Spatiotemporally-Resolved Velocimetry for the Study of

Spatiotemporally-Resolved Velocimetry for the Study ofLarge-Scale Turbulence in Supersonic Jets

Ashley J. Saltzman

Dissertation submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Mechanical Engineering

K. Todd Lowe, Co-chair

Wing F. Ng, Co-chair

Ricardo A. Burdisso

Joseph W. Meadows

December 11, 2020

Blacksburg, Virginia

Keywords: Doppler global velocimetry, large-scale turbulence, jet noise

Copyright 2021, Ashley J. Saltzman

Spatiotemporally-Resolved Velocimetry for the Study of Large-ScaleTurbulence in Supersonic Jets

Ashley J. Saltzman

(ABSTRACT)

The noise emitted from tactical supersonic aircraft presents a dangerous risk of noise-induced

hearing loss for personnel who work near these jets. Although jet noise has many interacting

features, large-scale turbulent structures are believed to dominate the noise produced by

heated supersonic jets. To characterize the unsteady behavior of these large-scale turbu-

lent structures, which can be correlated over several jet diameters, a velocimetry technique

resolving a large region of the flow spatially and temporally is desired. This work details

the development of time-resolved Doppler global velocimetry (TRDGV) for the study of

large-scale turbulence in high-speed flows. The technique has been used to demonstrate

three-component velocity measurements acquired at 250 kHz, and an analysis is presented

to explore the implications of scaling the technique for studying large-scale turbulent be-

havior. The work suggests that the observation of low-wavenumber structures will not be

affected by the large-scale measurement. Finally, a spatiotemporally-resolved measurement

of a heated supersonic jet is achieved using large-scale TRDGV. By measuring a region

spanning several jet diameters, the lifetime of turbulent features can be observed. The work

presented in this dissertation suggests that TRDGV can be an invaluable tool for the dis-

cussion of turbulence with respect to aeroacoustics, providing a path for linking the flow to

far-field noise.

Spatiotemporally-Resolved Velocimetry for the Study of Large-ScaleTurbulence in Supersonic Jets

Ashley J. Saltzman

(GENERAL AUDIENCE ABSTRACT)

During takeoff, the intense noise emitted from tactical supersonic aircraft exposes personnel

to dangerous risks of noise-induced hearing loss. In order to develop noise-reduction tech-

niques which can be applied to these aircraft, a better understanding of the links between

the jet flow and sound is needed. Laser-based diagnostics present an opportunity for study-

ing the flow-field through time and space; however, achieving both temporal and spatial

resolution is a technically challenging task. The research presented herein seeks to develop a

diagnostic technique which is optimized for the study of turbulent structures which dominate

jet noise production. The technique, Doppler global velocimetry (DGV), uses the Doppler

shift principle to measure the velocity of the flow. First, the ability of DGV to measure

the three orthogonal components of velocity is demonstrated, acquiring data at 250 kHz.

Since turbulent structures in heated jets can be correlated over long distances, the effects

on measurement error due to a large field-of-view measurement are investigated. The work

suggests that DGV can be an invaluable tool for the discussion of turbulence and aeroa-

coustics, particularly for the consideration of full-scale measurements. Finally, a large-scale

velocity measurement resolved in time and space is demonstrated on a heated supersonic jet

and used to make observations about the turbulence structure of the flow field.

Acknowledgments

I would first like to thank my advisors, Dr. Todd Lowe and Dr. Wing Ng. Their technical

expertise and encouragement have helped me to become a researcher as well as shaped this

dissertation tremendously. It was truly an honor to work under you both. I would also like to

thank my dissertation committee members, Dr. Joseph Meadows and Dr. Ricardo Burdisso,

for providing valuable advice aiding in the research focus and dissertation. I would also

like to acknowledge the support of the AOE machine shop, Randall Monk, and both AOE

and ME administration, without whom this work could not have been completed. I have

been privileged to work beside many other graduate students, whose advice and friendship

enriched my time at Virginia Tech. I would like to thank Dr. Agastya Balantrapu, Anthony

Millican, Dr. Chi Moon, Dr. David Mayo Jr., Dillon Sluss, Kevin D’Souza, Matthew

Boyda, Mathew Ruda, Nandita Hari, Russell Repasky, Sean Shea, Sean Powers, Stephen

Edelmann, Dr. Tamy Guimarães, Dr. Tyler Vincent, and Will Perez. A special thanks to

my officemates of McBryde 616, Dr. Kyle Daniel and Dr. Christopher Hickling, for the

daily coffee, encouragement, and conversations at the LUG. I am so lucky to have met you

all and I wish you the best of luck in your careers. I would like to thank my family and

friends for their support throughout my life, especially my parents, Scott and Jo Saltzman.

Finally, I would like to thank my husband, Aaron Defreitas, for his unwavering support in

our relationship. Journeying graduate school together has not always been easy, but I am

thankful to have gone through it with you.

iv

Contents

List of Figures vii

List of Tables x

1 Introduction 11.1 Structure and Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Attributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Review of Literature 52.1 Jet Noise Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Components of Jet Noise . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Large-Scale Turbulent Mixing Noise . . . . . . . . . . . . . . . . . . 62.1.3 Noise Reduction Techniques . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Velocimetry Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Intrusive Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Particle-based Techniques . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Molecular-based Techniques . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Bibliography 13

3 250 kHz three-component Doppler velocimetry at 32 simultaneous points:a new capability for high speed flows 173.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 Principle of DGV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.2 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.3 Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.1 Mean flow quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.2 Time-resolved flow quantities . . . . . . . . . . . . . . . . . . . . . . 28

v

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Finite control volume and scalability effects in velocimetry for applica-tion to aeroacoustics 314.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.1 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1.2 Objectives of the Study . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.1 DGV and Scattering Principles . . . . . . . . . . . . . . . . . . . . . 354.2.2 Effect on Mean Velocity Measurements . . . . . . . . . . . . . . . . . 354.2.3 Effect on Spectral Measurement . . . . . . . . . . . . . . . . . . . . . 364.2.4 Flows of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2.5 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3.1 Mean Velocity and Turbulence Error . . . . . . . . . . . . . . . . . . 384.3.2 Spectral Resolution Effects and Comparison to Experiment . . . . . 394.3.3 Extension of the Analysis for Large-Scale TRDGV . . . . . . . . . . 42

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5 50 kHz, large field of view imaging of heated supersonic jets usingDoppler global velocimetry 475.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2.1 Doppler Global Velocimetry . . . . . . . . . . . . . . . . . . . . . . . 505.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.2.3 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.1 Mean Velocity Results . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.2 Instantaneous Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . 575.3.3 Velocity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.3.4 Space-Time Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6 Conclusions and Outlook 676.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

vi

List of Figures

2 Review of Literature

1 Far-field narrow-band supersonic jet noise spectrum measured by Seiner [39] 6

3 250 kHz three-component Doppler velocimetry at 32 simultaneous points:a new capability for high speed flows1 Light scattering geometry of the DGV principle. . . . . . . . . . . . . . . . . 212 Theoretical transmission spectrum of iodine gas and theoretical observed spec-

trum, shifted in frequency due to the Doppler effect. . . . . . . . . . . . . . 213 Experimental setup of the TRDGV system, including the laser conditioning

and observer subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Laser sheet multiplexing cycle showing alternating pulses of laser light. . . . 225 Flow chart showing the data processing routine for the incident and observed

signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Theoretical transmission spectrum compared to the incident transmission

measured by the photodetectors during the experiment. . . . . . . . . . . . . 247 Snippet of the raw time series signal from a single sensor in the PMT array

showing different pulses of laser light . . . . . . . . . . . . . . . . . . . . . . 248 A portion of the time series from a single sensor in the PMT array after initial

pulse processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Uncalibrated mean transmission from the observer during the experiment.

Each line is the mean transmission signal from one pixel on the PMT array. 2510 Calibrated mean transmission from the observer. The black line is the incident

laser transmission, measured by the photodetector. Each other line is themean signal from one pixel of the PMT array. . . . . . . . . . . . . . . . . . 25

11 Measurement plane orientation in jet flow, showing measurement downstreamof the potential core collapse. . . . . . . . . . . . . . . . . . . . . . . . . . . 26

12 Mean jet velocity profiles measured using TRDGV (three-component), hotwire (single-component), and Pitot probe (single-component). . . . . . . . . 27

13 Mean turbulence intensity profiles measured using TRDGV (three-component)and hot wire (single-component). . . . . . . . . . . . . . . . . . . . . . . . . 27

14 Fluctuating velocity spectra for varying transverse positions at x/D = 8. (a)Axial velocity, (b) Transverse velocity, and (c) Azimuthal velocity. . . . . . . 28

15 Comparison of axial velocity spectra to literature for (a) y/D = 0.5 and (b)y/D = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Finite control volume and scalability effects in velocimetry for applicationto aeroacoustics1 Illustration of observable flow features based on the measurement domain. . 342 Depiction of measurement over a finite control volume. . . . . . . . . . . . . 363 Percent error of mean velocity due to changing control volume size for Cases

A and B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Percent error of turbulence amplification due to changing control volume size

for Cases A and B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 (a) Filtered spectra for Case A and (b) corresponding frequency response

function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Filtered and aliased spectra for varying pixel sizes in Case A. . . . . . . . . . 417 Percent error of measured Reynolds normal stress due to changing control

volume size for Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 Comparison of predicted spectrum from the current work to experimental

data from the subsonic jet case. . . . . . . . . . . . . . . . . . . . . . . . . . 429 Filtered and aliased spectra for Case B with varying FOV. . . . . . . . . . . 4310 Percent error of measured Reynolds normal stress due to changing control

volume size for Case B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4311 Filtered and aliased spectrum for Case B showing wavenumber which sepa-

rates radiating components. Wavenumbers to the left of the vertical lines canradiate sound to the far-field. . . . . . . . . . . . . . . . . . . . . . . . . . . 44

12 Filtered and aliased spectrum for Case C showing wavenumber which sepa-rates radiating components. Wavenumbers to the left of the vertical lines canradiate sound to the far-field. . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 50 kHz, large field of view imaging of heated supersonic jets using Dopplerglobal velocimetry1 Theoretical transmission of light through iodine gas, illustrating the principle

of the Doppler shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 Experimental setup of the TRDGV measurement (not to scale) . . . . . . . 523 Sensitivity vector maps of the measurement plane of the current work. . . . 534 Data processing workflow for the signals in the DGV measurement. . . . . . 535 Raw images of the heated supersonic jet after performing spatial calibration. 546 Frequency response function of the expected spectrum compared to the model. 557 Radial profiles of U/Uj for the supersonic jet measured by PIV and TRDGV. 578 Radial profiles of u′u′/U2

j for the supersonic jet measured by PIV and TRDGV. 57

9 Sequence of 9 instantaneous snapshots of velocity in the heated supersonic jet. 5810 Comparison of TRDGV velocity spectra with measurements from literature. 5911 Map of spectral energy distribution in the heated supersonic jet (a) with radial

profiles of constant frequency for F = 2 kHz (b) and F = 5 kHz (c). . . . . . 5912 Axial space-time correlations computed at y/D = 0 (a) and y/D = −0.5

(b). Cropped correlation to show detail near zero lag for y/D = 0 (c) andy/D = 0.5 (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

13 Space-time correlations of the velocity for probe position x/D = 7 and y/D =−0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

14 Axial location of maximum correlation for each time delay shown by Fig. 8. 6215 Space-time correlations of the low-pass filtered flow-field (marked by ‘o’) with

correlations of the low-pass filtered density near-field (marked by ‘x’) from [32]. 62

List of Tables

4 Finite control volume and scalability effects in velocimetry for applicationto aeroacoustics

1 Description of jet flows used for analysis . . . . . . . . . . . . . . . . . . . . 392 Control volume dimension based on desired axial length of jet to image . . . 433 Energy attenuation by the measured 10D spectrum . . . . . . . . . . . . . . 44

x

Chapter 1

Introduction

The noise from tactical aircraft can exceed 140 dB during takeoff. Without hearing pro-tection, the permissible exposure time for noise of this magnitude is less than one minute.This presents a risk for Navy personnel who typically work around these engines, and as aresult, noise-induced hearing loss is a growing concern for the Navy. Additionally, renewedinterest in commercial supersonic travel by NASA and others means public noise pollutionconcerns will be a driving factor in their success. Therefore, research on understanding thenoise-producing mechanisms in a jet flow and noise reduction techniques remains relevant.Although much progress has been made in terms of identifying the fundamental compo-nents of noise in jets, a better understanding of the connection between the flow-field andthe acoustics is needed, which would identify specific turbulent mechanisms which producenoise. This remains a challenge due to the need to measure the flow in time and spacesimultaneously.

Non-intrusive, laser-based diagnostic techniques, such as laser Doppler anemometry (LDA),Doppler global velocimetry (DGV), and particle image velocimetry (PIV), use the scatteringof light by seeding particles to measure the velocity of the flow field. The listed techniqueshave shown promise for achieving either high spatial or temporal resolution of the threevelocity components; however, a single technique combining these qualities has not yet beenachieved. In this work, the DGV technique will be developed to provide large field-of-viewvelocity measurements resolved in space and time. The developments described throughoutthis dissertation will provide a unique opportunity for studying the lifetime of large-scaleturbulence in heated supersonic jets and studying the noise-production mechanisms behindjet noise reduction techniques.

1.1 Structure and Content

Chapter 1: The current chapter introduces the main topics of this dissertation. The mainachievements of the dissertation, attributions, and publications are addressed.

Chapter 2: This chapter reviews the relevant research concepts and previous work in theliterature. The gap in the research and motivation for the dissertation work is presented.

Chapter 3: This chapter presents a research paper published in Measurement Science and

1

2 Chapter 1. Introduction

Technology titled, “250 kHz three-component Doppler global velocimetry at 32 simultaneouspoints: a new capability for high speed flows”. The paper serves as a demonstration of thethree-component capability of the TRDGV technique.

Chapter 4: This chapter presents a research study under review by Experiments in Fluidstitled, “Finite control volume and scalability effects in velocimetry for application to aeroa-coustics”. This study analyzes how a time-resolved measurement will be affected by scalingto a large field-of-view.

Chapter 5: This chapter presents a manuscript which will be submitted for publicationtitled, “50 kHz, large field of view imaging of heated supersonic jets using Doppler globalvelocimetry”. The manuscript applies TRDGV to measure a large field of view of the heatedsupersonic jet, resolved in space and time. The research study discusses observations of theturbulence structure of the flow-field.

Chapter 6: This chapter summarizes the work presented in the dissertation and discussesthe outlook and suggested future work.

The formatting and content style of each chapter may vary due to requirements of the journalin which they are or will be published.

1.2 Attributions

The research content detailed in this dissertation has been aided by many colleagues andprofessors, namely the two co-chairs of the dissertation committee. A description of theircontributions is provided:

Dr. K. Todd Lowe is the primary advisor and committee co-chair for this project. Hesupervised the research and provided extensive technical guidance on the experiments anddata analysis presented in the dissertation. He also provided revisions and reviews of thepapers presented in this dissertation.

Dr. Wing F. Ng is a co-advisor and committee co-chair for this project. He supervisedthe research and provided considerable guidance on the research direction and goals of theproject. He also provided revisions and reviews of the papers presented in this dissertation.

1.3 Achievements

The major accomplishments of the research presented in this dissertation include:

• Three-component velocity measurements have been successfully demonstrated and val-idated at 250 kHz for 32 planar points in a high subsonic jet flow. To the author’s

1.4. List of Publications 3

knowledge, this is the highest framerate sustained for multipoint, three-componentmeasurements. These results highlight the suitability of TRDGV for studying flowthree-dimensionality in high-speed flows.

• Analytical efforts toward quantifying the errors present in large-scale, time-resolvedmeasurements due to the increased size of the control volume have been achieved. Theresults have shown that although a large-scale measurement would result in some addederror, the most relevant, noise-producing turbulent structures would be unaffected.This work synthesises analysis of large-scale, time-resolved measurement techniques,and provides the foundation for development of a large-scale TRDGV system.

• One-of-a-kind measurements have been achieved in a heated supersonic jet, measuringvelocity for 8 jet diameters at 50 kHz. This work scaled the field of view and increasedspatial resolution for the DGV, providing a new facility capability. Additionally, exist-ing flow measurements in heated supersonic jets are sparse, so this dataset can providefurther opportunities for validation or improvements to noise models.

• Direct observation of the lifetime of turbulence in the heated supersonic jet flow is nowpossible, and the space-time turbulence structure has been examined. Low-frequencyenergy was shown to increase and spread transversely in the jet with increasing axialdistance. Space-time correlations in the flow field show clear evidence of wavepacketstructures, which are correlated in a similar manner as the density near-field.

1.4 List of Publications

The following list presents the scientific publications produced by the author during her timeas a Ph.D. student.

Peer-reviewed Journal Publications

• Saltzman, Ashley J., Lowe, K. Todd, and Ng, Wing F., 250 kHz three-componentDoppler global velocimetry at 32 simultaneous points: a new capability for high speedflows. Measurement Science and Technology, 2020. doi: 10.1088/1361-6501/ab8ee9

• Boyda, Matthew T., Byun, Gwibo, Saltzman, Ashley J., and Lowe, K. Todd, Ge-ometric scattering removal in cross-correlation Doppler global velocimetry by struc-tured illumination. Measurement Science and Technology, 2020. doi: 10.1088/1361-6501/ab6b4f

• Saltzman, Ashley J., Lowe, K. Todd, and Ng, Wing F., Finite control volume andscalability effects in velocimetry for application to aeroacoustics. Experiments in Fluids,(under review)

4 Chapter 1. Introduction

• Saltzman, Ashley J., Lowe, K. Todd, and Ng, Wing F., 50 kHz, large field of viewimaging of heated supersonic jets using Doppler global velocimetry. (not yet published)

Conference Proceedings

• Saltzman, Ashley J., Lowe, K. Todd, and Ng, Wing F., Doppler global velocimetryfor 50 kHz, large field of view measurement of high-speed flows. To be presented atAIAA Scitech 2021 Forum.

• Boyda, Matthew T., Byun, Gwibo, Saltzman, Ashley J., and Lowe, K. Todd, In-fluence of Mie and Geometric Scattering Contributions on Temperature and DensityMeasurements in Filtered Rayleigh Scattering AIAA Scitech 2020 Forum, AIAA Paper2020-1516, 2020. doi: 10.2514/6.2020-1516

• Boyda, Matthew T., Byun, Gwibo, Saltzman, Ashley J., and Lowe, K. Todd, Ge-ometric scattering removal in CC-DGV by structured illumination 13th InternationalSymposium on PIV (ISPIV 2019), 2019.

• Saltzman, Ashley J., Boyda, Matthew T., Lowe, K. Todd, and Ng, Wing F., Fil-tered Rayleigh Scattering for Velocity and Temperature Measurements of a HeatedSupersonic Jet with Thermal Non-Uniformity. AIAA/CEAS 2019 Aeroacoustics Con-ference, AIAA Paper 2019-2677, 2019. doi: 10.2514/6.2019-2677

• Saltzman, Ashley J., Lowe, K. Todd, and Ng, Wing F., Demonstration of 250 kHzThree-Component Velocity Measurements using TRDGV at 32 Simultaneous Points.AIAA Scitech 2019 Forum, AIAA Paper 2019-1819, 2019. doi: 10.2514/6.2019-1819

Chapter 2

Review of Literature

2.1 Jet Noise Fundamentals

Researchers have sought to understand the noise production characteristics of supersonic jetssince nearly their invention in the 1950s [34]. To understand the motivation and underlyinggoals behind the diagnostic development research in this dissertation, the fundamentals ofjet noise and state of jet noise reduction research will be reviewed to follow.

2.1.1 Components of Jet Noise

Supersonic jets exhibit different noise characteristics to their subsonic counterparts. Thenoise from supersonic jets can be generalized into three principal categories: broadbandshock-associated noise (BBSAN), screech tones, and turbulent mixing noise [45]. A typicalfar-field narrow-band supersonic jet noise spectrum, shown in Fig. 1, depicts the distinctcharacteristics of these noise components. Although one observer angle is shown in the figure,the intensities of the individual components will be strongly dependent on the direction ofobservation.

BBSAN is caused by the interaction of quasi-periodic shock cells with coherent turbulentstructures [45]. This component radiates noise in all directions, but most intensely in theupstream direction. Tam has shown a reliable method for predicting BBSAN using instabilitywave theory [44]. Screech tones are formed by a feedback loop between shock cell structuresand shear layer instability. The interaction of the propagating shear layer instability withshock cells generates a disturbance which travels upstream to again interact with the shearlayer. This causes the distinct high amplitude narrowband tone which can be seen in thenoise spectrum of Fig. 1 [36]. Screech tones will radiate noise most intensely to the upstreamdirection, and it is widely accepted that screech tone intensity decreases with increasing jettemperature.

