3D RECONSTRUCTION OF TURBULENT FLAMES BY
STEREOSCOPIC PHOTOGRAPHY
Noémi László1, Pál Tóth2
MSc student, 2 professor’s assistant,
Dep. of Combustion Technology and Thermal Energy, University of Miskolc, Hungary;
[email protected], [email protected]
1
ABSTRACT
From the combustion technology point of view, most industrial flames can be
classified as turbulent-diffuse flames. The surface of a luminous flame can be
defined as the instantaneous isoconcentration surface of glowing soot or hydroxy
radicals. The properties and location of this surface characterizes the reaction
kinetics and fluid mechanics of the flame. In this work, stereoscopy as an imaging
method was used to reconstruct the surface of a turbulent flame. Stereoscopy uses
two different two-dimensional (2D) images of the same scene, taken from different
view angles, to obtain three-dimensional (3D) information (depth) of the scene. We
used a digital single lens reflex camera equipped with a stereoscopic adapter, that
simulated two virtual views by splitting the camera sensor in two parts using a
right-angle mirror. The geometry of the adapter closely resembled that of the human
eyes. With the properly calibrated stereoscopic camera system, the spatial
coordinates of the image can be calculated. After camera calibration, images of a
small Bunsen burner, producing a turbulent-diffuse flame, were acquired. The 2D
images were transformed to 3D images by a custom MATLAB code. Stereoscopic
imaging proved to be an effective method for obtaining depth information from
image pairs of turbulent flames. The exact nature and properties of the depth
information that can be extracted by stereoscopy from partly transparent objects,
such as flames, remains the target of future studies.
1. INTRODUCTION
A flame is the visible gaseous part of fire [1]. The exoterm reaction within the
combustion zone causes the visibility of the flame. Most flames are hot enough to
be considered lower energy-density ionized plasma. Flames may be different in the
aspect of mixing fuel and oxidant, and the flow velocity.
Previously the shape of the flame had been defined with different methods. In
one of these a long-exposure and high-speed color camera was used to study the
premixed turbulent flames. The camera allows the examination of dynamics and
structure of different flame types [2]. The combustion and spread of the flame was
studied with the Schlieren method and stereo imaging [3]. The CCD method is used
to determine the vortex number generated by coal powder burners. This
visualization system is based on spatial characterization of spectral and statistical
parameters to provide information on the flame’s turbulent nature through
recirculation and flow features [4]. Digital cameras produce two-dimensional
images of a three-dimensional object. A stereo camera is a projective device, a set
of two digital cameras engaged in a special non-centered projection. [5]. There is an
important geometric relationship between the two cameras represented in Fig.1. [6].
Fig.1. The geometric relationship between the two
cameras [6]
Point X, its projections x and x ', and camera centers C and C ' are positioned
on the same plane as part of the projective features. The intersection of the
projection lines of points x and x ' in the epipolar plane give point X. The line
connecting the camera centers C and C’ is the base line, a special line that creates
the image of one center in the other camera. Through triangulation with camera
matrixes and point pairs the 3D image is generated. The principle of triangulation is
illustrated on Fig.2. [5].
Fig.2. The principle of triangulation [5]
The point is projected along the camera’s focus point (O1,O2), resulting in two
points (y1, y2). If y1, y2 are predetermined and the camera geometry is known, the
two projection lines can be defined. Ideally the projection lines intersect at point X.
In knowledge of depth the 3D point is determined.
2. EXPERIMENTAL MATERIALS AND PROCEDURE
The 3D reconstruction is based on the mapping of corresponding points and
their 2D images. Using a calibration sample with known 3D attributes these
corresponding points are easily aligned. The sample is shown on in Fig. 3.
Fig. 3. The calibrration pattern
with detected corner points
The calibration of the stereo camera system requires the independent
calibration of both cameras. This is achieved through turning the calibration sample
into different positions. Accurate calibration requires tens of positions to be
detected. Assuming standard calibration the corresponding pixels on both images
are found in the same row. The easiest way of comparison is done with grey-scale
images where the intensity of each pixel is used. In this case the following relation
is applicable [5]:
𝑥 ↔ 𝑥 ′ → 𝑓 (𝑥) = 𝑔(𝑥 ′ )
(1)
The intensity is influenced by various factors. As a result, comparison is not
carried out on a pixel level but in small areas using average intensities. The method
used for stereo matching is cross-correlation which pairs smaller or larger areas. On
one image a window is applied to a specific point. On the second image a window
is chosen to the presumed point [7].
Correlation can be calculated between the two areas inside the windows [7].
The calibration of the left stereo camera and the stereo calibration is shown on
Fig. 4.a and 4.b.
A
Z [mm]
B
Z [mm]
Y [mm]
Y [mm]
X [mm]
X [mm]
Fig.4. The left stereo camera calibration (a) and the stereo calibration (b).
Geometric distortion (distortion of the lens) may degrade the quality of 3D 2D imaging. These errors however can be compensated and the remaining distortion
is minimized.
At times the projection lines do not intersect in the 3D space. Intersection
comes true when the points fit the epipolar limit given by the fundamental matrix.
