Development of Doppler global velocimetry for the ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2016/finalworks2016/papers/02.2_3... · Measurements in both a small scale supersonic jet

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

Development of Doppler global velocimetry for the measurement of eddy convective velocities

Tobias Ecker1,*, K. Todd Lowe2, Wing F. Ng3

1: Institute for Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen, Germany 2: Department of Aerospace and Ocean Engineering, Virginia Tech, VA, USA

3: Department of Mechanical Engineering, Virginia Tech, VA, USA

* Correspondent author: [email protected]

Keywords: DGV, instrumentation development, supersonic jet

ABSTRACT

A new Doppler global velocimeter (DGV) for high-speed flow applications was developed for the measurement of

eddy convective velocities in supersonic jet flows for aeroacoustic studies. The key technologies for this instrument

are spatially resolving, high sensitivity photomultipliers, field programmable gate array (FPGA)-based signal

processors and a continuous wave laser, which can be frequency tuned. The instrument presented in this study is

based upon the classic DGV technique but with technology enhancements that allow instantaneous and long time

span velocimetry at a 250 kHz sampling rate. The instrument has been matured to deliver a robust performance

even with low signal-to-noise ratios, as may be encountered in high-speed flows and large-scale facilities.

Measurements in both a small scale supersonic jet facility as well as a large-scale multi-stream nozzle at NASA

Glenn are presented to demonstrate the instrument capabilities in delivering robust measurement of convective

velocities within high-speed turbulent shear flows.

1. Introduction

Doppler global velocimetry is a technique based on the selective absorption characteristics of

molecular gases that is capable of direct measurement of the Doppler effect. DGV relies on the

detection of the Doppler shift of laser light scattered off tracer particles within the local flow. Its

capability to detect multiple particles within the measurement volume, while its temporal

resolution and scale up is only limited by particle response and signal to noise ratio, make it a

suitable instrument for time-resolved measurements of high speed flows.

The measurement of convective velocities, the speed at which eddies within the turbulent

flow convect, has been of particular interest due to its significance in the interpretation and the

development of aero-acoustic analogies (Lighthill, 1952). While hotwire anemometry, due to its

frequency response, can still be considered a standard for experiments in many experimental

studies on turbulent flow, its use in heated, supersonic shear layers has become obsolete with the

advent of optical and non-intrusive measurement techniques. The use of laser based instruments

like laser Doppler velocimetry (LDV), particle image velocimetry (PIV) and Doppler global

velocimetry DGV or other optical instruments (Kuo et al., 2011) avoid many of the issues


intrusive instrumentation in supersonic flows have. LDV has been used for doing two-point

correlations, which is the basis for the determination of the convective wavespeed, in hot and

cold high-speed jets in early studies by Lau et al. (1980), and most recently by Kerhervé et al.

(2004a, 2004b) in a cold supersonic jet. As LDV is a single point instrument, two LDVs had to be

operated simultaneously at varying separation distances within the flow. PIV, being a planar

technique, allows the correlation of the voxels with one another, reducing the complexity in the

measurement and determination of correlation functions and convective wavespeeds. Wernet

(2007) has successfully demonstrated the of use temporally resolved PIV for space-correlations in

cold and hot jet flows within a large scale facility, usually operating at 25-50 kHz. Like LDV,

DGV is a velocimetry technique based on the direct measurement of the Doppler effect. The

technique was first invented by Komine (1990) and subsequently refined by Komine et al. (1991)

and Meyers and Komine (1991). Detailed uncertainty analyses and flow studies have been

carried out by Meyers et al. (2001) in the early 1990s at NASA Langley, mainly for the

measurement of mean flow components. Smith (1998) and Clancy et al. (1999) first showed the

application of DGV to obtain instantaneous velocity vectors in several continuous frames in a

supersonic flow. However while these measurements were instantaneous, they were not

continuous and did not allow the capture of time-resolved flow features. The first to

demonstrate the application of a high repetition rate DGV system in a high-speed facility was