Turbulent mixing noise is caused by the self-interaction of the turbulence in the flow, byboth fine- and large-scale structures. Turbulent mixing noise is associated with Strouhalnumbers (St = fD/Uj, where f is frequency, D is the nozzle diameter, and Uj is the jet exitvelocity) between 0.1 and 0.4. The dominant part of turbulent mixing noise for heated jets,large-scale turbulence mixing noise, radiates most intensely in the downstream direction,

5

6 Chapter 2. Review of Literature

Figure 1: Far-field narrow-band supersonic jet noise spectrum measured by Seiner [39]

120◦ to 135◦ from the jet axis [40]. Since this component radiates primarily in the directiontypically occupied by personnel during takeoff, and is most dominant in heated flows, it isof particular interest for the research in this dissertation.

2.1.2 Large-Scale Turbulent Mixing Noise

The foundation of aeroacoustics research comes from Lighthill’s acoustic analogy, where herearranged the Navier-Stokes equations to describe the relationship between fluid dynamicsand the radiated sound field [26].

∂2ρ

∂t2− c2∞ ▽2 ρ =

∂2 (ρUiUj − σij + (p− c2∞ρ) δij)

∂xi∂xj

(2.1)

The left hand side of Lighthill’s equation describes the density (also pressure) propaga-tion, while the right hand side describes the forces which produce the waves. The termin the parentheses is known as Lighthill’s stress tensor, where ρUiUj is the turbulence self-interaction term, σij is the viscous shear stress, and p− c2∞ρ is the compressive stress tensor.Without the presence of solid surfaces, the noise produced from a high Reynolds numbersand low Mach number (M = Uj/c∞, where c∞ is the speed of sound) jet will be dominatedby the convective turbulence term. This means that to predict the sound field, the space-time correlation of the stress tensor for every point in the flow must be known. Such a

2.1. Jet Noise Fundamentals 7

measurement would be extremely challenging, which will be discussed in the next section.

Although powerful, limitations do exist in Lighthill’s equation, particularly the low Machnumber assumption. Ffowcs Williams and Hawkings later extended the acoustic analogy toinclude the effect of convection in sonic and supersonic speeds by modeling a radiator surfacesurrounding the jet flow in order to capture the space-time history of pressure and densityfluctuations [16]. This foundational work has been expanded upon by many researchers topredict jet noise from source models, some of which have been reviewed by Bailly et al.[3]. The main conclusion to reach from this very brief overview of acoustic propagation isthat large-scale turbulence self-interaction is the dominant contributor to noise in heatedsupersonic jets.

Large-scale turbulent structures, or wave packets, are flow disturbances which are correlatedfor lengths much larger than the integral turbulence length scales and convect with nearlyconstant velocity [19]. The experimental evidence for these organized turbulence structureswas first observed by Mollo-Christensen, who foreshadows the need for advanced measure-ment and analysis techniques in saying, “It is suggested that turbulence, at least as far assome of the lower-order statistical measures are concerned, may be more regular than wethink it is, if one only could find a new way of looking at it,” [32]. The high coherence of thesestructures makes them extremely efficient at radiating noise, even though they contain a lowamount of the flow’s total fluctuation energy. Although evidence of these wavepackets canalso be observed in the near-field, distinguishing them from highly energetic, finer-scale tur-bulence, typically requires the use of decomposition methods. Papamoschou et al. suggeststhrough the space-time correlation equation that the strength of a source could primarily bereduced by a reduction in radiative efficiency [35]. This provides a path for evaluating noisereduction mechanisms, provided the space-time correlation term, and thus the convectionterm, can be measured.

2.1.3 Noise Reduction Techniques

In the interest of suppressing jet noise, researchers have studied techniques which modify theturbulence characteristics of jets to affect the sound. Nozzle geometry modifications, such aschevrons, can be a relatively simple, yet effective method of reducing noise in subsonic jets.In supersonic flows, however, the increased turbulence intensity can lead to an increase inhigh frequency noise contribution. Additionally, the interaction with the shock cell structureleads to an increase in BBSAN, essentially cancelling out the positive effects of chevrons[17]. For this reason, alternative techniques must be used for supersonic jets.

Fluidic injection, where a secondary fluid is injected into the nozzle or jet plume, is anappealing technique due to its potential for active control of noise reduction. The techniquewas shown to promote mixing near the jet exhaust and reduce noise by up to 5 dB overall SPLin laboratory-scale experiments [37]. Inverted velocity profile (IVP) jets are multi-streamjets where the core jet stream has lower axial velocity than the bypass flow, as opposed to


normal velocity profile jets (NVP). By matching effective mass flow rates, thrust, and exitarea, IVP jets have been shown to reduce noise by up to 4 dB [46]. Actual implementationof an IVP jet would be very challenging due to the need to redesign an engine with a fanstream operating faster than the core, with large compromises to aircraft performance. Thus,jet noise reduction techniques which can be implemented into real engines are needed formeaningful impact.

Building on the idea that disrupting the formation of large-scale structures can reduce theiracoustic efficiency, researchers at Virginia Tech have investigated the ability of locally colderflow to induce perturbations in free jets. In their work, a total temperature non-uniformityis introduced in the otherwise heated jet flow through the injection of unheated air intothe diverging portion of the jet nozzle [28]. Both streams accelerate through the supersonicnozzle, resulting in a region of lower total temperature, at the nozzle exhaust plane. The flowperturbations caused by the non-uniformity show modifications to the jet’s shear structureand suggest an increase in three-dimensionality [28]. Far-field acoustic measurements showeda reduction of 2 ± 0.5 dB in peak noise directions, with up to 2.5 dB OASPL reduction inangles upstream of the peak noise direction [9]. Through an investigation of the density near-field, the non-uniformity showed a decorrelation of Mach waves, suggesting a disruption inthe formation of large-scale structures [8]. The research to be discussed throughout thisdissertation shows promising applicability to studying the spatiotemporal structure of thenon-uniform flow field, which has previously not been possible. In measuring the flow fieldspatiotemporally, direct links between it and the pressure field could be investigated.

2.2 Velocimetry Techniques

To study complex fluid flows, such as supersonic jets, researchers need a way to measurethem. Many techniques have been developed to accomplish the task of measuring fluidvelocity, ranging in cost, complexity, and typical application. Velocimetry techniques cangenerally be split into two categories: intrusive methods, which involve inserting probehardware into the flow, and non-intrusive techniques, which enable measurement of the flowspeed using alternate methods. A variety of intrusive and non-intrusive techniques willbe addressed to follow, with a focus on time-resolved measurements due to the interest instudying the lifetime of turbulent structures in supersonic jets.

2.2.1 Intrusive Techniques

Pitot probes are widely used in various environments ranging from racecars to aircraft. In itssimplest form, the flow speed is determined by measuring the pressure differential throughthe tube, although modern probes have been developed which are capable of measuringthe fluid velocity vector. By using multiple holes located around a center hole, the three-

2.2. Velocimetry Techniques 9

dimensional velocity vector can be found based on calibration curves of the probe [33].Pressure probes are commonly time-averaged measurements, although specialized probes formeasuring turbulent fluctuations with higher frequency response (up to 50 kHz) do exist[23]. In a supersonic flow, a shock will be formed in front of the probe due to its intrusivenature and shock relations must be used to determine the pressure upstream of the shock.

With the desire to reliably measure time-dependent statistics, thermal anemometry includinghot-wire probes became a standard instrument for measuring compressible flows. In hot-wire anemometry, a thin wire filament is supplied constant temperature or voltage andfluctuations from the setpoint are measured with high temporal response. Calibration ofthe anemometer is first performed by measuring a flow with a known speed, where therelationship between voltage and velocity can be found using King’s law [20]. The flowvelocity in the measurement can then be found using the deviation from the setpoint andthe calibration. Hot-wire probes have been used in a variety of applications over the pastfew decades [42]. Using multiple wires on a single probe enables the measurement of allthree velocity components using a calibration for velocity and a calibration to account forthe geometry of the probe [52]. Although hot-wire probes are widely applicable to manyflows, the fragile instrument will experience limitations in harsh flow environments such asa heated or highly turbulent flow [49]. Bare tungsten wires will begin to oxidize around600K, and thus Smits et al. found constant temperature anemometers to be unsuitable forheated flows due to low allowable overheat ratio [41]. Other wire materials, such as platinumor platinum-rhodium, have higher oxidation temperatures, but may still produce unreliablemeasurements in heated flows [27].

2.2.2 Particle-based Techniques

With the limitations of intrusive techniques, and advances in laser technology and opti-cal instrumentation, much research has been done to develop particle-based velocimetrytechniques. The techniques discussed in this section detect laser light scattered by seedingparticles added to the flow in order to measure the velocity of the flow. These techniquesexhibit potential for achieving high resolution in time or space non-intrusively.

Laser Doppler velocimetry (LDV), also known as laser Doppler anemometry (LDA), wasdeveloped in the 1960s and widely adapted to suit a variety of measurement applications.LDV is based on the principle of the Doppler effect, which states that the frequency of awave changes relative to a moving observer. If the Doppler frequency shift due to the flowcan be detected, then the velocity of the flow can be measured. To detect the frequencyshift, LDV uses a pair of intersecting laser beams of a known frequency. Seeding particleswhich pass through the intersection (the measurement volume) will scatter light of differentfrequencies which can then be detected by a photodetector or PMT observer. A more in-depth description of the LDV principles can be found in [1]. Although one pair of beamsprovides the velocity magnitude in the sensed direction, additional velocity components can


be measured by the addition of multiple laser beams [48]. Since its invention, LDV hasproven valuable in a variety of flow applications, from computing correlations in subsonicand supersonic jets [24], [25], to measurement of swirl to study blood coagulation [18].

Similarly, Doppler global velocimetry (DGV) is a non-intrusive technique based on theDoppler shift principle. The working principles of DGV will be described in detail through-out this dissertation. Developed in the 1990s as an alternative laser-based method, DGVuses the absorption characteristics of a molecular gas filter to directly measure the frequencyshift [21]. When the scattered light passes through the gas filter, some of its intensity willbe absorbed by the gas, depending on the frequency of the light. The velocity of the flowcan be determined by the following equation [29],

∆fD =

−→U · (o− i)

λ(2.2)

where ∆fD is the shift in frequency, −→U is the velocity vector, o is the direction of observation,i is the direction of the incident laser propagation, and λ is the incident frequency of the laser.Since the frequency shift is measured directly, the velocity can be determined for multiplepoints simultaneously, as opposed to the single-point LDV technique. Three orthogonalvelocity components can be resolved using three independent measures of the frequencyshift; however, research efforts have been made to reduce the number of required sensors[12]. DGV exhibits low absolute uncertainties, making it suitable for high-speed flows. Tofurther reduce measurement uncertainties, researchers have utilized frequency scanning totune the laser to an optimal frequency and cross-correlate the transmission signal in orderto find velocity [7, 15]. Time-resolved DGV (TRDGV) can be achieved through imagingvia high-speed sensors or cameras. Due to their high light sensitivity, photomultiplier tube(PMT) arrays were used to develop a high-speed DGV system, demonstrated at 100 kHz fora single-point, three-component measurement [12]. PMT cameras were later developed byEcker et al. [13], and utilized by the author to demonstrated a multipoint, three-componentTRDGV measurement, which will be discussed in Chapter 3. DGV measurements have beenachieved with high spatial and temporal resolution previously using high-speed cameras,although technology at the time limited the dataset to 28 frames and a single componentmeasurement [47]. In Chapter 5, a spatiotemporally-resolved DGV system is presented andmeasurements on a supersonic jet are discussed.

Particle image velocimetry (PIV) has become increasingly popular for measuring velocity,thanks to digital photography developments in the 1990s [51], as well as commercializationefforts [2]. In PIV, two images are taken with a known time delay. The light scattered byseeding particles in the two sequential frames can then be cross-correlated to find the velocityof within the interrogation region. High spatial resolution is achievable with PIV, provingvaluable for mean flow measurements; however, time-resolved PIV is becoming more widelyavailable due to camera framerate and computational developments. A time-resolved PIV(TRPIV) measurement for highly subsonic or supersonic flow speeds was first demonstrated

2.3. Concluding Remarks 11

at NASA Glenn, where the system was used for computation of two-point space-time corre-lations in a high subsonic heated jet at 25 kHz [50]. Ultrafast data acquisition rates rangingfrom 400 kHz to 1 MHz have also been achieved using pulse-burst lasers, although typicallyat the expense of spatial resolution or record length [4, 5, 6].

2.2.3 Molecular-based Techniques

Due to limitations in particle response time and potential difficulties seeding the flow,molecular-based velocimetry techniques are increasingly attractive. Rayleigh scattering oc-curs off particles much smaller than the wavelength of light, the molecules in the flow [31].The interaction is elastic, meaning no energy is transferred, allowing for properties of theflow such as temperature or density to be measured, in addition to velocity. As in otherDoppler-based techniques, a molecular gas filter can be used to determine the frequencyof the scattered light, in an implementation known as filtered Rayleigh scattering (FRS).The signal measured by the camera will be the convolution of the gas filter’s transmissionspectrum and the light scattering spectrum, including contributions of Rayleigh scattering,Mie scattering, and background scattering. The ability to measure multiple flow propertiessimultaneously and non-intrusively has led the technique to be used in various time-averagedmeasurements: combustion environments [14], subsonic jet exhausts [11], nozzle guide vanecascades [10], and in heated supersonic jets [38]. The low scattering intensity of the Rayleighspectrum makes a time-resolved measurement very challenging without the use of a high-powered laser; however, measurements up to 32 kHz have been achieved using light-sensitivePMT arrays [30], with proof-of-concept work completed for measurements up to 100 kHz[53].

Molecular tagging velocimetry (MTV) is an optical technique which excites molecules in theflow using fluorescence or phosphorescence. Using flow molecules as tracers eliminates therisk of particle lag in the measurement. In MTV, a pulsed laser is used to tag regions in theflow, which are then measured at two instances within the lifetime of the tracer. The velocityfield can then be estimated by the Lagrangian displacement field. For this reason, MTV canbe thought of as a molecular counterpart to PIV [22]. Two-component velocity measurementscan be achieved using several intersecting laser beams, which provide intensity fields withspatial gradients in multiple directions [43]. MTV offers the ability to measure the velocityfield, as well as other flow variables such as pressure, temperature, and concentration, andfurther explanation and examples of the technique can be found in [22].

2.3 Concluding Remarks

The review has discussed the fundamental principles of jet noise, including that turbulentmixing noise radiates most intensely in the downstream direction. Importantly, it is believed


that large-scale turbulent structures dominate the noise production in heated supersonic jets.Modern jet noise reduction approaches discuss the need for disrupting the formation of theselarge-scale coherent structures and reducing their radiative efficiency to make meaningfulimpacts in noise. Researchers suggest that the success of jet noise reduction studies has beenlimited by the “lack of conceptual framework connecting flow perturbations near the nozzleexit to the far field” [19]. The task of linking flow to acoustics would require measurementresolution in both space and time, in addition to measuring all three velocity components.Up to this point, such a measurement suitable for use in heated supersonic jets has not beenachieved.Various velocimetry techniques have been developed for use in measuring high-speed flows,as was discussed in the literature review. Many of these techniques possess the ability toresolve time-scales of interest in supersonic flows; however, no single technique has beenoptimized to achieve the spatial and temporal resolution desired for studying large-scaleturbulence. Of the discussed techniques, a few of the inherent characteristics of DGV makethe technique suitable for this purpose. DGV exhibits absolute, rather than relative, uncer-tainties, meaning that errors will not scale with high flow speeds present in supersonic jets.Additionally, resolution of individual particles, as in PIV, is not necessary for DGV, sug-gesting the ability for scaling to large measurement regions. Finally, as each light-scatteringparticle in the measurement volume contributes to the signal, the signal-to-noise ratio (SNR)of the measurement can be improved with higher concentrations of particles. These qualitiessuggest the potential of DGV for achieving a large-scale, spatiotemporally-resolved measure-ment. The studies which will be presented in Chapters 3 – 5 seek to fill the research gapsby demonstrating the time-resolved, three-component capability of TRDGV and achievinga spatiotemporally-resolved large-scale measurement in heated supersonic jets. The furtherdevelopment of TRDGV as a diagnostic technique could lay the groundwork for exploringthe mechanisms linking flow to sound.

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Chapter 3

250 kHz three-component Dopplervelocimetry at 32 simultaneous points:a new capability for high speed flows

The content of this chapter was published in Measurement Science and Technology (Saltz-man, A.J., Lowe, K.T., and Ng, W.F., “250 kHz three-component Doppler global velocimetryat 32 simultaneous points: a new capability for high speed flows,” Measurement Science andTechnology (2020) 31(9):12, doi: 10.1088/1361-6501/ab8ee9). The material is reproducedwith the permission of IOP Publishing Ltd.

17

Measurement Science and Technology

PAPER

250 kHz three-component Doppler velocimetry at 32 simultaneouspoints: a new capability for high speed flowsTo cite this article: Ashley J Saltzman et al 2020 Meas. Sci. Technol. 31 095302

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Measurement Science and Technology

Meas. Sci. Technol. 31 (2020) 095302 (12pp) https://doi.org/10.1088/1361-6501/ab8ee9

250 kHz three-component Dopplervelocimetry at 32 simultaneous points: anew capability for high speed flows

Ashley J Saltzman1, K Todd Lowe2 and Wing F Ng1

1 Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, United States of America2 Crofton Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA, UnitedStates of America

E-mail: [email protected]

Received 12 March 2020, revised 24 April 2020Accepted for publication 30 April 2020Published 15 June 2020

AbstractTime-resolved Doppler global velocimetry (TRDGV) is used to demonstrate three-componentvelocity measurements of 32 planar points, acquired simultaneously at 250 kHz.Photomultiplier tube arrays are used to detect the flow signal, with each array having eight rowsof four pixels. The system utilizes frequency scanning of a continuous wave laser, allowing forsimple calibration of the signals used to determine the incident and Doppler-shifted frequency.The TRDGV system is used to measure an unheated, Mach 0.91 free jet downstream of thepotential core collapse. Axial mean velocities were measured within a root-mean-square error of7 m s−1 compared to Pitot probe validation measurements. Additionally, axial turbulenceintensities showed agreement to hot wire validation measurements and exhibited typicalmagnitudes reported in the literature. Velocity spectra were obtained for the three componentsof velocity, revealing a − 5/3 decay in the axial velocity spectra in the inertial subrangefrequencies, and generally less decay present in the transverse component spectra. Hot wiremeasurements and spectra from literature were used for validation of the TRDGV spectralresults, showing broadband spectral agreement. The instrument described in this work showspromising capability for multi-point, time-resolved velocity vector measurement in high speedcompressible flows with acceptable levels of uncertainty.

Keywords: Doppler global velocimetry, time-resolved velocity, three-component velocity

Some figures may appear in colour only in the online journal

1. Introduction

The goal of observing fluid dynamic behavior has driveninnovation in the field of optical instrumentation. For higherflow speeds, such as in high subsonic and supersonic free jets,the short timescale of the flow requires measurements withhigh frequency response in order to further describe turbulentflow behavior and gain insight into unsteady flowmechanisms.

Laser-based velocimetry techniques have been developedextensively for studying flow behavior, due to their potential toachieve high spatial and temporal resolution non-intrusively.One such technique, Doppler global velocimetry (DGV) util-izes the absorption characteristics of molecular gas cells to

measure the Doppler-shifted frequency based on scattering offof particles. DGVwas first developed by Komine [1], and thenrefined by Meyers and Komine as an alternative method toother laser velocimetry techniques, including particle imagevelocimetry [2]. A key advantage of the DGV technique is thatvelocity is determined from the scattered light from a collec-tion of particles, instead of relying on signals from discreteparticles, as in PIV. This allows for the use of smaller particlesand also larger fields of view. Three dimensional velocity isdiscernible without ambiguity by relating the geometry of theobserver cameras to the incident laser direction. Since thefundamental measurement exhibits absolute, rather than relat-ive, instrument uncertainties, the technique is well-suited for

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Meas. Sci. Technol. 31 (2020) 095302 A J Saltzman et al

high-speed flows. The characteristics of the DGV techniquemake it befitting of time-resolved measurements in flows withshort timescales.

