Dynamics of aluminum combustion

A study has been performed modeling both steady and unsteady combustion of aluminum. Law's steadystate aluminum combustion model has been expanded to include the effects of multiple oxidizers and their products, oxide accumulation on the surface of the burning aluminum particle, and convection. Both transport and thermodynamic properties are calculated internally for varying temperatures, relaxing the normal assumption of unity Lewis number. The aluminum combustion model has been compared to experimental data from burners, laser-ignited particles, and propellant under a variety of conditions, showing a reasonable degree of agreement. Calculations with the model show that O2 is a stronger oxidizer than H2O, which in turn is stronger than CO2. The aluminum combustion model was incorporated into a computer model for predicting acoustic effects in a Rijke burner. Calculations have shown that a significant part of the increase in acousticgrowth due to the addition of aluminum is due strictly to the change in the gas temperature profile. The change in temperature profile apparently causes the location of the velocity antinode to shift relative to the Rijke burner flame and thereby cause an increase in the flame response. The acoustic model agrees reasonably well with available acoustic growth rates for data where aluminum particles have been added to a propane Rijke burner. Nomenclature ak = sum of the mole fractions of the oxidizers in Eq. (1) Cp = heat capacity, J/kg D = diffusivity, irr/s d = particle diameter, m F = ratio of total mass flux to mass flux aluminum H = total flux of energy in aluminum combustion model, W/m2; heat of reaction, J/mol j = mass flux due to diffusion, kg/m2/s k =. arbitrary constant in Eq. (1) M = nondimensional mass flux used in Law's aluminum combustion model /?2 = mass flux, kg/m2/s Nu = Nusselt number p = pressure, N/m2 Qr = heat production due to a reaction, W/m3; heat caused by radiation, W/m2 <92 = enthalpy in the region from the flame to infinity q = heat flux, W/m2 Re = Reynolds number r = radial distance, m; reaction rate, kg/mVs T = temperature, K t = time, s v — velocity, m/s; volume, m3 \v = transport property weighting factor A- = mole fraction 77 = fraction of vaporized oxide that moves toward the particle surface 0 = fraction of metal oxide that vaporizes at the flame A = fraction of metal that reacts with the particular oxidizing species v = stoichiometric mass ratio of oxide or oxidizer to metal f = fraction of condensed products with move inward or outward p = density, kg/m3 T = characteristic time lag, s