Development and Application of Advanced Optical Diagnostics in High Speed Jets

Transcription

1 The 10th International Symposium on Flow Visualization August 26-29, 2002, Kyoto, Japan F0501 (Plenary Lecture) Development and Application of Advanced Optical Diagnostics in High Speed Jets Samimy, M., Thurow, B., Hileman, J., and Lempert, W. Gas Dynamics and Turbulence Laboratory Department of Mechanical Engineering The Ohio State University, Columbus, Ohio 43210, USA Tel: / FAX: Abstract: Development of a MHz rate planar flow imaging system for real-time high-speed flow diagnostics is briefly described. The system has been utilized in supersonic jets with Mach numbers of 1.3 and 2.0 (convective Mach numbers of 0.59 and 0.85) to explore compressibility effects on large-scale turbulence structures. In addition to the loss of coherency due to compressibility, results show the convective velocity in the Mach 2.0 jet is bi-modal with a fast mode and a slow mode. The system has also been used in simultaneous flow imaging and acoustics measurements in a supersonic jet to explore sources of large peaks in the far acoustic field. The results have provided some new insight into the far-field acoustic waveform and the processes within the jet by which the peak acoustic radiation is generated. Keywords: Visualization, Real-time, Supersonic, Jet, Acoustics, Compressibility, High-Speed 1. Introduction High-speed jets are utilized in a myriad of engineering applications. They range from gaseous fuel injectors in school buses; to the coating of surfaces in manufacturing processes using high-pressure particle laden jets; to commercial and military jet engines. The size of these jets varies from a millimeter in a passenger size automobile fuel injector to a meter in a commercial airplane jet engine. These jets are turbulent and almost always have a high Reynolds number. Depending upon the specific application, one would desire to understand and perhaps control mixing and entrainment characteristics; kinetic energy/impact; interaction among turbulence structures and with shock/expansion waves within the jet; and the far-field noise radiation. The understanding of these characteristics takes greater importance as our needs and desires to actively control these flows increase. The understanding of large-scale coherent structures, which are responsible, for example, for entrainment, mixing, and noise generation, in planar two-dimensional mixing layers and the effects of compressibility on their nature has increased significantly over the last 25 years. The understanding of such structures in jets, particularly in axisymmetric jets, which are more complex due to the existence of additional instability modes, has also increased substantially over the last 25 years in incompressible cases. Unfortunately, one cannot make such a claim in compressible cases, which almost always possess a high Reynolds number and have more operating regimes (i.e. fully expanded, overexpanded, and underexpanded). The lack of appropriate computational and experimental tools has been at the root of this problem. While the computational capabilities are inching toward being able to deal with high Reynolds number jets, it will take quite a while for its full realization. On the other hand, experimental capabilities have improved significantly and can be quite helpful in tackling these issues. Experiments are also essential for the advancement and validation of numerical techniques. We have been working on various compressible flow problems for quite sometime and have recently initiated a multifaceted program with both short and long term goals of developing technologies to advance our understanding and control of high-speed and high Reynolds number jets. The program includes (1) development of advance laser

