Three-dimensional visualization and quantitative

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geometric parameters of a flame over a range of combustion conditions. Keywords: flame, CCD ... combustion engineers for improved understanding and on-line.
INSTITUTE OF PHYSICS PUBLISHING

MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 13 (2002) 1643–1650

PII: S0957-0233(02)33912-2

Three-dimensional visualization and quantitative characterization of gaseous flames H C Bheemul, G Lu and Y Yan1 Advanced Instrumentation and Control Research Centre, School of Engineering, University of Greenwich at Medway, Chatham Maritime, Kent ME4 4TB, UK

Received 15 February 2002, in final form and accepted for publication 21 August 2002 Published 19 September 2002 Online at stacks.iop.org/MST/13/1643 Abstract This paper presents a novel instrumentation system for the three-dimensional visualization and quantitative characterization of gaseous flames. The system consists of three monochromatic CCD cameras, a frame grabber and a computer with dedicated software. The three cameras, placed equidistant and equiangular from each other around the flame being monitored, capture the two-dimensional images of the flame simultaneously from the three different directions. Dedicated computing algorithms have been developed to reconstruct three-dimensional models of the flame using its contours extracted from the two-dimensional images. A set of geometric parameters, including volume, surface area, orientation, length and circularity, are defined to characterize the flame from the model generated. The accuracy and spatial resolution of the system are evaluated using purpose-designed templates. A series of experiments was conducted on a gas-fired combustion rig to evaluate the performance of the system. The results obtained demonstrate that the system is capable of measuring three-dimensional geometric parameters of a flame over a range of combustion conditions. Keywords: flame, CCD camera, digital imaging, contour extraction,

three-dimensional model (Some figures in this article are in colour only in the electronic version)

1. Introduction Fossil-fuel-fired combustion systems are widely used in many industries to generate electrical power and thermal energy. Optimized operating conditions in such systems are required to enhance furnace safety, improve combustion efficiency and reduce pollutant emissions. A flame is the central reaction zone of a combustion process and its geometrical, luminous and thermodynamic characteristics provide instantaneous information on the quality and performance of the combustion process. Monitoring and characterization of combustion flames have therefore become increasingly important to combustion engineers for improved understanding and on-line optimization of combustion conditions. 1

Author to whom any correspondence should be addressed.

Several instrumentation systems operating on digital imaging and image processing techniques have recently been developed for the measurement of geometric, luminous and thermodynamic parameters of fossil-fuel-fired flames [1–3]. Industrial trials of such systems have also been undertaken recently and results obtained have demonstrated their operability and effectiveness [4–7]. The systems, however, use a single monochromatic CCD camera that allows a flame to be visualized from one direction only. The information obtained is therefore limited to two dimensions— the third dimension has not been taken into account. A flame is a three-dimensional flow field and can be either laminar or turbulent depending upon the Reynold’s number of the combustion flow. The shape of the burner outlet contributes enormously to the irregularity of the flame shape. As the flame emerges from the burner, the root of the flame usually shapes

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out according to the structure and geometry of the burner outlet. However, the burner outlet is not always practically perfect and depends on various factors such as wear and tear, corrosion of the burner material and its inelastic expansion at high temperature. The flame parameters, measured from different viewing locations using a two-dimensional imaging system, may not be identical and this fact has been confirmed by recent experimental work [8]. To achieve an in-depth understanding of a flame and subsequent optimization of combustion conditions, the flame should ideally be monitored three-dimensionally. Such an approach would also lead to the acquisition of ample practical data for the validation of computational fluid dynamics (CFD) models of flames and furnaces, which are now being developed by many research groups worldwide. Very limited work has previously been reported on three-dimensional monitoring and characterization of fossil fuel flames. Preliminary work on the reconstruction of three-dimensional models of a flame using digital imaging techniques has been described by Annunzotia et al [9], where only two flame parameters—volume and surface area— were determined. The tomographic approach has also been applied in an attempt to reconstruct three-dimensional models of a flame, but no measurement of the aforementioned flame parameters has been made [10]. Three-dimensional temperature measurement has been performed through multispectral tomographic image analysis [11], but the work has not been extended for the measurement of geometric and luminous parameters. In this paper, the design, implementation and experimental evaluation of a novel instrumentation system for the threedimensional visualization and quantitative characterization of gas-fired flames are described. Three identical CCD cameras are placed equidistantly around the furnace walls. The cameras capture two-dimensional images of the flame simultaneously from three different directions. A contour extraction method has been devised to extract the contours of the flame from each two-dimensional image. Based upon the data provided by the contours, algorithms have been developed for the threedimensional reconstruction of the flame model. A set of threedimensional geometric parameters is defined and computed from the model using various image processing techniques. Experimental results obtained on a combustion test rig under a range of operating conditions are also presented.