Thurow et al. (2005). His implementation used a high-speed camera (128 x 64 pixels) to obtain

one-component time-resolved velocity data as well as convective velocities in a rectangular

Mach 2.0 jet. Based upon this previous work Ecker et al. (2014) introduced a point Dopper

velocimeter (Cavone, 2006) operated in a cold supersonic jet at 100 kHz effective data rates and a

reduced number of sensors using a time-multiplexed technique. This work has been matured to

include a novel sensor system based on a 64 channel Photomultiplier (PMT), enabling spatially

and temporally resolved measurements in high-speed flows. The instrument has since been

applied to the measurement of convective velocities within heated small (Ecker et al. 2015b,c,d)

and large scale facilities (Ecker et al., 2016a,b) and is described in detail in this paper.

In this paper, we present the details of a novel 64-simultaneous-point, 250 kHz repetition

rate Doppler global velocimeter. The attributes of this development are particularly well suited

for measurements of turbulent eddy convective velocity in high speed flows. Given the

aeroacoustics interest in convective velocity due to the impact this parameter has on radiation

efficiency, the applications are those of relevance to jet noise for high speed propulsion. An

analysis of the operating principles and measurement uncertainties of this technique for

convective velocities is provided. Results are presented for convective velocity measured in

supersonic heated jets and in three-stream subsonic jets near Mach 1. These results reveal the


value of the method for obtaining quantitative turbulence structure information of developing

shear layers of relevance to the jet noise community.

2. Doppler global velocimetry

For the classic implementation of DGV (as first proposed by Komine (1990)), the

frequency of a single-longitudinal-mode laser is set so that the Doppler shifted frequency lies

optimally in the absorption spectrum of a molecular gas filter. A reference light path is used to

normalize the intensity of the filtered scattering by the intensity of the local scattering based on

particle density and laser light amplitude. The Doppler shift of the scattered light depends upon

the laser frequency, vector particle velocity, and laser propagation and observation directions

(see Fig. 1) and is related by the Doppler equation (Ecker et al., 2014) as:

𝑓𝐷 = 𝑓0�� ∙𝑒

𝑐 (1)

Fig. 1 Vector definitions of the DGV principle.

The Doppler shifted frequency is obtained by applying the intensity-frequency transfer function

of the molecular as filter to the intensity based sensor signals. An experimental scan compared to

a model fit by Forkey et al. (1997) is shown in Fig. 2 (Ecker et al., 2014).

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


3. Instrumentation

The presented instrument uses Doppler shift measured from a pair of co-planar laser sheets at 45

deg to the streamwise axis, which are time multiplexed to achieve three-velocity component

operation. Two receiver systems using novel 64 channel PMT cameras in a Doppler sensitive and

reference layout to record the light scattered from the particles in the measurement volume.

Recent studies have successfully shown the scale up of the instrument for the use in mid and

large-scale jet geometries.

(a)

(b)

Fig. 3 TR-DGV basic operating principle (a), sensitivity vectors within the facility coordinate

system for TR-DGV instrument (b). Image courtesy Ecker et al. (2015b).

To time multiplex the arrangement, acousto-optical modulators (AOMs) are used to chop

the incident laser beam into 4 μs, or shorter, pulses. The pulsed laser light is routed via free space

optics to laser sheet generating optics. The laser optics are arranged in a 45-degree configuration

to the jet centerline and create the measurement. Light receiver units are placed on both sides of

the flow, perpendicular to the measurement plane. In each receiver unit, the light collected by a

camera lens is first split into two paths—a signal path passing through a starved iodine cell and

-1-0.5

00.5

11

0.5

0

-0.5

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8-1

unit vectorssensitivity vectorsobservation vectorslaser direction vectors


a reference path with no cell. The basic sensor configuration and laser sheet timing is shown in

Fig. 3 (a) and the four measurement vectors for this instrument are shown within the facility

coordinate system in Fig. 3 (b). For a receiver system with a measurement plane parallel to the

stream-wise axis the maximal sheet width is dictated by the 45 deg angle position (for a square

sensor), which was also found as the angle with the lowest overall uncertainty by Ecker et al.