2 based flow diagnostics, (2) development of high bandwidth and high amplitude actuators for flow control, (3) development of low dimensional models for high-speed flows, and finally, (4) development and design of controllers that can use the actuators and low dimensional models for closed-loop flow control. We will briefly discuss the progress made in topic (1) and will present and discuss the application of the developed laser based diagnostics to explore compressibility effects in high-speed axisymmetric jets. We will also provide a brief discussion of the application of these diagnostic tools to better understand jet noise sources. Under topic (2) we have been working on Hartmann tube based fluidic actuators (Kastner and Samimy, 2002) and very recently on plasma actuators. Initial results on topic (3) can be found in Caraballo et al. (2001). Topic (4) is part of a very recent program and is still in its infancy. 2. Development of Real-Time Laser Based Flow Diagnostics Over the last two decades, quite a few researchers have used pulsed lasers to visualize large-scale coherent structures within high-speed flows (e.g. Elliott et al., 1992 & 1995 and Clemens and Mungal, 1995). However, the repetition rate of commercially available lasers is too low to provide any information on the development of and interaction between such structures. Some success in this arena has been achieved by using double-pulse lasers or two lasers, but the results are still limited to two time resolved images, which are not sufficient for the exploration of the development and interaction of these structures. In the last few years, some advances have been made in both laser and camera technologies that have made possible a MHz rate imaging system. This MHz rate imaging system incorporates a pulse burst Nd:YAG laser and a MHz frame-rate CCD camera. Used in conjunction with one another, these technologies have been utilized to visualize the flow of Mach 1.3 and 2.0 ideally expanded axisymmetric jets (Thurow et al., 2001a & 2002) and to explore jet noise sources in a Mach 1.3 ideally expanded axisymmetric jet (Hileman et al. 2001a & b). The two major components of the system, the laser and the CCD camera, will be briefly discussed below, followed by a discussion of the applications of this MHz rate imaging system. 2.1 MHz Rate Pulse-burst Laser A schematic diagram of the laser that we currently use is shown in Fig. 1. It is a home-built second generation system based on that described previously by Lempert et al. (1996 & 1997), Wu et al. (2000), and Thurow et al. (2001b). A continuous wave Nd:YAG ring laser serves as the primary oscillator, the output of which is pre-amplified in a double-pass, flashlamp-pumped, pulsed amplifier. The resulting approximately 150 µs duration pulse is formed into a burst of pulses using a dual-pockel cell beam-slicer. The flexible pulse train can have a variable number of pulses, between 1 and 99, with inter-pulse timing as short as 1 µs. The individual pulse durations can be varied between 5 ns and 10 µs. The pulse-train is further amplified by a pair of additional double-pass amplifiers with an overall gain of approximately The pulse-train is then reflected off of a phase conjugate mirror (to be described) and passed through two single-pass, double-flashlamp, amplifiers with single-pass gains of approximately 4 each. It is then converted to the second harmonic at a wavelength of 532 nm using a KTP crystal. The phase conjugate mirror (PCM) and the 5 th amplifier are recent additions to the laser and were not part of the laser system used to acquire the flow visualization images presented in this paper. Figure 2 shows a typical burst train, consisting of 17 pulses, each having duration of 10 ns. The inter-pulse timing is 5 µs. The output energy, at the second harmonic (532 nm), was approximately 7 mj in each of the individual pulses for this specific case. Typical pulse energies varied between 2 and 10 mj/pulse depending on the time separation between the pulses for the initial set up. Longer separations between pulses correlate to higher pulse energies. Furthermore, the timing of the four amplifiers can be varied relative to one another in order to distribute the power evenly over the entire burst. The overall burst process has a repetition rate of 10 Hz. In the initial set-up of the laser system, the conversion efficiency from the first harmonic (1064 nm) to the second harmonic (532 nm) was less than 15%. This relatively low conversion efficiency is mainly due to the presence of a low intensity pedestal superimposed upon the high-intensity pulses, which make up the desired output of the burst train. This pedestal occurs because the Pockel cell switcher leaks ~ 0.1% when it is nominally off. Since it is on for only ~ 10 ns out of ~ 10 µs, a substantial amount of leaked energy is contained in the pedestal. Although the pedestal is a few orders of magnitude less intense than the pulses, the integrated power of the pedestal is estimated to be as high as 50% of the total power in the laser. Thus, the energy of the laser was limited to the order of 2-10 mj/pulse at 532 nm. To overcome this problem and to increase energy per pulse, a phase conjugate mirror (PCM) has been incorporated into the laser system. The PCM acts as a non-linear reflector where the intense light of the pulses is reflected through backward Brillouin scattering. The low intensity pedestal, however, is below the threshold for this process and is consequently transmitted through the PCM. The PCM consists of an optical quality glass cell filled with Fluorinert (FC-75), which is a heavy fluorocarbon with a relative low threshold for Brillouin scattering, and a lens to focus the beam to a point in the fluid. With the addition of the PCM, the pedestal can be eliminated from the pulses and the remaining amplifiers in the laser system can be used more efficiently to amplify the pulses. 2

3 Conversion efficiencies are now better than 35%, a significant improvement. Furthermore, a 5 th amplifier has been added to the system to provide even more power. With the current set-up, pulse energies as high as 50 mj have been measured, providing over a factor of 5 improvement from the initial system. As will be discussed shortly, even with the 5 to 10 mj/pulse of the initial set up, the laser power was quite adequate for flow visualization (Thurow et al., 2001a & 2002; Hileman et al. 2001a&b), but not for quantitative measurement (Thurow et al., 2001b). CW laser λ/2 Fast Pockel Cells λ/2 λ/4 Telescope To Application (532 nm) λ/4 Harmonic Crystal λ/2 Telescope λ/2 λ/2 λ/2 λ/4 PCM Assembly λ/4 Focusing Lens Telescope Amplifier Optical Isolator Waveplate Focal/ Expanding Lens Polarizer Mirror Figure 1: Schematic Diagram of Pulse Burst Laser Relative Powe Tim e (microseconds) Figure 2: Typical Burst Train with Pulse Separation of 5 µs and Energy per Pulse of ~7 mj 2.2 MHz Rate CCD Camera The camera that we have used with the MHz imaging system so far is manufactured by Silicon Mountain Design (SMD), which is now a subsidiary of Dalsa, Inc. The camera can acquire 17 images at a variable frame rate up to 1 MHz. Each image in the sequence has a resolution of 245 x 245 pixels. The camera is based on a 1024 x 1024, 12-bit CCD chip, in which 16 of 17 pixels are masked. By appropriate shifting of charge, individual images are initially stored in pixel locations under the mask. After accumulation of all the images, a PC reads the output as one large image, containing all 17 frames. The output signal is transferred via four parallel data ports, each comprising a 3