Velocimetry meaurements are commonly limited by theirrepetition rates, although much progress and innovation hasoccurred over the past few decades [3]. Sampling the flow atthese high repetition rates has been a limiting factor. Pulseburst laser systems, which concentrate a large amount ofenergy over a short amount of time, have been developed toachieve high repetition rates. This provides the opportunity forvirtually instantaneous measurement of the flow, and has beenused in many applications of time-resolved velocimetry [4–6].Pulse burst laser systems can be quite complex and costly,leading some researchers to explore alternate techniques usingcontinuous-wave lasers [7]. Additionally, high-speed imagingnecessitates a rapid-response sensor to measure with high tem-poral resolution. Photomultiplier tube (PMT) arrays have beenwidely used in the biomedical and physics fields; however,their qualities of light sensitivity and rapid response have beenshown to be useful for fluid dynamics measurement as well.Ecker et al utilized field-programmable gate arrays (FPGA)to develop a high-speed flow velocimetry system, capable ofmeasurement up to 10MHz at 64 channels [8]. Recently, high-speed CMOS cameras have become available, which havedemonstrated frame rates in the tens of thousands up to over abillion [9]. The cost of commercially-available cameras can beprohibitive, and has led researchers to look toward developinglow-cost cameras for high-speed imaging [10]. These devel-opments provide the foundation for the current work and thefuture of high-speed flow velocimetry techniques.

Using the developments in laser technology and increasedsensor capabilities has resulted in improvements in spatial andtemporal resolution for laser-based flow measurements, lead-ing to promising results. Ecker et al demonstrated 100 kHzDGV with a reduced number of required sensors for three-component velocity measurements of a single point [7]. Thisapplication utilized multiplexing of laser sheets, alternatingpulses of laser light, to achieve the desired sampling rate, whileonly requiring two observers to measure three-componentvelocity. The use of PMT arrays to measure the scattered lightwas then implemented by Ecker et al in order to measure mul-tiple flow points simultaneously, providing the opportunityfor a spatially resolved measurement [8]. The time-resolvedDGV (TRDGV) system was used to measure heated super-sonic jets at Virginia Tech, and through a study of eddy con-vection velocities, experimentally demonstrated a mechanismfor the role of heating in jet noise reduction [11]. Scaling thetechnique for use at NASA Glenn’s Aero-Acoustic PropulsionLab (AAPL) allowed for spatial correlation of flow signals toestimate convection velocities solely from the scattered lightsignal of adjacent pixels, with the assumption that the seedingparticles would exactly follow the flow for short time scales[12]. Using the signal directly measured by the PMT arrays,as opposed to the Doppler signal, good agreement was shownbetween convection velocity measurement and PIV measure-ment of axial velocity in multi-stream jets [13].

Multi-point measurements have been achieved at higherrepetition rates using high-speed cameras and pulse-burst

laser systems, although these highly time-resolved demon-strations have typically been single component measure-ments. Recently, a pulse-burst laser was used to measurea small velocity field at 400 kHz, dubbed ‘postage-stampPIV’ [6]. In increasing the temporal resolution, field of viewwas thus reduced to a 6 mm × 6 mm region, an array of128 × 120 pixels. This configuration exhibited very high fre-quency response in a high speed flow, although at the expenseof a small field-of-view, limited by camera capabilities. Usinga pulse-burst laser for Doppler measurements, Thurow et alcompared the results of planar Doppler velocimetry for botha single camera and two camera configuration [4]. Singlecomponent velocity measurement was achieved at 250 kHz,with combined random and bias errors totaling between 13–15 m s−1. High temporal and spatial resolution provided theability to observe dynamics of fluid entrainment, with the ideathat even shorter-lived structures could be observed with thepulse-burst laser having the ability to measure up to 1 MHz.

Further working to minimize measurement uncertainty, aDGV system can be tuned to an optimal frequency by adjust-ing the frequency of the incident laser light. Frequency scan-ning also improves the dynamic range of the DGV system.Scanning through multiple laser frequencies provides a data-set which can be cross-correlated in order to find the velocity,as in cross-correlation DGV (CC-DGV) [14]. The techniquewas found to be robust against changes in vapor cell pressureand has been recognized as a high dynamic range implement-ation of DGV [15]. A several-gigahertz sweep of the vaporabsorption spectrum resulted in mean three-component velo-cities acquired in a wind tunnel with uncertainties less than2 m s−1. In a recent implementation using a pulse-burst laser,the time needed to perform a frequency scan for CC-DGVwasreduced from 2–4 min to 10 ms [16]. This development canlead to increased frequency response capability and adds to theappeal of frequency scanning as a useful tool for DGV meas-urements.

The previous works have made progress towards fluiddynamic measurements with increased temporal and spatialresolution; however, a multi-point measurement with highrepetition rates, as well as resolving three-components of velo-city, has yet to be achieved. In the interest of capturing aflow’s three-dimensional complexity, we focus on demon-strating the three-component capability of DGV in the cur-rent work, while still retaining a time-resolved, multipointsystem. We combine previous efforts in the development ofTRDGV systems which include multiplexing of a continu-ous wave laser to reduce the number of views required, andfast response PMT cameras to add a spatial component to thesystem. Additionally, we implement laser frequency scanningtechniques during the collection of data, resulting in a calibra-tion method for each pixel based on the signal’s fit to a theoret-ical model of gas cell absorption. This work is the first demon-stration of the three-component velocity measurement capab-ility of the TRDGV system repeated at 250 kHz, acquired for32 planar points simultaneously. To the authors’ knowledge,this is the highest sustained sampling rate ever demonstratedfor multi-point, three-component flow velocity measurements.The TRDGV system is used to measure an unheated subsonic

2


free jet, operated at a Mach number of 0.91, downstream ofthe potential core collapse. A hot wire probe, with estimatedfrequency response of 20 kHz, and a Pitot probe were used toprovide measurement validation.

The paper is organized as follows: experimental methods,including system instrumentation, data processing techniques,and an uncertainty analysis, are discussed in section 2. Theexperimental results and comparison to validation measure-ments as well as literature are shown in section 3, followed byoverall conclusions in section 4.

1.1. Principle of DGV

Doppler global velocimetry relies on the principle of the Dop-pler effect; the frequency of a wave will be shifted an amountproportional to the cosine of the angle between the wave andthe observer. In a velocimetry application, light scattered offof particles will be shifted in frequency proportional to thespeed of the particle. The frequency shift of scattered light isdependent on the velocity vector, observer direction, and laserpropagation direction [2],

∆fD =

⇀

U ·(o− i

)λ

(1)

where⇀

U is the pixel velocity vector, o is the direction of obser-vation by the camera, i is the laser propagation direction, andλ is the incident laser light frequency. For a three-componentvelocity measurement, three independent signals are neededto distinguish the velocity vector components. The velocityvector can be reconstructed from the measured signal by acoordinate transformation using the measurement componentdirection,

⇀

U=

eT1eT2eT3

−1 u1u2u3

=

R11 R12 R13

R21 R22 R23

R31 R32 R33

u1u2u3

(2)

where e is the measurement component direction (o− i), ui isthe magnitude of the measured velocity component consistentwith equation (1), and R is the geometric calibration for theinstrument configuration. Figure 1 shows the geometry of thescattering principle with labeled nomenclature.

In practice, two key measurements are needed to distin-guish the frequency shift for DGV. There must be a methodfor measuring the incident laser frequency and also for meas-uring the scattered, Doppler-shifted frequency. In most applic-ations, laser frequency is determined by measuring the trans-mission of light, scattered by seeding particles, through a vaporcell. Iodine gas is commonly used as the vapor cell because itsabsorption qualities have the range needed for measuring Dop-pler shifts, and its absorption features have been well char-acterized [17]. By taking the ratio of light passing throughthe cell to unfiltered light, the transmission through the filteris obtained. By comparison of this transmission to a theoret-ical iodine transmission spectrum, e.g. Forkey et al [17], an

Figure 1. Light scattering geometry of the DGV principle. Conceptadapted from [7].

Figure 2. Theoretical transmission spectrum of iodine gas andtheoretical observed spectrum, shifted in frequency due to theDoppler effect.

estimate of the light’s frequency can be found. This practice isused to determine frequency for both the incident light and theobserved, Doppler-shifted light. The incident laser frequencycan be tuned in order to find the desired centered location of thetransmission spectrum. Ideally, the chosen centered frequencyshould have distinct transmission features for easier detectionof the shifted frequency, meaning the expected frequency shiftshould have an easily identifiable transmission. The frequencyof incident light should be tuned in steps to compare to the the-oretical absorption spectrum, an example of which is shown infigure 2. In the figure, one can observe that for each incidentfrequency, the frequency measured in the flow is shifted leftby a constant wavenumber.

3


Figure 3. Experimental setup of the TRDGV system, including the laser conditioning and observer subsystems.

2. Experimental methods

2.1. Instrumentation

In the system used in the current work, there are two parts: thelaser conditioning subsystem which delivers the intense laserlight, and the observer subsystem which records the scatteredlight. The laser conditioning subsystem, shown in figure 3, isisolated from the jet set up, as previous experience has shownthis to reduce the interference of the jet acoustics on the laserfrequency stability. This subsystem is utilized to determinethe incident laser frequency, necessary for measurement ofthe Doppler-shifted frequency. A continuous-wave CoherentInc. Verdi V6 model is used with a maximum output power of6 W at 532 nm. Contemporary diode-pumped solid-state lasertechnology exhibits the desired characteristics for this meas-urement with a linewidth of 5MHz, a coherence length greaterthan 100 m, and intensity fluctuation noise of less than 0.03%RMSThe frequency of the continuous-wave laser can be finelytuned by applying voltage to a piezoelectric element (PZT) inthe laser head, using a BK Precision DC power supply with avoltage range of 0 to 72 V. A small amount of laser light isdiverted from the primary beam in order to monitor the incid-ent frequency. This beam is then split equally, with one pathdirected onto a photodiode and the other passing through amolecular gas filter at a known pressure and then onto a secondphotodiode (ThorLabs, PDA100 A, free-space amplified pho-todetector). A starved vapor iodine cell, ISSI I2 S-5, with alength of 15 cm, at a constant pressure of 0.67 Torr is used asthe molecular filter.

The primary beam is then directed through two IntraAc-tion Corp. model ATM-80A1 80 MHz acousto-optical mod-ulators (AOM) with 77 ns rise times, which act as opticalswitches. The AOM uses sound waves to diffract the beam,creating multiple, frequency-shifted beams with a diffraction

Figure 4. Laser sheet multiplexing cycle showing alternating pulsesof laser light.

efficiency of 85%. The beam diffracted to the first order isdiverted and expanded through a cylindrical lens to form alaser sheet. The zeroth order beam then continues into a secondAOM, creating another diffracted beam which will form thesecond laser sheet. The intersection of the laser sheets, shownin the observer subsystem of figure 3, constitutes the measure-ment plane of the system. The laser sheets are multiplexed ina cycle, shown in figure 4. The first laser sheet is pulsed for1 µs (P1), followed by 0.5 µs of dark time. The second lasersheet is then pulsed for 1 µs (P2), followed by 1.5 µs of darktime before the cycle repeats. In this cycle, the effective repe-tition rate of the instrument is 250 kHz. The multiplexing iscontrolled with a BNC 565 delay generator, and triggered by

4


the DAQ system. Further description of the multiplexing cyclecan be found in Ecker et al [7]. Using the AOM, fewer camerasare needed for distinguishing the three components of velocitybecause there are two pulses of light captured by two cameras,a total of four signals. Three of these signals were used fordetermination of the velocity vector in the current work; how-ever, utilizing a fourth signal has previously been shown toreduce error propagation in the calculation of the orthogonalvelocity components [18].

The layout of the cameras is shown in detail in the topview of figure 3. For determination of the Doppler-shifted fre-quency, the scattering signal is collected by camera lensesperpendicular to either side of the measurement plane. Thescattered signal is split by a non-polarizing beam-splittingcube, with one path passing directly to the cameras, the particlescattering (reference) signal. The other path is passed throughthe iodine gas filter, resulting in the filtered signal. The ratio ofthese two signals provides a measure of the amount of trans-mission through the vapor filter, which is then compared toincident transmission measured by the photodetectors. Mag-nification by the lenses in this experiment was equal to 2.8;however, this value can be adapted based on application of themeasurement technique. The scalable nature of the DGV tech-nique makes it easily adjustable for small and large scale rigs,one of the strong benefits of using this technique.

Each camera in the system is a rapid-response photomulti-plier tube (PMT) array based on flat panel type HamamatsuH8500 C and H10966 series PMTs. The reader is referredto Ecker et al [8] for an in-depth technical description ofthe cameras and triggering; however, a summary is providedhere. There are 64 sensors on the PMT array, arranged in an8 × 8 grid of ‘pixels’. The four inner columns of pixels, an8 × 4 grid consisting of 32 pixels, have been utilized for thecurrent work. Four PMT arrays are used for this measure-ment: two arrays perpendicular to each side of the measure-ment plane. The PMT arrays have single electron responsetimes of 0.5 ns, notably smaller than the sampling rate andtimescales of interest in this measurement. The photocath-ode voltage for the gain of the PMT was chosen to maximizedynamic range of the instrument without oversaturating thePMT arrays, approximately 700 V. The PMT arrays shouldbe specified to exhibit high quantum efficiency for the desiredwavelength of light in the system. High-speed amplifier boardsamplify the anode signals and transmit them to the adaptermodule of the data acquisition system. Field programmablegate arrays (FPGA, FlexRIO PXIe-7965 R) allow for stream-lined acquisition of multiple channels with preprocessing toreduce the acquired data from 50 million samples-per-secondto 10 million samples-per-second. For one second of meas-urement, approximately 2.5 GB of data are generated. Thedata are processed, as described in section 2.3, to obtain the250 kHz velocity signal, resulting in 250 000 samples per cam-era pixel in the standard 1 s acquisition.

2.2. Data processing

The data processing routine for the current work is shown infigure 5. In summary, the signal from the photodetector pair

Figure 5. Flow chart showing the data processing routine for theincident and observed signals.

is used to determine the incident frequency, and the PMT sig-nals from each camera pair are used to determine the shiftedfrequency. Equation (1) is then used to relate the incident fre-quency, shifted frequency, and the geometry of the system inorder to find the instantaneous velocity vector for each pixel.Scripts for the data processing routine can be acquired by con-tacting the corresponding author.

The first step in the data processing routine is to determinethe incident laser frequency using the laser conditioning sub-system. The absorption of iodine gas as a function of laser fre-quency, modelled by Forkey et al [17] is used for this determ-ination. The incident transmission during the experiment iscalculated as the ratio of the signal from the filtered photo-detector to the unfiltered photodetector. To determine the cor-responding laser frequency associated with this transmission,the laser frequency is tuned to measure the transmission atmultiple frequencies, known as frequency scanning. A broadbandwidth of the absorption spectrum, 4.2 GHz for this exper-iment, is scanned in order to identify distinct characteristicswithin the spectrum. These characteristics typically includeregions of high and low transmission by the iodine cell, knownas transmission peaks and troughs, respectively. Photodetectormeasurements are recorded for each adjustment of the incid-ent laser frequency; so, the features can be used to determinethe incident frequency delivered by the subsystem by compar-ison to the theoretical model. Figure 6 shows the mean incid-ent transmission scan compared to the theoretical spectrum,with each distinct incident frequencymarked via symbols. The

5


Figure 6. Theoretical transmission spectrum compared to theincident transmission measured by the photodetectors during theexperiment.

experimental scan shows little deviation from the theoreticalmodel. Any frequency from this scan can be chosen for a velo-city calculation; however, it is preferred to choose the incidentfrequency based on the expected Doppler-shifted frequency.For this work, an incident frequency corresponding to 50%transmission was used.

The light scattered by the flow, collected by the observersubsystem, must be used to determine the Doppler-shifted fre-quency. This procedure is slightly more involved, as the pulsesof laser light are visible in the raw PMT signal as a con-sequence of the laser multiplexing. As shown in figure 7, thedistinct pulse of each laser sheet can be identified, as well asthe dark time between pulses of the laser sheet, according tothe multiplexing cycle described previously.

The duration of the measurement determines the numberof laser pulses in the signal. A processing algorithm writtenin MATLAB extracts the mean intensity value, time-averagedduring each pulse. When the laser sheet is off, a base levelof counts is still read as signal by the PMT arrays. Thus, theintensity during the laser’s dark time must be subtracted fromthe mean pulse intensity in order to find the instantaneousintensity from the flow, as shown by equation (3),

Iflow = Ipulse− Idark (3)

where Iflow is the measured instantaneous intensity of lightscattered by the flow, Ipulse is the time-averaged intensity overthe duration of the pulse, and Idark is the time-averaged intens-ity over the duration of the dark time. Figure 8 shows the cam-era intensity after the initial pulse processing, for the filteredand reference signals of one pixel pair.

Expectedly, the intensity of the filtered signal is less thanthe intensity from the reference (unfiltered) signal, since someof the light has been absorbed by the vapor cell. To find thetransmission of the Doppler-shifted light through the cell, the

Figure 7. Snippet of the raw time series signal from a single sensorin the PMT array showing different pulses of laser light.

Figure 8. A portion of the time series from a single sensor in thePMT array after initial pulse processing.

filtered PMT signal is divided by the unfiltered signal. For ref-erence, the incident laser frequency chosen for the measure-ment is 18 789.88 cm−1, corresponding to a transmission ofapproximately 50%.

The pulse processing routine is performed on each of data-sets in the scan, which results in calculation of the uncalib-rated transmissions. Figure 9 shows the mean value of theuncalibrated transmission for each sensor on the PMT cam-eras, for multiple incident frequencies. The shape of this spec-trum exhibits similarity to the reference photodetector trans-mission, figure 6. However, due to differences in amplificationof each PMT sensor, the magnitude of the transmission spec-trum varies for each pixel, as shown by figure 9. The signalsmust be calibrated in order to calculate the Doppler shift, andthe calibration procedure is described as follows.

6


Figure 9. Uncalibrated mean transmission from the observer duringthe experiment. Each line is the mean transmission signal from onepixel on the PMT array.

During the measurement, data is collected by both the pho-todetector pair (incident light) and the PMT arrays (observedlight) for each frequency of the laser scan. The mean trans-mission from the photodetector should exactly reconstruct thetheoretical transmission spectrum, as shown by figure 6. Themean transmission from each pixel on the PMT array shouldalso reconstruct this transmission spectrum, albeit shifted infrequency by the mean flow velocity due to the Doppler shift.As shown by figure 9, the mean PMT transmissions show sim-ilar shape to the model spectrum, with varying magnitudescaused by differences in amplification of each sensor. A scal-ing factor between the peak transmission of the theoreticalspectrum and the peak of the mean observed spectrum is com-puted, and the PMT signals are normalized by this constant.As shown in figure 10, the transmission spectra have been col-lapsed by the scaling factor. Additionally, the Doppler shiftdue to the flow is clearly visible as the observed spectra areshifted left of the incident signal (black line). The instantan-eous transmission signal is subjected to variations in the Dop-pler shift caused by the flow turbulence; therefore, the meantransmission signal is used for the calibration. Since sufficientlight scattering by seed particles is not as easily achieved withthe flow off, the data from the flow measurement is used.

Each time-resolved pixel signal is then normalized byits individual scaling factor, resulting in a vector of calib-rated, instantaneous transmissions. The instantaneous laserfrequency is calculated by finding the frequency which mostclosely matches the measured transmission in a portion of themodel spectrum, centered around the incident frequency. Theshift from the AOM is accounted for by adding 80 MHz tothe Doppler-shifted frequency. To find the magnitude of theinstantaneous frequency shift, the incident frequency is simplysubtracted from the Doppler-shifted frequency. The instantan-eous velocity is then determined as in equation (1).

Figure 10. Calibrated mean transmission from the observer. Theblack line is the incident laser transmission, measured by thephotodetector. Each other line is the mean signal from one pixel ofthe PMT array.

To determine the three-component velocity, a minimumof three distinct signals are needed. With two laser pulsesmeasured by two cameras, four signals are obtained from thismeasurement. The three best camera signals are chosen byfinding the minimum root mean square error between the the-oretical spectrum and each pixel. From there, the calibratedtransmissions can be used to calculate velocity according toequation (1).

2.3. Facility

A free jet was used at Virginia Tech’s Advanced Power andPropulsion Lab (APPL) for this experiment. The unheated airexits through a 3D-printed, converging, axisymmetric nozzlewith an exit diameter of 12.7 mm, at a Mach number of0.91. For this jet condition, the diameter Reynolds number is275 000 and the exit velocity is 288 m s−1 assuming isentropicrelations. The jet condition is monitored by total pressure andtemperature probes just upstream of the converging nozzle,with values read by a digital manometer (Dwyer, input pres-sure from 0–100 psi, 0.5% uncertainty) and a digital thermo-meter (Omega, type K, 1/8” diameter, 0.5 ◦C full-scale uncer-tainty). Flow seeding is introduced far upstream of the nozzleexit in the form of diethylhexl-sebacate (DEHS) particles withdiameters less than 1 µm. Error due to the particle responsetime is discussed in section 2.4.

