Comparison of Numerical Iterative Algorithms for Two-Dimensional Absorption Spectral Reconstruction
ZHANG Li-fang1, YANG Yan-xia1, ZHAO Guan-jia1, MA Su-xia1, GUO Xue-mao2
1. Department of Thermal Engineering, College of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2. Post-Doctoral Scientific Research Workstation of Taiyuan Boiler Group Co. Ltd., Taiyuan 030024, China
Abstract：Two-dimensional (2D) temperature and component concentration distribution based on tunable diode laser absorption spectroscopy is significant for combustion diagnosis, and the iterative algorithm plays an important role in the reconstruction of temperature and component concentration. It is found that the adaptive algebraic reconstruction technique and the least-square QR decomposition algorithm have good advantages in constructing 2D temperature and H2O concentration distribution. The simulated results show that four spectral absorption lines of H2O with wavelengths at 7 154.35, 7 153.75, 7 185.60 and 7 444.36 cm-1 are very suitable for measuring temperature and water vapor concentration distribution in high-temperature premix flame. Compared with the absorption lines at 7 444.36, 7 185.60, 7 154.35 and 7 153.75 cm-1, the absorption lines of CO2 and CH4 are very weak, the absorption lines of O2 and CO are almost no absorption in this band. Therefore, CO2, CH4, O2, CO and other gases in the combustion environment do not affect the absorption spectrum of H2O. By comparing the optimal relaxation factor, calculation time and reconstruction error of different algorithms, we find that the adaptive algebraic reconstruction technique has better reconstruction quality and shorter calculation time than the least square QR decomposition algorithm. Based on the AART algorithm, this paper further compares the 2D reconstruction effects of different absorption line pairs (7 444.36 and 7 185.60 cm-1, 7 154.35 and 7 153.75 cm-1) at 16, 32, 48 and 64 ray beams. The results show that the reconstruction results obtained from absorption lines 7 153.75 and 7 154.35 cm-1 are better than those obtained from absorption lines 7 185.60 and 7 444.36 cm-1. With the increased laser beams, the reconstructed results are closer to the assumed temperature and concentration distributions. The 32-beam arrangement is more suitable for the actual flame’s 2D temperature and concentration reconstruction. In order to analyze the ability of the AART algorithm to reconstruct different temperature and concentration distributions, this paper further simulates bimodal temperature and concentration distributions. The results show that with the increase of the ray beam, the temperature reconstruction error is always greater than the concentration reconstruction error, indicating that the ray number has a more obvious effect on temperature. In the bimodal distribution, the reconstruction error is the largest when the projected ray beam is 16, but the reconstruction results can also reflect temperature and concentration distribution trend.
Key words：Tunable diode laser absorption spectroscopy; Reconstruction algorithm; Temperature distribution; Concentration distribution
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