(2014) for this type of sensor geometry. This configuration could be extended to volumetric

operation by using a moving light sheet and a lens configuration with sufficient depth of field.

Using three of the four measurement velocity vectors the three component velocity vector

within the facility coordinate system can be extracted by using a transformation matrix:

�� = [

𝑒 1𝑇

𝑒 2𝑇

𝑒 3𝑇

]

−1

(

𝑢1

𝑢2

𝑢3

) = [𝑅11 𝑅12 𝑅13

𝑅21 𝑅22 𝑅23

𝑅31 𝑅32 𝑅33

] (

𝑢1

𝑢2

𝑢3

) (2)

The main sources of uncertainty of DGV are attributed to the characterization of the molecular

gas cell, laser line stability and signal to noise ratio of the sensor. Progresses in the development

of advanced DGV techniques, which address these issues, have been made since and lead to new

derivate DGV technologies (Fischer et al. 2007, 2008, Charret et al. 2004, Cadel et al. 2015). The

uncertainty of the velocity components along the sensitivity vectors is found to be a combination

of systematic and random uncertainties, and can be expressed as:

𝛿𝑢𝑖 =𝑐

𝑓0√(

𝑑𝑓

𝑑𝑇)𝑖

2(𝛿𝑇𝑖)2 + 𝑇𝑖

2 [𝛿 (𝑑𝑓

𝑑𝑇)𝑖]2

+𝑓𝑖

2

𝑓02 {(

𝑑𝑓

𝑑𝑇)0

2(𝛿𝑇0)2 + 𝑇0

2 [𝛿 (𝑑𝑓

𝑑𝑇)0]2

} (3)

Applying the transformation matrix to this analysis allows obtaining uncertainties within the

facility coordinate system as:

∆�� = (

𝛿𝑢𝑥

𝛿𝑢𝑦

𝛿𝑢𝑧

) = √([𝑅11 𝑅12 𝑅13

𝑅21 𝑅22 𝑅23

𝑅31 𝑅32 𝑅33

])

2

(

𝛿𝑢1

𝛿𝑢2

𝛿𝑢3

)

2

+ ([

𝛿𝑅11 𝛿𝑅12 𝛿𝑅13



])

2

(

𝑢1

𝑢2

𝑢3

)

2

(4)

For the instrument used in this study, two receiver systems using 64 channel PMT

cameras are used to record the light scattered from particles in the measurement volume. Recent

studies have successfully shown the scale up of the instrument for the use in mid and large-scale

jet geometries. The system consist of three essential subsystems:

1. Laser system, which enables conditioning of the Laser beam

2. Camera system, which receives the Doppler shifted light

3. DAQ system, which records the data and interfaces all subsystems


Fig. 4 DGV system electric and optical signal overview (Ecker et al., 2016b).

The signal flow and functional integration of the Laser multiplexing system (1), as well as

of the two camera systems (2) and the data acquisition system (3) for the DGV instrument are

shown in Fig. 4. The laser system is based on a Verdi V18 single frequency diode pumped


continuous wave laser which is time multiplexed using two IntraAction Corp. 80 MHz AOMs.

This laser has a line width of approximately 5 MHz over 20 ms (Coherent Inc white paper). The

time multiplexing of the laser sheets is controlled via a BNC 565 delay generator, which is

triggered by a digital output from the DAQ system. Continuous triggering from the FPGA

Adapter module, which is also used for recording of the PMT data, ensures a maximum of

synchrony between laser multiplexing and data recording.

The 1 MHz trigger signal is recorded by the multipurpose DAQ card as a reference. A reference

beam is extracted from the multiplexing system via a beamsplitter and used to record the light

intensity from two Thorlabs PDA100A photodiodes which are setup around a reference Iodine

(ISSI Inc.) cell in a similar configuration as described for the DGV camera system.

