Development of Doppler global velocimetry for the measurement of ...

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Development of Doppler global velocimetry for the measurement of eddy convective velocities Tobias Ecker1,*, K. Todd Lowe2, Wing F. Ng3 1: Institute for Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen, Germany 2: Department of Aerospace and Ocean Engineering, Virginia Tech, VA, USA 3: Department of Mechanical Engineering, Virginia Tech, VA, USA * Correspondent author: [email protected] Keywords: DGV, instrumentation development, supersonic jet

ABSTRACT A new Doppler global velocimeter (DGV) for high-speed flow applications was developed for the measurement of eddy convective velocities in supersonic jet flows for aeroacoustic studies. The key technologies for this instrument are spatially resolving, high sensitivity photomultipliers, field programmable gate array (FPGA)-based signal processors and a continuous wave laser, which can be frequency tuned. The instrument presented in this study is based upon the classic DGV technique but with technology enhancements that allow instantaneous and long time span velocimetry at a 250 kHz sampling rate. The instrument has been matured to deliver a robust performance even with low signal-to-noise ratios, as may be encountered in high-speed flows and large-scale facilities. Measurements in both a small scale supersonic jet facility as well as a large-scale multi-stream nozzle at NASA Glenn are presented to demonstrate the instrument capabilities in delivering robust measurement of convective velocities within high-speed turbulent shear flows.

1. Introduction Doppler global velocimetry is a technique based on the selective absorption characteristics of molecular gases that is capable of direct measurement of the Doppler effect. DGV relies on the detection of the Doppler shift of laser light scattered off tracer particles within the local flow. Its capability to detect multiple particles within the measurement volume, while its temporal resolution and scale up is only limited by particle response and signal to noise ratio, make it a suitable instrument for time-resolved measurements of high speed flows. The measurement of convective velocities, the speed at which eddies within the turbulent flow convect, has been of particular interest due to its significance in the interpretation and the development of aero-acoustic analogies (Lighthill, 1952). While hotwire anemometry, due to its frequency response, can still be considered a standard for experiments in many experimental studies on turbulent flow, its use in heated, supersonic shear layers has become obsolete with the advent of optical and non-intrusive measurement techniques. The use of laser based instruments like laser Doppler velocimetry (LDV), particle image velocimetry (PIV) and Doppler global velocimetry DGV or other optical instruments (Kuo et al., 2011) avoid many of the issues


intrusive instrumentation in supersonic flows have. LDV has been used for doing two-point correlations, which is the basis for the determination of the convective wavespeed, in hot and cold high-speed jets in early studies by Lau et al. (1980), and most recently by Kerhervé et al. (2004a, 2004b) in a cold supersonic jet. As LDV is a single point instrument, two LDVs had to be operated simultaneously at varying separation distances within the flow. PIV, being a planar technique, allows the correlation of the voxels with one another, reducing the complexity in the measurement and determination of correlation functions and convective wavespeeds. Wernet (2007) has successfully demonstrated the of use temporally resolved PIV for space-correlations in cold and hot jet flows within a large scale facility, usually operating at 25-50 kHz. Like LDV, DGV is a velocimetry technique based on the direct measurement of the Doppler effect. The technique was first invented by Komine (1990) and subsequently refined by Komine et al. (1991) and Meyers and Komine (1991). Detailed uncertainty analyses and flow studies have been carried out by Meyers et al. (2001) in the early 1990s at NASA Langley, mainly for the measurement of mean flow components. Smith (1998) and Clancy et al. (1999) first showed the application of DGV to obtain instantaneous velocity vectors in several continuous frames in a supersonic flow. However while these measurements were instantaneous, they were not continuous and did not allow the capture of time-resolved flow features. The first to demonstrate the application of a high repetition rate DGV system in a high-speed facility was Thurow et al. (2005). His implementation used a high-speed camera (128 x 64 pixels) to obtain one-component time-resolved velocity data as well as convective velocities in a rectangular Mach 2.0 jet. Based upon this previous work Ecker et al. (2014) introduced a point Dopper velocimeter (Cavone, 2006) operated in a cold supersonic jet at 100 kHz effective data rates and a reduced number of sensors using a time-multiplexed technique. This work has been matured to include a novel sensor system based on a 64 channel Photomultiplier (PMT), enabling spatially and temporally resolved measurements in high-speed flows. The instrument has since been applied to the measurement of convective velocities within heated small (Ecker et al. 2015b,c,d) and large scale facilities (Ecker et al., 2016a,b) and is described in detail in this paper. In this paper, we present the details of a novel 64-simultaneous-point, 250 kHz repetition rate Doppler global velocimeter. The attributes of this development are particularly well suited for measurements of turbulent eddy convective velocity in high speed flows. Given the aeroacoustics interest in convective velocity due to the impact this parameter has on radiation efficiency, the applications are those of relevance to jet noise for high speed propulsion. An analysis of the operating principles and measurement uncertainties of this technique for convective velocities is provided. Results are presented for convective velocity measured in supersonic heated jets and in three-stream subsonic jets near Mach 1. These results reveal the


