Modelling the combustion of a sub-micron aluminium particle

Abstract

We pose the following question: ‘Within the context of the classical shrinking-core model for sub-micron aluminium combustion, allowing only for the diffusion of atomic oxygen (no aluminium diffusion), but with two non-classical ingredients (large Knudsen number heat losses to the ambient atmosphere and a fractal reacting surface), are the solutions consistent with four experimental facts and data sets: (i) burn times; (ii) particle temperatures; (iii) maximum temperatures independent of particle size for small Damköhler numbers; and (iv) also for small Damköhler numbers a burn law of the form d^{1 − ν}–t (where d is the particle diameter and ν ∼ 0.7 or so)?’ In the analysis we first consider a non-fractal model and scale the lengths with (where is the diffusion coefficient and k is the reaction-rate constant) and time with (where ρ⁻ is the aluminium density and c_o is a characteristic value of the O density within the alumina). Burn times are calculated which follow a linear d–t law for small values of kL/D(L = D/2), the Damköhler number, and a quadratic d²–t law for large values of . Enhanced temperatures (greater than the ambient) arise for small values of with maximum values that are size independent. Since the small Damköhler d–t law does not agree with experimental data, we introduce a fractal concept into the model, as this can generate a burn law of the observed form. However, we then find that the maximum temperature is not independent of particle size.

Keywords:

• nano-aluminium
• large Knudsen number
• combustion
• burn-time/diameter laws
• fractals

Notes

1. We shall draw some conclusions about the value of later in the paper.

Additional information

Funding

This work was supported in part through IllinoisRocstar LLC [grant FA9300-33-M-2004 under a Phase II program with the Air Force], program manager S. Alexander Schumaker. Thomas L. Jackson was also supported in part by the Defense Threat Reduction Agency [Basic Research Award No. HDTRA1-13-0010] to the University of Illinois at Urbana-Champaign, program manager Dr Suhithi Peiris. The work of [6], important ingredients of which were supplied to us before its publication for which we are most grateful, was also supported by IllinoisRocstar LLC under the Phase II program with the Air Force.