Three-dimensional dynamic measurements of CH* and C2* concentrations in flame using simultaneous chemiluminescence tomography

Ying Jin; Yang Song; Xiangju Qu; Zhenhua Li; Yunjing Ji; Anzhi He

doi:10.1364/OE.25.004640

1. Introduction

Due to advantages as non-intrusiveness and instantaneity, chemiluminescence based combustion diagnostics can be utilized as a well-suited inherent monitor for active combustion control in practical industrial environments [1–5]. As luminous emission in flames can be attributed to the transform of excited radicals, formed during the breakdown of reactant from an excited energy state to their ground energy state, instantaneous radiation emission at specific wavelengths is considered as flame chemiluminescence, which can be analyzed and correlated to combustion properties directly [6, 7]. For hydrocarbon flames, the radical chemiluminescence emissions of CH*, C2* and OH* can be treated as “finger prints” for flame diagnostics [8–11], especially CH* and C2*, corresponding to blue and green colors in visible spectrum. Flame chemiluminescence reflects flame information as equivalence ratio [12–15], heat release [16–18] and level of additives [19–21], etc. Therefore, quantitative measurements on these chemiluminescence signals are important in combustion studies and applications.

Early mature detections for flame chemiluminescence were based on the Photo Multiplier Tube (PMT) [22, 23]. However, limited by only one-dimensional radiation detection, they cannot provide adequate spatial resolution in combustion measurements. For two-dimensional methods, the well-established technique is planar laser-induced fluorescence (PLIF) [24]. Aldén et al. recorded CH*/CH₂O and OH* PLIF images to investigate the local flame front structures of turbulent premixed methane/air jet flames as well as turbulence and flame interaction [25, 26]. Miller et al. analyzed transient ignition processes using the formaldehyde PLIF and CH* chemiluminescence imaging [27]. Moreover, Allison et al. used CH₂O PLIF and high-speed CH* chemiluminescence to observe flame structures and combustion dynamics in a premixed ethylene combustor [28].

Compared to those one- or two-dimensional detecting tactics, flame chemiluminescence tomography (FCT) which can retrieve three dimensional (3D) spatial distributions provides more details in flames, thus attracting increasing interest in combustion research. Floyd et al. measured instantaneous 3D structure of CH* emission of matrix burner and turbulent opposed jet flame [29, 30]. Upton et al. presented high-resolution 3D measurements of the flame surface in a turbulent reacting flow [31]. Cai et al. [32, 33] and Li et al. [34, 35] recorded CH* chemiluminescence to reconstruct the instantaneous flame structures. Besides structure measurements, Ishino et al. designed a forty-lens camera to acquire the emission light intensity and recovered the distribution of local burning velocity of turbulent flame [36]. These researches only focus on the measurement of single component information, more information can be extracted from multispectral chemiluminescence measurements. To realize multi-channel detection, tactic based on optical system improvements is a potential way. Gao et al. diagnosed temperature field according to dual-wave spectrum tomography with 4 CCD cameras arranged in two orthogonal arrays, each was filtered through a dedicated wave (696.5nm and 763.5nm, respectively) to capture multispectral images of the combustion field instantaneously [37]. Cignoli et al. developed a two-dimensional soot diagnostic technique as the extension of two-color pyrometry [38]: flame images were acquired by a two-faceted quartz prism through two suitably chosen optical filters facing two sides of the prism. In order to ensure the accuracy of measurement, the arrangements of the prism and filters should be determined accurately, often leading to complex diagnostic system. Additionally, spectral separation according to image processing is another way to extract specific chemiluminescence spectrum from color images. Recently, Huang et al. proposed both RGB (red, green, blue) and HSV (hue, saturation, value) color models to characterize the color spectrum of methane flame under various burning conditions [39–41]. However, both CH* and C2* intensities were extracted from blue and green layer directly ignoring the crosstalk between layers, leading to errors in CH* and C2* concentration detecting.