value of the method for obtaining quantitative turbulence structure information of developing shear layers of relevance to the jet noise community. 2. Doppler global velocimetry For the classic implementation of DGV (as first proposed by Komine (1990)), the frequency of a single-longitudinal-mode laser is set so that the Doppler shifted frequency lies optimally in the absorption spectrum of a molecular gas filter. A reference light path is used to normalize the intensity of the filtered scattering by the intensity of the local scattering based on particle density and laser light amplitude. The Doppler shift of the scattered light depends upon the laser frequency, vector particle velocity, and laser propagation and observation directions (see Fig. 1) and is related by the Doppler equation (Ecker et al., 2014) as: 𝑓𝐷 = 𝑓0

⃗ ∙𝑒 𝑈 𝑐

(1)

Fig. 1 Vector definitions of the DGV principle. The Doppler shifted frequency is obtained by applying the intensity-frequency transfer function of the molecular as filter to the intensity based sensor signals. An experimental scan compared to a model fit by Forkey et al. (1997) is shown in Fig. 2 (Ecker et al., 2014).

Fig. 2 Experimental Iodine cell transmission scan (black) compared to numerical model fit (red).


3. Instrumentation The presented instrument uses Doppler shift measured from a pair of co-planar laser sheets at 45 deg to the streamwise axis, which are time multiplexed to achieve three-velocity component operation. Two receiver systems using novel 64 channel PMT cameras in a Doppler sensitive and reference layout to record the light scattered from the particles in the measurement volume. Recent studies have successfully shown the scale up of the instrument for the use in mid and large-scale jet geometries.

(a) unit vectors sensitivity vectors observation vectors laser direction vectors

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -0.5

0 0.5 1

1

0.5

0

-0.5

-1

(b) Fig. 3 TR-DGV basic operating principle (a), sensitivity vectors within the facility coordinate system for TR-DGV instrument (b). Image courtesy Ecker et al. (2015b). To time multiplex the arrangement, acousto-optical modulators (AOMs) are used to chop the incident laser beam into 4 μs, or shorter, pulses. The pulsed laser light is routed via free space optics to laser sheet generating optics. The laser optics are arranged in a 45-degree configuration to the jet centerline and create the measurement. Light receiver units are placed on both sides of the flow, perpendicular to the measurement plane. In each receiver unit, the light collected by a camera lens is first split into two paths—a signal path passing through a starved iodine cell and


a reference path with no cell. The basic sensor configuration and laser sheet timing is shown in Fig. 3 (a) and the four measurement vectors for this instrument are shown within the facility coordinate system in Fig. 3 (b). For a receiver system with a measurement plane parallel to the stream-wise axis the maximal sheet width is dictated by the 45 deg angle position (for a square sensor), which was also found as the angle with the lowest overall uncertainty by Ecker et al. (2014) for this type of sensor geometry. This configuration could be extended to volumetric operation by using a moving light sheet and a lens configuration with sufficient depth of field. Using three of the four measurement velocity vectors the three component velocity vector within the facility coordinate system can be extracted by using a transformation matrix: 𝑒1

𝑇 −1 𝑇

⃗ = [𝑒2 ] 𝑈 𝑒3

𝑇

𝑢1 𝑅11 (𝑢2 ) = [𝑅21 𝑢3 𝑅31

𝑅12 𝑅22 𝑅32

𝑅13 𝑢1 𝑅23 ] (𝑢2 ) 𝑅33 𝑢3

(2)

