Analytical Formulation-Based Soot Modelling in Ethylene Laminar Jet Diffusion Flames

Abstract

Soot volume fraction predictions through simulations carried out on OpenFOAM® are reported in diffusion flames with ethylene fuel. A single-step global reaction mechanism for gas-phase species with an infinitely fast chemistry assumption is employed. Traditionally soot formation includes inception, nucleation, agglomeration, growth, and oxidation processes, and the individual rates are solved to determine soot levels. However, in the present work, the detailed model is replaced with the soot formation and oxidation rates, defined as analytical functions of mixture fraction and temperature, where the net soot formation rate can be defined as the sum of individual soot formation and oxidation rates. The soot formation/oxidation rates are modelled as surface area-independent processes. The flame is modelled by solving conservation equations for continuity, momentum, total energy, and species mass fractions. Additionally, separate conservation equations are solved to compute the mixture fraction and soot mass fraction consisting of source terms that are identical and account for the mixture fraction consumption/production due to soot. As a consequence, computational time can be reduced drastically. This is a quantitative approach that gives the principal soot formation regions depending on the combination of local mixture fraction and temperature. The implemented model is based on the smoke point height, an empirical method to predict the sooting propensity based on fuel stoichiometry. The model predicts better soot volume fraction in buoyant diffusion flames. It was also observed that the optimal fuel constants to evaluate soot formation rates for different fuels change with fuel stoichiometry. However, soot oxidation strictly occurs in a particular region in the flame; hence, they are independent of fuel. The numerical results are compared with the experimental measurements, showing an excellent agreement for the velocity and temperature. Qualitative agreements are observed for the soot volume fraction predictions. A close agreement was obtained in smoke point prediction for the overventilated flame. An established theory through simulations was also observed, which states that the amount of soot production is proportional to the fuel flow rate. Further validations underscore the predictive capabilities. Model improvements are also reported with better predictions of soot volume fractions through modifications to the model constants based on mixture fraction range.