4 quarter size column of the image. The video signal out can have either a gain of 1 or 4 applied to it. Effective pixel size is less than 10 µm, and the quantum efficiency and fill factor are less than 20% and 3%, respectively. In comparison with a typical scientific grade 16-bit CCD camera, the ultra-fast SMD CCD camera has a few drawbacks. First, the relatively small spatial resolution of 245 x 245 limits the spatial scale of the measurements. Second, a pixel size of less than 10 µm is relatively small and contributes significantly to speckle noise, which scales inversely with pixel size (Smith 1998). Third, the low quantum efficiency and very low fill factor necessitate a more intense signal. Compounded with the limited amount of available laser power, this leads to a low signal to noise ratio. To improve the real-time imaging capabilities and to move towards quantitative real-time imaging, a new CCD camera manufactured by Princeton Scientific Instruments (PSI) has been recently acquired. Three major advantages of this camera over the SMD camera are: (1) the number of images/frames in a real-time sequence has increased from 17 to 28; (2) the fill factor is increased from less than 3% to over 45%; and (3) the effective pixel size is increased from less than 10 µm to about 80 µm. As will be discussed next, the last two improvements would help to significantly improve the overall signal to noise ratio and will reduce the speckle noise by a factor of approximately Real-Time Qualitative and Quantitative Flow Visualizations The initial pulse burst laser, which had low pulse energy, has been successfully used with the SMD camera to obtain flow visualizations of Mach 1.3 and Mach 2.0 axisymmetric jets (Thurow et al., 2001a & 2002 and Hileman et al. 2001a&b). In these experiments, seed particles of order 50 nm in diameter were introduced into the flow naturally through a product formation technique where condensed water particles formed in the mixing layer of the jet due to the entrainment and mixing of warm, moist, ambient air with the cold, dry jet core air. The laser was formed into a sheet to illuminate various cross-stream and streamwise planes of the jet. Sample results from these experiments will be presented and discussed later in the paper. The pulse burst laser / SMD camera system that was used for MHz imaging also showed a great potential for quantitative planar velocity measurements, but there were also some major problem areas (Thurow et al. 2001b). These issues along with the potential of a new system with the upgraded pulse burst laser and a new ultra-fast CCD camera will briefly be discussed below. There are two conceptual optical techniques that one can use to measure flow velocities. The first concept requires measuring the shift in the frequency of the illuminating laser light that is scattered by seed particles in the flow (Adrian, 1983). The idea of measuring the Doppler shift due to the motion of particles in the flow was originated by Cummins et al. (1964) and Yeh and Cummins (1964) after the advent of lasers. The widely used laser Doppler velocimetry (LDV), which is a point-measurement, is based on this concept. A new class of velocimetry technique based on a spectral molecular filter, which was originated by Komine et al. (1991) and Meyers and Komine (1991), has been developed within the past several years that can measure the Doppler shift of scattering particles on an illuminated plane. This technique is called planar Doppler velocimetry (PDV), or Doppler global velocimetry (DGV). Details of this technique can be found in recent review articles by McKenzie (1996), Elliott and Beutner (1999), and Samimy and Wernet (2000). The second concept is based on measuring the transit time between two points of seed particles in the flow (Adrian, 1991). The widely used particle imaging velocimetry (PIV) and its many variations are based on this concept. Both PDV and PIV can be used in high-speed flows. Our preference has been PDV for the reasons detailed in Samimy and Wernet (2000), and we have been active in its development for quite a few years (Elliott et al., 1994, Clancy and Samimy, 1997, Arnette et al., 1998, Clancy et al. 1999). The main components of PDV include a narrow spectral linewidth pulsed laser and a CCD camera. In a typical PDV set-up, the repetition rate of both of these elements is sufficiently low to preclude it from real-time measurements in high-speed flows. The possibility of incorporating the MHz rate laser and camera that were discussed above to develop a real-time PDV technique termed RTPDV were explored recently (Thurow et al., 2001b). The findings and the current status of this work will be briefly discussed in the next few paragraphs. A set of experiments was designed to take the first steps in the development of RTPDV. The first experiment consisted of using the pulse burst laser to take an iodine filter profile. This spectral filter profile is an essential part of the PDV techniques, as it is used to convert image intensity into Doppler shift. The ratio of filtered and unfiltered images provides a map of Doppler shift/a component of velocity, on the illuminated plane in the flow. The experiment was successful and demonstrated the laser s single-frequency capabilities, which is very important for the PDV technique. The second experiment used a stationary target to simulate a realistic RTPDV setup. It incorporated both the pulse burst laser and the ultra-fast SMD camera. A commercial Nd:YAG laser was also used for direct comparison with the pulse burst laser. Preliminary results showed the presence of excessive image noise. The relative inefficiency of the camera, as discussed above, and the low laser power both contributed to image noise 4