The main sources of uncertainty of DGV are attributed to the characterization of the molecular gas cell, laser line stability and signal to noise ratio of the sensor. Progresses in the development of advanced DGV techniques, which address these issues, have been made since and lead to new derivate DGV technologies (Fischer et al. 2007, 2008, Charret et al. 2004, Cadel et al. 2015). The uncertainty of the velocity components along the sensitivity vectors is found to be a combination of systematic and random uncertainties, and can be expressed as: 𝑐

2

𝑑𝑓

2

𝑑𝑓

𝑓2

2

𝑑𝑓

𝛿𝑢𝑖 = 𝑓 √(𝑑𝑇) (𝛿𝑇𝑖 )2 + 𝑇𝑖2 [𝛿 (𝑑𝑇) ] + 𝑓𝑖2 {(𝑑𝑇) 0

𝑖

𝑖

0

0

2

𝑑𝑓

(𝛿𝑇0 )2 + 𝑇02 [𝛿 ( ) ] } 𝑑𝑇 0

(3)

Applying the transformation matrix to this analysis allows obtaining uncertainties within the facility coordinate system as: 𝛿𝑢𝑥 𝑅11 ⃗ √ 𝛿𝑢 𝑅 ∆𝑈 = ( 𝑦 ) = ([ 21 𝑅31 𝛿𝑢𝑧

𝑅12 𝑅22 𝑅32

𝛿𝑅11 𝑅13 2 𝛿𝑢1 2 𝑅23 ]) (𝛿𝑢2 ) + ([𝛿𝑅21 𝑅33 𝛿𝑢3 𝛿𝑅31

𝛿𝑅12 𝛿𝑅22 𝛿𝑅32

𝛿𝑅13 2 𝑢1 2 𝛿𝑅23 ]) (𝑢2 ) 𝑢3 𝛿𝑅33

(4)

For the instrument used in this study, two receiver systems using 64 channel PMT cameras are used to record the light scattered from particles in the measurement volume. Recent studies have successfully shown the scale up of the instrument for the use in mid and large-scale jet geometries. The system consist of three essential subsystems: 1. Laser system, which enables conditioning of the Laser beam 2. Camera system, which receives the Doppler shifted light 3. DAQ system, which records the data and interfaces all subsystems


Fig. 4 DGV system electric and optical signal overview (Ecker et al., 2016b). The signal flow and functional integration of the Laser multiplexing system (1), as well as of the two camera systems (2) and the data acquisition system (3) for the DGV instrument are shown in Fig. 4. The laser system is based on a Verdi V18 single frequency diode pumped


continuous wave laser which is time multiplexed using two IntraAction Corp. 80 MHz AOMs. This laser has a line width of approximately 5 MHz over 20 ms (Coherent Inc white paper). The time multiplexing of the laser sheets is controlled via a BNC 565 delay generator, which is triggered by a digital output from the DAQ system. Continuous triggering from the FPGA Adapter module, which is also used for recording of the PMT data, ensures a maximum of synchrony between laser multiplexing and data recording. The 1 MHz trigger signal is recorded by the multipurpose DAQ card as a reference. A reference beam is extracted from the multiplexing system via a beamsplitter and used to record the light intensity from two Thorlabs PDA100A photodiodes which are setup around a reference Iodine (ISSI Inc.) cell in a similar configuration as described for the DGV camera system. The scattered light is sensed by two photomultiplier (PMT) array detectors, one for each the signal and reference paths. A 2 in beamsplitter cube is used to divide the received between light paths. The PMT array detectors and the high bandwidth data acquisition system used to measure the PMT anode signals form a unique system for very high repetition rate, low light measurements. The PMT array detectors are Hamamatsu H8500C PMT modules, each with 64 anodes. Custom 16-channel, high-speed amplifier boards from Ectronic GmbH amplify the anode signals and transmit them to the adapter module of the data acquisition system. On each module, 32 anodes were used and the flow was imaged such that the points were distributed in a rectangular grid that was 30.32 mm in the stream-wise direction and 61.22 mm in the radial direction.