In order to achieve quantitative concentration distribution of CH* and C2* simultaneously with simple diagnostic system and credible accuracy as well, 3D dynamic flame detecting method for double species concentration measurements is proposed in this paper. Firstly, a quantitative flame chemiluminescence multispectral separation algorithm is proposed to extract intensities of both CH* and C2*. Furthermore, FCT system established with 12 digital color cameras is adopted to acquire 3D CH* and C2* concentration distribution of propane flame simultaneously. Theory as well as its verification of flame chemiluminescence multispectral separation algorithm is detailed provided in Section 2. Section 3 proposes the apparatus of the 12-camera experimental system and its calibration. In Section 4, both CH* and C2* components of a non-axisymmetric propane-air diffusion flame are measured. Certificated by practical measurements, it is believed the proposed 3D dynamic measurement of double species concentrations by FCT can be further applied in combustion diagnostics for both high resolution observations and quantitative detections.

2. Flame chemiluminescence multispectral separation algorithm

The central radiation wavelengths of CH* and C2* in propane-air flame are 431.5 nm and 516.5 nm, respectively [42]. Here, customized double-channel bandpass filter is implemented before CMOS camera (MER-231-41U3C, 1920 × 1200, pixel size 5.86 μm) in order to collect both chemiluminescence emission intensities of CH* and C2* as I_CH and I_C2. The spectrum of filters is shown as the yellow line in Fig. 1 with central wavelengths of 431.5 nm and 516.5 nm owning the full width at half maximum (FWHM) of 35 nm. Moreover, the spectral sensitivity of employed color camera is also demonstrated in Fig. 1 by means of red, green and blue lines corresponding to RGB channels.

Fig. 1 The transmissivity of double-channel bandpass filter and the spectral sensitivity of the color camera.

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In this work, the captured images are recorded in Bayer pattern, generally, to get images corresponding to each channel, the Bayer pattern image should be converted into a RGB image via algorithms as linear interpolation depicted in Fig. 2(a). However, the classical linear interpolation simply treat blue and green channel signals as CH* and C2* intensities without considering crosstalk between channels, leading to errors in both I_CH and I_C2 retrieval. In order to avoid such errors and acquire credible accuracy in quantitative flame measurements, here, we propose multispectral separation algorithm to obtain the separated signals representing the actual intensities of CH* and C2*, as illustrated in Fig. 2(b).

Fig. 2 CH* and C2* intensity retrieval. (a) conventional method using linear interpolation, (b) multispectral separation algorithm.

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Considering the transmissivity of RGB channels in color CMOS, the intensity recorded by green channel p_g as well as that collected by blue channel p_b are the mixture of I_CH and I_C2 as illustrated in Eq. (1).

ε I = P

Where

ε = [\begin{matrix} ε_{11} & ε_{12} \\ ε_{21} & ε_{22} \end{matrix}], I = [\begin{matrix} I_{C H} \\ I_{C 2} \end{matrix}], P = [\begin{matrix} p_{b} \\ p_{g} \end{matrix}] .

The parameters in Eq. (2) are defined in Eq. (3).

{\begin{cases} ε_{11} = \sum_{λ \in w_{b}}^{} (f_{λ} \cdot b_{λ}) / w_{b} \\ ε_{12} = \sum_{λ \in w_{g}}^{} (f_{λ} \cdot b_{λ}) / w_{g} \\ ε_{21} = \sum_{λ \in w_{b}}^{} (f_{λ} \cdot g_{λ}) / w_{b} \\ ε_{22} = \sum_{λ \in w_{g}}^{} (f_{λ} \cdot g_{λ}) / w_{g} \end{cases}

Where w_b and w_g are defined as bandwidths of double-channel corresponding to B and G channels, λ indicates the wavelength in the range of bandwidth, the transmissivity of double-channel bandpass filters is considered as f_λ, b_λ and g_λ refer to the spectral sensitivity of B and G channels according to λ. Thus I_CH and I_C2 can be computed as shown in Eq. (4).

{\begin{cases} I_{C H} = \frac{p_{b} ε_{22} - p_{g} ε_{12}}{ε_{11} ε_{22} - ε_{12} ε_{21}} \\ I_{C 2} = \frac{p_{g} ε_{11} - p_{b} ε_{21}}{ε_{11} ε_{22} - ε_{12} ε_{21}} \end{cases}

According to Eq. (4), both I_CH and I_C2 can be extracted from simultaneously captured color images. To certificate its performance, a dual-wavelength solid laser (440 nm/515 nm) was used for experimental verification.