5 and made the measurements more challenging. The results also indicated that the pulse burst laser has better frequency stability than the commercial laser, thus eliminating the immediate need for a frequency monitoring system. A third experiment using a Mach 2.0 rectangular nozzle was conducted to examine the effectiveness of the technique on taking measurements in an actual flow. While the results seemed to be marred by the presence of image noise, the experiments at least provided an initial proof of concept that RTPDV has potential. As was discussed earlier, significant improvements have been made on both the pulse burst laser side by incorporating a phase conjugate mirror and adding a 5 th amplifier, and the ultra fast camera side by purchasing a higher quality (and more expensive, of course) camera. A factor of approximately 5 increase in the energy per pulse of the laser (from the order of 10 to 50 mj/pulse) and a factor of 15 increase in the fill factor of the camera (from approximately 3% to 45%) should help to improve the overall signal-to-noise ratio and to reduce the overall image noise. In addition, a factor 8 increase in the effective pixel size (from about 10 to 80) should reduce the speckle noise by a factor of almost 8, as speckle scales inversely with pixel size (e.g. Smith 1998). For a preliminary evaluation of the effects of these improvements, an experiment was set up to visualize a Mach 1.3 rectangular jet (exit dimensions of 38.1 x 14.7 mm). Both the SMD and PSI cameras were set-up with identical lenses and placed about 65 cm away from and perpendicular to the laser sheet, which was aligned with the streamwise direction. Figure 3 shows the images acquired by these cameras, before and after post-processing a) b) c) 0 d) Figure 3: Comparison of Images Taken of the same Flow but not at the same Time Instance by SMD and PSI MHz Rate Cameras. Images a) and c) are the raw outputs from the cameras while b) and d) are the images after post-processing procedures, which included background subtraction. Unfortunately, the PSI camera currently in use has a region of inactive pixels; visible on the right hand side of the images. Ignoring this defect in the PSI camera, the images clearly depict the advantages of the PSI camera over the SMD camera. It should be noted that the appearance of the post-processed SMD camera image (b) was enhanced with a smoothing filter (3 x 3 pixel moving average) in order to reduce the grainy appearance. The PSI camera did not need this filtering. This grainy appearance is mostly due to speckle noise. The speckle noise is estimated to be over 30% of the magnitude of the signal and makes quantitative diagnostics very challenging. The PSI camera, however, does not exhibit this noise. This improvement can be seen in comparing images a) and c). Furthermore, even after post-processing, the quality of the images from the SMD camera is limited by low signal levels. This is clear in image b) where the image is quite grainy. Image d) from the PSI camera, is a much higher quality image of the jet. Detailed assessment of the improvements and their effect on 5

6 RTPDV is forthcoming. 2.4 Correlation of Flow Images with Far-Field Acoustic Radiation It is a known fact that the exhaust jet is responsible for the majority of noise during the takeoff phase of a jet aircraft. Therefore, it has been a topic of research over the past fifty plus years (e.g. Tam, 1995). A major portion of the exhaust noise from a typical jet engine is created by the turbulent mixing between the high-speed flow from the jet engine and the ambient air entrained into the jet. Many of the average properties of jet noise are well known, but the underlying mechanisms responsible for its creation are not well understood and are the subject of intense current research. The main goal of this element of the research effort at GDTL is to determine how turbulence structures create mixing noise and to devise control schemes to reduce it. In an unconventional manner, the acoustic data is examined in the time domain, and is only taken to the frequency domain as necessary when comparison between individual dynamic features and the overall properties of the jet is desired. The jet in this study has a Mach number of 1.3 (measured Mach number is 1.28), a Reynolds number of 1.06 x 10 6, and an exit diameter of 2.54 cm. For background and details see Hileman and Samimy (2001) and Hileman et al. (2001a&b; 2002). For subsonic or ideally expanded supersonic jets, the dominant noise source is the large coherent structures within the mixing layer. If the convective velocity of these structures is subsonic, this component of jet noise is commonly referred to as turbulent mixing noise. However, if the convective velocity is supersonic relative to the ambient, then the large-scale structures will radiate Mach waves. Since the convective Mach number for the jet in this study is subsonic (M c =0.59), Mach wave radiation should not be present, and as such the focus is on turbulent mixing noise. Turbulent mixing noise is highly directional. The noise emission is greatest at angles close to the downstream jet centerline. The peak radiation angle has been measured to vary from 25 to 45 with respect to the downstream jet axis. This angle is approximately 30 in the current Mach 1.3 jet. A microphone array consisting of four 6.35 mm, model 4939 B & K microphones that were separated by 3.81, 5.08, and 6.35 cm, was located at 30 in the acoustic far field. The time delay between when an individual sound signal was recorded by two different microphones (phase lag) was combined with knowledge of the array geometry to determine the angle with which the sound wave had approached the array. This angle was then used to determine the location of the noise source assuming they were all located on the jet centerline (this linear array cannot resolve its transverse position). We currently use a three-dimensional microphone array to more accurately locate the noise source in space (Hileman et al. 2002). The mixing layer of the jet was visualized with the MHz rate imaging system described above simultaneously with the acoustic measurements. Scattering of light from the pulse burst laser by the naturally generated particles within the mixing layer of the jet, due to mixing of the entrained moist ambient air into the jet with the cold and dry jet air, was used to visualize the flow. The scattered light was captured with the ultra-fast SMD camera. The laser was located outside of the anechoic chamber and its beam was redirected into the chamber through a small hole. The SMD camera was placed inside of the chamber, perpendicular to the laser sheet, capturing the jet over a range of downstream locations from 4.5 to 10.5D; D being the nozzle diameter. The camera could not be placed outside of the anechoic chamber since the signal level dropped significantly at large distances. Both the camera stand and the camera were wrapped in acoustic foam to minimize acoustic reflections. 2.5 Experimental Facilities All of the experiments were conducted at The Ohio State University s Gas Dynamics and Turbulence Laboratory (GDTL). The facility consists of a jet stand and stagnation chamber to which a variety of nozzles may be attached. Air is supplied to the stagnation chamber from two four-stage compressors; it is filtered, dried and stored in two cylindrical tanks with a total capacity of 42.5 m 3 at 16.5 MPa (1600 ft 3 at 2500 psi). The stagnation chamber contains a perforated plate and two screens of varying porosity to condition the flow to be as uniform as possible prior to entering the nozzle. The experiments were conducted within the optically accessed anechoic chamber of GDTL. The inner dimensions of the chamber measure, from wedge tip to wedge tip, 3.12 meters in width and length, and 2.69 meters in height. Additional details of the anechoic chamber and jet flow facility can be found in Hileman and Samimy (2001) and Kerechanin et al. (2001). The two jet nozzles that were used in this study have design Mach numbers of 1.3 and 2.0. The nozzles have a 25.4 mm exit diameter with the diverging section contour designed using the method of characteristics. The nozzle Mach numbers were experimentally determined using a pitot probe to be 1.28 and 2.06, respectively. The jet exhausts into the anechoic chamber and exits the facility through a large bell-mouth at the opposite end of the chamber. Pressure to the stagnation chamber is controlled manually through the actuation of a Fisher control valve and can be maintained at constant pressure within 0.3 psi. Pressure was set for an ideally expanded flow and held constant through each set of experiments. 6