Fig. 5 CAD of TR-DGV instrument configured for small-scale supersonic hot jet. Image courtesy Ecker et al. (2015b).


Depending on the application and required laser output, the optical routing of the laser beams can be done via fiber optics or mirror configurations. Fig. 5 portraits the basic instrument geometry for the use in a small-scale facility using 8 μm telecommunication grade fiber optics. Pictures of the scaled up system using a mirror configuration are shown in the applications section. 4. Data processing for convective velocities The multi-point PMT (effective area 24.12 x 48.7 mm2, configuration is displayed in Fig. 6) (Ecker 2015a) allows space/time cross-correlation processing of the experimental data over all 32 sensor pixels. The time-resolved data s(x,r,t) acquired on each sensor pixel were processed and correlated to reference locations throughout the shear layer. The second-order cross-correlation (Morris and Zaman, 2010) is defined as 1

𝑇/2

𝑅𝑖𝑗 (𝑥, 𝑟, 𝜍, 𝜉, 𝜏) = ∫−𝑇/2 𝑠𝑖 (𝑥, 𝑟, 𝑡)𝑠𝑗 (𝑥 + 𝜍, 𝑟 + 𝜉, 𝑡 + 𝜏)𝑑𝑡 = ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 𝑠𝑖 (𝑥, 𝑟, 𝑡)𝑠𝑗 (𝑥 + 𝜍, 𝑟 + 𝜉, 𝑡 + 𝜏) 𝑇

(5)

where 𝜍 and 𝜉 are the spatial separation and 𝜏 the delay timescale from the reference location. As used in equation (2), further uses of the ( ) notation indicate time averaging. The correlation function exhibits maxima along the convective ridge. These points lie on the locus of 𝜍𝑟 = 𝑢𝑐 𝜏𝑟 , and the correlation function along this locus, 𝑅(𝜏𝑟 ) = 𝑅(𝜍𝑟 = 𝑢𝑐 𝜏𝑟 )

(6)

characterizes the decay of the spatio/temporal extent of integral scale eddy correlation. The space/time correlations maps measured allow the determination of equation (7) from which the integral convective velocity (Fisher and Davies, 1964) can be determined, given the known stream-wise measurement position spacing, 𝑢𝑐 = 𝜍𝑟 ⁄𝜏𝑟 = 𝑘Δ𝑥/𝜏𝑟

(7)

Fig 6. PMT sensor configuration (left), example space/time correlation across the sensor (right).


Processing for frequency dependent convective velocities as well as intermittency has been demonstrated by Ecker et al. (2015c,d) in previous studies. The uncertainty within the measurement of the convective wavespeed behaves much differently than the uncertainty within the instantaneous velocity component. The uncertainty within the determination of the convective wavespeed from the correlation function Rij is primarily dependent on the time accuracy of the data acquisition and the sensor spacing. Propagation of error analysis yields the following uncertainty for the convective velocity: 1 2

Δ𝑥 2

𝛿Δ𝑥 2

𝛿𝜏 2

𝛿𝑢𝑐 = ±√(𝜏 ) (𝛿Δ𝑥)2 + ( 𝜏2 ) (𝛿𝜏)2 = ±𝑢𝑐 √( Δ𝑥 ) + ( 𝜏2 )

(8)

Ecker et al. (2015b) analyzed the uncertainty within the processing algorithms used to obtain the lag time. By applying a Monte-Carlo simulation using synthetic flow data they found that noise has a very low impact on the lag time estimation. For a case with mean flow and turbulence properties representative to supersonic shear layers, they found the error within the lag time estimate to approach values of about 4% at signal to noise ratios (SNR log) above 0. As can be seen from equation 8, the normalized uncertainty for convective velocity is a combination of the relative uncertainties of the sensor spacing and lag time estimate. As long as the relative uncertainties can be held constant, scale up of the instrument for the use in larger scale facilities does not lead to increased uncertainties. 5. Applications The TR-DGV instrument has to date been used for the measurement of the eddy convective velocity in two facilities, the Virginia Tech hot supersonic jet facility (Ecker et al. 2015b) and the High Flow Jet Exit Rig (HFJER) at the NASA Aeroacoustic Propulsion lab (AAPL). An overview of the very different optical instrument parameters is shown in table 1, demonstrating the scalability of the TR-DGV technique. Table 1. Instrumentation parameters for two facilities used.

