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