2. System description 2.1. System set-up Figure 1 shows a schematic diagram of the system developed. The system consists of three monochromatic CCD cameras, a frame grabber and a computer with associated software. The cameras are placed at fixed locations A, B and C, separated by equal angles of 120◦ . Each camera has a 2/3 inch CCD panel with a resolution of 816 × 606 pixels. The frame grabber converts the analogue signals from the three cameras into two-dimensional digital images simultaneously with eightbit digitization at up to 45 MHz. Combined with the high performance computer system, the frame grabber supports a transfer rate of 132 MB s−1 , providing real-time transfer of 1644

Computer

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Figure 1. System set-up.

the images to the host computer memory. The entire imaging system provides a frame rate of 60 frames s−1 . It is worth pointing out that other possible sensing arrangements have also been considered. For instance, a single CCD camera coupled with a trifurcated image fibre bundle could be used to capture three flame images from three different viewing locations. However, the optical fibre may not provide a very suitable optical path due to significant signal attenuation with respect to the length and bending of the fibre, small field of views and its excessive cost [12, 13]. A special optical assembly incorporating beamsplitters and converging/diverging lenses may also be designed to capture multiple images using a single CCD camera. However, the portability of such a system would be very poor due to the complexity of the three-dimensional optical sensing arrangement. Compared to these two possible sensing arrangements, the multi-camera approach offers obvious advantages and has, therefore, been adopted for the prototype system. 2.2. System calibration The calibration of the system was conducted by reproducing the geometrical relationship between the cameras and the flame. Although the cameras meet the same technical specifications, each camera had to be calibrated separately due to tolerances in image sizes of the CCD sensor originated from the manufacturing process, and natural degradation of semi-conductors. Several rectangular templates of known dimensions were placed where the flame was to be located, and faced the camera being calibrated. The length and width of the template were measured in pixels. Transformation factors in both the horizontal and vertical directions, designated by Ht and Vt , were then determined from the ratios between the pixel numbers measured and the actual dimensions of the template. Ht and Vt are effectively the indicators of the spatial resolution of the system, i.e., the sizes of the small region of the object surface represented by a single pixel. It is understood that the spatial resolution of the system is dependent upon the radial distance of the cameras from the flame. Figure 2 shows variations of Ht and Vt with the objective length over the range between 230 and 380 mm. It is clear that both Ht and Vt increase almost linearly with the objective length, indicating that the system has a good linearity in the spatial resolution. In this study, the objective length is

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set at 280 mm so that the spatial resolution of the system is 0.48 mm/pixel in the horizontal direction and 0.46 mm/pixel in the vertical direction. These values are incorporated into the system software so that the flame parameters measured in pixel numbers can be converted into absolute values. The accuracy of the dimensional measurement of the system was evaluated using a number of other reference templates. The results obtained, each of which is an average of 25 readings, are plotted in figure 3. An ideal straight line is also plotted to give a direct comparison between the measured results and the reference values. The maximum deviation of the measured length from the reference length is less than 2%. The repeatability of the system was also evaluated by recording 25 consecutive readings for a given reference length. For instance, the normalized standard deviation of the 25 readings for a reference length of 150 mm was 0.27%, equivalent to 0.4 mm along the longitudinal direction.

3. Reconstruction of flame models 3.1. Contour extraction The detection of flame contours using a suitable method is crucial before any reconstruction of the flame model is performed. The outer contour of a flame can be defined as the boundary between the luminous region of the flame and its surroundings, and corresponds to one-fifth of the maximum heat released [14–16]. Unlike a solid object, the flame contour is not clearly defined due to the inherent dynamic nature of the gas phase and the combustion process. This makes conventional edge detection techniques, such as threshold settings and low-pass filtering [14, 17], ineffective in the extraction of the flame contour from its images. Theoretically, the luminous region of the flame is generated by hot soot derived from the combustibles in unison with intensive thermal reactions and heat exchanges [14]. The boundary of the luminous region is considered to be where the combustion has completed. The variation of the flame luminosity is then expected to present a significant gradient nearby the boundary. The detection of the maximum gradients of the grey-level variations is achieved by scanning horizontally along the flame image, starting from the top-left