The TRDGV measurement plane in this experiment wasa streamwise-oriented plane, centered eight diameters down-stream of the nozzle exit. The plane, shown schematicallyin figure 11, consists of 8 transverse rows and 4 streamwisecolumns, resulting in 32 positions of measurement for this sys-tem. Each pixel in the plane measures a 2 mm × 2 mm regionin the flow.

7


Figure 11. Measurement plane orientation in jet flow, showingmeasurement downstream of the potential core collapse.

For validation of the results, two different measurementtechniques were used to measure a transverse profile: a Pitotprobe was used to characterize the jet mean flow, and a single-component Auspex hot wire anemometer was used to obtaintime-resolved information. Based on the input range of themanometer, the total pressure measurement is read to an accur-acy of 0.5% of the reported pressure, corresponding to lessthan 1 m s−1 error. The hot wire was oriented parallel to theazimuthal axis and had a wire length of 1.2 mm. The frequencyresponse of the hot-wire probe was limited to 20 kHz, determ-ined by performing a square-wave test at jet operation condi-tions. Calibration of the hot wire was performed at the nozzleexit, varying the velocity of the jet from ± 30% of the axialvelocity at the 8D station. King’s law was then used to determ-ine a relationship between the voltage from the hot wire andfluid velocity [19].

2.4. Uncertainty

Uncertainty will affect each term in the Doppler equation[equation (1)]; however, only the frequency shift is directlymeasured. Ecker et al [7] previously quantified several errorsin the TRDGV measurement system using a simulated velo-city signal, generated using Pope’s model turbulent powerspectrum [20], with integral and Kolmogorov timescales rep-resentative of supersonic jets. The analysis showed that tem-poral averaging was the main contributor to random error inthe instantaneous velocity measurement, proportional to theratio of the multiplexing time interval to the flow timescaleof interest. For the flow in this experiment, the integral times-cale, found by integrating the autocorrelation of the velocitysignal, is approximately 96 µs. Using the analysis from Eckeret al, the RMS uncertainty (i.e. the 68% confidence interval)in instantaneous velocity measurement due to temporal aver-aging is estimated to be less than 1 m s−1 for each componentof velocity [7]. This error will scale with the nature of the flow,decreasingwith longer timescales, as in cold or subsonic flows,and increasing with shorter timescales, as in heated jets.

The bias uncertainty of the measurement will be affected bythe geometric configuration of the instrument and the uncer-tainty in the transmission. The uncertainty due to geometricconfiguration of this measurement system is most affected bythe angle of the intersecting laser sheets, shown in figure 3.Ecker et al found that an angle between 30◦ and 50◦ minimizedthree-component velocity RMSuncertainty [7]. The geometricerror is not expected to vary with the flow velocity; however,

the uncertainty in transmission determination and the slope ofthe transmission line will be affected by the velocity of theflow.

The error in determination of the transmission (and there-fore the frequency) will manifest in the measurement as arti-ficial turbulence. A Monte Carlo simulation of signal-to-noise

ratio (SNR = 10log10(PsignalPnoise

); power, P) was used by Ecker

et al to calculate the uncertainty in vapor cell transmission,and accordingly, the measured frequency [7]. To calculate theSNR for this work, we utilize the measurement occurring inthe trough of the transmission spectrum. At this frequency, thesignal collected by the filtered PMT is entirely noise becauseall scattered light has been absorbed by the iodine filter; andso, the variance of this signal can be used to estimate Pnoise.The signal’s power is estimated as the sum of its real varianceand the variance of the signal’s noise. We can approximate theSNR for the current work using the following equations.

SNR= 10log10

(σ2Tt

σ2Tn

)(4)

σ2Tt =

(∂T∂ft

)2

σ2ft+

(∂T∂rt

)2

σ2rt (5)

σ2Tn =

(∂T∂fn

)2

σ2fn+

(∂T∂rn

)2

σ2rn (6)

where σ2 is the variance of the signal, T is the measured trans-mission, t is the ‘true’ contribution of the signal, n is the noisecontribution of the signal, f is the filtered camera signal, andr is the reference camera signal in the trough. Evaluating thisratio for each camera, SNR was estimated to be 24 dB for thismeasurement, corresponding to an RMS uncertainty in trans-mission of less than 2% according to the study by Ecker et al[7] From equation (1), the velocity measured is a function ofthe Doppler shift, incident frequency, and geometric arrange-ment of the observers; therefore, the uncertainty in transmis-sion corresponds to an uncertainty in velocity dependent on theslope of the chosen transmission line. Using the chosen trans-mission line, jet velocity, and geometric arrangement from thisexperimental configuration, this error is estimated to be within4 m s−1. The absolute error values presented by the DGV tech-nique make it well-suited for high-speed flows, although thepractical limitations for DGV in low-speed applications havebeen explored in literature [21]. For low flow speeds, a smallerDoppler shift will occur, and this small shift could be obscuredby measurement noise. A steeper transmission line would bedesired to maximize sensitivity to the change in velocity, sincethe Doppler shift will be smaller. An alternate measurementtechnique may be desired for these low-speed applications.

The scattered light signal is averaged over the size of eachpixel, which will act as a low-pass filter and influence themeasurements [22]. Using the kinetic energy budget for air jetsderived by Panchapakesan and Lumley [23], the dissipationrate can be estimated for this jet as ϵ= 0.016 U3

r1/2, where U is

the local centerline jet velocity and r1/2 is the half-width of thejet. The dissipation rate was estimated to be 12.8× 106 m2 s−3,

8


Figure 12. Mean jet velocity profiles measured using TRDGV(three-component), hot wire (single-component), and Pitot probe(single-component).

resulting in a Kolmogorov timescale of 1.2 µs. This timescaleis nearly resolved by our sampling rate (4 µs); however, thespatial resolution of the current implementation is not as wellresolved. Using the dissipation rate estimate, the Kolmogorovlength scale is estimated to be 4 µm. This scale is approxim-ately 500 times smaller than the size of the pixel in real space;so, it is clear that some level of aliasing will occur due to spa-tial under-sampling. The effect of aliasing will be observed inthe high-frequency region of the velocity spectra, as describedby Gamba and Clemens [22]. Since the authors primarily seekto develop an instrument that is capable of sensing the dynam-ics of large-scale turbulence and flow instability features, thislimitation for the smallest scales of turbulence is tolerated inthe current work.

The ability of the seeding particles to follow the flow willalso contribute to the measurement uncertainty, and can beshown by the Stokes number. Ideally, the response time of theparticle should be faster than the flow’s smallest timescale foraccurate measurement of seeded flow. The diameter of seedingparticles in the current work is less than 1 µm, leading to anestimated particle relaxation time of 2.3 µs. The Stokes num-ber based on the jet’s velocity and diameter is 0.03, meaninglarge-scale motion is captured well by the particles. Calculat-ing the Stokes number based on the smallest scales, the Stokesnumber is approximately 115. This magnitude indicates thatthe particles will not follow the smallest scales of turbulence;however, the effects of the spatial filtering, described previ-ously, are expected to dominate the high-frequency error.

Uncertainty in hot wire measurement, assuming survivalof the wire, is predominantly dependent on the turbulenceintensity of the flow and also the error due to spatial averaging.The hot wire used in this experiment was 1.2 mm in length,comparable to the pixel size in the TRDGV measurement. A

Figure 13. Mean turbulence intensity profiles measured usingTRDGV (three-component) and hot wire (single-component).

detailed uncertainty analysis for hot wire measurements wasconducted by Tutu and Chevray, in which they investigatederrors in instantaneous velocity, mean quantities, and turbu-lence intensity both in single hot wires and in cross wires [24].For a flow with axial turbulence intensity of 20%, instantan-eous velocity errors totaled 1.3% of the flow velocity. For flowspeeds in this experiment, approximately 3m s−1 error in velo-city measurement would occur.

3. Results and discussion

The subsonic jet was measured using the TRDGV systemand data were obtained for 32 points in the flow, arranged inthe grid previously described. Mean and time-resolved meas-urements are presented from one column of the PMT arrayin order to demonstrate the validity of the technique. Thecoordinate system for this measurement is defined in figures3 and 11.

3.1. Mean flow quantities

Figure 12 shows the mean jet velocity profiles in the regionmeasured for three velocity components. The axial direction,has been measured with three different techniques. Uncertain-ties in the mean velocity for the three measurements are pre-viously discussed in section 2.4. The peak jet velocity at thisaxial station is approximately 0.72Uj, indicating a region wellbeyond the collapse of the potential core. The mean axial velo-city measured using TRDGV compares within 12 m s−1 ofthe probe and hot wire, in the most extreme point, while RMSerror between the probe and TRDGV was 7 m s−1. Second-ary mean velocities are expectedly low in magnitude, rangingwithin 10% of Uj. These velocities are approximately equal toeach other, indicating an axisymmetric expansion of the jet.

9


Figure 14. Fluctuating velocity spectra for varying transverse position at x/D = 8. (a) Axial velocity, (b) Transverse velocity, and (c)Azimuthal velocity.

The azimuthal direction has a slightly positive bias, indicatingthe measurement plane could have been radially offset fromthe jet’s center.

Turbulence intensity, the square root of the squared fluc-tuating velocity term, is shown in figure 13. For a developingfree jet, lower turbulence levels are expected near the jet axisdue to still existing remnants of the potential core [25]. Asthe jet expands, turbulence intensity increases as a result ofentrainment with the surrounding air. In figure 13, turbulenceintensity is lowest in the center of the jet for each velocity com-ponent, as expected. Axial turbulence intensity measured byhot wire and TRDGV compare well, within 0.6% RMS Themagnitude and shape of the turbulence profile compares wellto previously documented values of subsonic jets as presentedby Lau, Morris, and Fisher [26], as well as Bridges and Wer-net [27]. Secondary velocity turbulence intensities showmuchlower turbulence levels than the axial direction, ranging from6% to 10%. These components show the same overall trend oflower intensity in the center, which increases through the shearlayer. The asymmetry of these components about the jet’s cen-ter indicate that the measurement plane may have been angledfrom the vertical direction.

3.2. Time-resolved flow quantities

The strongest appeal for using this instrument is its ability toobtain time-resolved flow information. Spectra of the time-resolved velocities were calculated using Welch’s method forestimating power spectral densities, implemented in MAT-LAB, with the time signal divided into 300 bins. Detailedexplanation of Welch’s method can be found in Bendat andPiersol [28]. After processing the data, two spectral tones (withfrequencies of 4 kHz and 12 kHz) appeared in the signals. Todetermine if the tones were flow related, the data collected bythe filtered PMT at a laser frequency in the transmission troughwere examined. At this frequency, all the intensity of the laseris absorbed by the iodine cell, and so the filtered signal can-not contain any flow information. The presence of the tones inthese data indicated that they could not be flow-related. The

tones were then manually removed from the spectra so theywould not affect any comparisons.

Figure 14 presents the spectra for each velocity compon-ent, at varying radial position. In the axial velocity spectra,figure 14(a), a transfer in spectral energy to higher frequen-cies occurs due to the presence of the potential core, as hasbeen observed in literature [29]. Additionally, near the cen-ter of the jet, we see −5/3 power-law dependence indicativeof the inertial subrange of isotropic turbulence [20]. The mag-nitude of spectral energy increases through the shear layer dueto increased levels of turbulence. Figures 14(b) and (c) showthat the fluctuating v and w velocity spectra have lower energythan the axial component, due to slower velocities and lessturbulence intensity. These spectra do not appear to exhibitpower-law dependence. Although the magnitudes of spec-tral energy in these two directions are similar to each other,the spectra exhibit different behavior in lower frequencies.In these components we again see increased spectral energythrough the shear layer. The noise-limited spectral responseof this measurement appears to be approximately 40 kHz.The behaviour of these spectra show similarities to the aliasedspectra presented by Gamba and Clemens [22]. It is evid-ent that the spatial under-sampling in this measurement res-ults in aliasing of the turbulent signal, most noticeably by thereduction of high-frequency roll-off in the transverse velocityspectra.

Figure 15 shows a comparison of the axial velocity spec-tra measured using TRDGV to various spectra from literat-ure [30–34], plotted non-dimensionally for better comparison.Axial distance from the nozzle exit is used as the length scaleof the Strouhal number, to account for differences due to prox-imity to the potential core. Figure 15(a) compares the spectraat the lipline position. The axial velocity spectrum measuredwith TRDGV compares very well to the hot wire measure-ment. The spectral shape generally follows the spectra fromliterature; however, −5/3 decay is not observed in the liplinespectra of the current work. Instead, the lipline data followsa − 1 power-law ‘, which has also been observed by Bereshet al [6].

10


Figure 15. Comparison of axial velocity spectra to literature for (a) y/D = 0.5 and (b) y/D = 0.

Figure 15(b) shows axial velocity spectra at the jet center-line. Note that the hot wire measurement for this radial pos-ition is not shown due to a malfunction of the anemometer.It is first noticeable that the characteristic increase in spectraldensity near Strouhal number of 0.25, as shown by Morris andZaman [34], is not as prominent sufficiently downstream ofthe potential core breakdown. This is evident in the TRDGVspectrum from this experiment (blue) and in previous work byNarayanan et al (green) [33], which both show measurementsin axial stations beyond the breakdown of the potential core.The TRDGV spectral shape compares very well to the datafrom [33], with the slope in the inertial subrange in the currentdata at x/D= 8 lying between the slopes from the comparisondata which were acquired at x/D= 5 and 10.

4. Conclusions

The current work expanded upon previous efforts towards tem-poral and spatial resolution to demonstrate a TRDGV instru-ment capable of measuring three-component velocities at 32simultaneous points in a high speed flow with a repetition rateof 250 kHz. Implementing laser frequency scanning withinthe TRDGV system resulted in a simple and robust way tocalibrate the raw intensity signals. Data were collected ona high subsonic jet at an axial location downstream of thepotential core collapse. Mean velocity measurements werevalidated using a hot wire and Pitot probe and showed excel-lent agreement within 7 m s−1 RMS Measurements of turbu-lence intensity showed good agreement between the TRDGVmeasurements and the hot wire probe. Instantaneous velocit-ies were assessed by calculating power spectra of the three-component velocity using Welch’s method. The axial velocityspectra revealed broadband spectral agreement to the hot wiredata, as well as spectra from literature, both showing the−5/3power law dependence of the inertial subrange of turbulence.Secondary velocity spectra revealed lower energy magnitudes,as well as evolving spectral behavior through the shear layer.

The velocimetry instrument described in this paper showspromising capability for obtaining measurements in highspeed compressible flows, including transonic and super-sonic flows. Simultaneous multipoint measurements provid-ing spatial resolution to the instrument can be used to studyhow turbulent structures convect in the flow. With the three-component capability, experimental investigation of time-resolved vorticity and azimuthal modes are possible. In addi-tion to providing numerous analysis opportunities to developmore insight into the evolution of turbulent structures, theinstrument is suitable for studying other fluid mechanics prob-lems. Transient and unsteady flow behaviors such as shockwaves can also be observed using this instrument. Combin-ing these qualities into one instrument makes for a robust,widely applicable measurement system. Additionally, sinceDGV does not rely on sensing of individual particles, thetechnique is scalable. This point gives this instrument astrong appeal in measuring flows in ranging from laborat-ory settings to full-scale gas turbine engine rigs. Continueddevelopment of the system will further improve the meas-urement. Utilizing additional channels of the PMT arrayswould be a simple way to increase the number of measure-ment points; however, replacing the PMT arrays with highspeed cameras would increase the spatial resolution of thesystem as well as the ease of data processing, better suit-ing the instrument for commercialization. The abilities ofthis TRDGV instrument, combining spatial resolution, three-component measurement, and high temporal resolution, makefor a diverse and valuable instrument for measuring high speedflows.

Acknowledgments

The work described was supported by Navy grants N00014-16-1-2444 and N00014-14-1-2836, which was funded by theOffice of Naval Research and managed by Dr Steven Martens.The authors would also like to acknowledge Sean Shea, Dr

11


David Mayo Jr, and Dr Kyle Daniel for providing guidanceand numerous conversations regarding the experiment, as wellas Agastya Balantrapu for the hard work in collecting the hot-wire measurements.

ORCID iDs

Ashley J Saltzman https://orcid.org/0000-0001-9599-2986K Todd Lowe https://orcid.org/0000-0002-0147-4641

References

[1] Komine H 1990 System for measuring velocity field of fluidflow using a laser Doppler spectral image converter USPatent No. 4919536

[2] Meyers J F and Komine H 1991 Doppler global velocimetry: anew way to look at velocity Laser Anemometry 1 289–96

[3] Thurow B, Jiang N and Lempert W 2013 Review of ultra-highrepetition rate laser diagnostics for fluid dynamicmeasurements Meas. Sci. Technol. 24 012002

[4] Thurow B S, Jiang N, Lempert W R and Samimy M 2005Development of megahertz-rate planar Doppler velocimetryfor high speed flows AIAA J. 43 500–11

[5] Wernet M P 2007 Temporally resolved PIV for space-timecorrelations in both cold and hot jet flowsMeas. Sci.Technol. 18 1387–403

[6] Beresh S J, Henfling J F, Spillers R W and Spitzer S M 2018‘Postage-stamp PIV’: small velocity fields at 400 kHz forturbulence spectra measurements Meas. Sci. Technol.29 034011

[7] Ecker T, Brooks D R, Lowe K T and Ng W F 2014Development and application of a point doppler velocimeterfeaturing two-beam multiplexing for time-resolvedmeasurements of high speed flow Exp. Fluids55 1819–33

[8] Ecker T, Lowe K T and Ng W F A rapid response 64-channelphotomultiplier tube camera for high-speed flowvelocimetry 2015 Meas. Sci. Technol. 26 027001

[9] El-Desouki M, Deen M J, Fang Q, Liu L, Tse F andArmstrong D 2009 CMOS image sensors for high speedapplications Sensors 9 430–44

[10] Duke D J, Knast T, Thethy B, Gisler L andEdgington-Mitchell D 2019 A low-cost high-speed CMOScamera for scientific imagingMeas. Sci. Technol. 30 075403

[11] Ecker T, Lowe K T and Ng W F 2015 Eddy convection indeveloping heated supersonic jets AIAA J. 53

[12] Ecker T, Lowe K T and Ng W F 2016 Scale-up of thetime-resolved doppler global velocimetry technique 54thAIAA Aerospace Sciences Meeting AIAA 2016-0029

[13] Stuber M, Lowe K T and Ng W F 2019 Synthesis ofconvection velocity and turbulence measurements inthree-stream jets Exp. Fluids 60 5

[14] Cadel D R and Lowe K T 2015 Cross-correlation Dopplerglobal velocimetry (CC-DGV) Opt. Lasers Eng.71 51–61

[15] Fischer A 2017 Model-based review of Doppler globalvelocimetry techniques with laser frequency modulationOpt. Lasers Eng. 93 19–35

[16] Fahringer T W F Jr , Burns R A, Danehy P M, Bardet P M andFelver J 2019 Pulse-burst cross-correlation Doppler globalvelocimetry AIAA Aviation 2019 Forum

[17] Forkey J N, Lempert W R and Miles R B 1997 Corrected andcalibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths Appl. Opt. 36 6729–38

[18] Charrett T O H, Nobes D S and Tatam R P 2007 Investigationinto the selection of viewing configurations forthree-component planar Doppler velocimetry measurementsAppl. Opt. 46 4102–16

[19] King L V 1914 Determination of the convection constants ofsmall platinum wires with applications to hot-wireanemometry Proc. R. Soc. Lond. A 90 563–70

[20] Pope S B 2000 Turbulent Flows (Cambridge: CambridgeUniversity Press)

[21] McKenzie R L 1997 Planar Doppler Velocimetry performancein low-speed flows AIAA 35th Aerospace Sciences MeetingExhibit

[22] Gamba M and Clemens N T 2011 Requirements, capabilitesand accuracies of time-resolved piv in turbulent reactingflows AIAA Aerospace Sciences Meeting 2011

[23] Panchapakesan N R and Lumley J L 1993 Turbulencemeasurements in axisymmetric jets of air and helium. Part1. Air jet J. Fluid Mech. 246 197–223

[24] Tutu N K and Chevray R Cross-wire anemometry in highintensity turbulence 1975 J. Fluid Mech. 71 785–800

[25] Bridges J and Wernet M P 2010 Establishing consensusturbulence statistics for hot subsonic jets 16th AIAA/CEASAeroacoustics Conf. AIAA 2010-3751

[26] Lau J C, Morris P J and Fisher M J 1979 Measurements insubsonic and supersonic free jets using a laser velocimeterJ. Fluid Mech.