Lens focal length

Small scale jet facility

NASA AAPL

85 mm

200 mm

𝛥𝑡 (Laser)

4 𝜇𝑠

Measurement area (PMT coverage)

12 x 24 mm2

30.32 x 61.22 mm2

𝛥𝑥 (horizontal)

3 mm

7.58 mm

As shown by Ecker et al. (2014), the instantaneous measurement uncertainty can be estimated for this configuration as ±9.2 m/s for the streamwise velocity component from equation (3) and (4),


similarly the mean bias uncertainty is ±1.5 m/s for all components. The uncertainties, as well as the condition number for the transformation matrix and the minimally required Iodine line frequency width are summarized in table 2. Table 2. Uncertainties and Doppler frequency range. Uncertainty (inst.)

9.2 / 6.5 / 6.2 m/s

Uncertainty (mean)

1.5 / 1.5 / 1.5 m/s

Uncertainty [𝛿𝑢𝑐 /𝑢𝑐 ]

0.065

Uncertainty [𝛿𝛥𝑥 /𝛥𝑥 ]

0.05

Uncertainty [𝛿𝜏 /𝜏 ]

0.04

Max Condition number

4.2

Range (Doppler freq)

0.12 GHz

The properties of the Iodine cells of the DGV instrument were optimized for their respective use. The reference cell, which is located on the optical table and used to obtain the reference frequency, was operated at 65 °C. At this temperature and the relatively low filling pressure, this cell is ideally suited to track the initial Laser frequency due to its gentle transmission slopes. The measurement cells, which are located in both DGV camera units inhibit a much higher sensitivity to frequency change and therefore to the velocity fluctuations within the flow. The properties of the Iodine cells used are summarized in table 3. Table 3. Iodine cell properties. reference cell

measurement cell (O1/O2)

Pressure

0.1 Torr

1.0 / 1.2 Torr

Body temperature

65 °C

35 / 35 °C

Small-scale supersonic hot jet facility at Virginia Tech The TR-DGV setup for this particular experiment is displayed in Fig. 5 and Fig 7 (a). The distribution of the convective velocity and Mach number for several streamwise stations was measured by Ecker et al. (2015b) for two heated conditions (TTR = total temperature / ambient temperature = 1.6 and TTR = 2.0) in a small scale (d = 2 in) supersonic hot jet facility. The results of the colder (TTR = 1.6) condition are shown in Fig. 7 (b). The structure of the eddy convective velocity and Mach number profiles indicates several noteworthy aspects of the flow physics of heated supersonic jets. The convective speeds within the potential core at x/D = 4 and 6 for both TTR conditions are approximately uniform and equal to the jet exit velocity. In


comparison to the mean velocity distribution it was found that the convective velocity data exhibits a clear difference in spreading of the convective velocity profile. Between both TTR cases, a measurable reduction in the scaled eddy convective velocity is found for the hotter TTR case at the downstream stations, which is believed to be leading to a reduction in convective amplification and contributing to the reduced noise emissions. Specifically, the density ratio is believed to play a direct role in scaling due to dependency of the ‘symmetric’ convective Mach number (Papamoschou, 1997) on this quantity. More analysis and data can be found in Ecker et al. (2015b).

(a)

(b) Fig 7. Measurement of convective velocity in a small-scale supersonic hot jet (TTR=1.6) at several streamwise stations. Large-scale supersonic hot jet facility at NASA Glenn Research Center Multi-stream nozzles are currently under investigation for application in the future supersonic aircraft. In order to demonstrate the scalability of the TR-DGV instrument, measurements were performed at a three-stream nozzle with and without axial offset of the third stream.