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Figure 3. Comparison between the measured length and the reference length.

corner. To reduce the effect of random noise in the image, the grey-level of each pixel being processed is replaced with the average grey-level of its nearest eight neighbouring pixels. The ratio between the grey-levels of two adjacent regions (i.e. the grey-level of the left pixel over that of the right pixel) is computed from the left edge to right edge of the image. If the brightness of a region of the image is uniform, the ratio is one. Any change in brightness will result in an increase or reduction in the ratio. Figure 4 shows the ratios of grey-levels between two neighbouring regions for three typical sections along the flame height. It is clear that the ratio varies significantly within the flame luminous region whilst it remains unity outside the region. The highest and lowest ratios, namely a, a , b, b , c and c , corresponding to sections A–A , B–B and C–C respectively, are marked in figure 4. The locations of the peak ratios are considered to be the maximum gradients of the greylevel variations, and therefore the right and left boundaries of the flame at the corresponding section. By joining all the points where peak ratios are detected, the extraction of the flame contour is achieved. It was noted that several peak ratios might exist at one image section due to the variation of inner structure of the flame. However, only the first and last peak points are recognized because only the outer contour of the flame is required in this study. This generalized contour extraction method has been evaluated using various flame images obtained under different combustion conditions and proven very effective. 3.2. Model reconstruction Conventional methods for three-dimensional reconstruction of an object are mainly based on projection and spectroscopy. These techniques are inappropriate for the reconstruction of a flame because of the lack of required features, such as edges and textures, in the flame images. To achieve the threedimensional visualization of a flame, an innovative algorithm, which relies on the information provided by the contours extracted from the flame images, has been proposed. As shown in figure 5(a), the three images captured by the imaging system can be considered as projections of the flame on the three 1645

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Figure 4. Variation of the grey-level ratio between successive neighbouring regions. z n=N

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Figure 5. Contour arrangement and segmentation. (a) Arrangement of flame contours. (b) Enlarged view of the nth segment.

planes, which are perpendicular to the optical axes of the three cameras and intersect at the burner axis. The flame contours are obtained from the images using a contour extraction method (section 3.1). The burner axis divides each contour into two sections, making a total of six main sections with an adjacent angle of 60◦ (figure 5(b)). Each pixel of the contour is given in the ‘x–y’ coordinate system. By introducing transformation matrices, the two-dimensional data of the contours can be converted into three-dimensional coordinates, which are then plotted in an ‘x–y–z’ co-ordinate system. The six main sections of the flame contours, arranged in the ‘x–y–z’ coordinate system, are used to reconstruct the three-dimensional model of the flame. The model is obtained by covering the entire contour arrangement with a ‘fishnet’ surface, which is generated using mesh-generation techniques [18, 19]. Assuming the change between the main sections is constant, intermediate sections with an adjacent angle θ (θ = 0◦ –60◦ ) are created and arranged in the same coordinate system. During contour extraction, a number of segments of equal height h have already been defined along the burner axis. For a given nth segment (figure 5(a)), the contours are joined to form a mesh by β-spline curves [20], which are computed from the set of coordinates provided by each section. The size of the ‘mesh’ is dependent upon the angle between 1646

the two adjacent sections (θ ) and the height of the segment (h). Larger values of h require less computation time, but lead to low quality of the reconstructed flame model. Smaller values of h and θ allow a more accurate model to be reconstructed but entail longer computation time. It is therefore necessary to define smaller grids for critical and more complicated regions of the model, and larger grids for simpler regions. The visual representation of the reconstructed flame model depends on the point of view. In order to visualize other parts of the flame such as the back and side views, six points of view have been defined. Continuous rotation of the entire contour arrangement by 60◦ allows the three-dimensional visualization of the flame at the six different points of view (Pv ) with Pv = 0◦ chosen as a viewer reference point. Pseudo-colours are applied to the monochromatic models for better representation. At Pv = 0◦ , the middle part of the model is represented by a dark red and the two outer sides with a pale yellow. This convention is chosen because the central reaction zone is darker than the outer part of the flame. Figure 6(a) shows a typical example of the instantaneous flame images simultaneously captured at locations A, B and C. The corresponding threedimensional model reconstructed is illustrated in figure 6(b), which is viewed from three different points of view.

