Spline-based Abel Transform (SAT) radial property reconstruction for noise and trapping correction: Application to axisymmetric sooting flames

In combustion research, optical diagnostics often necessitate Abel inversion to deconvolve the measurements of axisymmetric flames, especially to determine local soot temperature fields from integrated flame radiative emission measurements. However, traditional Abel inversion methods can considerably amplify experimental noise, especially towards the flame centerline. Although various strategies exist to mitigate this issue, they typically do not address the correction of signal trapping within the flame. The present paper introduces an adapted Abel inversion tool that combines resistance to experimental noise with a mechanism to correct signal trapping effects. The tool employs noise-free Abel inversion using piecewise spline functions. Its effectiveness is validated through numerical comparisons with conventional methods. The practical application is demonstrated in the measurement of soot temperature in a canonical laminar diffusion ethylene flame. This is achieved by using multi-wavelength line-of-sight attenuation (LOSA) and emission measurements. The tool corrects for the signal trapping effect in emission data by integrating extinction profiles, thus enabling a more precise soot temperature analysis. The current study also compares two techniques of temperature measurement based on thermal emission: traditional two-color pyrometry and a calibrated emission and absorption ratio method. The study further explores the effects of signal trapping, scattering contribution, and the absorption function ratio on soot temperature determination based on experimental profiles. The findings suggest that signal trapping and scattering contributions have a negligible impact on measurements at the wavelengths examined. However, the choice of absorption function ratio significantly influences the outcomes of two-color pyrometry, highlighting the advantage of the one color emission/absorption technique for the determination of sooting flames temperature measurements. •A new Abel transform based on cubic splines considering signal trapping is proposed.•This method, slightly slower, is more robust than classical Onion-Peeling.•The method is applied to determine soot temperature in a canonical ethylene flame.•One-color SAT method is compared to classical 2C pyrometry.•The one-color approach is advantageous because it is independent of optical index.