A novel single-pixel imaging method for two-dimensional soot volume fraction measurements in axisymmetric flames

Abstract

This paper initially utilizes a Fourier single-pixel imaging (FSI) optical method to measure the soot volume fraction ($f_v$) field in flames, which is based on the theorems of Fourier transform and Beer-Lambert law. Unlike the conventional two-dimensional sensor used for imaging, a spatially unresolvable detector, such as a photomultiplier tube (PMT), is utilized to reconstruct flame images. The current prototype optical measurement system is detailed and further validated by a proof-of-concept experiment on a benchmark laminar diffusion flame. It is found that the sample rate and the loop number significantly affect the quality of flame image reconstruction, and it is recommended to use thresholds of 25 % and 20 for these two parameters. In addition, the maximum standard deviation $f_v$ of 0.025, as calculated through error propagation in five repeated experiments, demonstrates the robustness of the FSI technique. Nevertheless, the present optical layout could be further optimized in terms of improving the quality of reconstructed images, shortening the sampling duration, and replacing the near-infrared light source to achieve more precise $f_v$ distributions and reduce uncertainties. Moreover, the potential for single-shot resolution improvements deserves further investigation of temporal flame measurements in the near future.