1. Introduction

Due to turbulent and non-symmetric flows in practical combustion, diagnostic techniques nowadays are developing towards a high-speed (generally at a repetition rate of ∼kHz) and three–dimensional detection [1–5]. Up to now the measured quantities have covered chemiluminescence [5], fluorescence [3], incandescence [4] and velocity [2], etc. As one of the most important combustion parameters, temperature plays a central role in understanding combustion processes and controlling combustion pollutants. Most steps of the soot evolution process are closely linked to temperature, governing soot and gas-phase reaction kinetics [6]. Tracking the evolution of soot properties in turbulent flames is of paramount interest, as it can be seen by a number of experimental [7] and numerical [8] studies. To the best of our knowledge, these and other experimental investigations have not reported on high-speed soot temperature measurement. Yet the knowledge of local temperature is a prerequisite for accurate soot particle sizing by time-resolved laser-induced incandesence [9,10], which is a key technique for the measurement of soot volume fraction and primary particle size. So the provision of soot temperature is an essential intermediate step for comprehensive 4D soot diagnostics in turbulent flames. Regarding numerical investigations, Lagrangian soot tracking methods have become increasingly important [11,12], and in this context the provision of experimental local soot temperatures may be extremely beneficial. Therefore, there is a need to propose a feasible approach that can resolve 3D temperature field at the repetition rate of ∼kHz.

With the rapid development of imaging technologies in recent years, a number of camera-based techniques, such as phosphor thermometry [13,14], two-line atomic fluorescence (TLAF) [15–17], two-color pyrometry [18–22], have emerged to measure multi-dimensional temperature fields in combustion environments. Among these techniques, two-color pyrometry can favorably be combined with tomography due to its line-of-sight (LOS) character, and thereby provides an opportunity to realize a high-speed and 3D thermometry. Compared to existing volumetric thermometry techniques such as volumetric two-color laser-induced OH fluorescence [23] and tomographic two-line laser absorption imaging [24], this method does not need any laser excitation and therefore offers a comparatively simple experimental arrangement and ease of implementation. However, the method requires sufficient thermal radiation signals at two wavelengths [18–22]. Previous efforts [25,26] commonly established tomographic experimental setups based on multiple RGB cameras. The red, green and blue channels allow to capture emissions at different wavelength bands simultaneously. However, these approaches are hardly suited to carry out high-speed temperature determinations due to the formidably high experimental cost for high-speed RGB cameras. Thus, the challenge persists to achieve 3D, high-speed and time-resolved (4D) temperature measurements of turbulent flames.

The main objective of this work is to measure 4D temperature distributions for a turbulent flame by using tomographic two-color pyrometry. Compared to the previous investigations [25,26], the evolution of the 3D temperature field in a turbulent flame is to the best of our knowledge resolved at a high frequency of 7.5 kHz for the first time. Furthermore, the novel experiment employs only two cameras equipped with filters and a customized fiber bundle to obtain nine emission projections simultaneously at each wavelength band.

2. Methodology

2.1 Principle of two-color pyrometry

Two-color pyrometry for temperature determination is based on Planck’s law, in which the spectral emission I(${\boldsymbol {\lambda }}$,T) is a function of temperature T and emissivity ${{\boldsymbol {\varepsilon} }_{\boldsymbol {\lambda} }}$ [27,28]:

Taking the ratio of Eq. (1) at two different wavelengths and incorporating Eq. (2), Eq. (3) is derived and temperature can be evaluated using a look-up table:

2.2 Tomographic two-color pyrometry

Tomographic two-color pyrometry is a combined technique of two-color pyrometry and emission tomography, and can recover the 3D temperature distribution of a region of interest [25,26]. The 3D temperature distribution is calculated based on two 3D emission distributions at different wavelengths. For tomographic reconstruction, the flame emission at each wavelength needs to be recorded at multiple views, which indicates that a number of cameras (e.g., 6 [29]) should be employed. For steady flames, the emission can be recorded successively by one camera, equipped with a filter at the first wavelength, and recorded again after changing the filter. Yet, for turbulent flames, the emission must be captured at two wavelengths simultaneously, which usually requires double the number of cameras. Another possibility is to choose RGB cameras that can acquire emissions at three wavelength bands simultaneously. However, this method is not flawless as the bandwidths of most RGB cameras are relatively wide, resulting in a decreased accuracy of the temperature determination [30].