During the verification, the actual intensity ratio ρ_GBa between green (515 nm) and blue component (440 nm) was adjusted from 0.31 to 3.16 by changing intensity of each source as shown in Fig. 3(a), which lists captured mixed intensities of lasers. Applying the multispectral separation algorithm, Figs. 3(b) and 3(c), as well as Table 1, reveal the separated green and blue components. It is worth noting that the intensity of laser was recorded five times repeatedly with same ρ_GBa. The measured ρ_GBm are determined applying the proposed multispectral separation algorithm.

Fig. 3 Verification of flame chemiluminescence multispectral separation algorithm. (a) captured mixed intensities of lasers with various green to blue ratio, (b) and (c) retrieved green and blue intensities using proposed multispectral separation algorithm.

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Table 1. Verification details of flame chemiluminescence multispectral separation algorithm.

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Figure 4 illustrates the verification results of proposed algorithm. The black squares refer to the average measured ρ_GBm while the red dots represent the actual value of ρ_GBa, indicating measured ratios fit well with actual ones. Moreover, to quantitatively evaluate the precision of the proposed algorithm, root-mean-square (RMSE) was also adopted as shown in Eq. (5), in which N is the number of measurements, and (ρ_GBm)_max indicates the maximum value of ρ_GBm under the same condition. The RMSE and standard deviation computations listed in Table 1 show that the maximum RMSE is 2.68 × 10⁻², and the maximum standard deviation is lower than 3.90 × 10⁻², which prove that the proposed algorithm can distinguish I_CH and I_C2 with credible accuracy, thus providing a useful technique for quantitatively measuring CH* and C2* concentration of propane flame in real time combustion diagnostics.

Fig. 4 Verification results of flame chemiluminescence multispectral separation algorithm.

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R M S E = \frac{{{\sum_{i = 1}^{N} [{(ρ_{G B a})}_{i} - {(ρ_{G B}_{m})}_{i}]}^{2}}^{1 / 2}}{N \cdot {(ρ_{G B m})}_{\max}}

3. FCT system and its calibration

FCT system consisting of 12 color CMOS cameras covering ~180° was established as shown in Fig. 5. Moreover, lenses (Computar M0814) with focal length of 8 mm as well as double-channel bandpass filters were implemented to obtain the light intensity signal of CH* and C2* according to single-shot image combining with proposed multispectral separation algorithm. All CMOS cameras were connected to computers and triggered at the same time to capture the projections from 12 directions simultaneously. Here, the propane-air diffusion flame was used as the test sample.

Fig. 5 Experimental setup for propane combustion diagnostics.

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Both I_CH and I_C2in each direction can be extracted from simultaneously captured color images. Then, applying multiplicative algebraic reconstruction technique (MART), 3D structure of CH* and C2* intensities distribution can be computed for further flame detection and species analysis. However, due to inevitable errors from installation of different optical elements such as distortions and location deviations, both accuracy and resolution in CH* and C2* reconstructions will be decreased. Therefore, FCT system calibration [43] should be performed to remap these projections to a unified coordinate system before practical measurements, and those errors can be compensated using the calibration results. Here, a standard board shown in Fig. 6 was used in calibration. Moreover, in order to quantitatively characterize the calibration processing, three coordinate systems were used, as the world coordinate (x_w, y_w, z_w) (blue in Fig. 6), the camera coordinate (x_c, y_c, z_c) (green in Fig. 6) and the image coordinate (x_i, y_i) (red in Fig. 6). Origins of these coordinates O_w, O_c and O_i are located at centers of calibration board, imaging lens and CMOS chip, respectively. Both orientation and position of a CMOS camera in space are uniquely defined by Euler angles (ψ, θ, Φ) (“yaw”, “pitch”, and “roll” respectively) and three translations (T_X, T_y, T_z).

Fig. 6 Coordinate system used in FCT system calibration.

