A semi-analytical variable property droplet combustion model
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A multizone droplet burn model is developed to account for changes in the thermal and transport properties as a function of droplet radius. The formulation is semi-analytical—allowing for accurate and computationally efficient estimates of flame structure and burn rates. Zonal thermal and transport properties are computed using the Cantera software and pre-tabulated for rapid evaluation during run-time. Model predictions are compared to experimental measurements of burning n -heptane, ethanol and methanol droplets. An adaptive zone refinement algorithm is developed that minimizes the number of zones required to provide accurate estimates of burn time without excess zones. A sensitivity study of burn rate and flame stand-off with far-field oxygen concentration is conducted with comparisons to experimental data. Overall agreement to data is encouraging with errors typically less than 20% for predictions of burn rates, stand-off ratio and flame temperature for the fuels considered. The quiescent quasi-steady solution is extended to a convective transient solution without the need to solve an eigenvalue solution in time. The time history of the burning droplets show good comparison with experimental data. To further decrease computational cost, the source terms for the transient solution are linearized for an explicit time marching solution. An error convergence study was performed to show a time-step independent solution exists at a reasonable Δ t.