Apparently, emission tomography is the primary procedure in 3D temperature evaluation. Mathematically, an emission image recorded by camera can be formulated as a weighted summation of emission intensities as [31]:

3. Experimental setup

The experimental setup is presented in Fig. 1. As can be seen, this setup mainly contains a customized fiber bundle (manufactured by the Nanjing Chunhui Science and Technology Industrial Co. Ltd) surrounding a flame, a beam splitter and two cameras. Adopting fiber bundles for flame chemiluminescence tomography has been performed by Anikin et al. [34,35]. In this work, the fiber bundle has nine inputs and one output with a total length of 2 m. Each input end contains an array of 340 ${\times} $ 340 fiber elements with a size of ∼5.8 mm ${\times} $ 5.8 mm, resulting in an output end array of 1020 ${\times} $ 1020 fiber elements with a size of ∼17.4 mm ${\times} $ 17.4 mm. The fiber element resolution is ∼17 $\mathrm{\mu }$m. The nine inputs were arranged nearly along a semi-circle in a plane covering an angular range of ∼120° in a roughly equiangular manner. In front of each input, an AF Nikon lens (50 mm focal length and f/1.8) was used to collect the emission signals. With this arrangement, the emissions collected by the nine inputs can be transmitted to the same output end. By using a beam splitter cube, the signal was further split in two paths. One part of the signal was captured by a camera equipped with a AIS Nikon Micro lens (60 mm focal length and f/2.8) and a band-pass filter (${\mathrm{\lambda }_1}$=425 nm ± 25 nm, Edmund Optics). The other signal part was captured by a second camera equipped with another AIS Nikon Micro lens and another filter (${\mathrm{\lambda }_2}$=600 nm ± 25 nm, Edmund Optics).

 

Fig. 1. The experimental setup for 3D temperature determination.

Download Full Size | PDF

In order to determine the real emission intensity, a calibration procedure was carried out. Physically, the emission intensities were converted into voltage signals by the cameras. The conversion relationship between the two signals can be expressed as [19]:

The tomographic two-color pyrometry system for 3D temperature determination was tested in a premixed laminar flat flame and a weakly turbulent diffusion flame, respectively. For the premixed laminar flame, a commercial standard flat flame burner with bronze matrix (McKenna, Holthuis & Associates) was used. The details on the burner configuration can be found in [36]. A premixed gas flow of ethene and air was supplied with an equivalence ratio of 2.7. The total flow rate was set to be 10 SLPM (standard liters per minute). This gas flow was isolated from the surrounding by a shroud gas of nitrogen. To stabilize the flame, a stainless steel plate with a diameter of 60 mm and a thickness of 20 mm was mounted at 26 mm height above the burner (HAB) surface. During the experiment, the burner was cooled by circulated water at 18 °C. For this steady flat flame, the distance between the flame and the fiber bundle input was ∼0.57 m, and only one camera (Andor USB iStar model DH334T-18F-E3, 16 bit) was used. The exposure time was set to 10 µs. The signal acquisition at different wavelengths was achieved by changing filters.

For the experiment with the unsteady, weakly turbulent diffusion flame, the fuel was ethyne mixed with nitrogen, which was sent through a stainless steel tube with an inner diameter of 2 mm and an outer diameter of 6 mm. The flow rate was set to 4 SLPM, resulting in a Reynolds number of ∼3900. In order to isolate the flame from the surroundings, nitrogen was used as the shroud gas provided from the outer shield with a diameter of 35 mm. This burner configuration was also used in the works of Geitlinger et al. [37] and Oltmann et al. [38]. The distance between the flame and the fiber bundle input was ∼0.53 m. For the temperature determination of the turbulent flame, the emissions need to be captured at two wavelength bands simultaneously, requiring two high-speed cameras. One camera (No. 1) used in this work was a Phantom v2012 equipped with an intensifier (HS-IRO). The other (No. 2) was a Phantom v711 equipped with an intensifier (Goldlücke GmbH, integrated by Lavision GmbH). To freeze the transient temperature fields, both cameras were operated at a frame rate of 7.5 kHz and with an intensifier gate of 40 µs. The two cameras were synchronized with a timing unit (PTU) and monitored with an oscilloscope.