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Theoretically, the transform from the world coordinate system (x_w, y_w, z_w) to the camera coordinate system (x_c, y_c, z_c) can be expressed as

[\begin{matrix} x_{c} \\ y_{c} \\ z_{c} \end{matrix}] = R [\begin{matrix} x_{w} \\ y_{w} \\ z_{w} \end{matrix}] + T

Where R and T are regarded as rotation matrix and translation vector:

\begin{array}{l} \begin{matrix} R \end{matrix} = [\begin{matrix} r_{1} & r_{2} & r_{3} \\ r_{4} & r_{5} & r_{6} \\ r_{7} & r_{8} & r_{9} \end{matrix}] \\ = [\begin{matrix} \cos ϕ \cos ψ & \cos ψ \sin ϕ & - \sin ψ \\ \cos ϕ \sin ψ \sin θ - \cos θ \sin ϕ & \sin ϕ \sin ψ \sin θ + \cos ϕ \cos θ & \sin θ \cos ψ \\ \cos ϕ \sin ψ \cos θ + \sin ϕ \sin θ & \sin ϕ \sin ψ \cos θ - \sin θ \cos ϕ & \cos ψ \cos θ \end{matrix}] \end{array}

T = [\begin{matrix} T_{x} \\ T_{y} \\ T_{z} \end{matrix}]

Neglecting lens distortion, an object point and its corresponding image satisfy the pinhole camera model as demonstrated in Eq. (9):

x_{i} = z_{0} \frac{x_{c}}{z_{c}}, y_{i} = z_{0} \frac{y_{c}}{z_{c}} .

Where z₀ is regarded as the imaging distance of lens.

Based on Eq. (8) and (9), relation between the world coordinates of the sampling points in calibration board and the corresponding image coordinates can be described in matrix form:

B y = b

Where

B = [\begin{matrix} x_{w 1} & y_{w 1} & z_{w 1} & 1 & 0 & 0 & 0 & 0 & - x_{i 1} x_{w 1} & - x_{i 1} y_{w 1} & - x_{i 1} z_{w 1} \\ 0 & 0 & 0 & 0 & x_{w 1} & y_{w 1} & z_{w 1} & 1 & - y_{i 1} x_{w 1} & - y_{i 1} y_{w 1} & - y_{i 1} z_{w 1} \\ ⋮ \\ x_{w S} & y_{w S} & z_{w S} & 1 & 0 & 0 & 0 & 0 & - x_{i S} x_{w S} & - x_{i S} y_{w S} & - x_{i S} z_{w S} \\ 0 & 0 & 0 & 0 & x_{w S} & y_{w S} & z_{w S} & 1 & - y_{i S} x_{w S} & - y_{i S} y_{w S} & - y_{i S} z_{w S} \end{matrix}]

y = {[\begin{matrix} \frac{Z_{0} r_{1}}{T_{z}} & \frac{Z_{0} r_{2}}{T_{z}} & \frac{Z_{0} r_{3}}{T_{z}} & \frac{Z_{0} T_{x}}{T_{z}} & \frac{Z_{0} r_{4}}{T_{z}} & \frac{Z_{0} r_{5}}{T_{z}} & \frac{Z_{0} r_{6}}{T_{z}} & \frac{Z_{0} T_{y}}{T_{z}} & \frac{r_{7}}{T_{z}} & \frac{r_{8}}{T_{z}} & \frac{r_{9}}{T_{z}} \end{matrix}]}^{T}

b = {[\begin{matrix} x_{i 1} & y_{i 1} & \dots & x_{i S} & y_{i S} \end{matrix}]}^{T}

Since the world coordinates (x_wn, y_wn, z_wn) of the sampling points n = {1, 2,..., S} are pre-defined and the corresponding image points (x_in, y_in) can be acquired from the images, thus according to Eq. (10), all camera parameters are determined as demonstrated in Table 2.

Table 2. Calibrated camera parameters.

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Finally, to estimate the accuracy of calibration, re-projection processing based on the retrieved camera parameters in Table 2 was adopted. Shown in Fig. 7, re-projection points (red dots in zoomed-in figures) match well with the sampling points.

Fig. 7 Re-projection results in all 12 directions. Red dots in zoomed-in plots indicate re-projected results.