The scattered light is sensed by two photomultiplier (PMT) array detectors, one for each

the signal and reference paths. A 2 in beamsplitter cube is used to divide the received between

light paths. The PMT array detectors and the high bandwidth data acquisition system used to

measure the PMT anode signals form a unique system for very high repetition rate, low light

measurements. The PMT array detectors are Hamamatsu H8500C PMT modules, each with 64

anodes. Custom 16-channel, high-speed amplifier boards from Ectronic GmbH amplify the

anode signals and transmit them to the adapter module of the data acquisition system. On each

module, 32 anodes were used and the flow was imaged such that the points were distributed in

a rectangular grid that was 30.32 mm in the stream-wise direction and 61.22 mm in the radial

direction.

Fig. 5 CAD of TR-DGV instrument configured for small-scale supersonic hot jet. Image courtesy

Ecker et al. (2015b).


Depending on the application and required laser output, the optical routing of the laser

beams can be done via fiber optics or mirror configurations. Fig. 5 portraits the basic instrument

geometry for the use in a small-scale facility using 8 μm telecommunication grade fiber optics.

Pictures of the scaled up system using a mirror configuration are shown in the applications

section.

4. Data processing for convective velocities

The multi-point PMT (effective area 24.12 x 48.7 mm2, configuration is displayed in Fig. 6) (Ecker

2015a) allows space/time cross-correlation processing of the experimental data over all 32 sensor

pixels. The time-resolved data s(x,r,t) acquired on each sensor pixel were processed and

correlated to reference locations throughout the shear layer. The second-order cross-correlation

(Morris and Zaman, 2010) is defined as

𝑅𝑖𝑗(𝑥, 𝑟, 𝜍, 𝜉, 𝜏) =1

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

𝑇/2

−𝑇/2𝑠𝑖(𝑥, 𝑟, 𝑡)𝑠𝑗(𝑥 + 𝜍, 𝑟 + 𝜉, 𝑡 + 𝜏) (5)

where 𝜍 and 𝜉 are the spatial separation and 𝜏 the delay timescale from the reference location. As

used in equation (2), further uses of the ( ) notation indicate time averaging.

The correlation function exhibits maxima along the convective ridge. These points lie on the

locus of 𝜍𝑟 = 𝑢𝑐𝜏𝑟, and the correlation function along this locus,

𝑅(𝜏𝑟) = 𝑅(𝜍𝑟 = 𝑢𝑐𝜏𝑟) (6)

characterizes the decay of the spatio/temporal extent of integral scale eddy correlation.

The space/time correlations maps measured allow the determination of equation (7) from which

the integral convective velocity (Fisher and Davies, 1964) can be determined, given the known

stream-wise measurement position spacing,

𝑢𝑐 = 𝜍𝑟 𝜏𝑟⁄ = 𝑘Δ𝑥/𝜏𝑟 (7)

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


Processing for frequency dependent convective velocities as well as intermittency has been

demonstrated by Ecker et al. (2015c,d) in previous studies. The uncertainty within the

measurement of the convective wavespeed behaves much differently than the uncertainty within

the instantaneous velocity component. The uncertainty within the determination of the

convective wavespeed from the correlation function Rij is primarily dependent on the time

accuracy of the data acquisition and the sensor spacing.

Propagation of error analysis yields the following uncertainty for the convective velocity:

𝛿𝑢𝑐 = ±√(1

𝜏)2(𝛿Δ𝑥)2 + (

Δ𝑥

𝜏2)2(𝛿𝜏)2 = ±𝑢𝑐√(

𝛿Δ𝑥

Δ𝑥)2

+ (𝛿𝜏

𝜏2)2

(8)

Ecker et al. (2015b) analyzed the uncertainty within the processing algorithms used to obtain the

lag time. By applying a Monte-Carlo simulation using synthetic flow data they found that noise

has a very low impact on the lag time estimation. For a case with mean flow and turbulence

properties representative to supersonic shear layers, they found the error within the lag time

estimate to approach values of about 4% at signal to noise ratios (SNRlog) above 0. As can be

seen from equation 8, the normalized uncertainty for convective velocity is a combination of the

relative uncertainties of the sensor spacing and lag time estimate. As long as the relative

uncertainties can be held constant, scale up of the instrument for the use in larger scale facilities

does not lead to increased uncertainties.