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Figure 7. Definition of flame parameters α f and L f .

where ri (n) is the distance between the boundary of the contour and the burner axis at the segment, h is the height of the segment, N is the total number of segments, θ is the adjacent angle between two sections of the contours and equal to 15◦ in this study, and k = 360◦ /θ is the total number of contour sections. (b) Surface area (S f ). The area that is covered by the ‘fishnet’ surface is defined as the surface area of the flame, and is the sum of the surrounding surface areas of all the segments, as shown in figure 5(a), i.e. Pv=0°

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Figure 6. Typical flame images and their corresponding reconstructed three-dimensional model. (a) Typical flame images captured by the three cameras. (b) Three-dimensional visualization of the flame at three different points of view.

An animated flame model is also created so that the viewer can see all round the flame at different times. The colour scheme chosen for the reconstructed model gives an extra visual effect during its rotation. It is worth mentioning that the laboratory-scale gaseous flame is of low soot density and its effects on the flame shape are insignificant [15, 16]. Therefore, factors such as emissive properties of the flame have not been taken into account in this study.

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(c) Orientation (α f ). The flame may drift away from the burner axis because of its dynamic nature. This characteristic of the flame can be represented in terms of its orientation, which is the angle between the flame axis and the burner axis (figure 7). To obtain the flame axis, the geometric centre of each segment, (X n , Yn , Z n ), is computed from the following equations: Xn =

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(3.1)

4. Definition and quantification of flame parameters

Yn =

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Following the three-dimensional reconstruction of the flame model, a set of geometrical parameters of the flame is defined as follows.

Zn =

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(a) Volume (Q f ). The volume of the flame is the space it occupies in the furnace. As shown in figure 5(a), the flame contour arrangement is divided into a number of segments along the burner axis. The volume of the flame is, therefore, the summation of the volumes of all the segments, i.e. Qf =

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where M is the total number of pixels over the cross section of the segment. The linear regression line that passes through the centre of the burner outlet and fits the geometric centres of all the segments is defined as the flame axis. α f is determined as follows:  √ 2 X + Y2 α f = tan−1 (4) Z where X, Y , and Z are the coordinates of any point on the flame axis. 1647

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(d) Length (L f ). The distance between the centre of the burner outlet and the furthest point of the flame intersecting the flame model is defined as the length of the flame (figure 7). L f is obtained by scanning along the flame axis. (e) Circularity (C f ). The circularity of a flame segment along the burner axis is a measure of its closeness to the circular shape. For a given segment (figure 5(b)), C f (n) is expressed as  K   2 1 i=1 (r i (n) − r¯ (n)) × 100% C f (n) = 1 − r¯ (n) K −1 (5) where ri (n) is the distance between the flame boundary and the centre of the segment, and r¯ (n) is the average value of ri (n). If the segment is perfectly circular, C f = 100%. (f) Uncertainty of a flame parameter (δ). It is noted that the instantaneous value of a flame parameter is fluctuating due to the inherent dynamic nature of the flame. In this study, the uncertainty of each flame parameter (δ) is defined as its standard deviation normalized to its mean value, i.e. δ(x) =

σ (x) × 100% x¯

(6)

where x¯ and σ (x) are the average value and standard deviation of the parameter x respectively.

5. Experimental results and discussion 5.1. Experimental conditions To evaluate the performance of the system, a series of experiments was conducted on a gas-fired combustion rig. The combustion chamber is designed in a hexagonal shape with an inner diameter of 220 mm, serving to create a desirable and safe experimental environment. The base of the chamber is left open for secondary air to circulate. A burner with an outlet diameter of 15 mm was placed in the centre of the chamber. Air is supplied by a compressor which has a reservoir of 0.15 m3 . The fuel used for the experiments was commercial butane stored in a cylinder. Five different fuel flow rates varying from 1.6 to 7.8 cm3 s−1 were chosen. For each fuel flow rate, a minimum of ten different air flow rates was set, resulting in at least ten air– fuel ratios (r). For each condition, the three-dimensional flame model was reconstructed for 50 times and the flame parameters were determined from each model. The average values of the parameters are then computed and their uncertainties calculated.