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The deviation in the camera calibration method is synthetically quantitatively evaluated by the re-projections of the sample points to the image planes with the calibration results.

The vertical deviation and horizontal deviation of the re-projected coordinates of sample points in the image plane are used to describe the errors. The projection deviation of the 324 sample points in all 12 directions are plotted in Fig. 8. It can be found that most of the sample points’ deviations concentrate in the range of plus or minus one pixel. In addition, the maximum vertical deviation is smaller than 1.5 pixel and the maximum horizontal deviation is no more than 2 pixel. The quantitatively evaluation of re-projection indicate that the calibrated FCT system can compensate deviations of CMOS cameras and provide accurate flame projections in various directions as well as detailed flame structures after 3D reconstruction.

Fig. 8 Re-projection deviation of the sample points in all 12 directions.

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4. 3D dynamic CH* and C2* measurements and analysis in propane-air diffusion flame

After calibration of the FCT system as well as certification of flame chemiluminescence multispectral separation algorithm, they were applied for 3D dynamic CH* and C2* component reconstruction in flame diagnostics. Figure 9 demonstrates full directional projections of non-axisymmetric propane-air diffusion flame with single-jet nozzle captured with exposure time of 20 μs at a rate of 5 fps. According to the proposed quantitative multispectral separation algorithm, intensities corresponding to CH* and C2* can be separated as depicted in Fig. 10.

Fig. 9 Projectons of non-axisymmetric propane-air diffusion flame from 12 directions at 0.4s.

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Fig. 10 Chemiluminescence emission intensity images of CH* and C2* from 12 directions at 0.4s.

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In order to analyze the flame configuration in details as well as its species concentration, both 3D concentration distributions of CH* and C2* need to be reconstructed. Here, the reconstructed volume (the purple cube in Fig. 7) is divided into 100 × 100 × 200 voxels in x, y, and z directions. The spatial resolution must satisfy the following relationship to ensure the distance between imaging centers of adjacent voxel cannot be larger than the size of a pixel.

Δ G \leq \frac{n \times Δ P}{Z_{0}} T_{z}

Where ΔG indicates the spatial resolution, ΔP represents the size of pixel, n is the aggregation number of pixel. In this work, the size of pixel is 5.86 μm and the aggregation number of pixel is chosen as 2. Z₀ is the minimum image distance of 12 cameras. Meanwhile, T_z refer to the minimum distance from the flame to the camera of 12 cameras. According to Table 2, Z₀ is 8.13 mm and T_z is 490.50 mm. Thus, the spatial resolution is chosen as 0.65 mm in this work.

Since the size of the weight matrix depends on discretization of the reconstructed volume as well as number of projections, considering the number of voxels and the projections recorded on ~1.2 × 10⁴ pixels (region of interest), the weight matrix at each view required more than 89.4 GB of memory. By removing zero elements in the weight matrix and taking into account the number of effective pixels on which a projection is recorded and resolved, the size of weight matrix at each view can be reduced to 25.8 MB of memory. Thus 3D FCT problem can be performed by MART, as described in Eq. (15).

f_{i}^{(h + 1)} = f_{i}^{(h)} \times (1 - \frac{α w_{i j}}{\sum_{i = 1}^{N} {(w_{i j})}^{2}} (1 - \frac{I_{j}}{\sum_{i = 1}^{N} w_{i j} f_{i}^{(h)}}) \begin{matrix} 1 \leq j \leq p \times q \end{matrix}

The voxel indices are represented by the single index i, j is defined as the projection direction. I_j is regarded as the projection in direction j, and f_i refers to the intensity of the voxel i. Weight factor w_ij can be considered as the contribution coefficient of the voxel i to the direction j. Where α is a relaxation factor in improving convergence with sensor noise, h is the index of iteration. The reconstruction is considered converged once the absolute difference of the sum of f from one iteration to the next, is below the threshold value Δc. In order to increase the speed of transfer of data from hard disk to memory, the memory mapping technology was adopted. Here, the time consumption in single frame reconstruction was 3 min.

