ O XI n te r fa c e PowerXStage Drive Logic RSHTGsTX RSHTGsRX Mo to r XF e e d b a c k PDIBL8x8WsbCYPBY7 PDIBH8Gs)sbPWM)sVsSTEP)sV DIR)sVsYUXsENCsY8Bs)sV CYPBB8Cs)7 PDIBH8Gs?bPWM?VsSTEP?V DIR?VsYUXsENCsY8Bs?V CYPBB8Cs?7 PYIBLs)sbREF)7 PYIBLs?bREFB7 DZXSERVOXDRIVE MC1XDZR02-QDXMOUNTINGXCARD F e e d b a c k X C o n n e c to r Mo to r Po w e r C o n n e c to r Po w e r C o n n e c to r Lzk Lzk Lzk )GV xzk xzk )GV Lzk )GV xzk xzk )GV )GVsLOGICsSUPPLYsINPUT GND Communication Interface GND I/ O XC o n n e c to r Logic Power C MechanicaloSpecifications MountingsSignalsConnectorAsPLs WzBpin8sdualBrow8sx?GHsmmspitchssocket MountingsPowersConnectorAsPxs xHBpin8sdualBrow8sx?GHsmmspitchssocket MountingsPowersConnectorAsPWs xHBpin8sdualBrow8sx?GHsmmspitchssocket IVOsConnectorAsPH(s LNBport8sdualBrow8sx?zzsmmsspacedsplugsterminal CommunicationsConnectorAsPG(s LzBport8sdualBrow8sx?zzsmmsspacedsplugsterminal FeedbacksConnectorAsPN(s LxBport8sdualBrow8sx?zzsmmsspacedsplugsterminal MotorsPowersConnectorAsPDsbmatingsconnectorsincluded7s HBport8sG?zTsmmsspacedsinsertsconnector PowersConnectorAsPTsbmatingsconnectorsincluded7s WBport8sG?zTsmmsspacedsinsertsconnector BussCapacitance Lzz?FsVsxzzsV SizesbLsxsWsxsH7s x?GsxsW?zsxsL?zsinches Weights Gz?DsgsbL?Tsoz7 2MatingoConnectoroKit Matingfconnectorfhousingfandfcrimpfpinsfcanfbeforderedfasfafkitfusing ADVANCED MotionfControlsfpartfnumber KC8MC1XDZ026 ThisfincludesfmatingfconnectorfhousingfandfcrimpfstylefcontactsfforfthefI#OFfFeedbackFfandfCommunicationfconnectors6fThe recommendedftoolfforfcrimpingfthefcontactsfisfMolexfpartfnumber 63811863006 Figure B.4: AMC Mounting Card Block Diagram 56 Appendix C Velocity Contour The following images are the snapshot velocity contours acquired from the PIV analysis of the forced cases. Figure C.1: Velocity Contour, St = 0:12 57 Figure C.2: Velocity Contour, St = 0:09 58 Appendix D Cross-Spectra Figure D.1: Cross-Spectra, Unforced 59 Figure D.2: Cross-Spectra, St = 0:12 60 Figure D.3: Cross-Spectra, St = 0:09 61 Appendix E Mode Distribution 62 (a) Unforced (b) St = 0:12 (c) St = 0:09 Figure E.1: Energy distribution 63 (a) Unforced (b) St = 0:12 (c) St = 0:09 Figure E.2: Energy distribution at y=D = 4 64 Appendix F Shear layer PSD Below are additional PSD plots with the CTA probe located within the shear layer at a series of locations downstream. frequency m a g n i t u d e 10 1 10 2 10 3 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 y/D = 1 y/D = 4 y/D = 6 Figure F.1: Shear layer PSD, no forcing 65 frequency m a g n i t u d e 10 1 10 2 10 3 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 y/D = 1 y/D = 4 y/D = 6 Figure F.2: Shear layer PSD, St = 0:12 66 frequency m a g n i t u d e 10 1 10 2 10 3 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 y/D = 1 y/D = 4 y/D = 6 Figure F.3: Shear layer PSD, St = 0:09 67 Appendix G POD Contour Plots 68 (a) First mode, St = 0:12 (b) 2525 mode, St = 0:12 Figure G.1: Modal energy for azimuthal cuts at y=D = 4 with streamtracers superimposed (St = 0:12) 69 (a) First mode, St = 0:09 (b) 25th mode, St = 0:09 Figure G.2: Modal energy for azimuthal cuts at y=D = 4 with streamtracers superimposed (St = 0:09) 70 Figure G.3: No forcing, 25th mode at y=D = 6 with streamtracers superimposed 71 Figure G.4: St = 0:12;25th mode at y=D = 6 with streamtracers superimposed 72 Figure G.5: St = 0:09;25th mode at y=D = 6 with streamtracers superimposed 73 Appendix H Turbulent Kinetic Energy Following are similar contour plots of the turbulent kinetic energy with contour lines superimposed. Figure H.1: Turbulent Kinetic Energy for non-forcing 74 (a) St = 0:12 (b) St = 0:09 Figure H.2: Turbulent Kinetic Energy for forced cases 75