Reconstruction Algorithm of Absorption Spectral Field Distribution Based on a Priori Constrained Bivariate Polynomial Model

Computed Tomography–Tunable Diode Laser Absorption Spectroscopy (CT-TDLAS) is an effective diagnostic method for analyzing combustion flow fields within engines. This study proposes an adaptive reconstruction algorithm utilizing constrained polynomial fitting within the CT-TDLAS framework. Based on existing polynomial fitting models, the proposed algorithm integrates physical boundary constraints on temperature and concentration fields, optimizing integrated absorbance errors. This method significantly enhances reconstruction accuracy and computational efficiency, while also lowering computational complexity. The adaptive strategy dynamically adjusts the polynomial order, effectively mitigating issues of overfitting or underdetermination typically associated with fixed polynomial orders. Numerical simulations demonstrate reduced temperature reconstruction errors of 2%, 1.6%, and 2% for single-peak, dual-peak, and mixed distribution flow fields, respectively. Corresponding concentration errors were 2%, 1.8%, and 2.6%, which are all improvements over those achieved by the Algebraic Reconstruction Technique (ART). Experimental results using a McKenna flat-flame burner revealed an average reconstruction error of only 0.3% compared to thermocouple measurements for high-temperature regions (>1000 K), with a minimal central temperature difference of 6 K. For lower-temperature peripheral regions, the average error was 188 K, illustrating the practical applicability of the proposed algorithm.