Flamelet modeling of aluminum particle combustion

To facilitate comprehensive numerical studies on metal fuel combustion within large-scale burners, a novel flamelet model is formulated for aluminum (Al) particle combustion using Flamelet Generated Manifold (FGM). The new FGM model for Al particle combustion is referred as Al-FGM model. The model introduces an oxidizer depletion parameter ${\hat{Z}}_O$ that quantitatively captures oxygen consumption mechanisms through both heterogeneous surface reactions and alumina deposition processes. This key advancement complements three fundamental combustion descriptors: fuel-oriented mixture fraction ${\hat{Z}}_{\mathrm{Al}}$, reaction progress variable ${\hat{Y}}_c$, and normalized enthalpy deficit ${\hat{h}}_t$. The resulting four-variable manifold (${\hat{Z}}_{\mathrm{Al}}$, ${\hat{Y}}_c$, ${\hat{Z}}_O$, ${\hat{h}}_t$) establishes a thermochemical state space for efficient flamelet tabulation. The flamelet library is constructed by solving a series of one-dimensional (1D) gaseous counterflow flames. To accurately represent the significant gas-phase enthalpy changes due to intense interphase and radiative heat transfer within Al particle cloud combustion, the temperature boundary conditions of the 1D counterflow flames and the proportion of energy released by chemical reactions in the gas-phase energy equation are synergistically adjusted during the solution process. The proposed Al-FGM model undergoes validation using a dust counterflow flame setup. Using solutions derived from detailed chemistry as reference data, the Al-FGM model is validated across various dust concentrations through both a priori and a posteriori analysis. In the a priori studies, the proposed Al-FGM model is first validated on a pure gas Al counterflow flame setup, demonstrating perfect agreement. At a low Al particle concentrations ($\varphi$ = 300 ${\mathrm{g/m}}^3$), Al-FGM results match perfectly with reference data, as evidenced by both a priori and a posteriori analysis. As dust concentration increases ($\varphi$ = 400 ${\mathrm{g/m}}^3$), minor discrepancies emerge in mid-flame regions, where premixed combustion dominates. At higher concentrations ($\varphi$ = 500 ${\mathrm{g/m}}^3$), these discrepancies amplify in the midstream and downstream regions of the counterflow flames, while the upstream region remains highly accurate. Despite these deviations, the maximum error in average temperature predictions at $\varphi$ = 500 ${\mathrm{g/m}}^3$ remains a mere 95 K, corresponding to a relative error of 2.7% in the a posteriori analysis. Computational cost analyses indicate that the tabulated chemistry framework achieves a 4-5 fold increase in computational speedup compared to detailed chemistry simulation for the studied 2D setup.

Novelty and Significance Statement

In the present study, a novel four-control-variables flamelet model is proposed for aluminum particle combustion for the very first time. The validity of this proposed model is robustly established through comparisons with solutions derived from detailed chemical kinetics. This study represents a significant advancement in flamelet modeling for metal fuel combustion, providing a promising framework for future simulation-based investigations in this field.