[27] Bridges J and Wernet M P 2011 The NASA subsonic jetparticle image velocimetry (PIV) dataset. NASA ReportNo. NASA/TM-2011-216807

[28] Bendat J S and Piersol A G 2011 Random Data (Hoboken, NJ:Wiley)

[29] Davies P O A L, Ko N WM and Base B 1967 The localpressure field of turbulent jets. Aero. Res. Counc.Paper 989

[30] Power O, Kerherve F, Fitzpatrick J and Jordan P 2004Measurements of turbulence statistics in high subsonic jets10th AIAA/CEAS Aeroacoustics Conf. AIAA 2004-3021

[31] Kerherve F, Jordan P, Gervais Y and Valiere J C 2004Two-point laser Doppler Velocimetry measurements in amach 1.2 cold supersonic jet for statistical aeroacousticsource model Exp. Fluids 37 419–37

[32] Morris P J A note on noise generation by large scale turbulentstructures in subsonic and supersonic jets 2009 Int. J.Aeroacoust. 8 301–16

[33] Narayanan S, Barber T J and Polak D R 2002 High subsonicjet experiments: turbulence and noise generation studiesAIAA J. 40 3

[34] Morris P J and Zaman K B Velocity measurements in jets withapplication to noise source modeling 2010 J. Sound Vib.329 394–414

12

Chapter 4

Finite control volume and scalabilityeffects in velocimetry for applicationto aeroacoustics

The content of this chapter is under review for Experiments in Fluids. (Ashley J. Saltzman,K. Todd Lowe, and Wing F. Ng, “Finite control volume and scalability effects in velocimetryfor application to aeroacoustics”).

31

Experiments in Fluids manuscript No.(will be inserted by the editor)

Finite control volume and scalability effects in velocimetry forapplication to aeroacoustics

Ashley J. Saltzman · K. Todd Lowe · Wing F. Ng

Received: date / Accepted: date

Abstract The ability to scale the field of view for velocimetry methods is particularly attractive for aeroacousticsstudies, where turbulence contributions in long-lived, low wavenumber structures account for the most important

sources of radiated noise. Thanks to its core operating principles, Doppler global velocimetry (DGV) offers in-teresting opportunities for large-scale flow measurements. As is well known, a larger field-of-view (FOV) in themeasurement will change the spatial resolution, meaning that each measurement is integrated across a largercontrol volume. This finite size will affect the velocity and turbulence measurements, as well as the observable

wavenumbers in the measurement. The present study confirms the viability of DGV for studying low wavenum-bers while examining the influence on higher wavenumbers of the less coherent turbulent structures also present inhigh-speed flows. In the flows examined by the current work, mean velocity bias error due to integration over the

measurement region was shown to be small, less than 0.005%, for control volume heights up to 4 mm. Althoughsignificant energy attenuation occurs for high wavenumbers, the low wavenumber turbulent structures which dom-inate far-field noise are found to be unaffected by the size of the control volume required for large measurementof both laboratory- and full-scale supersonic jet flows. The results indicate a large-scale velocimetry system such

as DGV can be a valuable tool for researchers to study aeroacoustics in high-speed flows.

Graphic Abstract

Advanced Propulsion and Power LaboratoryVirginia TechBlacksburg, VA USA 24061Tel.: +540-231-7650Fax: +540-231-9632E-mail: [email protected]

2 Ashley J. Saltzman et al.

1 Introduction

Large-scale turbulent structures are believed to domi-

nate the noise produced by heated supersonic jets. De-spite contributing less to the total turbulence kineticenergy of the flow than more energetic, shorter-scale

turbulence, the high coherence of large-scale structuresmakes them extremely efficient at radiating noise (Jor-dan and Colonius (2013)). Because these structures canbe correlated over several axial lengths, a large region of

the flow must be measured, in addition to resolving theflow temporally, to further characterize the unsteadybehavior of these structures and their relationship to

far-field noise.

Laser-based velocimetry techniques are invaluable

to the study of flow due to their ability to measurethe flow non-intrusively. Techniques such as particle im-age velocimetry (PIV) and Doppler global velocimetry(DGV), which will be discussed throughout this work,

have shown to be effective for relating flow behavior toacoustics (e.g. Koschatzky et al. (2011); Moore et al.(2010); Moore et al. (2011); Gurtler et al. (2016)). For

example, Koschatzky et al. (2011) utilized Curle’s equa-tion to estimate the pressure field from PIV measure-ments and showed good agreement to microphone mea-surements of an open cavity in a low-speed flow. A chal-

lenge emerges in using these diagnostic techniques tostudy aeroacoustics of high-speed flows. Fundamentally,any velocimetry technique will measure the flow with a

defined spatial resolution: a control volume which has afinite size. Scaling a system to a larger measurement re-gion, which would be key for observation of long-lived,

highly correlated structures, typically necessitates eachpixel to measure a larger area. The size of this con-trol volume undoubtedly will affect the measurements.This concept is illustrated on a free jet shown by Fig.

1. Although the smaller field-of-view (FOV) capturespart of the large-scale instability feature, the evolutiondownstream of the potential core will be missed. The

larger FOV facilitates observation of lasting, large-scaleturbulent structures, at the expense of spatial resolu-tion. The effect of the increasing integration volume onthe mean, instantaneous, and turbulence measurements

must be characterized to assess the validity of a large-scale measurement for the study of aeroacoustics.

Uncertainty analyses of measurement techniques havesought to explain error contributions based on the spe-cific principles of the technique, such as seeding uni-

formity for PIV, or laser frequency stability in DGV.However, the finite control volume influence has con-ventionally been examined for laser Doppler velocime-try (LDV) measurements, in which the velocity is mea-

sured from scattering of particles which pass through

intersecting laser beams. Representing this problem an-

alytically, Durst et al. (1995) expressed the velocitymeasurement in the form of a truncated Taylor expan-sion to derive corrections for LDV turbulence intensity

measurements. Considering the ellipsoidal shape of theLDV control volume and the discreteness of particledetection, Fischer et al. (2000) also derived mean ve-locity and turbulence intensity corrections, as well as

corrections for higher-order moments. In the interestof determining the integration effect on spectral mea-surements by PIV, Gamba and Clemens (2011) repre-

sented the control volume as a three-dimensional (3D)box filter applied to the flow field. The effects of alias-ing were also considered on the PIV measurement at aspatial frequency corresponding to the control volume’s

height, as a way to approximate error in local velocitygradient PIV measurements. For prediction of acous-tics, the effects of spatial resolution were investigated

by Moore et al. (2010) through comparison to direct nu-merical simulation (DNS) of incompressible flows. Us-ing achievable control volume sizes of their PIV system,

the estimated pressure fields were shown to agree wellfor Strouhal numbers (St, a non-dimensional frequency)up to 1 (Moore et al. (2010)). The reviewed works, ex-amining lower Reynolds number flows, have concluded

that the size of the control volume has a quantifiableeffect on the measurements. The question which per-sists is how these findings will scale when considering a

larger measurement region in a high-speed flow.

1.1 State of the Art

To expand the ideas of finite control volume effects tolarge-scale measurement of high-speed flows, it is neces-sary to review relevant implementations of velocimetry

techniques. Two widely used planar techniques, PIVand DGV, observe light scattered by seeding particlesto measure the flow at many points in space and time.PIV compares the particle locations between two (or

more) images separated by a known timestep to mea-sure velocity. With the progression of camera and com-puting technology, researchers have been able to push

the limits of temporal resolution. Notably, state-of-the-art PIV systems can acquire images at framerates upto 100 kHz, and the technique shows promising abilityto measure space-time correlations in heated flows. In a

heated subsonic jet, a field-of-view (FOV) of 0.3 × 0.15m was measured using TR-PIV up to 25 kHz and com-pared well to hot-wire validation measurements (Wer-

net (2007)). On a larger scale, time-averaged PIV hasbeen utilized for measurement of rotorcraft in NASA’ssubsonic wind tunnel (Jenkins et al. (2009)). This work

measured three-component mean velocity in a 1.5 m ×

Finite control volume and scalability effects in velocimetry for application to aeroacoustics 3

Fig. 1: Illustration of observable flow features based on the measurement domain.

0.9 m region and observed complex interaction of thebody and rotor wakes. Details of a full-scale rotor wakemeasurement reveal challenges to large-scale applica-

tion of PIV (Wadcock et al. (2011)). In PIV, individualseeding particles must be imaged by the camera, whichcan limit the field of view and scalability of the tech-nique. The previous works experienced some practical

limits towards uniform seeding concentration and mea-suring particles in the large region of interest. A reviewof full-scale PIV rotor measurements also showed in-

creased noise levels as compared to smaller-scale PIVapplications (Raffel et al. (2012)).

As an alternative to tracking particle movement to

determine velocity, DGV uses absorption characteris-tics of a reference vapor to measure the frequency shiftof particles in a flow, by the Doppler effect. Early ef-

forts towards using DGV for large wind tunnel applica-tions were focused on mitigating instrumentation issuessuch as frequency stability, the need for beam-splitting

optics, and inadequate particle seeding (Meyers et al.(2004); Beutner et al. (1998)). Additionally, DGV hasbeen investigated as a technique capable of high tempo-ral resolution. Time-resolved DGV (TRDGV) in a high-

speed flow was first demonstrated as a single componentmeasurement, through the development of a megahertz-rate pulse-burst laser, and the more widespread avail-

ability of high-speed cameras (Thurow et al. (2005)).Using a continuous-wave laser, a more cost-effective al-ternative to pulse-burst lasers, a three-component TRDGVsystem was developed for studying convection in su-

personic heated jets (Ecker et al. (2014)). Multipoint,three-component velocity measurements were recentlydemonstrated by the current authors at a repetition

rate of 250 kHz in a laboratory-scale subsonic jet, albeitat a small region of interest (Saltzman et al. (2020)).In DGV, light scattering from multiple seeding parti-

cles can contribute to the signal measured by a singlepixel. This is distinct from PIV, which directly mea-

sures particle movement. Therefore, DGV is well-suitedto be scaled to large measurement regions because it isnot necessary to distinguish individual particles. Thischaracteristic was utilized for TRDGV measurements

of the Nozzle Acoustics Test Rig at NASA Glenn, andmean convection velocity measurements compared wellto PIV mean velocity data (Ecker et al. (2016); Stuber

et al. (2019)). Although DGV is inherently compati-ble for scaling to fit the desired application, limited re-search has been done to study how the measurement isfundamentally affected by the size of the measurement

region.

1.2 Objectives of the Study

From the review, we have shown the potential of DGV

as a valuable technique for measuring large-scale turbu-lent structures; however, the effect of spatial resolutionin a large-scale, high-speed measurement system is not

yet understood. In the current work, we will review theanalyses used to characterize finite control volume ef-fects on velocity measurements. These analyses will beused as the foundation for a case study presented on

TRDGV. To validate the methods for high-speed flows,experimental TRDGV data of a high subsonic jet willbe used. Finally, the work is extended to predict the

effects on a large-scale TRDGV measurement. With aninterest in aeroacoustics application, we will examinethe instrument’s ability to capture noise-radiating tur-

bulent structures in a heated supersonic jet, consideringboth a laboratory- and full-scale setup. This work willserve as a guide for understanding the effects of a finitecontrol volume in large-scale, time-resolved measure-

ment.


2 Methods

2.1 DGV and Scattering Principles

Although the analyses presented in the current workcan apply to any time-resolved velocimetry system, wewill focus on the specific application to a large-scale

TRDGV measurement. The principle of DGV has beendescribed extensively by other works (e.g. Meyers andKomine (1991); Fischer et al. (2007)) and will be sum-marized to follow. To take a measurement, seeding par-

ticles, which scatter light, must be added to the flow.When laser light is scattered by the particles, its fre-quency will be shifted proportional to the velocity of

the particle,

∆fD =

−→U · (o− i)

λ(1)

where−→U is the velocity vector measured by the pixel,

o is the direction of observation by the camera, i is the

laser propagation direction, and λ is the incident laserlight frequency. Frequency of the laser light for DGVis measured by observing the transmission through amolecular vapor filter. Through known models for the

vapor absorption spectrum, the frequency can be deter-mined. The frequency shift is found by comparison toan incident measurement at zero velocity, obtained si-

multaneously. Since the geometry configuration of thesetup is known, the velocity can then be determined.Additional components of velocity can be resolved with

additional observation directions, which would requireadditional cameras. The reader is referred to Saltzmanet al. (2020) for an in-depth discussion of typical exper-imental setup and example procedures for a TRDGV

measurement.

As the system has a finite measurement volume,multiple seeding particles can move within the boundsduring the measurement, as depicted by Fig. 2. There-

fore, the velocity measured by Eq. (1) represents the av-erage of the velocities of all particles which are presentin the control volume during the measurement timestep.This velocity will differ from the true velocity in the

center of the volume, Uy0 . In planar velocimetry, thecontrol volume is formed by the region of the flow mea-sured by each pixel of the camera, and the thickness of

the laser sheet. In the current work, a camera pixel isconsidered to lie in the x-y plane, with the x coordinatealong the jet axis and the y coordinate in the trans-

verse direction. The z coordinate is in the azimuthaldirection, defined by the thickness of the laser sheet.

2.2 Effect on Mean Velocity Measurements

First, the effect of the finite control volume on themean velocity measurement will be investigated analyt-

ically. Each velocity measured by one pixel representsa volume- and time-integrated quantity, shown by Eq.(2). The analysis to follow is guided by the work shownby Durst et al. (1995), where they quantified the effects

of an elliptical control volume in LDV measurements.There are some key differences to this analysis to applyto DGV measurements, which will be discussed.

The measured velocity is first defined as the timeand volume integrated quantity,

Umeas = limT→∞

1

T

∫ T

0

{1

V

∫∫∫V

gUy0dV

}dt (2)

where Umeas is the mean velocity measured in the con-trol volume, T is total averaging time, V is the size ofthe control volume, g is an expression for the distri-

bution of seeding particles in the control volume, andUy0 is the true flow velocity of the center of the controlvolume.

The velocity in a jet flow, and all turbulent flows,will vary across all dimensions. However, the largestgradients will occur perpendicular to the jet axis, as

the jet entrains the surrounding ambient air. For thecurrent analysis, the velocity is assumed to vary onlyin the y-direction across the control volume. This as-sumption greatly simplifies the error modelling in the

current work; however, the authors note that the con-clusions drawn may not apply for flows with large az-imuthal gradients. We simplify Eq. (2) to

Umeas =1

h

∫ h/2

−h/2g(y)Uy0dy (3)

where h is the vertical (y) dimension of the control vol-ume. In the DGV measurement, multiple seeding parti-

cles can contribute to scattering the light to detect thefrequency shift. For small dimensions of the control vol-ume, both the distribution of particles and the intensityof the signal (scattered light) are uniform. Therefore,

the particle distribution in Eq. (3) multiplied by thedetection probability is assumed to be unity, g(y) = 1.By Taylor series expansion of the velocity, and neglect-

ing terms higher than the second order,

Umeas = Uy0 +1

h

∫ h/2

−h/2

[(∂U

∂y

)y +

(∂2U

∂y2

)y2

2!

]dy

(4)

One can obtain an expression for the mean velocity er-ror due to the finite control volume through evaluation


Fig. 2: Depiction of measurement over a finite control volume.

of the integral and simplification of Eq. (4). The er-ror will depend on the second derivative of the velocitywith respect to the normal direction and the height of

the control volume. Thus, the mean velocity measuredacross the control volume compared to the true veloc-ity in the center of the control volume will be larger

if the second derivative is positive, and smaller if it isnegative.

Umeas = Uy0 +h2

24

(∂2U

∂y2

)(5)

The authors note that Eq. (5) can be scaled with the

reference velocity, thus the percent error of mean veloc-ity could be written as,

UmeasUy0

− 1 =h2

24

(∂2U

∂y2

)/Uy0 (6)

The finite control volume will also affect the measuredturbulence intensity. To derive this error analytically,general expressions for the fluctuating velocity term inthe measurement are first written,

umeas = Uy0 − Umeas (7)

uy0 = Uy0 − Uy0 (8)

Combining the previous expressions, the measured fluc-tuating term is described by,

umeas = Uy0 + uy0 − Umeas (9)

By Taylor series expansion of the fluctuating term, andsubstitution of Eq. (5), the following expression (shown

in sigma notation for compactness) is found,

umeas = Uy0 +∞∑n=1

∂nU

∂ynyn

n!+ uy0

+∞∑n=1

∂nu

∂ynyn

n!− Uy0 −

h2

24

(∂2U

∂y2

) (10)

Noting that some terms can simplify and neglectinghigher-order terms,

umeas =∂U

∂yy +

∂2U

∂y2y2

2!+ uy0 +

∂u

∂yy +

∂2u

∂y2y2

2!

−h2

24

(∂2U

∂y2

) (11)

The expression for turbulence intensity error can thenbe obtained by squaring Eq. (11) and taking the ex-pected value. The error will depend on the mean veloc-ity gradient and the second derivative of the velocity

variance. From Eq. (12), one can observe that the firstterm in the brackets will manifest as turbulence ampli-fication in the measurement, while the second term can

act as either amplification or reduction, depending onthe sign. Thus, the overall error due to the finite con-trol volume size will depend on the magnitude of the

second term. This error represents the variance error inthe control volume due to inhomogeneous flow.

u2meas = u2y0 +h2

12

[(∂U

∂y

)2

+

(∂2u2y0∂y2

)](12)

The turbulence error shown by Eq. (12) can also bescaled by the reference velocity to show the non-dimensional

percent error due to the control volume,

u2meas − u2y0Uy0

=h2

12

[(∂U

∂y

)2

+

(∂2u2y0∂y2

)]/Uy0 (13)

2.3 Effect on Spectral Measurement

In addition to creating error in the mean flow measure-ments, the finite size of the control volume will also af-

fect spectral behavior, as turbulent fluctuations occur-ring at frequencies higher than the corresponding spa-tial frequency will not be detected. Gamba and Clemens(2011) proposed that the control volume will act as 3D

box-type filter on the velocity measurement, where itsvalue is 0 outside the control volume, and 1 inside the


control volume. By starting with a model for the tur-bulence spectrum, the effects of the size of the controlvolume on the spectral measurement can be quantified.The velocity-spectrum tensor for isotropic turbulence is

defined as

Φij (κ) =E (κ)

4πκ2

(δij −

κiκjκ2

)(14)

where κ is the 3D wavenumber vector, κi is the wavenum-ber component, δ is the Kronecker delta, and E(κ) is

the 3D energy spectrum. For homogeneous, isotropicturbulence, a model for the 3D energy-spectrum func-tion was proposed by Pope (2000),

E(κ) = Cε23κ−

53 fL(κL)fN (κη) (15)

where C = 1.5, ε is the dissipation term, η is the Kol-mogorov length scale, and fL and fη are the non-dimensional

functions,

fL(κL) =

(κL√

(κL)2 + cL

) 55+p0

(16)

fη(κη) = exp{−β[(κη)4 + c4η

] 14 + cη

}(17)

where cL = 6.78, cη = 0.40, p0 = 2, β = 5.2, and L =

k3/2/ε, with k defined as the turbulent kinetic energy.The corresponding 1D spectrum is then,

E11(κ1) =

∫∫ ∞−∞

Φ11(κ)dκ2dκ3 (18)

where Φ11(κ) is found using Eq. (14). For the presentwork, this integral will be evaluated using a trapezoidalnumerical integration method, computed for a maxi-

mum wavenumber of 2/η. Following the description ofthe 3D box filter from Gamba and Clemens (2011) toconsider the effect of the control volume, the filteredvelocity-spectrum tensor is

Φf11 = |H(κ)|2 Φ11(κ) (19)

where H(κ) is the form of the control volume filter.The control volume is the space defined by V = d1d2d3,where d is the physical size, and 1, 2, and 3 are the or-

thogonal directions of the flow. In the spectral domain,H(κ) will take the form of a sinc function,

H(κ) =sin(πκ1

κd1)

πκ1

κd1

sin(πκ2

κd2)

πκ2

κd2

sin(πκ3

κd3)

πκ3

κd3

(20)

where κd1 , κd2 , and κd3 are the wavenumbers corre-sponding to the control volume’s dimensions, 2π/d1,

2π/d2, and 2π/d3, respectively. Based on these defini-tions, the filtered 1D spectrum can be found,

Ef11 =

∫∫ ∞−∞|H(κ)|2 Φ11(κ)dκ2dκ3 (21)

The effect of the spatial filter will manifest as a re-duction in measured turbulence. The authors note thatthis spectral error addresses the filtering effect which

would occur in either homogeneous or inhomogeneousflows, which is distinct from the variance error shownby Eq. 12. To better show the effect relative to thewavenumber, the comparison of the filtered spectrum

to the model will be represented by the frequency re-sponse function,

T11(κ1) =

∫∫∞−∞ |H(κ)|2 Φ11(κ)dκ2dκ3∫∫∞

−∞ Φ11(κ)dκ2dκ3(22)

In addition to acting as a spatial filter, the size of thecontrol volume will also limit the sampling frequency of

the measurement. The sampling wavenumber is definedby

κs =2π

h(23)

where h is again the vertical dimension of the controlvolume. Because of our assumption of velocity variationsolely along the radial dimension of the control volume,we will use that dimension to determine the spatial

wavenumber. The Nyquist frequency, κs/2, describesthe highest wavenumber which can be measured indis-tinguishably by the signal. Within the control volume,

any turbulent fluctuation which occurs at wavenumbershigher than the Nyquist will be aliased by the measure-ment. Aliasing will be modeled for the current workby folding the filtered 1D spectrum, Eq. (21), at the

Nyquist frequency. The combined effect of the spatialfiltering and aliasing will represent the actual measuredspectrum in the experiment. Scripts for evaluating the

effects of the finite control volume described throughoutthis work can be acquired by contacting the correspond-ing author.