Figure 11 reveals 3D CH* and C2* concentration distributions of non-axisymmetic propane-air diffusion flame at 0.4 sec. Additionally, since the CMOS camera array can record images covering complete flame variation process, thus 3D concentration distributions at different time can be monitored as shown in Fig. 12, illustrating the combustion process of the non-axisymmetic propane-air diffusion flame.

Fig. 11 3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame from four directions at 0.4s. (A movie is available online. See Visualization 1)

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Fig. 12 3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame at different moments. (A movie is available online. See Visualization 2)

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Additionally, quantitative species component can be determined according to reconstructed 3D distribution of CH* and C2* intensities. Figure 13 describes C2* to CH* ratios at 0.4s, 1.0s, 5.4s and 17.4s. Moreover, to quantitatively analyze details of species component distributions, Fig. 14 reveals normalized CH* (blue line) and C2* (green line) components at cross sections at 6.50 mm (A), 42.90 mm (B) and 72.15 mm (C) above the nozzle marked in Fig. 13, indicating that the value of C2* component is always higher than CH* in these sections of flame. Certified by both verification and practical measurements, it is believed the proposed 3D dynamic CH* and C2* concentration measuring technique can be well applied in real time composition testing in combustion diagnostics.

Fig. 13 3D C2* to CH* intensity ratio of non-axisymmetic propane diffusion flame at different moments.

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Fig. 14 Normalized reconstructed C2* and CH* components of selected sections.

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5. Summary

In summary, we proposed 3D dynamic CH* and C2* concentration measuring technique combining with chemiluminescence multispectral separation algorithm and calibrated FCT system. Firstly, accuracy of chemiluminescence multispectral separation algorithm based on digital color cameras coupled with double-channel bandpass filters was certificated by dual-wavelength solid laser, proving that it can acquire both CH* and C2* intensity of propane flame from single-shot color images. Furthermore, real time FCT system consisting of 12 color CMOS cameras covering ~180° was realized for dynamic 3D information reconstruction with MART. Moreover, system calibration was also implemented thus error due to optical element installation deviations can be compensated for credible resolution and accuracy in 3D reconstruction. Finally, multispectral separation algorithm was adopted to extract CH* and C2* intensities of a non-axisymmetic propane-air diffusion flame from 12 directions. Then, dynamic 3D chemiluminescence emission structure of CH* and C2* with volume of 65 × 65 × 130 mm³ can be reconstructed from simultaneously captured projections. Additionally, quantitative analysis of CH* and C2* components in flame was provided to study the propane-air diffusion flame in details. Considering the capability of the proposed technique in 3D dynamic quantitative species measurements, we believe it can be further applied in combustion studies and applications for crucial physical parameters measurements.

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Name	Description
Visualization 1: AVI (464 KB)	3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame at 0.4s
Visualization 2: AVI (3792 KB)	3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame in the combustion process

Experiments		1	2	3	4	5	6	7	8	9
Intensity of G channel (mw)		96.3	112.2	135.7	181.1	202.7	209.7	279.4	279.4	279.4
Intensity of B channel (mw)		301.4	277.0	277.0	277.0	203.3	140	140	114.1	88.3
Actual ρ_GB		0.31951	0.40506	0.48989	0.65381	0.99701	1.49790	1.99570	2.44870	3.16290
Measured ρ_GB	1	0.31950	0.40563	0.48974	0.65083	0.98087	1.49970	1.99170	2.42780	3.01090
	2	0.31956	0.40558	0.48993	0.65210	0.97943	1.50060	1.99370	2.44090	3.03030
	3	0.31956	0.40525	0.48998	0.65325	0.98145	1.49830	1.99640	2.44070	2.99120
	4	0.31949	0.40507	0.48986	0.65210	0.97800	1.49720	1.99310	2.44320	2.93540
	5	0.31947	0.40526	0.48974	0.65342	0.95030	1.49670	1.99440	2.44500	2.95620
RMSE		5.57E-05	4.10E-04	9.44E-05	1.20E-03	1.18E-02	4.73E-04	5.39E-04	2.00E-03	2.68E-02
Standard Deviation		4.16E-05	2.38E-04	1.09E-04	1.05E-03	1.33E-02	1.64E-03	1.73E-03	6.79E-03	3.89E-02