4. Results and discussion

4.1 Premixed steady flat flame

The emission images of the premixed steady flat flame were taken at the 425 nm $\, \pm $25 nm and 600 nm $\, \pm $25 nm wavelength bands, respectively. A set of example images can be found in Fig. S2 of the supplementary material. The internal and external parameters of the nine viewpoints were obtained by performing a camera calibration procedure. Specifically, a checkerboard was placed at the position where the flame was present and imaged by the tomographic system. The obtained image was split into nine sub-images, each of which corresponds to an individual viewpoint. The parameters of each viewpoint were fitted by using the Camera Calibration Toolbox for Matlab [39]. Although the calibration plate is different from the work of Wang et al. [40], the output parameters describe almost the same physical processes. The field of view was ∼65 mm${\times} $65 mm and occupied ∼325${\times} $325 image pixels, resulting in a pixel resolution of 0.2 mm. The emission images of each wavelength were averaged over 50 frames and the corresponding background was subtracted. Based on these images, the 3D emission distributions at the two wavelength bands were reconstructed and used for 3D temperature evaluation. The tomographic regions of both wavelength bands were referenced to the same checkerboard. The voxel resolution was set to be 0.6 mm along the x and y axes, and 0.25 mm along the z axis.

Figure 2 presents the 3D temperature distribution of the premixed steady flat flame. Following the work of Yon et al. [41], who carefully evaluated the wavelength-dependence of the absorption function for two types of flames, the values of E($\tilde{\textrm{m}}$) at the wavelengths of 425 nm and 600 nm were set to 0.37 and 0.30, respectively. As can be seen, the symmetric feature of the temperature distribution was recovered faithfully. In addition, in each vertical slice (e.g., the slice at Y = 36 mm, corresponding to the flame center) the temperature distribution presents a decreasing trend from the bottom to the top due to the radiative cooling and influence of the stabilization plate mounted at 26 mm HAB. Setting aside the outliers near the flame boundaries, the overall temperature range was from 1500 K to 2000K. These observations conform with the results reported by Reimann et al. [42]. In order to validate the temperature determination of the steady flame, a quantitative comparison against other studies is given here. For the position of 12 mm HAB on the central line of the middle slice, a temperature of 1652 K was obtained, which is in good agreement with 1690 K determined by Reimann et al. [42] for the same position within a flame at the same equivalence ratio ($\phi $=2.7). Furthermore, this value is within the range of temperatures measured by other researchers for somewhat lower or higher equivalence ratios (1750 K by Xu et al. [43] for $\phi $=2.64, 1750K by Malarski et al. [44] for $\phi $=2.3 and 1600 K by Kearney and Jackson [45] for $\phi $=3.1). This comparison demonstrates that the tomographic method introduced in this work can obtain reasonable accurate 3D temperature distribution for a sooting flame. Additionally, the 3D temperature distribution derived from tomographic two-color pyrometry is compared with that calculated based on an inverse Abel transform [46] and that of an LOS evaluation. The fifth sub-images as shown in Fig. S2(a) and S2(b) of the supplementary material were used for 3D emission reconstructions with the inverse Abel transform. The LOS temperature distribution was also derived from the fifth sub-images in Fig. S2(a) and S2(b).

 

Fig. 2. 3D temperature distribution determined based on tomographic two-color pyrometry.

Download Full Size | PDF

Figure 3 shows a comparison of the temperature distributions in the center slice at Y = 36 mm calculated by the three methods. In general, the three temperature distributions present a good agreement. This point could be supported by the temperature comparison along the central lines shown in Fig. 4. The differences of two temperature distributions each, i.e., $\mathrm{\Delta }$T-distributions, are also presented. As can be seen, similar temperature distributions such as a decreasing trend of temperature from the low HAB region to the high HAB are obtained from all different methods. The internal differences between the temperature from tomography and LOS temperature lie in the range from -25 K to 90 K. In comparison, the internal differences between temperature from tomography and that based on inverse Abel transform lie in the range from -70 K to 105 K for the central region, and in the range from -22 K to 25 K for the other regions. However, the inverse Abel transform results in a smaller width of the temperature distribution compared to the other two, which may be caused by the symmetry assumption, the uncertainties in determining the central line and flame diameter. The temperature contour from tomography conforms better with the LOS temperature. This is because no symmetric assumptions were used in these two methods. The pronounced errors on the flame contours can be attributed to the inconformity from LOS data and a single slice. It should be noted that the LOS temperature distribution was determined based on the LOS emission projections directly. Such a result represents the mean temperature values along the recording view, i.e. cannot reveal depth information. In comparison, the tomographic two-color pyrometry enables 3D-resolved temperature evaluation, which is the main advantage. These comparisons suggest that the temperature distribution is resolved sufficiently by the tomographic method.

 

Fig. 3. A comparison of temperature determinations calculated by three different methods.

Download Full Size | PDF

 

Fig. 4. A comparison of temperature determinations along the central lines calculated by three different methods.

