1

Photonic Doppler VelocimetryWorkshop IV

Measuring Projectile Balloting in a Gas-gunLauncher Using 2-channel PDV

Scott Levinson and Sikhanda Satapathy

Institute for Advanced TechnologyAustin, TX

Nov 6, 2009

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Quick Review of Photonic Doppler Velocimetry (PDV)

• PDV1 developed recently for short range (~20 cm) high velocity shock experiments.

• PDV measures velocity by determining beat frequency f by “mixing” unshifted laser (f0 = c/λ0) with Doppler-shifted signal (f1) that reflects off moving surface.

• Calculated Velocity v(t) is proportional to known or measured variables: f (t) or λ0 having high precision & accuracy.

• Robust highly resolved & accurate alternative to VISAR & Fabry-Pérot.

• Has advantages w/o many liabilities of other techniques.

1O. Strand, D. Goosman, C.Martinez, and C. Whitworth, Rev. Sci. Inst. 77, 83108, 2006.

laser

detectordigitizer v

fo fo

fo f1f1

probemovingsurfacef(t)= |f0-f1|

f(t) = |f0−f1| = 2v(t)/λ0

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Objectives

Exploit the robust, precise qualities of PDV to quantify long-range axial gun-launch dynamics:

o Velocity v(t)o Position x(t)o Acceleration a(t)

And, using multi-channel PDV, we measure in-bore balloting angle profiles θ(t), dθ(t) /dt.

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IAT’s 2-Stage Light Gas Gun & PDV Layout

Probe 2

Probe 3

Beam Positions & Diameters at

Muzzle

Probe 2

Probe 3

Probe 1

Beam Positions & Diameters at

Target

Accurate PDV measurements exploited for first time at long range

MeasuredIndependent

Beams & PDV Signals

@ 16 mBeam Positions &

Diameters at Breech

Probe 2

Probe 3

V(t)

Trigger Signal at Muzzle

Probe 1Probe 3

Probe 2

Probes In

Target

(Blast Tank) (Flight tube)

(ProjectileWith Retro-reflective

tape)

(38 mm Launch Tube)

10 m launch 6 m flight

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PDV Analyses of LGG in Vaccum & Full Atmosphere

• Digitally Sample “Mixed” PDV signal (∆t=.16 ns)• Break record into (214 sample ↔2.6 µs) sub-records, • FFT each sub-record k, noting vi= λ0/2×fi = 0.77465 (m/s)/MHz×fi• Display signal amplitude Sk(Vi) as 2-D Spectrogram with axes: frequency fi (velocity vi)

& sub-record k (time Tk)

• Narrow spectral signal Sk(Vi) identifies velocity Vi at each time Tk• Large (125 M-sample) data set required under-sampling. But aliasing will be

corrected since a and v must be continuous

Time (ms), (∆t= 1/fs =0.16 ns, ∆T= Nfft ∆t = 2.6 µs)

Vel

ocity

(m/s

) (∆

V=

λ ∆

f/2 =

( λ/2

) 0.3

8 M

Hz

= 0.

3 m

/s)

CxLG1114Ch2 Nfft:16384 nov lap: 8192

-8 -6 -4 -2 0 20.148

500

1000

1500

2000

2421.1

-10

-5

0

5

10

15

20

25

30

35

40

(dB)

CxLG1109Ch2 Nfft:16384 novlap: 8192

-8 -6 -4 -2 0 2

Tk Time (ms) Tk Time (ms)

v i(m

/s)

10 Torr Vacuum 760 Torr N2

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Figure of Merit of Test (Full Atmosphere)

• Velocity detected throughout bore - even with low S/N• Signal is lost for 1 ms before muzzle, but recovers outside of bore

-8 -6 -4 -2 0 20

10

20

30

40

50

60

Time (ms)

dB

Cxlgg1109Ch1 S/N, Noise

Signal Power in 381.5 kHz or 0.2955 m/s BandS/N PeakPower/<Noise>

Signal and Signal/Noise

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Detected Displacement, Velocity and Acceleration Profiles at Full Atmosphere

Acceleration and Error bars

• In Bore: 2 distinct acceleration stages Evidence of projectile ringing early in shot

• in free flight: ~ 4 kgee deceleration whichcorresponds to in full atmosphere

Velocity & DisplacementPeaks at Full Atmosphere

-8 -6 -4 -2 0 2-20

0

20

40

60

80

100

Time (ms)k

G

PDV Acceleration - 5pt Stencil Ch2 1 Atm

Acceleration (smoothed over 39.3 µs)50 % error bars (if normally distributed)

Alias correction when T>TNyq: V= 2*VNyq - V for V > VNyq

-8 -6 -4 -2 0 20

750

1500

2250

3000

velo

city

- m

/s

-8 -6 -4 -2 0 20

5

10

15

20

time - ms

disp

lace

men

t - m

Velocity and Displacement at Full Atm.

