Development of an Abel Transform Algorithm for Combustion Characterization and Data Analysis

The present study purpose is to develop an Inverse Abel Transform algorithm for combustion diagnostics. In order to develop and optimize a liquid rocket engine, the combustion process of the propellents combination GOX/CH4 and GOX/H2 are experimentally and numerically investigated at the Technical University of Munich to have a better knowledge about performance for this propellent pair. The combustion processes are studied by means an optical diagnostics technique, called Chemiluminescence, that allows to detect by means an ICCD camera the hydroxyl radicals OH* emission spontaneously producted in the chemical reactions within the combustion chamber and use it as a flame marker. Because this optical diagnostics technique is a line-of-sight technique, in which each measured quantity is an integrated emission along each line-of-sight, emission local measurements are not directly possible but require a post-processing deconvolution of the measured intensities to obtain spatial information. One of the existing deconvolution techniques is the Inverse Abel Transform, applicable only in case the object under examination is axysimmetric and solvable only in approximate way. An overview of some methods of problem resolution is presented, including the Fourier Method presented by G. Pretzel (1991) choosen for this thesis. Based on it a Matlab algorithm for the Inverse Abel Transform has been developed. It has been tested with the known radial distribution functions taken from the literature. Once checked algorithm, it has been applied to the intensities images recorded from ICCD camera to recover the emission radial distribution. Finally, the deducted results about the combustion process are be discussed and validated finding confirmation in the literature and previous studies, demonstrating the validity of the code itself.