2.4 Flows of Interest

To investigate the effects of changing control volumesize on mean and spectral measurements, the methods

described in Sect. 2.2 – 2.3 will be applied to three dif-ferent flows of interest, shown in Table 1. The first flowcase, A, was chosen based on availability of experimen-

tal data collected by a TRDGV system, the results ofwhich are shown in Saltzman et al. (2020). These data


will be used to validate the analyses shown in the pre-vious sections. The authors note that this flow case hadan exit Mach number of 0.9; however, at the axial sta-tion measured, x/D = 8, the local Mach number was

0.6. The second flow case, B, was chosen based on thedesire to use large-scale TRDGV for characterizing thelarge-scale turbulence structures in heated supersonic

jets. The analysis presented in the current work will beused to predict behavior in the heated jets, as well as toassess the ability of large-scale TRDGV to resolve tur-

bulence likely to radiate noise to the far-field. The flowconditions for Case B were based on previous exper-iments conducted at Virginia Tech’s Advanced Powerand Propulsion Lab (APPL), although time-resolved

velocity data was not available for this case (Mayo Jr.et al. (2019); Daniel et al. (2019)). Finally, Case Cwill be used to investigate the suitability of large-scale

measurement to a full-scale, afterburning jet engine.This jet flow would have a much larger nozzle diame-ter and total temperature ratio (TTR = T0/T∞, whereT∞ is the ambient temperature) than the laboratory-

scale measurements. Large-eddy simulation data wasused to estimate the flow quantities for Case C (Liuet al. (2016)). The differing quantities in these flows

such as Reynolds number, dissipation rate, and TTRwill change the effect that the finite control volume hason each measurement and are also shown in Table 1.

Note that the Strouhal number of 1 for the full-scale jetoccurs at a much lower frequency than the laboratory-scale jets, indicating Case C will be characterized bylower frequencies.

2.5 Uncertainty

The uncertainties in the measurement due to the prin-ciples of DGV have been thoroughly examined by otherworks (Ecker et al. (2014); Saltzman et al. (2020)). To

assess the significance of errors due to the control vol-ume size, the uncertainties due to the DGV principlewill be discussed briefly to follow. Using a simulated

velocity signal, Ecker et al. (2014) investigated severalsources of error in TRDGV measurements. Temporalaveraging was shown to be the greatest contributor torandom error, ranging from 1 - 6 m/s in the instan-

taneous axial velocity measurement, depending on theratio of the averaging time to the flow timescales. Biaserror was affected by the geometric configuration of the

measurement and the uncertainty in the slope of thetransmission line, which varies with the flow velocity.Considering the error contributions from all aspects ofthe technique, the inherent instantaneous velocity un-

certainty is estimated to be within 7 - 11 m/s (Ecker

et al. (2014)). Note that this error is absolute, inde-

pendent of flow velocity, making DGV more suitablefor high-speed flows. For further discussion of measure-ment uncertainties in DGV, the reader is referred to

Ecker et al. (2014) and Saltzman et al. (2020).

For the current work, we are interested in evaluat-

ing the uncertainties of the analysis based on the statedassumptions. The effect of the control volume is investi-gated by comparison to a model of the turbulence spec-trum. Pope’s model for the energy-spectrum function

has been widely accepted as representative for model-ing the distribution of scales within a turbulent flow.A possible error source emerges from the accuracy of

this model for jet flows; however, comparison of Pope’smodel to experimental data has shown good agreementin round jets (Pope (2000), Fig. 6.14).

Additionally, velocity is measured based on the scat-tering of light by particles for the DGV measurement.

The analysis of the control volume effects is valid onlyif the seeding particles accurately follow the flow withinthe control volume. This ability is characterized by Stokesnumber. The seeding particles have a diameter less than

1 µm and a particle relaxation time of 2.3 µs (Saltzmanet al. (2020)). For scales on the magnitude of the nozzlediameter and Uj , the Stokes number for Case A and B

is approximately 0.03, indicating that the particles ad-equately capture the large-scale behavior of the flows.Based on the Kolmogorov timescale of the flow, 1.2 µsfor Case A and 0.4 µs for Case B, the Stokes numbers

are respectively 1.9 and 5.8. These numbers are largerthan 1, meaning the particles will not follow the small-est scales of the flow exactly. For the large-scale mea-

surement application, these small scales will be filteredby the control volume.

3 Results and Discussion

For the present study, we seek to quantify the effect of

a changing measurement volume on the resulting tur-bulence statistics. First, the integration effect on meanvelocity and turbulence is investigated for the two flowsof interest using the analyses presented in Sect. 2.2. The

filtering effect, described in Sect. 2.3, is then applied toCase A in order to validate the method experimentallyfor high-speed flows. Finally, the same filtering analysis

is applied to Case B and C to study how the chang-ing FOV will affect the instrument’s ability to measurelarge-scale turbulent structures which contribute to far-

field noise production.


Table 1: Description of jet flows used for analysis.

Case Description M TTR D [m] Re×106 Uj [m/s] η [µm] ε×106 [m2/s3] St = 1 [kHz]

A Unheated, subsonic jet 0.6 1 0.013 0.23 206 3.3 1.1 16.2B Heated, supersonic jet 1.5 2 0.038 0.85 578 3.2 15.6 15.2C Full-scale engine 1.5 7 0.610 3.4 1132 18 7.6 1.9

3.1 Mean Velocity and Turbulence Error

Following Eq. (5), the mean velocity error was found tobe dependent on the squared height of the control vol-ume and the second derivative of velocity with respect

to the y direction. The second derivative was approxi-mated for the flow cases of interest based on experimen-tal data. Figure 3 shows the estimated percent error of

mean velocity based on the control volume size for thetwo flow cases. Larger velocity errors occur for Case Bthan Case A due to the larger value of the velocity gra-

dient in the supersonic flow case. Although the error inthe mean velocity measurement grows proportionallyto the squared control volume height, the overall errorcontribution is rather small. The figure shows an over-

estimate of the mean velocity of less than 0.005% forthe maximum control volume size shown. Consideringthe high flow speeds for which TRDGV is well suited,

these errors are practically negligible, especially whencompared to inherent technique uncertainties. Thus,the finite control volume size is not expected to be a

significant source of mean velocity error in a large-scalemeasurement.

The error in the Reynolds normal stress is depen-dent on the squared control volume height, the squaredvelocity gradient, and the second derivative of the nor-

mal stress with respect to the y direction, as shownby Eq. (12). The contribution of the second derivativeterm is generally small compared to the square of themean velocity gradient. The error in measurement of

the mean Reynolds normal stress is shown in Fig. 4 forvarying control volume size in Case A and B. From thederivation, it was shown that the finite control volume

has a turbulence amplification effect on the measure-ment. The error is scaled on the true Reynolds normalstress value to show the percent error of amplification.For Case A, percent error of the measured Reynolds

normal stress can be up to 4% for the maximum con-trol volume height considered. Case B will experiencehigher turbulence amplification for the same control

volume size, again due to the larger velocity gradientmagnitude occurring in the supersonic jet. For Case B,percent error of turbulence amplification will be up to

8.5% for the maximum control volume size shown. Thisamplification in Reynolds stress due to averaging over

the control volume will oppose the reduction caused bythe spatial filtering effect, which will be shown in Sect.3.2.

Fig. 3: Percent error of mean velocity due to changingcontrol volume size for Cases A and B.

Fig. 4: Percent error of turbulence amplification due tochanging control volume size for Cases A and B.


3.2 Spectral Resolution Effects and Comparison toExperiment

To explore the effect of the control volume size for eachflow case, the 3D energy spectrum was generated usingPope’s model for the appropriate flow conditions. For

Case A, the 3D model spectrum was filtered accordingto Eqs. (18) – (21) based on control volume sizes repre-sentative of high, medium, and low spatial resolutions.Figure 5 shows the effect of changing the control volume

dimensions for Case A. In Fig. 5a, the spectra show areduction in energy at high wavenumbers. With largermeasurement volumes, the energy attenuation begins

to occur at increasingly lower wavenumbers. The lobedbehavior observed in the filtered spectra is a result ofsidelobes in the box filter, and the lobes would likelybe obscured by noise thresholds in a typical DGV mea-

surement. By examining the frequency response func-tions (FRF), shown in Fig. 5b, we see that the energycontribution from the lobes is very small. For a control

volume height of 2 mm, over 50% of the energy is beingsuppressed at κ1η=0.003. The FRF indicates that forvery small control volumes (0.2 mm), 50% of the energy

is attenuated at κ1η=0.013.

To relate this wavenumber to sampling rates of atime-resolved measurement, a constant convection ve-

locity of 0.6Uj is assumed on the lip line, estimatedbased on values from literature (Morris (2009)). It shouldbe noted that the constant convection velocity assump-

tion is based on Taylor’s frozen flow hypothesis, whichcan be considered a source of error in this analysis. Typ-ically, it is expected for high frequencies to follow Tay-

lor’s hypothesis, while non-local large-scale motions willdominate lower frequencies. In the region of the shearlayer highlighted in this study, Taylor’s hypothesis isperhaps most valid as the local mean and large-scale

convection velocity begin to converge near the criticallayer of the jet, which is the region of particular interestfor aeroacoustic applications. These cutoff wavenum-

bers correspond to 18 and 60 kHz, respectively. Thesefrequencies are within typical sampling rates for a time-resolved measurement, and so the effects of this reduc-

tion must be considered when designing an experiment.

The filtered spectra are then aliased based on the

corresponding spatial sampling frequency, according toEqs. (23). Figure 6 shows how the aliasing alters thespectral shape. For low wavenumbers, the aliased, fil-

tered spectra do not differ from the filtered spectra,or the model spectrum. For wavenumbers approachingthe spatial frequency, the spectral energy magnitude

slightly increases due to the folding of the spectrum atthe Nyquist wavenumber, κs/2. It is evident that the

size of the control volume will have the effect of reduc-

ing the measured turbulence of the flow.

To further quantify the effect of the finite control

volume, the filtered and aliased spectra can be inte-grated to find the measured Reynolds normal stress.The true variance of the flow signal is found by the in-tegral of the model turbulent spectrum over the range

of wavenumbers from 0 to 2/η. Figure 7 shows the per-cent error of turbulence reduction due to the filteringbehavior of the control volume for Case A. The turbu-

lence reduction effect is compared with the turbulenceamplification due to the averaging over the control vol-ume, which was previously shown in Fig. 4. Note thatFig. 7 shows the absolute value of these errors for com-

parison. For the flow conditions of Case A, the filteringand aliasing has a much greater effect than the aver-aging. Even for a very small control volume height, 0.2

mm, the percent error in Reynolds stress is 18%. Thepercent error of the reduction for the maximum controlvolume height considered was 45%, while the percent

error of turbulence amplification is minor, at only 1.6%.

Considering these effects to be independent bias er-rors, the total error in the Reynolds stress measurement

is simply the sum of the reduction and the amplificationerror. For the control volume sizes and flow conditionsshown here, the total percent error ranges from 18 –

43%. Since the turbulence reduction is proportional tothe square of the volume height, these estimates willchange for different combinations of the spatial resolu-tion and flow conditions. This loss of energy occurs in

higher wavenumbers, or the fine scale turbulence, whichwill not contribute much noise (Morris (2009)).

The filtered and aliased spectra in Fig. 6 representsthe spectra we would expect to measure in a TRDGVexperiment due to the effect of the finite control volume.

We can validate this analytical method by comparingthe filtered and aliased spectrum, for h = 2 mm, toexperimental data from the same flow conditions. Thesetup and details of the TRDGV experiment used for

method validation are described in a previous publica-tion by the authors, which also compares the TRDGVresults to hot-wire measurements and data from liter-

ature (Saltzman et al. (2020)). Figure 8a shows Pope’smodel spectrum, with the combined effect of filteringand aliasing for h = 2 mm and h = 4 mm. Also shownis the experimental TRDGV data from the centerline

of the jet, with a control volume height of 2 mm. Tovalidate the method, filtering errors are artificially in-troduced to the experimental data by binning the sig-

nal from 4 pixels together, resulting in a control volumewith a height of 4 mm. The authors note that the tur-bulence in a jet is not expected to strictly agree with

Pope’s model for isotropic turbulence; in fact, looking at


10-4

10-2

100

1

10-5

100

105

E11 /

(5

)1/4

Model Spectrum

h = 0.2 mm

h = 1 mm

h = 2 mm

(a)

10-4

10-2

100

1

0

0.2

0.4

0.6

0.8

1

T11

Model Spectrum

h = 0.2 mm

h = 1 mm

h = 2 mm

(b)

Fig. 5: (a) Filtered spectra for Case A and (b) corresponding frequency response function.

Fig. 6: Filtered and aliased spectra for varying controlvolume sizes in Case A.

the experimental data shows noticeable differences such

as a low frequency dip in energy as well as the presenceof some peaks. The peaks in the TRDGV spectra areknown to be caused by measurement noise, unrelatedto flow phenomena (Saltzman et al. (2020)). Thus, the

purpose of this comparison is simply to validate themethod by showing similar behavior between the tworesults.

As observed previously, the filtering and aliasingof Pope’s model shows larger energy attenuation for

higher frequencies by the larger control volume. Thisbehavior is also shown by the TRDGV results. TheDGV spectra exhibit low frequency agreement, but the

effect of the larger control volume is evident for fre-quencies greater than 10 kHz, where the energy is re-

duced. To highlight the similarities between the modeland experimental data, the frequency response func-tion between the h = 4 mm and h = 2 mm spectra

is shown in Fig. 8b. It is important to note that theresponse function shown in this figure is distinct fromFig. 5b, as it compares the response of two control vol-

ume sizes, rather than comparison to the infinitely smallcontrol volume. The model shows a smooth decay inresponse across all frequencies, while the experimentaldata have seemingly been impacted by the noise floor

of the measurement, occurring for frequencies greaterthan 45 kHz, in addition to the visible peaks in theTRDGV data. Although the TRDGV data do exhibit

some low-frequency differences, the response decay be-tween 5 and 15 kHz compares very well to the behav-ior predicted by filtering and aliasing of Pope’s model.

With the same overall characteristics shown by the ex-perimental TRDGV data, we can conclude that the as-sumed filtering and aliasing behavior of the control vol-ume is representative of what is occurring in the real

measurement. Therefore, this analysis can be a valu-able tool for predicting the spectral effect that a finitecontrol volume size will have on the given measurement

and interpreting the experimental results.

3.3 Extension of the Analysis for Large-Scale TRDGV

With the analytical method validated, and its valuedemonstrated, we can now use the method for predic-

tion of the measurement performance of a large-scaleTRDGV measurement applied to a heated supersonicjet.

In the interest of measuring large-scale turbulent

structures, it is desired to image a large portion of


Fig. 7: Percent error of measured Reynolds normal stress due to changing control volume size for Case A.

103

104

105

Frequency [Hz]

10-3

10-2

10-1

Gu

u [m

2/s

2/H

z]

Pope's Model, h = 2 mm

Pope's Model, h = 4 mm

TRDGV, h = 2 mm

TRDGV, h = 4 mm

(a)

103

104

105

Frequency [Hz]

0

0.2

0.4

0.6

0.8

1

Guu(h

= 4

mm

) /

Guu(h

= 2

mm

)

Pope's Model

TRDGV

(b)

Fig. 8: Comparison of predicted spectra and experimental spectra for the subsonic jet case (a) and frequencyresponse function for the different control volume sizes (b).

the flow. Using pixel counts achievable by a high-speed

camera at high framerates, the size of the control vol-ume needed to capture a large length of the jet can beapproximated. Control volume dimensions are shown inTable 2 for varying FOV, based on specifications of a

Photron Fastcam Nova high-speed camera operating at50,000 fps. The laser sheet thickness is not expected tochange for the large-scale measurement.

Repeating the procedure described in Sect. 2.3, Fig.9 shows the effect of a changing FOV in a large-scalemeasurement of Case B. The filtered and aliased spec-

tra are shown compared to the model turbulent spec-trum. As the measurement FOV increases, the cut-offwavenumber decreases due to the required larger con-

trol volume. The spectral behavior in these results issimilar to Fig. 6. For the largest FOV of 10D, the mea-

surement will not be able to resolve scales in the iner-tial subrange or dissipation range; however, the energy-

containing region is well-resolved.

The effect of the FOV on the measured turbulence is

calculated as in the previous section. The percent errorof Reynolds stress reduction is shown in Fig. 10, com-pared with the amplification due to averaging. Again,the filtering and aliasing has a larger effect on the Reynolds

stress error than the averaging. Based on the FOV ex-amined, the Reynolds stress measurement is reducedby 30 – 47%. Interestingly, since the control volume is

larger for Case B, the averaging effect does somewhatbalance the filtering effect. For a measurement of 10D,the total percent error in the measured Reynolds stress

is 38%. Although this error is still considerably large, itis smaller than the total error from Case A. These re-


Table 2: Control volume dimension based on desired axial length of jet to image.

Axial FOV h (mm)

3D 15D 1.410D 3

Fig. 9: Filtered and aliased spectra for Case B with

varying FOV.

sults could change depending on the size of the control

volume and the flow conditions; however, for the ex-pected spatial resolution of a large-scale supersonic jetmeasurement using current technology, the finite con-

trol volume has a large effect on the measured overallvelocity variance. These results indicate that one couldfind an optimal size of the control volume based on theflow conditions to limit the error in the measurement.

The implications of these effects must be evaluated bythe researcher, based on the application and require-ments of the measurement.

Although it is clear that a large-scale TRDGV mea-surement will not be capable of capturing the dissipa-

tion scales of the energy spectrum in this flow, a large-scale measurement can still be of value. For the pur-poses of seeking to develop an instrument optimizedfor the study of large-scale, long-lived structures in jet

flows, we must confirm such a measurement can stillcapture the scales of turbulence which radiate noise.

For a disturbance in the flow field to cause a pressurefluctuation which radiates to the far-field and producesnoise, it must have energy in the supersonic region of

wavenumber/frequency space (Crighton (1975)). Thewavenumber which separates radiating and non-radiatingcomponents is defined, κa=ω/a∞ , where ω is the an-

gular frequency and a∞ is the ambient speed of sound.Wavenumbers less than κa∞ at any given frequency

Fig. 10: Percent error of measured Reynolds normalstress due to changing control volume size for Case B.

have the potential to radiate sound to the far field ifpopulated with energy. To assess the ability to detectnoise-radiating structures, first the Strouhal number inthe jet is defined, St = fD/Uj . Since angular frequency

is related to linear frequency by the factor 2π, we candefine the radiating wavenumber for any value of theStrouhal number. Figure 11 shows these wavenumbers

relative to the model and predicted turbulent spectrafor the case of the heated supersonic jet. Only the pre-dicted spectrum for the 10D FOV is shown becauseit is the largest considered FOV; so, it will have the

largest effect on the measurements. The Strouhal num-bers shown in the figure are 0.15, 0. 24, 0.33, and 0.44,respectively. Note that these Strouhal numbers corre-

spond to peak noise frequencies in the far-field acousticspectra measured by Daniel et al. (2019) for the flowcase of interest. These values also compare well to peak

Strouhal numbers found in the literature for a variety ofdifferent jet conditions, where the peak Strouhal num-ber varies based on the direction of observation (Tamet al. (2008); Morris (2009); Liu et al. (2016)).

Table 3 shows the amount of energy attenuation in

Case B resulting from the large FOV for each Strouhalnumber. For lower Strouhal numbers, on the range of0 to 0.24, the spectrum is relatively unaffected by the

large FOV, as the reduction in energy measured is lessthan 2%. Thus, the large-scale TRDGV measurement


Table 3: Energy attenuation by the measured 10D spectrum.

