Volumetric reconstruction of soot volume fraction through 3-D masked Tikhonov regularization

The ill-posed nature of the tomographic inverse problem for soot volume fraction reconstruction often creates artifacts and provides lower reconstruction accuracy, particularly when viewing angles are limited. In this study, a volumetric masked-based 3-D Tikhonov regularization method is proposed to reconstruct soot volume fraction in a purely absorbing flame. The 3-D Tikhonov regularization method addresses the ill-posedness by penalizing unrealistic variations in the soot volume fraction, thus enhancing the robustness of the reconstruction. Additionally, volumetric masking derived from light field ray-tracing refines the reconstruction by accurately defining the flame's boundaries and improving the soot volume fraction inversion accuracy. Numerical simulations were conducted on a bimodal asymmetric flame to analyze the effects of varying viewing angles and volumetric masking strategies. Experimental studies were also performed to reconstruct soot volume fraction under different combustion operating conditions. Both numerical simulations and experimental studies demonstrate that the proposed method not only works on a limited number of viewing angles but also mitigates the reconstruction artifacts and decreases the computational costs.