7 3. Experimental Results and Discussions 3.1 Compressibility Effects in Jets Significant progress has been made over the last two decades on the effects of compressibility, characterized by convective Mach number (Papamoschou and Roshko, 1988; Bogdanoff, 1983), in mixing layers. The overall findings are that as the convective Mach number is increased: (1) the growth rate of mixing layers drops significantly (Papamoschou and Roshko, 1988); (2) Reynolds stresses are decreased substantially (Elliott and Samimy, 1990); and (3) the structures in the mixing layer become less organized and more three-dimensional (Clements and Mungal 1995; Elliott et al & 1995). Similar observations on the lower growth rate and three-dimensionality of structures at higher convective Mach number have also been made using stability analysis (e.g. Ragab and Wu, 1989) and numerical simulations (e.g. Sandham and Reynolds, 1991). While the convective Mach number has been widely used to characterize compressibility, experiments performed predominantly on planar shear layers have indicated a significant deviation of the convective velocity from its theoretical value. This deviation has appeared as either a fast or a slow mode and has led to the stream selection rule that states that for a supersonic/subsonic stream combination, the convective velocity will err closer to the high-speed stream while for a supersonic/supersonic combination the velocity will err to the lower speed stream (Murakami and Papamoschou, 2000). The majority of work on compressibility effects that were cited above has been based on observations and measurements in planar mixing layers. The results presented here are on compressibility effects in axisymmetric jets, which are studied using real-time imaging system discussed above. One would expect to see some similarities and some difference between the results in planar and axisymmetric cases, as the axisymmetric case possesses additional instability modes. In addition to visual observations, spatial correlations of planar images are used to objectively track spatial features of the flow through the sequence of images and to obtain convective velocity of structures within axisymmetric jets. Figure 4 is a sequence of 16 images, each separated by 10 µs, of the Mach 1.3 (M c =0.59) jet, covering 4.25 to jet diameters downstream of the nozzle exit. Flow is from left to right, and the bright regions correspond to areas where moisture in the ambient air that is entrained into the mixing layer has condensed. Thus, only the mixing layer, in fact a major portion of the mixing layer, is being visualized. It is more informative to observe the development and interaction of structures within the mixing layer in movie format (Movie # 1 in the List of Movies). As seen in this image set (particularly in the upper half of the mixing layer in the 9 th to 12 th images), one observes only occasional appearance of structures that resemble the familiar core and braid regions associated with structures in incompressible shear layers. Furthermore, the superposition of many smaller scales is evident by the jagged edges at the high- and low-speed boundaries of the mixing layer. Figure 4 depicts an event that typifies the dynamics of structures in this compressible mixing layer. In the second frame, three structures are identified, labeled as A, B and C. These eddies are not typical roller type structures seen in incompressible flows, but are distinguishable. By the 6 th frame, structures A and B are slightly tilted and stretched in the direction of the shear. Structure C, meanwhile, appears roughly the same as it did in frame 2, possibly tilting and stretching slightly. By the 10 th frame, structure B is dramatically tilted and stretched from its original shape and now overlaps A on the low-speed side of the mixing layer and C on the high-speed side. By the 14 th frame, no evidence of structure B exists as it has been torn apart by the pairing interaction with A and C. Two identifiable structures remain that are labeled A+B and B+C to indicate their origin. The developments and interactions characterized in this sequence of images shown in Figure 4 can be generalized as being composed of the basic processes of tilting, stretching, tearing, and pairing. These processes demonstrated in Figure 4 are very common and take place throughout the mixing layer on a wide variety of scales and occurrence. Obviously, one cannot explore these kinds of processes if a double-pulse laser or two lasers are utilized to obtain two images, as has been done in the past. 7

