Modeling and verification of astigmatic digital off-axis holography for burning droplet measurement in a flame tube

Abstract

It is difficult to measure fuel droplets in cylindrical combustors under combustion conditions, but of significance, since fuel behavior is related to combustion performance. In this study, digital off-axis holography and corresponding data treating algorithms are applied to quantify irregular spray droplets in combustion field inside a thick silica flame tube. The analytical expression of an off-axis hologram passing through a pipe is derived based on optic matrix theory and Fresnel diffraction transform. The interference fringes and phase distribution show consistency with the experimental results under the same condition. A modified convolution reconstruction method facing off-axis holography is proposed to locate and quantify the particles in a pipe. The theoretical simulation and experimental results indicate that the proposed method can obtain a clear reconstructed droplet. The image field of view does not change with the reconstruction distance. The particle field obtained through this method has distortion due to the refraction of the curved surface, and can be corrected through ABCD transfer matrix. The calibration method and modified results reveal that the overall droplet size error is lower than 1-pixel width, and real x and y locating errors after correction are lower than 1-pixel width. The depth position error is also discussed through experimental validation. The visualization and quantification results of fuel droplets in the real turbulent spray flame in a circular flame tube prove the feasibility of the proposed theoretical analysis and the reconstruction method.