A detailed of analysis of joint soot volume fraction/temperature statistics in non-premixed jet flame: Implication for soot emission turbulence/radiation interaction

Abstract

The main objective of this study is to provide insights on the modelling of soot emission Turbulence Radiation Interaction (TRI) through a detailed analysis of the joint SVF/temperature statistics in turbulent non-premixed flames. The analysis relies on RANS/Transported Probability Density Function (TPDF) simulation of the Sandia ethylene jet turbulent non-premixed flame. RANS/TPDF predictions reproduce with fidelity the exhaustive set of experimental data, namely the flame structure, the soot and temperature statistics including the soot intermittency, and the radiative outputs. The marginal PDF of SVF exhibits the typical shape of an intermittent process and can be decomposed into a non-sooting mode and a sooting mode, with this latter being reasonably represented by a truncated Gaussian PDF. As expected, the marginal PDF of temperature can be reasonably represented by a clipped Gaussian PDF whereas that of the soot temperature follows a significantly narrower PDF as soot is fully oxidized in the fuel rich side of the flame. Analysis of the joint SVF/temperature PDF shows that both SVF/temperature and SVF/soot temperature first-order cross correlations are positive in the soot formation region and becomes strongly negative in the region of strong soot emission. The TPDF predictions are analysed a priori to design a new joint presumed PDF (PPDF) of SVF and temperature through the Gaussian copula. The Gaussian copula-based PPDF depends on six parameters, namely the five related to the marginal PDFs of SVF and temperature added to the first-order cross-correlation coefficient of SVF and temperature. Mean soot emission term computed with the copula-based PPDF agrees very well with the reference TPDF solution over the entire flame and improves significantly the solutions obtained by neglecting either TRI or the correlation between SVF and temperature. These results indicate that the Gaussian copula-based joint PPDF model is a good candidate to interpret soot emission-related experimental data in turbulent non-premixed flames.