8 t = 0 µsec t = 10 µsec t = 20 µsec t = 30 µsec 4.3 x/d 10.6 x/d A B C t = 40 µsec t = 50 µsec t = 60 µsec t = 70 µsec t = 80 µsec t = 90 µsec t = 100 µsec t = 110 µsec t = 120 µsec t = 130 µsec t = 140 µsec t = 150 µsec A+B B+C Figure 4: A Sequence of Images with 10 µs Separation of Mach 1.3 Jet Figure 5 is a typical example of a sequence of cross-stream images located at 6 jet diameters downstream of the nozzle exit for the same Mach 1.3 jet. The images are separated by 4 µs and are approximately 5 cm in width and height. Since the developments on the cross-stream planes are much faster, the timing between pulses has been reduced from 10 to 4 µs. The three-dimensional nature of large-scale structures is quite obvious not only from observation of the development of the structures but also from observation of the development of the jet core (the dark region in the middle). The average end of the potential/jet core is located 6 jet diameter downstream of the nozzle exit, which is the location of the image plane in Fig. 5 (Hileman and Samimy, 2001). Note that the average end of the potential core obtained using these images would be downstream of the actual location, as a major portion but not the entire mixing layer is visualized due to the nature of the condensation processes in the mixing layer and the imaging technique. A key feature of the flow is the presence of streamwise vortices. This can be seen at a number of azimuthal locations in Fig. 5. In particular, the development of a counter-rotating streamwise vortex pair in the lower left corner of the images (the circled region) has been captured. This vortex pair has developed into a mushroom like structure by image # 8 in the sequence. Figure 6 shows a sequence of 16 images separated by 8 µs each, which are typical for the Mach 2.0 (M c =0.87) jet. Movie # 2 (see the List of Movies) shows the sequence in movie format. In comparison with the M c =0.59 case shown in Figure 4, structures are much less organized and evolve much more rapidly, which makes it difficult to identify them beyond a couple of frames, even though the timing between images has been reduced from 10 µs in Mach 1.3 case to 8 µs for this case. The tilting, stretching, tearing, and pairing processes depicted in Figure 4 still occur, but are more difficult to follow as the structures undergoing the processes are not as easy to identify and the events appear to happen more rapidly. As in the Mach 1.3 case, cross-stream image sequences indicate the presence of streamwise vortices. As in the M c =0.59 case, these observations agree relatively well with observations made on planar shear layers. 8

9 t=0 µsec t=4 µsec t=8 µsec t=12 µsec t=16 µsec t=20 µsec t=24 µsec t=28 µsec t=32 µsec t=36 µsec t=40 µsec t=44 µsec t=48 µsec t=52 µsec t=56 µsec t=60 µsec Figure 5: A Sequence of Streamwise Images Separated by 4 µs at 6D Downstream of the Nozzle Exit t = 0 µsec t = 10 µsec t = 20 µsec t = 30 µsec 5.5 x/d 11.8 x/d t = 40 µsec t = 50 µsec t = 60 µsec t = 70 µsec t = 80 µsec t = 90 µsec t = 100 µsec t = 110 µsec t = 120 µsec t = 130 µsec t = 140 µsec t = 150 µsec Figure 6: A Sequence of Images with 10 µs Separation of Mach 2 Jet 9

10 Spatial correlations were calculated using each sequence of images. For each sequence of images, there are 16 images and thus 16 spatial correlation contour plots can be determined; each of these plots has a peak correlation location that can be identified and taken as the location of the average moving structure. As opposed to showing all 16 two-dimensional contour plots, however, it is more convenient to only show the peak correlation level as it varies in the streamwise direction (one dimension). Figure 7(a) is a graph of the correlation level for selected time separations in the Mach 1.3 jet. This data was obtained by averaging the two-dimensional spatial cross correlation from an ensemble of about 250 individual movies/image sets. This graph is similar to some degree to a space-time correlation plot using two probes, where temporal correlations are plotted for various probe separations ( x). In Figure 7(a), spatial correlations are plotted for various time separations between laser pulses ( t). As expected, the maximum correlation for t = 0 µs is 1.0 at zero spatial separation and drops off with increasing streamwise separation distance. For a time separation of 10 µs, the peak is at a separation of approximately 5 pixels with a correlation level of about For increasing time separations, the peak correlation level drops and broadens. At t = 120 µs, the maximum correlation is about 0.35 and the peak is quite broad. If one were to plot the separation distance of this peak on an x-t diagram, the slope of the line fit through these points would be the average convective velocity for the Mach 1.3 jet. This plot is shown in Figure 7(b). The average convective velocity is determined to be 270 m/s, which is well above the theoretical prediction of 206 m/s Displacement (meters) t = 0 µ sec t = 10 µ sec t = 20 µ sec t = 40 µ sec t = 80 µ sec Streamwise Position (pixels) dx/dt = 270 m /sec (a) t = 120 µ sec (b) 000E6 40E-6 80E-6 120E-6 Tim e (sec) Displacement (meters) t = 0 µ sec t = 16 µ sec t = 32 µ sec Slow Mode Fast Mode t = 64 µ sec Streamwise Position (pixels) dx/dt = 422 m /sec (c) t = 112 (d) dx/dt = 185 m /sec 000E6 40E-6 80E-6 120E-6 Tim e (sec) Figure 7: Variations of Average Correlation Level with Streamwise Separation Distance for Different Separation Time Between Flow Images, and Convective Velocity for Mach 1.3 and Mach 2 Jets. Figure 7(c) is a plot of the streamwise correlation level versus distance for various time separations for the Mach 2.0 jet, obtained from a set of 100 individual movies/image sets. A similar trend to the Mach 1.3 case is initially observed as the maximum correlation decreases and the peak becomes increasingly broader. For a time separation of 64 µs, however, a very interesting event happens. The broad peak has developed into two distinct peaks. By individually charting the location of both peaks, two convective velocities were calculated, a fast mode and a slow mode. This is shown in Figure 7(d). The points marking the fast mode do not appear until a time separation of 64 µs. The average velocity of the fast mode is 422 m/s while the slow mode is 185 m/s. The theoretical value for the convective velocity is calculated as 303 m/s, which is approximately halfway between the fast mode and the slow 10