St Case B Case CEnergy Attenuation (%) Energy Attenuation (%)

0.15 0.8 1.60.24 1.7 2.70.33 2.7 4.00.44 4.0 6.2

Fig. 11: Filtered and aliased spectrum for Case B show-

ing wavenumber which separates radiating components.Wavenumbers to the left of the vertical lines can radiatesound to the far-field.

will resolve large-scale turbulent structures at these low

frequencies. Between Strouhal numbers of 0.33 to 0.44,the spectral energy attenuation is slightly greater, rang-ing from 2.7 – 4.0%. For higher Strouhal numbers, notmarked in the figure, the energy attenuation grows. The

ability to observe these structures is questionable dueto the size of the control volume. Although these higherfrequencies do not dominate the far-field noise from

turbulent mixing, they will be of interest when con-sidering the other two components of jet noise: screechtones and broadband shock-associated noise. This can

be considered a limitation of the large-scale TRDGVtechnique, but it indicates that the application wouldbe most valuable for the study of turbulent mixing noisein supersonic jets.

Finally, we show the effect of a large control volumeon a full-scale measurement (Case C) in Fig. 12. To im-age a 10D axial length of this flow, the height of the con-

trol volume is estimated to be 24 mm. The wavenumberwhich separates components radiating to the far-field isagain defined for relevant Strouhal numbers. In the full-

scale engine, both the temperature and the nozzle diam-eter have been increased compared to Case B. As a re-

sult, the Strouhal numbers which characterize the peakfar-field noise correspond to much lower frequencies.

Therefore, the resolved turbulence spectrum shown byFig. 12 is shifted left relative to the Strouhal number inthe full-scale engine. The energy attenuation for each

Strouhal number is again shown by Table 3. The energyattenuation is larger than Case B, with a reduction of6.2% for St = 0.44. The full-scale investigation recon-

firms that although higher wavenumbers are affected bythe large control volume, the lower wavenumber struc-tures are unaffected. These results show the plausibil-ity of large-scale TRDGV particularly for aeroacoustics

applications.

From this work, we have shown that although large-scale measurements are not without inherent errors,they can still be a valuable tool for observing fluctu-ations in the flow which produce noise in the far-field.

The purpose of this analysis has been to help the prac-titioner obtain an understanding of, and to establishfor, the effect of finite spatial resolution on measure-

ment errors. It may be of interest to the practitionerto correct their results based on analyses described inthe work. It is possible to refine the estimates, given

additional data. A deconvolution of the filter could beperformed for a partial correction of the experimen-tal data. However, since the filtering is applied in the3D wavenumber space, and the measurement obtains

a linear frequency component, a substantial amount ofmissing information would need to be assumed to cor-rect the measurement.

4 Conclusions

The current work has synthesized analyses to investi-

gate the fundamental effect of control volume size inlarge-scale, time-resolved velocity measurements. Specif-ically, DGV was investigated by the case study due to

its suitability to being scaled. Two flow cases were pri-marily considered: an unheated, subsonic jet for whichvalidation data was available, and a heated, supersonicjet for which a large-scale measurement system is de-

sired. Three sizes of the control volume were evaluated


Fig. 12: Filtered and aliased spectrum for Case C showing wavenumber which separates radiating components.Wavenumbers to the left of the vertical lines can radiate sound to the far-field.

for each flow case, corresponding to a small, medium,and large FOV. The mean velocity error was found to beless than 0.02 m/s for control volume heights between

0.1 and 4 mm, practically negligible considering the flowspeed. Amplification of the Reynolds stress measure-ment due to averaging over the control volume had a

percent error of up to 15% at 4 mm. However, the dom-inant effect of the control volume was the reduction inReynolds stress resulting from the filtering and aliasingbehavior of the control volume. For the subsonic flow

case, the total error in the Reynolds stress measure-ment was 43%, while the 10D FOV in the supersonicflow case was 38%. These results suggest an optimal

FOV could be found which would minimize the finitecontrol volume effect.

Velocity spectra were predicted by modeling the fil-tering and aliasing effect of the control volume on amodel turbulent spectrum. Good agreement was shown

to the subsonic jet validation measurements, indicatingthat the analysis is representative of the measurement.The analysis method was then used to predict behav-

ior of a large-scale measurement of a heated, supersonicjet. The large FOV showed large energy attenuation inthe high wavenumber portion of the predicted spectra.

To assess the effect of the control volume on the abil-ity to study noise-producing turbulent structures, thewavenumber which can radiate noise to the far-field wascalculated for a range of Strouhal numbers. For frequen-

cies which correspond to peak far-field noise, the spec-tra were shown to be unaffected by the control volumesize. The same behavior was observed when consider-

ing the flow conditions of a full-scale, afterburning jetengine.

This study provides a framework for determiningthe impact of spatial resolution in a large-scale, time-resolved measurement. The results have shown that al-

though the measurement is undoubtedly affected by thesize of the control volume, the errors are small com-pared to inherent technique uncertainties. Additionally,low wavenumber structures which dominate noise pro-

duction in heated jets are minimally affected by thecontrol volume size. The analysis gives support that thedevelopment of a large-scale, time-resolved velocimetry

system will be an invaluable tool for the discussion ofturbulence and aeroacoustics, particularly for the con-sideration of a full-scale measurement.

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Ecker T, Brooks D, Lowe KT, Ng WF (2014) De-velopment and application of a point doppler ve-locimeter featuring two-beam multiplexing for time-resolved measurements of high-speed flow. Exp Flu-

ids 55:1819–1833, doi:10.1007/s00348-014-1819-0Ecker T, Lowe KT, Ng W (2016) Scale-up of the

time-resolved doppler global velocimetry technique.

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Fischer A, Buttner L, Czarske J, Egger M, Grosche G,

Muller H (2007) Investigation of time-resolved sin-gle detector doppler global velocimetry using sinu-soidal laser frequency modulation. Meas Sci Technol18(8):2529–2545, doi:10.1088/0957-0233/18/8/029

Fischer M, , Jovanovic J, Durst F (2000) Near-wall be-haviour of statistical properties in turbulent flows. IntJ Heat Fluid Fl 21(5):471–479, doi:10.1016/S0142-

727X(00)00034-5Gamba M, Clemens NT (2011) Requirements, capabil-

ities, and accuracies of time-resolved piv in turbu-lent reacting flows. In: 49th AIAA Aerospace Sciences

Meeting, p 32, doi:10.2514/6.2011-362Gurtler J, Haufe D, Schulz A, Bake F, Enghardt L,

Czarske J, Fischer A (2016) High-speed camera-

based measurement system for aeroacoustic investi-gations. J Sens Sens Syst 5:125–136, doi:10.5194/jsss-5-125-2016

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65th Annual Forum, p 22Jordan P, Colonius T (2013) Wave packets and tur-

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Mayo Jr DE, Daniel KA, Lowe KT, Ng WF (2019)Mean flow and turbulence of a heated super-sonic jet with temperature non-uniformity. AIAAJ57(8):3493–3500, doi:10.2514/1.J058163

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50:877–885, doi:10.1007/s00348-010-0932-yMorris PJ (2009) A note on noise generation by

large scale turbulent structures in subsonic andsupersonic jets. Int J Aeroacoust 8(4):301–315,

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component doppler global velocimetry at 32 simul-taneous points: a new capability for high speed

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Meas Sci Technol 18(5):1387–1403, doi:10.1088/0957-0233/18/5/027

Chapter 5

50 kHz, large field of view imaging ofheated supersonic jets using Dopplerglobal velocimetry

The contents of this chapter are to be submitted for publication. (Ashley J. Saltzman, K.Todd Lowe, and Wing F. Ng, “50 kHz, large field of view imaging of heated supersonic jetsusing Doppler global velocimetry”).

47

50 kHz, large field of view imaging of heated supersonic jetsusing Doppler global velocimetry

Ashley J. Saltzman ∗, K. Todd Lowe † and Wing F. Ng ‡

Virginia Tech, Blacksburg, VA, 24060

Large-scale turbulent structures can be correlated over many jet diameters, and thus a

large field of view measurement resolved in time and space is desired to link their evolution

to aeroacoustic noise production. This work describes the development and demonstration of

a novel time-resolved Doppler global velocimetry system capable of spatially-resolving a large

field of view of the jet. The technique is applied to image a large axial extent of the flow-

field in a heated supersonic jet at 50 kHz. Mean velocity and turbulence intensity measured

within a root-mean-square error of 0.02*/* 9 and 0.01D′/* 9 , respectively, to PIV validation

measurements. Velocity spectra were validated by comparison to existing literature for free

jets. The spatial distribution of energy within the jet was also observed through the velocity

spectra, showing energy concentrated along the nozzle lip line for all frequencies. Space-

time correlations reveal evidence of wavepacket structures, characterized by their long axial

correlations and constant convection velocity. The measurement technique developed in this

work shows strong suitability for measurement of large-scale turbulent structures and could

be used for extensive analysis opportunities of heated supersonic jets in the future.

I. Introduction

Large-scale, unsteady flow structures are of interest to many fluid mechanics problems. Particularly, noise

production in heated supersonic jets is believed to be dominated by these structures [1]. As personnel working on

aircraft carrier decks can be exposed to more than 145 dB during takeoff and landing, novel noise reduction techniques

which can alter the formation of coherent turbulent structures are increasingly important.

Large-scale turbulent structures, also known as wavepackets, are characterized by their high coherence, making them

extremely efficient at radiating noise to the far-field in heated supersonic jets [1]. Linking turbulence to noise-production

events has long been desired in the aeroacoustic community, but success has been limited due to inability to measure

two-point space-time correlations in high-speed and heated flows [2]. Spatiotemporally resolving the flow field presents

an instrumentation challenge, due to harsh flow environments requiring a non-intrusive measurement and small temporal∗Graduate Research Assistant, Department of Mechanical Engineering, Virginia Tech, Student Member AIAA†Associate Professor, Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech, Associate Fellow AIAA.‡Alumni Distinguished Professor, Department of Mechanical Engineering, Virginia Tech, Fellow AIAA.

scales requiring high data repetition rates. Additionally, as large-scale turbulent structures can be highly correlated over

several axial jet diameters, a large field of view (FOV) would be required to fully study their lifetimes.

Advanced laser diagnostic techniques, such as particle image velocimetry (PIV) or Doppler global velocimetry

(DGV) have shown promising potential for flow observation with high spatial or temporal resolution. Both of these

techniques are particle-based, meaning particles added to the flow scatter laser light in order to determine the flow’s

velocity.

In PIV, two images of the flow field are acquired with a set time delay. The intensity distribution across a small

interrogation window in the frames is then cross correlated to determine the velocity [3]. Uniform flow seeding and

scalability have presented challenges for PIV, as was shown by wake measurements of a full-scale rotor by Wadcock et

al. [4]. Nonetheless, very large-scale measurements have been achieved at low repetition rates using natural snowfall as

seeding particles [5].

DGV was originally developed in the 1990s as an alternative to PIV [6]. It relies on the principle of the Doppler

effect to measure velocity, stating that the light scattered by seeding particles in the flow will be shifted in frequency

based on the flow’s velocity [7]. Multiple seeding particles can contribute to the measured signal, making DGV highly

suitable for scaling to a large measurement region since individual particle motion does not need to be identified.

Early development efforts sought to use DGV for application to large wind tunnels; however, they first experienced

instrumentation issues such as laser frequency instability and inadequate particle seeding [8, 9].

Over the past several years, researchers have demonstrated much progress towards either temporally- or spatially-

resolved measurements of high-speed flows thanks to developments in camera and laser technology. Time-resolved PIV

(TRPIV) for heated jets was demonstrated by Wernet et al. [10]. Prior to this work, the temporal limitation of PIV had

been overcome using multiple, independent PIV systems; however, a pulse-burst laser enabled the high repetition rate

of[10]. Velocity measurements were validated in a heated Mach 0.9 jet up to 25 kHz [10]. Higher acquisition rates

up to 100 kHz then followed, with large-scale measurements of a high subsonic jet imaged in 6 frames [11], as well

as an initial spatiotemporal analysis of turbulent jet flows [12]. Velocities in a supersonic jet were recently resolved

to 400 kHz by Beresh et al. using a pulse-burst PIV system [13]. This temporal resolution was only possible for a

resolution of 128 × 120 pixels (6 mm × 6 mm), resulting in the nickname ‘postage-stamp PIV’. Using a continuous

wave laser, a more economical option, repetition rates up to 250 kHz were achieved for a single point by Ecker et al.

with time-resolved DGV (TRDGV) [14]. This system, utilizing photomultiplier tube (PMT) arrays as cameras, was later

scaled-up for measurements of convection velocity of the Nozzle Acoustics Test Rig at NASA Glenn [15]. Recently, the

current authors demonstrated multipoint, three-component velocity measurements at 250 kHz using TRDGV, albeit

spatial resolution was limited to 32 simultaneous measurement points [16].

Although much diagnostic development progress has been made, a single measurement technique optimized for the

study of large-scale turbulent structures does not yet exist. Such a technique would require the "holy grail" combination

2

of high repetition rate, large FOV, and high spatial resolution. It has been shown by the review that DGV exhibits

characteristics making it suitable for a large-scale measurement; however, spatiotemporally-resolved measurements

have not yet been demonstrated with DGV. In the current work, the development of a large FOV TRDGV system is

described with the goal of spatiotemporally-resolving the velocity field. The measurement provides the novel capability

to study turbulent evolution over long axial distances and large time delays in heated supersonic jets. The measurement

described herein will enable extensive analysis opportunities for the detailed study of noise-production mechanisms by

large-scale turbulent structures. The paper is organized as follows: Section II describes the details of the DGV system

and experimental setup. Section III presents the results of the experiment and discusses their implications. Section IV

discusses the conclusions and recommendations for future work.

II. Methods

A. Doppler Global Velocimetry

The working principles of DGV have been described extensively by other works [14, 16, 17] and are summarized to

follow. DGV is a non-intrusive technique which relies on the Doppler shift principle, stating that the frequency of a

wave is shifted based on the motion of the observer. In velocimetry, this principle can be shown by, [7]

Δ 5� =

−→* · (> − 8)

_(1)

where Δ 5� is the Doppler-shifted frequency, −→* is the velocity of the flow, > is the direction of observation, 8 is the

direction of incident laser light, and _ is the incident laser frequency. In DGV, the laser frequency can be determined by

measuring the transmission of light through a vapor cell. Some of the intensity of the light will be absorbed based on

the absorption characteristics of the gas and its frequency. Using knowledge of the characteristics of the gas, commonly

molecular iodine, the corresponding laser frequency is determined by comparison to a theoretical transmission spectrum,

e.g. Forkey et al. [18]. Thus, to ascertain the velocity of the flow, the laser frequency must be measured twice:

prior to entering the flow (the incident measurement) and then again by the light scattered by the flow (the observed

measurement). This concept is illustrated by Fig. 1. The frequency of the incident light, 50, corresponds to 20%

transmission through the iodine vapor. A flow with velocity −→* shifts the frequency of the light to the Doppler-shifted

frequency, 5� , corresponding to 75% transmission. The Doppler shift, Δ 5� is simply the difference between these two

frequencies. In a DGV measurement, the incident laser frequency must be tuned to a desired frequency for which the

Doppler-shifted frequency can be distinguished, based on the expected velocity in the flow.

Since the direction of laser propagation and observation are known, the flow velocity can be determined. Additional

components of velocity can be measured by the addition of observer pairs, meaning three independent measurements

are required to resolve three orthogonal components of velocity. However, research efforts have been made to reduce the

3

Fig. 1 Theoretical transmission of light through iodine gas, illustrating the principle of the Doppler shift.

number of detectors required for the measurement [14], or to reduce measurement uncertainty using more than three

signals [19].

B. Experimental Setup

The heated supersonic jet rig at the Virginia Tech Advanced Propulsion and Power Laboratory (APPL) was used for

this experiment. The rig is capable of supplying flows up to Mach 2 and total temperature ratios of 3 using a 192 kW

heater. A converging-diverging nozzle with exit diameter of 38.1 mm was used to create a free jet operating at Mach 1.5

and a total temperature ratio ())') of 2. For this jet condition, the diameter Reynolds number is 850,000 and the jet

exit velocity is 578 m/s assuming isentropic relations. The jet condition is monitored by total temperature and pressure

measurements of the flow, recorded by a National Instruments 9213 thermocouple module and a Scanivalve Corp.

ZOC171P/8Px-APC pressure transducer, respectively. The jet rig has been used in other works and further description

can be found in the works by Mayo Jr. et al. and Daniel et al. [20, 21]. To scatter the laser light, alumina particles with

a nominal diameter of 0.3 `m were added to the flow upstream of the nozzle exit. The entrainment region surrounding

the jet flow was seeded using a Concept Colt smoke machine, producing mineral oil particles between 0.3 and 0.4 `m.

Figure 2 shows the experimental setup of the TRDGV system. A continuous-wave Coherent Inc. Verdi V18 laser,

isolated from the jet setup, is used with a maximum output power of 18 W at 532 nm. The laser is first tuned to the

desired incident frequency by applying voltage to a piezoelectric element (PZT) in the laser head. A laser line centered

at 18,789.88 cm−1 was chosen to ensure sufficient bandwidth for discerning the shifted frequency. A portion of the

beam is diverted using a beamsplitter cube for measurement of the incident frequency. This beam is split again, with

one path passing directly onto a photodiode, and the other passing through a starved vapor iodine cell (ISSI I2 S-5,

4

length 15 cm, 0.67 Torr) and then onto a second photodiode (ThorLabs, PDA100A, free-space amplified photodetector).

By taking the ratio of the filtered signal to the reference signal, the transmission of light through the iodine cell is found.

The laser beam is then directed to the free jet optomechanically and expanded to a laser sheet using a cylindrical lens.

The sheet enters the flow at a 9◦ angle from the horizon, centered in the jet.

Fig. 2 Experimental setup of the TRDGV measurement (not to scale).

The light scattered by the flow is observed by two high-speed cameras (Phantom v2512), located as shown in the

figure. The cameras are synchronized using the signal from a function generator (BNC Model 645) to record 100,000

images at 50 kHz. In switching from highly light-sensitive PMT arrays in previous work by the authors [16] to CMOS

cameras, the temporal resolution must be reduced to ensure sufficient signal can be achieved using the continuous-wave

laser, and so an exposure time of 20`s was used. Similar to the laser conditioning subsystem, one camera serves as the

reference signal and the other serves as the filtered signal by observing the flow through an iodine cell to determine the

transmission (frequency) of the light scattered by the flow. A laser line filter (Thorlabs FL532-3) was used on each

camera, and a neutral-density filter with an optical density of 0.5 was used with the reference camera to obtain more

equal image intensity with the filtered camera.

The streamwise-oriented measurement plane observed the jet from G/� = 5 to 13, providing a spatial resolution of

0.91 x 0.91 mm/pixel. The velocity vector sensitivity, determined by the > − 8 vector as shown by Eq. 1, will vary across

the large measurement plane and contains components in all directions, as shown by Fig. 3. Due to the geometric setup

of the experiment, the sensed velocity will be most sensitive to the azimuthal direction, although contributions from the

streamwise and transverse directions will also be captured. Measurement of the streamwise velocity component in a

streamwise-oriented measurement plane is not possible with a single-component TRDGV system [22]. As measurement

5

validation, the DGV sensed velocity will be compared with mean velocity measurements taken by Mayo Jr. et al. using

PIV in the same jet [20].

Fig. 3 Sensitivity vector maps of the measurement plane of the current work.

C. Data Processing

An overview of the data processing routine used by the current work is shown by Fig. 4 and is summarized in

this section. First, the incident laser frequency is determined using the photodetector signals in the laser conditioning

subsystem. The filtered photodetector signal is divided by the reference photodetector signal to find the transmission of

laser light through the iodine gas cell. The incident laser frequency is found using a model for iodine absorption of laser

light [18] . As there are multiple frequencies of the iodine spectrum which have the same transmission, the laser may be

scanned through multiple frequencies prior to the measurement to ensure the correct frequency is found.

Fig. 4 Data processing workflow for the signals in the DGV measurement.

6

The flow-scattered light is observed by two high-speed cameras in the observer subsystem. Before the Doppler-shifted

frequency can be found, the raw images must be calibrated and aligned. Spatial registration of the images was achieved

by first obtaining no-flow calibration images of a large checkerboard pattern (30 mm squares, Calib.io Calibration

Targets) with each camera. Spatial calibration was then performed using the open-source MATLAB camera calibration

toolbox [23] to register and dewarp the images. Lastly, the intensity of the reference camera signal is corrected to

account for the optical density of the ND filter. Figure 5 shows example images from the measurement after spatial

calibration was performed. Turbulent structures in the jet shear layer are clearly visible in the filtered and reference

images. In the filtered image, regions with higher intensity represent a faster flow velocity. Expectedly, the reference

images have a higher intensity than the filtered images. Although a large axial FOV is visible in these raw images, the

flow region was cropped to G/� = 5 to 13 to ensure sufficient signal-to-noise ratio ((#') was achieved.