5. Applications

The TR-DGV instrument has to date been used for the measurement of the eddy convective

velocity in two facilities, the Virginia Tech hot supersonic jet facility (Ecker et al. 2015b) and the

High Flow Jet Exit Rig (HFJER) at the NASA Aeroacoustic Propulsion lab (AAPL). An overview

of the very different optical instrument parameters is shown in table 1, demonstrating the

scalability of the TR-DGV technique.

Table 1. Instrumentation parameters for two facilities used.

Small scale jet facility NASA AAPL

Lens focal length 85 mm 200 mm

𝛥𝑡 (Laser) 4 𝜇𝑠

Measurement area (PMT coverage) 12 x 24 mm2 30.32 x 61.22 mm2

𝛥𝑥 (horizontal) 3 mm 7.58 mm

As shown by Ecker et al. (2014), the instantaneous measurement uncertainty can be estimated for

this configuration as ±9.2 m/s for the streamwise velocity component from equation (3) and (4),


similarly the mean bias uncertainty is ±1.5 m/s for all components. The uncertainties, as well as

the condition number for the transformation matrix and the minimally required Iodine line

frequency width are summarized in table 2.

Table 2. Uncertainties and Doppler frequency range.

Uncertainty (inst.) 9.2 / 6.5 / 6.2 m/s

Uncertainty (mean) 1.5 / 1.5 / 1.5 m/s

Uncertainty [𝛿𝑢𝑐/𝑢𝑐] 0.065

Uncertainty [𝛿𝛥𝑥 /𝛥𝑥 ] 0.05

Uncertainty [𝛿𝜏 /𝜏 ] 0.04

Max Condition number 4.2

Range (Doppler freq) 0.12 GHz

The properties of the Iodine cells of the DGV instrument were optimized for their respective use.

The reference cell, which is located on the optical table and used to obtain the reference

frequency, was operated at 65 °C. At this temperature and the relatively low filling pressure, this

cell is ideally suited to track the initial Laser frequency due to its gentle transmission slopes. The

measurement cells, which are located in both DGV camera units inhibit a much higher

sensitivity to frequency change and therefore to the velocity fluctuations within the flow. The

properties of the Iodine cells used are summarized in table 3.

Table 3. Iodine cell properties.

reference cell measurement cell (O1/O2)

Pressure 0.1 Torr 1.0 / 1.2 Torr

Body temperature 65 °C 35 / 35 °C

Small-scale supersonic hot jet facility at Virginia Tech

The TR-DGV setup for this particular experiment is displayed in Fig. 5 and Fig 7 (a). The

distribution of the convective velocity and Mach number for several streamwise stations was

measured by Ecker et al. (2015b) for two heated conditions (TTR = total temperature / ambient

temperature = 1.6 and TTR = 2.0) in a small scale (d = 2 in) supersonic hot jet facility.

The results of the colder (TTR = 1.6) condition are shown in Fig. 7 (b). The structure of the

eddy convective velocity and Mach number profiles indicates several noteworthy aspects of the

flow physics of heated supersonic jets. The convective speeds within the potential core at x/D =

4 and 6 for both TTR conditions are approximately uniform and equal to the jet exit velocity. In


comparison to the mean velocity distribution it was found that the convective velocity data

exhibits a clear difference in spreading of the convective velocity profile. Between both TTR

cases, a measurable reduction in the scaled eddy convective velocity is found for the hotter TTR

case at the downstream stations, which is believed to be leading to a reduction in convective

amplification and contributing to the reduced noise emissions. Specifically, the density ratio is

believed to play a direct role in scaling due to dependency of the ‘symmetric’ convective Mach

number (Papamoschou, 1997) on this quantity. More analysis and data can be found in Ecker et

al. (2015b).