11 mode. This is the first time that dual-mode convective velocity has been reported in an experimental work, and for the first time in an experimental or computational or theoretical work for a subsonic convective Mach number. This will be further discussed later. It is informative to further explore convective Mach number results for both cases by examining the histograms of the computed convective velocities from individual movies/ image sets (Figure 8); ~250 movies for the Mach 1.3 jet (Figure 8(a)) and ~100 movies for the Mach 2.0 jet (Figure 8(b)). As shown in Figure 8, the single peak of the histogram for the Mach 1.3 jet is centered around 275 m/s, which is close to the ensemble average velocity measurement given earlier, but the histogram for the Mach 2 jet is bimodal, with the two peaks centered around 200 m/s and 400 m/s. Approximately 2/3 of the measured convective velocities are of slow mode for the Mach 2.0 jet U c,theory =206 m/sec (a) U c,theory = 303 m/sec (b) Velocity (m/sec) Velocity (m/sec) Figure 8: Histograms of Convective Velocity for (a) Mach 1.3 and (b) Mach 2 Jets. These measurements add to the very limited experimental data that has been conducted to determine the convective velocity in supersonic axisymmetric jets. Fourgette et al (1991) used the same seeding technique used here and two single-pulse lasers to measure the convective velocity of a Mach 1.5 (M c =0.7) axisymmetric jet. Only 36 measurements were made and the reported average velocity was 350 m/s, which is greater than the theoretical velocity of 230 m/s. Murakami and Papamoschou (2000) utilized a two-laser set-up and laser induced fluorescence imaging of acetone seeded into a Mach 1.5 jet with co-flow to measure the convective velocity. Using air and helium mixtures, they were able to simulate a variety of convective Mach numbers between 0.43 and For each case, only a limited number of measurements were made. In all cases a fast mode was detected with the exception of the lower compressibility cases, which matched the theoretical value quite well. It should be noted that the presence of fast and slow modes has also been observed in three-dimensional linear stability analyses of compressible shear layers, but only for supersonic convective Mach numbers. For example, Jackson and Grosch (1989) and Day et al. (1998) show that for convective Mach numbers greater than 1, outer modes of instability waves (fast and slow modes) develop that become more amplified with increasing compressibility level. These modes are in addition to the central mode, which dominates at convective Mach numbers below 1. It is obvious that more experimental work is needed to further explore these issues. 3.1 Far-field Radiated Acoustic Sources In order to explore correlations between large amplitude far field noise radiated from the jet and large coherent structures within the jet, first the far field sound pressure peaks that were in excess of 1.5σ (σ is the standard deviation of far field sound pressure signal) were identified. To find out whether the acoustic wave associated with these peaks have any distinguishable waveform, these peaks then were phase-aligned and averaged. This was accomplished by taking one ms of data before and after every peak exceeding 1.5σ, phase aligning the peaks, and then ensemble averaging these acoustic signal segments. The result of this exercise for the positive peaks is shown in 11

12 Figure 9. A similar result was obtained for the negative peaks (Hileman et al., 2001b). The shape of the waveforms is quite remarkable because it has a sharp, distinct peak with two side lobes - a Mexican hat wavelet. Except for minor differences in the side lobes, the positive and negative waveforms are nearly mirror images of each other with respect to the abscissa. If the central part of the average waveform (-0.5 to 0.5 ms) in Figure 9 is transformed to the frequency space using Fourier transform, it shows a broad peak between 1 and 4 khz, which perfectly matches the range obtained from standard statistical analysis of the far field acoustic signal. The amplitude of the spectrum depends on the selected threshold level and the time length of the waveform used. Although what we are doing is unorthodox, the match of the peak in the waveform spectrum with the peak of the overall acoustic spectrum establishes that these peaks are from the large-scale turbulence structures in the jet. Our most recent work indicates that one can change the far field acoustic waveform, and thus its frequency content, by using, for example, vortex-generating tabs (Hileman and Samimy 2002). This finding is important in that it provides an avenue for determining what effect potential noise reduction devices have on the jet s radiated acoustic waveform. Through examination of the effect of devices on the acoustic waveform, a shift in the frequency content of the radiated noise might be obtained that could potentially reduce the perceived noise of the jet. Figure 9: Phase-averaged (peaks above 1.5 standard deviations lined up) positive large amplitude far field sound pressure waveform for the Mach 1.3 jet. The amplitude is normalized by the standard deviation of the acoustic data. Now a set of flow visualization images that were taken simultaneously with inline microphone array measurements will be presented and discussed. Figure 10 shows a sequence of 16 images with the consecutive images separated by 10 µs. This is the same Mach 1.3 jet that was discussed earlier. The flow is from left to right, and the tic marks at the bottom of the image are in jet diameters from the jet exit. The figure above the flow images is a far field sound pressure time trace from one of the microphones, which has a large rarefaction sound pressure (negative pressure peak) that is marked with a small circle. The flow visualization images in Fig. 10 show significant interaction between the two sides of the jet s mixing layer (Movie # 3 in the List of Movies). The interaction is between 7 and 9D within image 7. The origin of the marked peak was estimated as 7.9D (this is marked by a solid square on the top edge of image, rather than on the jet centerline so not to clutter the image, in all the images of Fig. 10), and it was created about 70 µs after the first image of the movie, which is 80 µs before the last image was taken. Taken a convection velocity of 270 m/s, which was measured experimentally and discussed earlier, a large structure at 7.3D in the first frame would be at 7.9D during noise emission. This same structure would be located at 9.0D in the last image (assuming a constant convection velocity). The location of such a hypothetical convecting structure has been marked in the images by an open square. Again this is marked toward the upper edge of each image rather than on the jet centerline so not to clutter the image. The sound wave was created when the two squares line up. The two sides of the mixing layer are experiencing significant interaction by the time the two squares are aligned and further the jet appears to be undulating as well in the interaction region. Thus, it appears that the intense interaction was responsible for the peak sound generation. 12

