A quantitative theory for heterogeneous combustion of nonvolatile metal particles in the diffusion-limited regime

TL;DR

This paper develops an analytical theory to accurately predict the burn time and temperature of nonvolatile metal particles during heterogeneous combustion in the diffusion-limited regime, validated by experimental data.

Contribution

It introduces a new analytical model that accounts for Stefan flow and provides quantitative predictions of burn time and temperature for metal particles.

Findings

Theoretical burn time matches experimental data closely.

Predicted particle temperature agrees at low oxygen levels.

Model overpredicts peak temperature due to neglected evaporation.

Abstract

The paper presents an analytical theory quantitatively describing the heterogeneous combustion of nonvolatile (metal) particles in the diffusion-limited regime. It is assumed that the particle is suspended in an unconfined, isobaric, quiescent gaseous mixture and the chemisorption of the oxygen takes place evenly on the particle surface. The exact solution of the particle burn time is derived from the conservation equations of the gas-phase described in a spherical coordinate system with the utilization of constant thermophysical properties, evaluated at a reference film layer. This solution inherently takes the Stefan flow into account. The approximate expression of the time-dependent particle temperature is solved from the conservation of the particle enthalpy by neglecting the higher order terms in the Taylor expansion of the product of the transient particle density and diameter squared. Coupling the solutions for the burn time and time-dependent particle temperature provides quantitative results when initial and boundary conditions are specified. The theory is employed to predict the burn time and temperature of micro-sized iron particles, which are then compared with measurements, as the first validation case. The theoretical burn time agrees with the experiments almost perfectly at both low and high oxygen levels. The calculated particle temperature matches the measurements fairly well at relatively low oxygen mole fractions, whereas the theory overpredict the particle peak temperature due to the neglect of evaporation and the possible transition of the combustion regime.