(a)

(b)

Fig 7. Measurement of convective velocity in a small-scale supersonic hot jet (TTR=1.6) at several

streamwise stations.

Large-scale supersonic hot jet facility at NASA Glenn Research Center

Multi-stream nozzles are currently under investigation for application in the future supersonic

aircraft. In order to demonstrate the scalability of the TR-DGV instrument, measurements were

performed at a three-stream nozzle with and without axial offset of the third stream.


For these large-scale measurements, both the laser itself and the reference Iodine cell are housed

in an acoustically treated box in order to reduce the influence of noise and vibrations onto the

laser stability. Similarly the box also serves to thermally insulate the system from outside

temperature influences. Despite the insulation, the high frequency jet noise negatively impacted

the Laser stability and lead to ambiguity in estimating both laser and Doppler-shifted flow

frequencies. Notwithstanding the difficulties in computing the velocity statistics due to noise

induced laser instabilities, the determination of the convective velocity was relatively unaffected

by the same issues due to the inherent robustness of using the cross correlation function for lag

time detection.

(a) (b)

(c)

Fig 8. Measurement of convective velocity in a large-scale multi-stream nozzle at NASA Glenn.

(a) Instrument placed the in facility (b) photo of the beam operation during measurement (c)

convective velocity profiles of a jet issuing from three-stream axisymmetric nozzle at several

streamwise stations.

Detector units

HFJER

Laser and laser monitoring

Laser sheets


As in previous work, the results for convective velocity differ in structure from the mean

velocity field, which was obtained using PIV. The distribution of the convective velocity in the

axisymmetric (non-offset) case and the instrument configuration is shown in Fig 8. A more

detailed dissemination of the flow results can be found in Ecker et al. (2016a,b).

6. Summary

A new instrument is presented which combines for the first time several unique features into a

powerful system for measuring convective velocities with low statistical uncertainties. While the

conventional operating methodology of DGV is preserved, newly available photonics and data

acquisition technologies transform it into a system with unique capabilities, which is

complementary to established instruments like PIV and LDV. Time-shift multiplexing is an

approach to reduce the number of required sensor devices while still providing data rates

suitable for high-speed applications and low mean uncertainties. The presented geometrical

configuration in combination with time-shift multiplexing is of interest, because it can be easily

extended to allow volumetric operation in the future. The presented data in both a small scale

and large scale hot jet facility showed the presence of high momentum, high velocity large scale

eddies downstream of the potential core. These regions of locally high convective Mach numbers

are expected to have a leading role in supersonic jet noise due to high convective amplification

factors causing higher noise intensity. The main challenges in the large-scale facility were

predominantly related to laser line stability due to vibration caused by the jet noise. This study

shows the benefits time-resolved DGV can provide for understanding dominant turbulent

structures for noise generation in supersonic jets, and it provides the basis for the ongoing

development of time resolved multi-point DGV instrumentation. The application of the

instrument in both a small scale and large-scale facility with only minor modifications

demonstrate the easy scalability and robustness for the measurement of convective velocities of

the DGV technique.

Acknowledgements

This work was supported by the NASA’s Commercial Supersonic Technology Project in

the Advanced Air Vehicles Program, and the Office of Naval Research through the Hot Jet Noise

Reduction Basic Research Challenge and DURIP, grants N00014-11-1-0754 and N00014-12-1-

0803. The authors gratefully acknowledge the support provided for acquisition of the data by

Drs. Brenda Henderson and Mark Wernet of the NASA Glenn Research Center.


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Development of Doppler global velocimetry for the ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2016/finalworks2016/papers/02.2_3... · Measurements in both a small scale supersonic jet