Reconstruction of flame permittivity distribution based on ECT and L_p regularized D-bar method

Abstract

The measurement of flame permittivity is significant in obtaining the combustion state. A method of Lp regularized D-bar is proposed in this article, which is used to reconstruct flame permittivity distribution by electrical capacitance tomography (ECT). Firstly, the distribution characteristic of flame permittivity is analyzed using the electric probe method. The simulation model of ECT flame measurement is set up based on the result of flame permittivity distribution. Then, the relationship model between the truncation radius of the D-bar algorithm and noise level is fitted based on the simulation reconstruction results of flame permittivity. The truncation radius of the D-bar algorithm for flame permittivity reconstruction is obtained by the relationship model. The Lp regularization is introduced into the scattering transformation solving of the D-bar algorithm, and the simulation results of flame permittivity reconstruction under different p-values are compared. In the experiment, the reconstruction of flame permittivity by the D-bar algorithm with different truncation radii is compared. The experimental results verify the truncation radius strategy based on noise level. Moreover, compared with L1 and L2 regularization methods, Lp regularization combined with the D-bar algorithm is more accurate in the experiment results of flame permittivity reconstruction.