Characterization of Engine Combustion Flames Using Inverse Abel Transform

Abstract

The present work involves the development and implementation of a mathematical transformation called inverse Abel transform and its application to diagnostics of reacting flow systems. Chemiluminescence is the phenomenon of emission of light during a chemical reaction. It takes place due to the formation of an intermediate excited state which further stabilizes and produces light. Chemiluminescence has a wide range of applications like analysis of inorganic species in a liquid phase, combustion analysis (concentration of CH* and OH*), glow sticks, etc. In combustion systems particularly, the location of maximum concentration of CH* and OH* is useful as they are considered to be the heat release markers in premixed flames. The concentration field of a given species can be obtained by viewing the reacting zone through an appropriate optical band-pass filter. This filter allows only the wavelength of light emitted by the species of interest. However, such an image contains the concentration of the entire volume, as each pixel captures the integrated light from the entire volume passing through its line of sight. In order to resolve an axisymmetric integrated line of the sight data distribution to one at a given azimuthal plane, a mathematical transformation called inverse Abel transform is used. The IAT takes a 2D projection and reconstructs a slice of the cylindrically symmetric 3D distribution. IAT also plays an important role in analyzing the projection of plasma plumes and flames. The major difficulties in implementing IAT are the discontinuity and its dependence on the first derivative of the original function. The latter is particularly challenging when used with experimental data, which is discrete and can be noisy. In order to remove these difficulties, several methods are available. Presently, a direct discretization method, implemented in MATLAB, is used to calculate the IAT. This method addresses the singularity by modifying a term suitably to avoid division by zero. The implemented algorithm was tested with various trial functions and was seen to provide an acceptable match. Subsequently, image processing of a CH* chemiluminescence data from literature is performed to obtain the azimuthal distribution of CH* relative concentration.