13 Figure 10: The top graph shows a short segment of the time trace from the far acoustic field of the Mach 1.3 jet, with a peak identified with o. The 16 real-time images of the jet are taken simultaneously with the far field noise measurement and are separated by 10 µs. The image set shows significant interaction between the two sides of the jet s mixing layer that is responsible for the marked peak in the time signature above the images. The strong interaction of the two sides of the mixing layer was determined to be the mechanism of sound generation in a large number of other data sets. In addition to cross mixing layer interaction, both large structure roll-up and sudden disintegration/tearing of a large structure have been observed to generate strong far field noise radiation. More details on this work can be found in Hileman and Samimy (2001) and Hileman et al. (2001a&b; 2002). 13

14 The inline microphone array that was used earlier for noise source localization assumed a jet centerline noise source distribution, and was sensitive to refraction errors (Hileman and Samimy, 2001, Hileman et al., 2001a, b). Based on these and other issues, a three-dimensional array that can locate the origin of individual sound waves in space has been designed, built, and tested (Hileman et al., 2002). Also, we have been working on Hartmann tube based fluidic actuators (Kastner and Samimy, 2002) and very recently on plasma actuators to force these jets. As part of the ongoing research effort in this area, these jets will be forced in order to further explore the nature of jet noise sources and means to alter them to eventually achieve jet noise reduction. 4. Concluding Remarks There is currently a comprehensive research program on compressible jets in the Gas Dynamics and Turbulence Laboratory. The program includes: (1) development of advance laser based flow diagnostics; (2) development of high bandwidth and high amplitude actuators for flow control; (3) development of low dimensional models for high-speed flows; and (4) development and design of controllers that can use the actuators and low dimensional models for closed-loop flow control. The progress made in the development of a MHz rate imaging system and its application to explore compressibility effects and far field noise sources in supersonic ideally expanded axisymmetric jets were presented and discussed. The MHz rate imaging system has been successfully used for qualitative flow visualizations. Problems associated with its applications for quantitative flow visualizations and steps taken to alleviate them were also discussed. Two ideally expanded axisymmetric jets with convective Mach numbers of 0.59 and 0.85 were examined. The first case is mildly compressible, as compressibility effects start around a convective Mach number of 0.5. The results for the lower compressibility case show the occasional presence of incompressible jets like rollers structures with well-defined braid and core regions. They also show that the development of structures is composed of the basic processes of tilting, stretching, tearing, and pairing, which can easily be followed. The measured convective velocity for this case has a single-mode distribution, but the average convective velocity is significantly higher than the theoretical value. Large-scale structures in the higher compressibility case are much less coherent, and very difficult to track. The measured convective velocity for this case exhibits a dual-mode distribution with fast and slow modes that are almost equally spaced on both sides of the theoretical velocity. Approximately 2/3 of the measured convective velocities are of slow mode. Some results and discussions were also presented on the application of the MHz rate imaging system to understand far field jet noise sources. The roll-up of structures, as well as strong interaction of structures across the jet core and sudden disintegration/tearing of large structures, has been observed to generate strong far field noise radiation Acknowledgements The authors would like to acknowledge support from the National Science Foundation (Major Research Instrumentation and Fluid Dynamics programs), the Air Force Office of Scientific Research (Unsteady Aerodynamics and Hypersonic program), and the State of Ohio Hayes Investment Fund. A National Defense Science and Engineering Graduate fellowship (for B. Thurow) and an Ohio Space Grant Consortium fellowship (for J. Hileman) are also acknowledged. List of Movies Movie 1: Visualization of Mach 1.3 jet in streamwise direction (Figure 4) (253 kb) Movie 2: Visualization of Mach 2 jet in streamwise direction (Figure 6) (348 kb) Movie 3: Visualization of a significant interaction between the two sides of the jet s mixing layer as a source of far field noise in a Mach 1.3 jet (Figure 10) (2793 kb) References Adrian, R. J., 1983, Laser Velocimetry, in Fluid Mechanics Measurements, edited by R. J. Goldstein, Hemisphere Publishing Corporation. Adrian R. J., 1991, ``Particle-imaging techniques for experimental fluid mechanics,'' Ann. Rev. Fluid Mech., Vol. 23, 261. Arnette, S.A., Samimy, M., and Elliott, G.S., 1998, Two-Component Planar Doppler Velocimetry in the Compressible Turbulent Boundary Layer, Experiments in Fluids, Vol. 24,