Download Full Size | PDF

4.2 Turbulent diffusion flame

In the experiment with the weakly turbulent diffusion flame, a total number of 500 frames were recorded. An example set of flame images can be found in Fig. S3 of the supplementary material. The field of view of Camera No. 1 was ∼59 mm${\times} $59 mm and occupied ∼245${\times} $245 image pixels, resulting in a pixel resolution of 0.24 mm; the field of view of Camera No. 2 was ∼60 mm${\times} $60 mm and occupied ∼220${\times} $220 image pixels, resulting in a pixel resolution of 0.27 mm. The turbulent flame height was ∼250 mm, which was out of the field of view. So three flame regions with a similar size were measured by lifting the burner. Considering the field of view a region of 50 mm height in each image was selected for the subsequent temperature determination.

Based on the consecutive emission images of the turbulent diffusion flame at the two wavelength bands, time-resolved 3D emission distributions of the turbulent flame at each band were reconstructed, based on which time-resolved temperature distributions were evaluated frame by frame. The voxel resolution for this turbulent flame was set to be 0.3 mm along the x and y axes, and 0.46 mm along the z axis. Figure 5 presents a 3D temperature evolution of every third frame for the time duration from 0 ms to 1.2 ms. In order to provide a better visualization of the 3D temperature evolution, an animation and a 3D temperature evolution at the repetition rate of 7.5 kHz (please see Fig. S4) are provided in the supplementary material. For each instant, the slices of Y = 17.6 mm, Y = 29.6 mm (where the nozzle outlet is), Y = 41.6 mm and HAB = 43 mm, HAB = 71 mm, HAB = 99 mm are displayed. As can be seen from Fig. 5, the instantaneous 3D temperature distribution exhibits a variety of spatial shapes and topologies. It should be noted that the temperature values in most combustion regions are 1500 K-1800K as suggested by the widespread blue areas. In the lower region where main combustion reaction occurs, the temperature values are larger than those in other parts. Furthermore, local regions with weak radiation intensity are identified based on a threshold value of 4% of the reconstructed maximum emission intensity (a heuristic value based on the ratio of average background and emission intensity). These will either grow or shrink, resulting in discontinuous soot structures. Thus, we assume that in those regions inside the flame only soot in low concentration is present, which is below the detection limit. By using the threshold value and relating the soot volume fraction data in the work of Reimann et al. [42], the detection limit of this work is roughly estimated to be 0.02 ppm. From a comparison of the slices at Y = 17.6 mm (or Y = 41.6 mm) and that at Y = 29.6 mm, one can see that these regions of low concentration in the outer parts of the flame are larger than those close to the central position. The spatial characteristics as shown in Fig. 5 are difficult to observe from traditional planar techniques.

 

Fig. 5. The 3D temperature evolution of every third frame for the time duration from 0 ms to 1.2 ms. The unit of this figure is Kelvin (K) (please see Visualization 1).