VNyq

TNyq

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Axial X(t), V(t) and dV/dt profiles in Vacuum

• Velocity detected throughout bore, reaching 2782 m/s

• Signal is lost for less than 0.40 ms near muzzle

• No drag is observed in Vacuum, confirming 37 km/s^2 drag is caused by air

8-8 -6 -4 -2 0 2

-20

0

20

40

60

80

100

Time (ms)

kG

PDV Acceleration - 5pt Stencil Ch2 1 Atm

1 AtmVac

-8 -6 -4 -2 0 20

750

1500

2250

3000

velo

city

- m

/s

-8 -6 -4 -2 0 20

5

10

15

20

Time - ms

Dis

plac

emen

t - m

Velocity & Displacement in Vacuum

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Pressures Estimates

-8 -6 -4 -2 0 2-5

0

5

10

15

20

25

30

Time - ms re Trigger by Laser 1 ( ∆T = 2.6 µs)

Pre

ssur

e - k

si, V

eloc

ity -

m/c

s

Measured and Predicted Pressure vs Shot 1114

Pressure near AR (measured)

Base pressure (derived - PDV)

Base pressure (predicted)

Velocity (measured - PDV)

AR pressure (predicted)

PB and PPDV in reasonable agreement <1 kHz(code predictions not valid at higher freq)

PB and PPDV exhibit spiky behavior -likely due to reflections of the shock structure in the hydrogen gas

Pg

2PDVm dPr dt

vπ

=

gP

( )BP code−

v

PDVP

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Velocity Fluctuations

t - ms

f - k

Hz

Spectrogram of Velocity - Shot 1114

-8 -6 -4 -2 00

2

4

6

8

10

12

14

16

18

20

20

22

24

26

28

30

32

34

36

38

40

(dB)

(Spectrogram of Spectrogram )

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Balloting Angle From Multiple High-Resolution Axial PDV Measurements

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x2

x3d23 = 13.5 mm

θ(t) = tan-1(x23(t)/d23) x23(t) ≡x3 – x2 θ’(t) = cos2(θ(t))·(v23(t))/d23

θ

Probe 2

Probe 3

• Tests prior to launch at 16 m established > 20 dB isolation between Probe 2 & Probe 3

• Precision & accuracy of balloting angle θ(t) is controlled by precision & accuracy probe separation d23, velocity measurement technique and numerical integration method.

Retro-reflective tape

0.75- in Aluminum leading edge on Lexan slug has ~0.5 mm smaller diameter

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Balloting Angle

-8 -6 -4 -2 0 2-5

-2.5

0

2.5

5

time - ms

Balloting

dθ/dt - 100s of Hzθ - Degrees

• Balloting is quiescent before launch (t <-8.5 ms) and in free flight (-0.54 m < x > 5.83 m): θ < 0.2°.

• θ(t) correlates with axial a(t) changes, reaching peak of nearly θ=-5°. balloting angle profile measurements appear feasible, even in

high G environments

-9.9 -8 -6 -4 -2 0 2 4 5.83-5

-2.5

0

2.5

5

Projectile Position - m

Balloting

dθ/dt - 100s of Hzθ - Degrees

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Power Spectrum of Balloting Angle

100 101 102-15

-10

-5

0

5

10

15

Frequency - Hz

dB

Power Spectrum of dθ/dt

• Balloting angle has broad, low frequency spectrum that peaks < 40 Hz

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Conclusions

• PDV analysis was successfully applied on launches over 16 m distances ~ 2-orders larger than used previously.

• Position, velocity, acceleration & Drag profiles were resolved

• New Non- disturbing, High-G measurements are now feasible with PDV• High frequency, Base-Pressure measurements • Multiple PDV signals: measurement of high-G

balloting angle profile now f.