Limitations of flamelet formulation for modeling turbulent pool fires

Abstract

A well-resolved database of a small-scale heptane pool fire is analyzed to assess the assumptions of flamelet models in fire simulations. The pool fire database features well-resolved turbulence fields, finite-rate chemistry for heptane using a 33-species skeletal mechanism, and a coupled Monte Carlo ray-tracing radiation solver with a line-by-line spectral model. A budget analysis of the flamelet equation is performed by transforming temperature and species to the mixture fraction space and extracting instantaneous flamelet solutions along flame-aligned directions. Five flame-aligned budget terms and one unsteady term are identified through transformation of the temperature equation. Three conditions are examined, including an adiabatic case, a case involving only gas radiation, and a case involving both gas and soot radiation. The budget analysis shows that preferential diffusion is non-negligible near the base of the pool. Radiation is found to be appreciable in the transition region of the fire, resulting in a reduction of flame temperature by as much as 270 K due to radiative heat losses. The curvature of the flame surface is found to have a minor impact on the temperature dynamics near the flame front. The extracted flame structures deviate from those predicted from a steady-state adiabatic laminar flamelet model, particularly in the profiles of CO, CO2, and OH. A time scale analysis is performed, indicating that steady state assumptions for chemical species are reasonable for this flame, although radiation is much slower compared to chemistry and requires consideration to correctly capture the temperature evolution. The source terms from radiative absorption and emission show pronounced non-proportionality between the two, where absorption can exceed emission, thereby serving as a heating source for the fuel and oxidizer streams. The controlling factors for radiative absorption are analyzed, based on which a non-local model is proposed to approximate absorption in pool fires. A priori assessment of this model shows good agreement with the pool fire database, demonstrating the feasibility of enhancing the flamelet formulation to account for radiative emission and absorption effects.