In some cases the epipolar requirement is not satisfied because of measurement
noise (detection error, sensor noise, etc) and results in no intersection.
During the study we used low-speed turbulent-dffuse flames. In order to
increase turbulence the flame was continuously blown by a fan to test the accuracy
of the 3D reconstruction – flame leaning is indicated by the depth coordinates
advancing towards greater Z values on the flame surface.
3. EXPERIMENTAL RESULTS AND DISCUSSION
The described method was tested in a laboratory using a Bunsen burner. The
burner produces a diffusion flame which is a low-speed, diffuse, laminar-turbulent
transitional flame greatly determined by buoyancy. On the flow images the periodic
bubbling motion caused by the Kelvin-Helmholtz instability was clearly visible.
The correctness and significance of the results produces by this method were
studied. The correctness of the coordinates was examined with an asymmetric
flame created with the use of the Bunsen burner combined with a fan. The
examinable phenomena can be improved through the use of motion images.
Thus a video was recorded from the flame that was compared with the stereo
reconstruction method.
A
B
C
Fig.6. Reconstructed images of turbulent flame [10 -1 mm]
Based on Fig. 6. the flame mostly leans towards greater Z values in one
direction. This suggests that the reconstruction was correct at least qualitatively.
The figure also shows the flame has a wrinkled surface that was well reproduced.
The resulting Z values were intuitive in the aspect of intensity as well.
The flame is also visible from the side and from the top on the 3D images. On
Fig. A. a side view of the flame is visible. On Fig. B. the flame is leaning forward
compared to Fig. A. On Fig. C. the flame is leaning backward. On the top-view
images the vortex-like nature of the flame is visible.
On Fig.7. the distribution of Z coordinates as a function of the Y coordinate is
shown, compiled from 50 pairs of images.
Fig. 7. The distribution of Z coordinates
as a function of the Y coordinate.
The black line indicates the Z coordinate of the output segment of the burner.
The white arrows indicate the direction of the blow with the fan. The Z coordinates
are shown as a bivariant density function of Y. Assuming a leaning flame the value
of the Z depth coordinate increases from the burner. As shown on figure 7, the
flame leans towards the increasing Z coordinates. According to the figures the
described method provides realistic results.
During the reconstruction errors can occur. Fig. 8. shows the standard
deviation of the reconstruction errors as a function of spatial coordinates. The grey
part indicates the field of vision of a camera, the colors indicate the rate of error.
Fig.8. The standard deviation o reconstruction errors as a function of the
spatial coordinates. The error is given in mm.
As shown on the figure the rate of error increases with the Z depth coordinate.
The reconstruction accuracy is determined by the base distance. The field of vision
decreases with the base distance increasing but the reconstruction becomes more
accurate. Decreasing the base distance point matching becomes easier but at the
expense of 3D reconstruction stability.
With the help of video analysis flame surface deformation rate, surface
curvature and its changes, and the spatial position flame split can be examined. The
images of Fig.9. show 50 frames from the video footage.
Fig.9. The Bunsen flame shooting footage in 3D reconstruction.
The video was recorder with 32 FPS. This rate allows a decent study of the
flame in space and time. Successive images show every change in the flame. As it
appears on these images the flame followed a Kelvin-Helmholtz wave-like motion.
Due to the instability of the flame it split. The determined parameters can be linked
to turbulent size scales.
4. CONCLUSIONS
3D reconstruction of turbulent flame surfaces using stereographic photography
is possible. The advantage of this method is the possibility to study flow
characteristics of a flame using a stereo device and 2D images.
The surface of a flame from a Bunsen burner was reconstructed. The flame
had a height of 15 cm. The reconstruction error of spatial coordinates was less than
1.5 mm. The reconstruction allows the study of the shape and surface curvature of
the flame. We were able to examine the motion of the flame surface using images
from the video footage.
The stereographic video analysis appears to be a promising tool for
investigating flow characteristics of complex flames, however, further studies are
required to determine what physical information do the spatial coordinates carry.
REFERENCES
Law, C. K. Laminar premixed flames, Combustion physics (2006)
Cambridge, England: Cambridge University Press. pp. 300.
[2]
T. Foat, K. P. Yap, and Y. Zhang: The Visualization and Mapping of
Turbulent Premixed Impinging Flames, Mechanical Engineering Department, P
O Box 88, UMIST, Manchester M60 1QD, UK
[3]
Qian Wang, Hua Wei Huang, Yang Zhang, Changying Zhao: Impinging
flame ignition and propagation visualisation using Schlieren and colourenhanced stereo imaging techniques, Fuel 108 (2013) pp.177-183.
[4]
A. González-Cencerrado, A. Gil, B. Peńa: Characterization of PF flames under
[1]
different swirl conditions based on visualization systems, Fuel 113 (2013) pp.798-809.
[5]
Kató Zoltán, Czúni László: Számítógépes látás (2011) pp.34-36, 45-53.
[6]
G. Gerig: Reconstruction and Triangulation (2013), pp. 2-9.
http://www.sci.utah.edu/~gerig/CS6320-S2013/Materials/CS6320-3DCV-S2013stereo-tringulation-animated.pdf
[7]
http://www.geier.hu/lila/KANDI/kandip.htm