For these large-scale measurements, both the laser itself and the reference Iodine cell are housed in an acoustically treated box in order to reduce the influence of noise and vibrations onto the laser stability. Similarly the box also serves to thermally insulate the system from outside temperature influences. Despite the insulation, the high frequency jet noise negatively impacted the Laser stability and lead to ambiguity in estimating both laser and Doppler-shifted flow frequencies. Notwithstanding the difficulties in computing the velocity statistics due to noise induced laser instabilities, the determination of the convective velocity was relatively unaffected by the same issues due to the inherent robustness of using the cross correlation function for lag time detection. Detector units

HFJER

Laser and laser monitoring

Laser sheets

(a)

(b)

(c) Fig 8. Measurement of convective velocity in a large-scale multi-stream nozzle at NASA Glenn. (a) Instrument placed the in facility (b) photo of the beam operation during measurement (c) convective velocity profiles of a jet issuing from three-stream axisymmetric nozzle at several streamwise stations.


As in previous work, the results for convective velocity differ in structure from the mean velocity field, which was obtained using PIV. The distribution of the convective velocity in the axisymmetric (non-offset) case and the instrument configuration is shown in Fig 8. A more detailed dissemination of the flow results can be found in Ecker et al. (2016a,b). 6. Summary A new instrument is presented which combines for the first time several unique features into a powerful system for measuring convective velocities with low statistical uncertainties. While the conventional operating methodology of DGV is preserved, newly available photonics and data acquisition technologies transform it into a system with unique capabilities, which is complementary to established instruments like PIV and LDV. Time-shift multiplexing is an approach to reduce the number of required sensor devices while still providing data rates suitable for high-speed applications and low mean uncertainties. The presented geometrical configuration in combination with time-shift multiplexing is of interest, because it can be easily extended to allow volumetric operation in the future. The presented data in both a small scale and large scale hot jet facility showed the presence of high momentum, high velocity large scale eddies downstream of the potential core. These regions of locally high convective Mach numbers are expected to have a leading role in supersonic jet noise due to high convective amplification factors causing higher noise intensity. The main challenges in the large-scale facility were predominantly related to laser line stability due to vibration caused by the jet noise. This study shows the benefits time-resolved DGV can provide for understanding dominant turbulent structures for noise generation in supersonic jets, and it provides the basis for the ongoing development of time resolved multi-point DGV instrumentation. The application of the instrument in both a small scale and large-scale facility with only minor modifications demonstrate the easy scalability and robustness for the measurement of convective velocities of the DGV technique. Acknowledgements This work was supported by the NASA’s Commercial Supersonic Technology Project in the Advanced Air Vehicles Program, and the Office of Naval Research through the Hot Jet Noise Reduction Basic Research Challenge and DURIP, grants N00014-11-1-0754 and N00014-12-10803. The authors gratefully acknowledge the support provided for acquisition of the data by Drs. Brenda Henderson and Mark Wernet of the NASA Glenn Research Center.


References Cadel DR, Lowe KT. (2015) Cross-correlation Doppler global velocimetry (CC-DGV). Opt Laser Eng 71:51-61. doi:10.1016/j.optlaseng.2015.03.012 Cavone AA, Meyers JF, Lee JW (2006) Development of point Doppler velocimetry for flow field investigations. In: Proceedings of the 13th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, 26–29 June. Coherent Inc. white paper, Wavelength control and locking with sub-MHz precision. http://www.coherent.com/download/6823/Wavelength-Control-and-Locking-with-Sub-MHzPrecision.pdf. Accessed 12 Aug 2014. Charrett TOH, Ford HD, Nobes DS, Tatam RP (2004) Two-frequency planar Doppler velocimetry (2v-PDV). Rev Sci Instrum 75:4487–4496. doi: 10.1063/1.1794451 Ecker T, Brooks DR, Lowe KT, Ng W (2014) Development and application of a point Doppler velocimeter featuring two-beam multiplexing for time-resolved measurements of high speed flow. Exp Fluids 55:1819 15pp. doi: 10.1007/s00348-014-1819-0 Ecker T, Lowe KT., Ng WF (2015a) A rapid response 64-channel photomultiplier tube camera for high-speed flow velocimetry. Meas Sci Technol 26(2):027001 6pp. Ecker T, Lowe KT, Ng WF (2015b) Eddy Convection in Developing Heated Supersonic Jets. AIAA J, 53(11):3305-3315. doi: 10.2514/1.J053946 Ecker T., Lowe KT, Ng WF (2015c) On the Distribution and Scaling of Convective Wavespeeds in the Shear Layers of Heated Supersonic Jet. In: Ninth International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9). Ecker T, Lowe KT, Ng WF (2015d) An experimental study of the role of core intermittency in equivalent jet noise sources. In: Ninth International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9). Ecker T, Lowe KT, Ng WF, Henderson BS, Leib SJ, (2016a) Velocity Statistics and Spectra in Three-Stream Jets. AIAA paper 2016-1633. In: Proceedings of the 54th AIAA Aerospace Sciences Meeting. doi: 10.2514/6.2016-1633 Ecker T, Lowe KT, Ng WF (2016b) Scale-up of the Time-Resolved Doppler Global Velocimetry Technique. AIAA paper 2016-0029. In: Proceedings of the 54th AIAA Aerospace Sciences Meeting. doi: 10.2514/6.2016-0029 Forkey JN, Lempert WR, Miles RB (1997) Corrected and calibrated I2 absorption model at frequency-doubled