Download Full Size | PDF

The uncertainty quantification of turbulent temperature determination was based on statistical analysis and the Monte Carlo method [47,48]. A temperature phantom was adapted from a direct numerical simulation (DNS) study [49] and is shown in Fig. 6(a). An example temperature slice at z = 25 is shown in Fig. 6(b). Based on the temperature phantom, the radiation phantoms at the bands of 425 nm and 600 nm were produced. The critical parameters that affect the tomographic reconstruction and the two-color pyrometry were considered as inputs, which included the camera calibration (intrinsic and extrinsic) parameters, image noise, and the values of E($\tilde{\textrm{m}}$) at 425 nm and 600 nm. These input parameters were assumed to follow Gaussian distributions. Note that the camera calibration parameters such as focal length, distortion factors, rotation and translation matrix, etc., only determine the pixel positions in image, as a simplification, these quantities were considered by the pixel position bias, which was obtained directly from the camera calibration procedure (the pixel error, i.e. the standard deviation). In this work, the probability distribution functions (PDFs) of pixel position followed ${\textrm{x}_1}\sim ({{{\bar{x}}_1},{\mathrm{\sigma }_{1\textrm{x}}}} )$, ${\textrm{y}_1}\sim ({{{\bar{y}}_1},{\mathrm{\sigma }_{1\textrm{y}}}} )$, ${\textrm{x}_2}\sim ({{{\bar{x}}_2},{\mathrm{\sigma }_{2\textrm{x}}}} )$, ${\textrm{y}_2}\sim ({{{\bar{y}}_2},{\mathrm{\sigma }_{2\textrm{y}}}} )$ with ${\mathrm{\sigma }_{1\textrm{x}}}$=0.77, ${\mathrm{\sigma }_{1\textrm{y}}}$=0.86, ${\mathrm{\sigma }_{2\textrm{x}}}$=0.71, ${\mathrm{\sigma }_{2\textrm{y}}}$=0.94. Based on the imaging model, the simulated images at the two bands were calculated, and pixel positions are biased based on the respective PDFs. Afterwards, the two simulated images were perturbed by Gaussian noise ${\textrm{p}_{\textrm{noise}}}\sim ({{{\bar{p}}_{\textrm{noise}}},{\mathrm{\sigma }_{\textrm{noise}}}} )$. The values of ${\bar{p}_{\textrm{noise}}}$ and ${\mathrm{\sigma }_{\textrm{noise}}}$ were estimated from the background region of the recorded flame image, and equaled to 3.57 and 4.24, respectively. The quantities of E($\tilde{\textrm{m}}$) at each band were assumed to follow the distribution calculated according to Yon et al. [41] as mean and a 5% value as standard deviation. Based on the Monte Carlo simulation the tomographic two-color pyrometry was repeated 500 times, yielding the same number of 3D temperature distributions. Figure 6(c) presents a comparison between the temperature phantom and one calculation along the gray line as shown in Fig. 6(b). The uncertainty was estimated by the sample standard deviation multiplied by a coverage factor of 2. In general, most uncertainty values were within the range between 60 K and 100 K. The uncertainty distribution of the 25^th layer along the z axis is shown in Fig. 6(d). Note that large uncertainties occur at edge regions.

 

Fig. 6. (a) The temperature phantom used for uncertainty analysis; (b) an example temperature distribution of the 25th layer along the z axis; (c) a comparison between the temperature phantom and one calculation along the gray line as shown in the panel (b); and (d) the corresponding uncertainty temperature distribution.

Download Full Size | PDF

In order to explicitly investigate the influence of the absorption function E($\tilde{\textrm{m}}$), which is a crucial parameter in pyrometry, on temperature determination, the temperature distribution at 0 ms was re-evaluated with constant values of E($\tilde{\textrm{m}}$) at each wavelength bands instead of the wavelength-dependent values of Yon et al. [41] and is shown in Fig. 7(a). Yon et al. performed a careful examination of the wavelength-dependence of the absorption function, using various fuels and dilution ratios in a hybrid burner and two different experimental approaches. While the wavelength dependence of E($\tilde{\textrm{m}}$) depends on many factors, such as fuel, location in the flame and soot maturity, the general trend of a smaller value at larger wavelength in the visible range corresponds with most observations in literature. The test case with constant values of E($\tilde{\textrm{m}}$) is being used here for comparative purpose to see how the choice of E($\tilde{\textrm{m}}$) would affect the temperature determination. As can be seen, with constant values of E($\tilde{\textrm{m}}$), the temperature values would be somewhat higher than those determined with wavelength dependent E($\tilde{\textrm{m}}$). The difference between the two temperature distributions at 0 ms shown in Figs. 5 and 6(a) is presented in Fig. 7(b), indicating a maximum difference of ∼120 K, underlining how crucial the choice E($\tilde{\textrm{m}}$) is. In addition, large differences can be observed at the positions with high temperature values. Similar results were also obtained in the temperature determinations of the premixed steady flat flame.

 

Fig. 7. (a): The temperature distribution at 0 ms with constant values of E($\tilde{\textrm{m}}$) at each wavelength bands; (b) The difference between the two temperature distributions. The unit of this figure is Kelvin (K).

Download Full Size | PDF

5. Conclusion

In summary, this work to the best of our knowledge represents the first attempt for 4D temperature determination where tomographic two-color pyrometry was used to evaluate temperature distributions in sooting flames. A novel approach combining the fiber bundles, beam splitter cube and two high-speed cameras was employed to obtain two sets of emission images at different wavelength bands. The approach was first successfully demonstrated on a steady flame produced by a laminar flat flame burner. The time-resolved temperature distribution of a weakly turbulent diffusion flame was evaluated at a repetition rate of 7.5 kHz. It should be noted that the temporal resolution achievable by this method is limited by the signal-to-noise ratio (SNR) of single-shot images as a short exposure gate results in a low SNR. However, such an approach has the ability to reach a repetition rate in the kHz range and is necessary to correctly depict the structures of the temperature distribution and its evolution in unsteady flames.