1 Photonic Doppler Velocimetry Workshop IV Measuring Projectile Balloting in a Gas-gun Launcher Using 2-channel PDV Scott Levinson and Sikhanda Satapathy Institute for Advanced Technology Austin, TX Nov 6, 2009
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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
2
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.