Folie 1 High precision image-based tracking of a rigid body moving within a fluid Stuart Laurence,...
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Folie 1
High precision image-based tracking of a rigid body moving within a fluid
Stuart Laurence, Jan Martinez Schramm
German Aerospace Center (DLR), Göttingen, Germany
APS/DFD, 23 November 2010
Folie 2
Motivation
Visualization-based techniques an attractive option for measuring displacements (and derived quantities) of rigid bodies in fluids, as they are completely non-intrusive
Particularly attractive for force-measurement in short-duration hypersonic facilities, as few other options available
However, measurement precision critical – in past (film-based analog techniques) displacement measurements limited to ~50 μm
Focus here on edge-detection-based techniques combined with least-squares fitting (suitable for silhouette images from schlieren, etc.)
Assumptions: no changes to body profile; motion two dimensional + one axis of rotation
Folie 3
Analytic-fitting technique
Edge detection Model edge
tracing and sub-pixel detection
Least-squares fitting
Folie 4
Free-flight measurements with analytic-fitting technique
Image-based measurements show reasonable agreement with accelerometer measurements
Response time for 14 kfps estimated to be ~0.5 ms
1 1.5 2 2.5 3 3.5 4
x 10-3
0
1000
2000
3000
4000
5000
t [s]
Dra
g ac
cele
ratio
n [m
/s2 ]
Accelerometers
Images
1 1.5 2 2.5 3 3.5 4
x 10-3
0
500
1000
1500
t [s]
Lift
acc
eler
atio
n [m
/s2 ]
Folie 5
Problems with analytic-fitting technique
Model cross-sectional profile must be expressible analytically (can be avoided by using, e.g., splines)
For all but simplest geometries, fitting procedure is iterative (slow!)
Reasonably complete profile required for convergence
Folie 6
Edge-tracking technique
Based on matching closest edge-points in reference and displaced images
Edge angle assumed to be the same for each edge-point pair
cos)(sin)(cossin eeee yyxxyx
Folie 7
Edge-tracking technique
Based on matching closest edge-points in reference and displaced images
Edge angle assumed to be the same for each edge-point pair
cos)(sin)(cossin eeee yyxxyx
linear least-squares problem for Δx and Δy
a) no errors b) with errors
Folie 8
Application of edge-tracking technique
2 4 6 8 10 12
x 10-3
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-3
Time [s]
Dis
plac
emen
ts [
m]
x
y
Folie 9
Error estimation through artificial image analysis
Errors introduced by pixellation/edge-detection (can be reduced through more precise algorithms) and CCD noise (unavoidable at given light conditions)
Such errors can be estimated through analysis of artificially constructed images
Folie 10
Error determination from calibrated sphere measurements
Precision-machined 40-mm diameter sphere controlled by linear displacement stepper
Magnification ~300 μm/pixelPosition determination from tracking techniques
compared with inputted displacementsStandard error ~1.3 μm
(A) Shimadzu HPV-1; (B) Telephoto lens; (C) Precision-machined sphere; (D) Linear displacement stage; (E) Light source; (F) Light-diffusing material
Folie 11
Errors in constant acceleration measurements
10-3
10-2
10-5
10-4
10-3
10-2
10-1
100
101
Measurement time [s]
Err
or in
mea
sure
d ac
cele
ratio
n: S
(a)/
a
20 kfps,a=1000 m/s2,s=1m
20 kfps,a=1000 m/s2,s=5m
20 kfps,a=1000 m/s2,s=50m
20 kfps,a=100 m/s2,s=1m
80 kfps,a=1000 m/s2,s=1m
Error in measured constant acceleration, a, can be determined from assumed displacement error (δ):
(n = number of measurement points)
For micron-level precision in displacement, accurate (~1%) acceleration measurements possible even for millisecond test times
2/1
56)(2ta
s
na
aS
Folie 12
Errors in constant acceleration measurements
10-3
10-2
10-5
10-4
10-3
10-2
10-1
100
101
Measurement time [s]
Err
or in
mea
sure
d ac
cele
ratio
n: S
(a)/
a
20 kfps,a=1000 m/s2,s=1m
20 kfps,a=1000 m/s2,s=5m
20 kfps,a=1000 m/s2,s=50m
20 kfps,a=100 m/s2,s=1m
80 kfps,a=1000 m/s2,s=1m
Error in measured constant acceleration, a, can be determined from assumed displacement error (δ):
(n = number of measurement points)
For micron-level precision in displacement, accurate (~1%) acceleration measurements possible even for millisecond test times
2/1
56)(2ta
s
na
aS
Folie 13
Conclusions
Technique originally developed for bodies with analytically expressible cross-sections
Generalized to arbitrary body geometries
Displacement measurements to micron level for wind-tunnel scale models – allows acceleration measurements to <1% under typical conditions
Generalization to three-dimensional motions?
Folie 14
Application of edge-tracking technique
2 4 6 8 10 12
x 10-3
0
0.1
0.2
0.3
0.4
0.5
t [s]
Vel
ocity
[m
/s]
vx
vy
Folie 15
Shock-wave surfing
-200 -150 -100 -50 0 50 100 150 200-0.015
-0.01
-0.005
0
0.005
0.01
0.015
(degrees)
(r -
r0)/
r 0
Corrected
Uncorrected
Optical distortions can become problematic for large fields-of-view
Can be corrected for using reference images
Error in edge-point locations
Folie 16
Shock-wave surfing
0 2 4 6 8 10 120
20
40
60
80
100
t [ms]
x [m
m]
Corrected
Uncorrected
0 2 4 6 8 10 12
-25
-20
-15
-10
-5
0
t [ms]
y [m
m]
Displacements
Optical distortions can become problematic for large fields-of-view
Can be corrected for using reference images
Folie 17
0 2 4 6 8 10 12
x 10-3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
t [s]
CD
Corrected
Uncorrected
0 2 4 6 8 10 12
x 10-3
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
t [s]
CL
Shock-wave surfing
Force coefficients
Optical distortions can become problematic for large fields-of-view
Can be corrected for using reference images