Nd:YAG

laser

wavelengths.

Appl

Opt

36:6729-6738.

doi:

10.1364/AO.36.006729 Fisher MJ, Davies POAL (1964) Correlation measurements in a non-frozen pattern of turbulence. J Fluid Mech 18:97–116. doi: 10.1017/S0022112064000076


Fischer A, Büttner L, Czarske J, Eggert M, Grosche G, Müller H (2007) Investigation of time-resolved single detector Doppler global velocimetry using sinusoidal laser frequency modulation. Meas Sci Technol 18(8):2529–2545. doi: 10.1088/0957-0233/18/8/029 Fischer A, Büttner L, Czarske J, Eggert M, Müller H (2008) Measurement uncertainty and temporal resolution of Doppler global velocimetry using laser frequency modulation. Appl Opt 47(21):3941–3953. doi: 10.1364/AO.47.003941 Kerhervé F, Jordan P, Gervais Y, Valiere, JC (2004a) Two-point laser Doppler velocimetry measurements in a Mach 1.2 cold supersonic jet for statistical aeroacoustic source model. Exp Fluids 37(3):419–437. doi: 10.1007/s00348-004-0815-1 Kerhervé F, Power O, Fitzpatrick J, Jordan P (2004b) Determination of Turbulent Scales in Subsonic and Supersonic Jets from LDV Measurements. In: Proceedings of the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon. Komine, H (1990) US Patent No. 4,919,536. U.S. Patent and Trademark Office, Washington, DC. Kuo CW, Powers R, and McLaughlin DK (2011) Space-time correlation of flow and acoustic field measurements in supersonic helium-air mixture jets using optical deflectometry. In: Proceedings of the 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), Portland, Oregon. doi: 10.2514/6.2011-2789 Lau JC (1980) Laser velocimeter correlation measurements in subsonic and supersonic jets. J Sound Vib 70(1):85–101. doi:10.1016/0022-460X(80)90556-8 Lighthill MJ (1952) On Sound Generated Aerodynamically. I. General Theory. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 211(1107):564– 587. doi: 10.1098/rspa.1952.0060 Meyers JF, Komine H (1991) Doppler global velocimetry: a new way to look at velocity. Laser Anemometry 1:289–296. Meyers JF, Lee JW, Schwartz RJ (2001) Characterization of measurement error sources in Doppler global velocimetry. Meas Sci Technol 12:357–368. Morris PJ, Zaman, Khairul BMQ (2010) Velocity measurements in jets with application to noise source modeling. J Sound Vib 329(4): 394–414. doi:10.1016/j.jsv.2009.09.024 Papamoschou D (1997) Mach wave elimination in supersonic jets. AIAA J 35(10):16041611. doi: 10.2514/2.19 Smith MW (1998) Application of a planar Doppler velocimetry system to a high Reynolds number compressible jet. In: Presented at the 36th AIAA aerospace sciences meeting and exhibit, Reno, NV.


Thurow BS (2005) On the convective velocity of large-scale structures in compressible axisymmetric jets. PhD Thesis, The Ohio State University, Columbus, OH. Wernet MP (2007) Temporally resolved PIV for space–time correlations in both cold and hot jet flows. Meas Sci Technol 18(5):1387. doi: 10.1088/0957-0233/18/5/027