Fig. 5 Raw images of the heated supersonic jet after performing spatial calibration.

For each pixel in the measurement plane, the observed transmission signal is found by taking the ratio of the filtered

to reference images. The Doppler-shifted frequency is then found in the same manner as the incident frequency, by

mapping the transmission to the corresponding frequency. The Doppler frequency shift is found simply by subtracting

the incident and observed frequencies. Finally, the instantaneous velocity is found using Eq. 1. This procedure is

repeated for each of the 100,000 images until the time-resolved velocity signal is found.

D. Uncertainty

Uncertainties in the DGV measurement technique have been investigated by several works in the literature

[14, 16, 24, 25]. Using a simulated velocity signal, Ecker et al. quantified several measurement errors in TRDGV for

heated supersonic jets [14]. The largest contributor to random error in an instantaneous measurement was shown to be

temporal averaging, which is proportional to the ratio of the time step to the timescale of the flow. The integral timescale

7

was estimated by the velocity autocorrelation and is approximately 35 `s in this flow, resulting in an instantaneous error

of between 3 and 7 m/s, based on a 68% confidence interval [14]. The bias uncertainty in this measurement will be

affected by the error in the determination of the transmission. Using a Monte Carlo simulation of signal-to-noise ratio

((#' = 10 log10 (%B86=0;

%=>8B4); power, P), the uncertainty in vapor cell transmission was estimated by Ecker et al. [14]. An

SNR of 22 for the current measurement corresponds to an RMS uncertainty in transmission of less than 3%. This error

will manifest as artificial turbulence in the measurement.

Since a larger measurement FOV means each camera pixel measures a larger region of the flow, the error effect due

to the finite control volume must be assessed. Previous work by the current authors investigated this effect analytically

for mean velocity, turbulence, and spectral results [26]. For the flow conditions and spatial resolution of the current

work, the analysis found that the percent error in mean velocity is less than 0.005%, and the percent error in mean

Reynolds stress is less than 2%, which are much smaller than inherent technique uncertainties. However, the finite

control volume will also have a combined filtering and aliasing effect on the measured velocity spectra, resulting in a

turbulence reduction effect for high wavenumbers. To assess this effect, a turbulence spectrum is modeled [27] and

analytically filtered to represent the spectrum which would be measured by a finite control volume. The frequency

response function (FRF) between the model and the filtered spectrum is shown in Fig. 6. From the figure, it is evident

that the large FOV measurement will be unable to capture high-wavenumber behavior, fine-scale turbulence. However,

the low wavenumber, large-scale structures are unaffected by the size of the control volume used in this measurement.

As the authors are primarily interested in studying the contributions of these large-scale turbulent structures to jet noise,

this limitation is tolerated for the current work. The reader is guided to Ref. [26] for further explanation of this error

contribution in the measurement.

10-2

100

102

104

1 [1/m]

0

0.5

1

E1

1,

Me

asu

red / E

11

, M

od

el

Fig. 6 Frequency response function of the expected spectrum compared to the model..

Lastly, in particle-based velocimetry techniques, the ability of the particle to accurately follow the flow must be

evaluated. The Stokes number can be used to define this quantity,

(C: =C0*

;0(2)

8

where C0 is the particle’s relaxation time, * is the fluid velocity, and ;0 is a characteristic length of the flow. For the

primary flow seeding, the particle diameter was less than 0.3 `m, yielding a Stokes number based on diameter (the

largest scales of the flow) of 0.03. This indicates that large-scale turbulent motion will be well-captured by the alumina

particles. Based on the smallest scales, the Stokes number will be much larger than 1. This indicates that the particles

will not follow the finest scales of turbulence; however, the filtering effect of the large FOV and the 50 kHz repetition

rate are expected to dominate the high-frequency error in this measurement.

III. Results and DiscussionThe large-FOV TRDGV system was used to measure the heated supersonic jet, resulting in 100,000 continuous

records for 264×39 planar measurements in the flow-field. The coordinate system for the measurement is defined in Fig.

2 and the results are shown and discussed to follow.

A. Mean Velocity Results

First, the mean velocity measurements are compared with existing PIV measurements collected by Mayo et al.

[20] in Fig. 7. Standard error uncertainties with a 95% confidence interval have been estimated as ±0.007*/* 9 and

±0.038D′/* 9 [20]. The PIV measurements are normalized by the jet exit velocity, while the DGV measurements

are normalized by the sensed velocity. The authors note that the PIV measurements were obtained by two separate

measurement planes, while the DGV results measured all axial stations contiguously. The marker size in Fig. 7 is

approximately indicative of the uncertainty in the mean velocity. The trend and magnitude of the DGV results show

good overall agreement with the PIV measurements. The jet exhibits expected top-hat profile characteristics in the

potential core region, with a gradual reduction downstream as the potential core collapses. The velocities further

upstream, G/� = 6, appear to have been impacted by the change in axial sensitivity across the measurement plane,

which was shown by Fig. 3. The root-mean-square error between the DGV and PIV measurements is 0.03*/* 9 at

this station. Further downstream, where there is greater axial sensitivity, the velocities show little deviation from PIV

measurements with an RMS error of 0.02*/* 9 . The DGV measurements show the greatest errors for H/� > 0.8,

particularly for G/� = 10 and 11. This discrepancy is likely a result of laser sheet intensity fluctuation or reduced (#'

in that region of the measurement.

Mean turbulence intensity profiles are shown in Fig. 8 for the PIV and DGV results, along with the corresponding

error bounds. Both measurements show expected turbulence trends in a free jet, with low turbulence in the jet centerline

due to the potential core and increasing turbulence moving radially outward. As the potential core collapses, turbulence

begins to increase in the center of the jet. Although the DGV and PIV measurements show similar magnitude and

behavior, the positions of maximum turbulence do not agree. The DGV technique measures contributions from radial

and azimuthal fluctuations, which would result in an increased turbulence measurement, while PIV measures solely the

9

Fig. 7 Radial profiles of*/* 9 for the supersonic jet measured by PIV and TRDGV.

axial fluctuations. Additionally, the large-FOV TRDGV technique is susceptible to measuring artificial turbulence due

to the error characteristics discussed in Sect. II.D. Overall, the RMS error in mean turbulence intensity between DGV

and PIV is 0.01D′/* 9 .

Fig. 8 Radial profiles of D′/* 9 for the supersonic jet measured by PIV and TRDGV.

B. Instantaneous Velocity

The appeal of this measurement is evident by its ability to observe turbulent structures over large time delays and

long axial distances. With these abilities, the DGV instrument is suitable for studying large-scale turbulence in heated

supersonic jets. To highlight this strength, Fig. 9 shows a series of 9 instantaneous frames of velocity in the heated

supersonic jet. In this measurement, 100,000 frames were acquired 20 `B apart, spanning a total time frame of 2 seconds.

The turbulent motions of the jet can be observed in the frames, with entrainment of surrounding air clearly visible by the

10

slower moving structures. A turbulence structure on the nozzle lip line is identified and circled as an example of a

feature which could be resolved and studied by this measurement. The circled stucture indicates an apparent ejection

event from the potential core region to the shear layer.

Fig. 9 Sequence of 9 instantaneous snapshots of velocity in the heated supersonic jet.

C. Velocity Spectra

Velocity spectra were calculated using Welch’s method for estimating power spectral densities [28]. The method

was implemented in MATLAB with the time signal divided into 150 bins. To validate these time-resolved quantities, a

spectrum measured by TRDGV is compared to some existing measurements from literature and is shown by Fig. 10.

All spectra shown in the figure were measured at the nozzle lip line for G/� = 6 and have been normalized by their

variance. The TRDGV results show excellent agreement across all frequencies with the measurement by Kerhervé et al.

[29] The spectral shape is similar to the measurement by Morris et al. [30], although the differences in frequency could

be explained by the drastically different Mach numbers.

With time-resolved velocities measured nearly continuously across the measurement plane, spectra can be computed

for each pixel to provide a quick overview of the energy distribution in the supersonic jet. The results from computing

the narrowband power spectral densities are shown in streamwise increments of 1D in Fig. 11(a). The spectral map

reveals several interesting features in the jet. In the potential core region (G/� < 7) near the center of the jet, the

energy is low. Peak energy across all frequencies appears to be concentrated on the nozzle lip line. Downstream of

this region, the energy increases, indicating increased turbulent fluctuations. Additionally, while the low-frequency

energy is increased downstream, the high-frequency energy remains constant throughout the jet. Figure 11(b) shows the

energy at each radial position for a constant frequency of 2 kHz. As the axial distance is increased, the energy becomes

distributed across the transverse direction, rather than concentrated at H/� = 0.5. For higher frequency, shown by Fig.

11(c), the energy is more evenly distributed in the transverse direction and does not greatly increase with axial distance.

The increased low-frequency fluctuation energy after G/� = 7 provides further support of the potential core collapse as

a strong region of noise production [31].

11

Fig. 10 Comparison of TRDGV velocity spectra with measurements from literature.

Fig. 11 Map of spectral energy distribution in the heated supersonic jet (a) with radial profiles of constantfrequency for � = 2 kHz (b) and � = 5 kHz (c).

12

D. Space-Time Correlations

With time-resolved velocity records obtained over the large measurement plane, the technique of the current work

provides the unique opportunity for measurement of two-point space-time correlations of the velocity field over large

delays in time. The second-order cross-correlation function is defined by, [28]

'8 9 (G, H, C, e, b, g) = D8 (G, H, C)D 9 (G + e, H + b, C + g) (3)

Where e and b are the spatial lags and g is the temporal lag. The cross-correlation function can be normalized by

the signal variances to find the correlation coefficient, d8 9 = '8 9/(D8D 9 ).

Figure 12 shows space-time correlations along the axial direction for two radial positions. By definition of the

correlation coefficient, both correlations begin at unity at the probe position and zero time delay. The correlations

then decrease across space and time due to the flow turbulence. Weak negative correalations are also shown by both

functions. Both functions show similar spatial extent of correlation, but their timescales are different. The slope of these

correlation functions are representative of the flow convection velocity. In the centerline correlation, the appearance

of two convective timescales can be observed in Fig. 12(c): a faster scale with*2 = 0.92* 9 , and a slower scale with

*2 = 0.54* 9 . This implies the presence of multiple turbulence mechanisms in the center of the flow as the potential

core breaks down. The correlation of the lip line reveals a slower convection velocity of*2 = 0.37* 9 .

Space-time correlations between the velocity signal of a reference probe point and the entire measurement plane

are shown in Fig. 13, for various time delays (g∗ = g*2/�). The color scale of the correlation coefficent is bound

by -0.5 to 0.5 to emphasize its behavior. Evidence of a large-scale turbulent structure is visible in the correlations,

showing alternating regions of positive and negative correlation. In the temporal range shown, the feature is correlated

for more than 2� in the streamwise direction. The shape of this correlation is unchanged for g∗ < 2.1. For g∗ > 2.1, the

correlation extends in the radial and axial directions, indicating the dissolution of this wavepacket-like structure.

Figure 14 shows the axial position of peak correlation from Fig. 13 for each time delay, which can be used to find

the convection velocity of this structure. The slope of this relationship is unchanged for g∗ < 2.1, indicating a nearly

constant convection velocity of 0.4* 9 . This convection velocity decreases for greater time delays, as was shown by the

change in correlation shape by Fig. 13. These characteristics support the expected behavior of wavepacket structures,

exhibiting constant convection velocity and long-lived axial correlations [1]. Additionally, these findings support the

research goals of the current work, showing that TRDGV is well-suited for studying wavepackets in great detail.

As a final demonstration of the unique capabilities of this measurement, the velocity signals are frequency-filtered in

an attempt to isolate the contributions from lower frequency, large-scale turbulent structures. A low-pass filter (FIR,

100th order) is designed using a cutoff frequency of 5.46 kHz, corresponding to a cutoff Strouhal number ((C) of

(C2DC = 0.36. In Fig. 10, (C2DC = 0.36 was chosen since it resides in the energy-containing region at frequencies below

13

Fig. 12 Axial space-time correlations computed at H/� = 0 (a) and H/� = 0.5 (b). Cropped correlation to showdetail near zero lag for H/� = 0 (c) and H/� = 0.5 (d).

Fig. 13 Space-time correlations of the velocity for probe position G/� = 7 and H/� = 0.5

the inertial subrange. The authors also note that this filtering follows the procedure used by Daniel [32] on schlieren

measurements of the density near-field, which showed that Mach waves dominated the low-frequency content of the

near-field. Figure 15 shows correlations of the low-pass filtered data, juxtaposed with the near-field correlations from

[32] shown on the same plot. To choose the probe position of the flow-field (G/� = 8.6 and H/� = 0.5), the source of

the Mach wave features shown by the near-field correlations was estimated by assuming refraction through an infinitely

14

Fig. 14 Axial location of maximum correlation for each time delay shown by Fig. 13.

thin shear layer [33]. The dashed line shows the approximate boundary of the jet shear layer. In Fig. 15, the correlations

shown above this dashed line correspond to correlation of the near-field data (using schlieren), while correlations below

the dashed line correspond to the correlations of the DGV turbulence data within the flow-field.

Fig. 15 Space-time correlations of the low-pass filtered flow-field (marked by ‘o’) with correlations of thelow-pass filtered density near-field (marked by ‘x’) from [32].

15

Across the shown time delays, the shape of the near-field correlation remains constant in angle and length-scale,

but the flow-field correlation is axially elongated for greater time delays. The correlation magnitude of the flow and

near-field are similar; however, the near-field shows greater negative correlations, suggesting a more highly organized

Mach wave structure than the turbulence for this region in the flow. The disorganization of correlations in the flow-field

is expected, given the many incoherent components of turbulence in the flow-field, such as flow three-dimensionality

and turbulent structure interactions. The acoustics of the near-field act as a filter, observing only the disturbances from

the wavepacket itself. Between the flow- and near-field for the low-pass filtered data, both the time- and length-scales

appear to be preserved. This observation provides further evidence that the near-field can be associated as a ‘footprint’

of the large-scale turbulence in the jet, previously shown using proper orthogonal decomposition by Arndt et al. [34].

Interestingly, not only does this suggest that the sound looks like the flow which created it [33], but also that the

sound is correlated in the same manner as the flow. Further analysis of the TRDGV flow measurements could lead to

identification of noise-production mechanisms in the near-field.

IV. ConclusionThe current work has developed a velocimetry system capable of high spatial and temporal resolution ideal for

non-intrusive measurement of high-speed and supersonic jets based on the DGV technique. Measurement of a heated

supersonic jet with high spatial resolution at 50 kHz was achieved using the velocimetry system. Mean velocity

measurements show good agreement with PIV results, and velocity spectra exhibited broadband agreement to spectra

from literature. A long axial length (8�) measurement enables the detailed study of large-scale turbulent structures in

the jet, showing structures which are correlated for more than 2� axially and convect with a constant velocity.

The capabilities of the TRDGV technique provide exciting opportunities for exploring the evolution of turbulence

in heated supersonic jets. Although a single-component measurement was achieved by the current work, additional

velocity components could be resolved with more high-speed cameras, fully-resolving the velocity field of a heated,

supersonic flow. Increased temporal resolution is possible and would likely required the use of a pulse-burst laser system.

Two-point space-time correlations, which have continued to be a challenge due to instrumentation complexity and

practicality, are achievable for large fields-of-view using this measurement technique. This work further demonstrates

scalability of the DGV technique and its usefulness for fluid mechanics and jet noise research. The developments of the

current work offer a pathway for linking turbulent flow fluctuations to noise production mechanisms, through detailed

study of the lifetime of large-scale turbulent structures.

AcknowledgementsThe authors would like to acknowledge Dr. David Mayo, Jr. for collecting the PIV measurements on the heated

supersonic jet rig which were used as measurement validation. The authors would also like to acknowledge Dr. Kyle

16

Daniel for collecting and processing the near-field results which were shown in the manuscript.

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19

Chapter 6

Conclusions and Outlook

This dissertation has focused on the further development of the time-resolved Doppler GlobalVelocimetry (TRDGV) technique for application to jet noise. The main conclusions fromeach study and suggestions for future work are discussed to follow.

6.1 Conclusions

The first study in the dissertation focused on demonstrating the three-component capabil-ity of the TRDGV technique. The TRDGV system used multiplexing of two laser sheets,allowing for a three-component measurement with a reduced number of required sensors.Frequency scanning of the continuous-wave laser provided a method for calibrating the rawintensity signals from the light-sensitive photomultiplier tube (PMT) sensors, which wereused to image the flow. The calibration by frequency scanning ensured an accurate measureof transmission for each signal, which was imperative for the success of the three-componentvelocity measurement. A high subsonic jet flow was measured using the TRDGV system at arepetition rate of 250 kHz. Mean velocity measurements were validated through comparisonto hot-wire and Pitot probe measurements. The velocity showed excellent agreement of 7ms−1 RMS of the validation measurements, within expected uncertainties of the technique.Secondary velocity components in the jet were low and of equal magnitude, indicating ax-isymmetric expansion of the jet. Axial velocity spectra revealed broadband agreement tohot-wire data and spectra from literature, while secondary velocity spectra showed lowerenergy magnitude and evolving behavior through the jet shear layer. This work showed thepromising applicability of TRDGV for measurement of high speed compressible flows. Addi-tionally, this work demonstrates the highest sustained sampling rate achieved for multi-point,three-component velocity measurements, to the author’s knowledge.

The second study in this dissertation provides an analytical approach to the understandingthe fundamental effect of scaling the TRDGV measurement to a larger field-of-view (FOV).Scalability is particularly important for aeroacoustics applications, where turbulent struc-tures can be long-lived and large-scale. Multiple light-scattering particles pass through thecontrol volume (pixel) in the measurement, and so the final measurement will be affected bythe size of this control volume. The analysis was performed using Pope’s model for isotropicturbulence. The error in mean velocity was found to be nearly negligible considering the flow

67

68 Chapter 6. Conclusions and Outlook

speed and inherent technique uncertainties; however, the spectral error due to the combinedfiltering and aliasing effect of the control volume was significant. For a large FOV mea-surement with a spatial resolution of 4×4 mm, the spectra experienced energy attenuationup to 40%. This energy attenuation occurred only in the high wavenumber portion of thespectrum, while low wavenumbers were unaffected. Undoubtedly, the ability for a large-scalemeasurement to observe high frequency turbulence is limited. However, for the purpose ofobserving large-scale, low wavenumber structures, this technique can still be an invaluabletool. Furthermore, this study presented a framework for a practitioner to understand theeffect of finite control volumes in their measurements.

The final study in this dissertation sought to scale-up the TRDGV technique for the studyof the lifetime of turbulence in heated supersonic jets. Using high-speed CMOS camerasto increase the technique’s spatial resolution, a long axial length (8D) of the velocity fieldwas measured at 50 kHz in a heated supersonic jet. Mean velocity measurements comparedwithin 0.03U/Uj RMS to PIV validation measurements. The time-resolved signal was val-idated through comparison of the velocity spectrum to literature and showed broadbandspectral agreement, as well as a -5/3 slope in the inertial subrange, expected of turbulencewith sufficiently high Reynolds numbers. Since time-resolved records were achieved nearlycontinuously over the large measurement plane, an overview of the spectral energy distribu-tion could be mapped and revealed increasing transverse spread of the low frequency energywith increasing axial distance. Space-time correlations were computed in the velocity fieldand showed evidence of a wavepacket structure convecting at constant speed, until its even-tual ejection from the shear layer. This work demonstrated the large-scale spatiotemporalcapability of TRDGV and provides exciting opportunities for further flow analysis.

6.2 Outlook

With the work presented in this dissertation, many opportunities exist for further analysisand technique expansion. Some suggestions for future work are described to follow:

• An obvious next step would be to resolve additional velocity components using theexperimental setup discussed in the third study. This development would fully-resolvethe flow field and allow for examination of the complex three-dimensional turbulencestructure of the jet.

• The experimental data provided by the third study should be evaluated using theanalysis presented in the second study, to experimentally quantify the uncertainty ina large-scale, time-resolved measurement.

• Jet noise-reduction techniques can be investigated experimentally using the large-scaleTRDGV technique. With simultaneous flow-field and far-field acoustic measurements,direct links could be observed between turbulence and noise production.

Documents

Spatiotemporally-Resolved Velocimetry for the Study of