Figure 9 illustrates the variations of the flame parameters with air flow rate for different fuel flow rates. As observed from the graphs, the flame parameters increase with fuel flow rate. It is also observed that under very air lean conditions (r  5), Q f , S f and L f increase with the air flow rate. This is due to the fact that the stoichiometric ratio of the butane gas is relatively high in comparison with other fuels such as methane and ethylene [15, 16]. In the case where the combustion flow is laminar (Re < 2000), a small amount of air has very little effect on the thermal/chemical reaction, but only increases the combustion flow velocity [14]. As the air–fuel ratio increases beyond 5, more air is mixed with the fuel giving the flame a premixed nature, resulting in a dramatic decrease in these three parameters. Similarly, α f increases with air flow rate for a given fuel flow rate when the air–fuel ratio is below 5. However, α f decreases gradually as the air–fuel ratio increases beyond 5. The increase in the amount of air mixing with the fuel stabilizes flame shape, directing the centre of each segment closer to the burner centre. Therefore, the regression line, which defines the flame axis, is converged towards the burner axis. This gives a decrease in α f . It is worth mentioning that the vertical alignment of the burner and the relatively stable laboratory environmental conditions lead to small values of α f throughout the experiment (4.75◦ is the maximum value of α f ). Figure 10 shows the variation of the circularity of the flame along the flame height with fuel flow rate under a constant air flow rate. It is observed that C f near the flame root is more than 95%, implying an almost circular shape. This accounts for the fact that the velocity of the air–fuel flow is uniformly distributed at the burner outlet and allows the flame to shape out according to the geometry of the burner. C f remains unaffected as the fuel flow rate increases from 1.6 to 7.8 cm3 s−1 . However, C f falls to 70% from its middle part to its tip, indicating unstable and inconsistent flame shape. Figure 11 exhibits the variation of the circularity of the flame with air flow rate under a constant fuel flow rate. Again, at an air flow rate of 15.7 cm3 s−1 , it is observed that C f decreases gradually down to 70%. This is attributed to the fact that, under a low air flow rate (r < 5), the flame is diffusive in nature. When the air flow rate increases (r  10), C f is more than 95%. This implies that the shape of a premixed flame is more stable than that of a diffusive flame. The uncertainty of each flame parameter under each condition is derived from 50 reconstructed flame models. The uncertainties of the flame parameters obtained at a fuel flow rate of 7.8 cm3 s−1 are plotted in figure 12. It can be observed that the uncertainties vary between 0.75 and 14%. A decrease in the uncertainty with air flow rate suggests a higher stability of a premixed flame compared to a diffusive flame.

6. Conclusion 5.2. Characterization of the flame After the contour extraction operation had been performed on the images of the flame, a three-dimensional model of the flame was reconstructed from its instantaneous images captured at each particular condition, as shown in figure 8. It is evident that the flame shape is very dynamic when r  5 because of the diffusive nature of the flame. When r  10 the flame has a more stable shape due to its premixed nature, although there is a decrease in the flame size. 1648

A novel instrumentation system operating on the latest optical sensing and digital imaging techniques has been described. The contours of the flame, obtained using the proposed contour extraction method, provide vital information needed to form the outer structure of the flame. A ‘fishnet’ surface, created using mesh-generating techniques, covers the entire flame structure and generates a three-dimensional reconstructed model of the flame. Dedicated software, based on various image processing techniques, has been developed to measure the defined

Three-dimensional visualization and quantitative characterization of gaseous flames

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Figure 8. Reconstructed three-dimensional models of the flame for different air-to-fuel ratios. (a) Fuel flow rate is 7.8 cm3 s−1 . (b) Air flow rate is 78.3 cm3 s−1 . (c)

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Acknowledgment

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The authors wish to acknowledge the British Coal Utilisation Research Association for providing a research grant (project B60) related to this work.

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References

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Figure 12. Uncertainties of flame parameters for fuel flow rate of 7.8 cm3 s−1 .

flame parameters. The results obtained from a series of experiments have demonstrated that the system is capable of measuring three-dimensional geometric parameters of the flame. It can therefore be deduced that, as expected, the quantitative characteristics of the flames are dependent on the operational conditions of the combustion rig. Further investigations are being undertaken to quantify luminous and thermodynamics parameters of a flame (brightness, uniformity, luminosity distribution, temperature distribution, soot concentration and flicker). It is envisaged that reconstructed three-dimensional flame models in conjunction with the measured flame parameters will enable combustion engineers to have a better understanding of the dynamic behaviour of flames under different operating conditions. 1650

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