Cam.	ψ	θ	Φ	$T x$	$T y$	$T z$	Im.dis
#	(^o)	(^o)	(^o)	(mm)	(mm)	(mm)	(mm)
1	279.53	0.43	−1.29	−8.79	29.77	−493.95	8.15
2	290.35	−0.31	−1.74	−8.41	30.00	–496.89	8.15
3	304.00	0.71	−1.67	−9.33	28.87	−494.66	8.13
4	318.49	0.71	−1.48	−8.16	28.78	−490.50	8.14
5	335.58	0.63	−0.99	−4.87	27.56	−506.14	8.14
6	353.75	0.09	0.34	1.77	31.37	−503.28	8.14
7	9.48	0.53	−0.30	2.17	29.45	−499.77	8.14
8	24.18	1.13	0.20	3.34	27.54	−493.38	8.14
9	37.52	1.16	0.04	3.14	25.83	−505.97	8.14
10	50.28	0.89	0.07	1.05	28.92	−501.37	8.14
11	64.91	1.01	0.44	1.23	29.33	−492.94	8.15
12	77.94	3.18	3.18	4.00	30.26	−491.04	8.15

Experiments		1	2	3	4	5	6	7	8	9
Intensity of G channel (mw)		96.3	112.2	135.7	181.1	202.7	209.7	279.4	279.4	279.4
Intensity of B channel (mw)		301.4	277.0	277.0	277.0	203.3	140	140	114.1	88.3
Actual ρ_GB		0.31951	0.40506	0.48989	0.65381	0.99701	1.49790	1.99570	2.44870	3.16290
Measured ρ_GB	1	0.31950	0.40563	0.48974	0.65083	0.98087	1.49970	1.99170	2.42780	3.01090
	2	0.31956	0.40558	0.48993	0.65210	0.97943	1.50060	1.99370	2.44090	3.03030
	3	0.31956	0.40525	0.48998	0.65325	0.98145	1.49830	1.99640	2.44070	2.99120
	4	0.31949	0.40507	0.48986	0.65210	0.97800	1.49720	1.99310	2.44320	2.93540
	5	0.31947	0.40526	0.48974	0.65342	0.95030	1.49670	1.99440	2.44500	2.95620
RMSE		5.57E-05	4.10E-04	9.44E-05	1.20E-03	1.18E-02	4.73E-04	5.39E-04	2.00E-03	2.68E-02
Standard Deviation		4.16E-05	2.38E-04	1.09E-04	1.05E-03	1.33E-02	1.64E-03	1.73E-03	6.79E-03	3.89E-02

Cam.	ψ	θ	Φ	$T x$	$T y$	$T z$	Im.dis
#	(^o)	(^o)	(^o)	(mm)	(mm)	(mm)	(mm)
1	279.53	0.43	−1.29	−8.79	29.77	−493.95	8.15
2	290.35	−0.31	−1.74	−8.41	30.00	–496.89	8.15
3	304.00	0.71	−1.67	−9.33	28.87	−494.66	8.13
4	318.49	0.71	−1.48	−8.16	28.78	−490.50	8.14
5	335.58	0.63	−0.99	−4.87	27.56	−506.14	8.14
6	353.75	0.09	0.34	1.77	31.37	−503.28	8.14
7	9.48	0.53	−0.30	2.17	29.45	−499.77	8.14
8	24.18	1.13	0.20	3.34	27.54	−493.38	8.14
9	37.52	1.16	0.04	3.14	25.83	−505.97	8.14
10	50.28	0.89	0.07	1.05	28.92	−501.37	8.14
11	64.91	1.01	0.44	1.23	29.33	−492.94	8.15
12	77.94	3.18	3.18	4.00	30.26	−491.04	8.15

Three-dimensional dynamic measurements of CH* and C2* concentrations in flame using simultaneous chemiluminescence tomography

Abstract

1. Introduction

2. Flame chemiluminescence multispectral separation algorithm

3. FCT system and its calibration

4. 3D dynamic CH* and C2* measurements and analysis in propane-air diffusion flame

5. Summary

References and links

Supplementary Material (2)

Cited By

Figures (14)

Tables (2)

Equations (15)

Optics Express