Hysteresis in the Vaporization-Controlled Inertial Regime of Nonpremixed Counterflow Spray Combustion

ABSTRACT

This numerical study uses a Lagrangian–Eulerian formulation employing the point-source approximation to investigate nonpremixed axisymmetric spray diffusion flames stabilized between a stream of hot air and a stream of nitrogen carrying a monodisperse spray of fuel droplets injected at a distance z_l from the stagnation plane. The computations consider moderately large values of the relevant thermal Peclet number, such that the thickness of the mixing layer separating both streams is much smaller than z_l. A one-step irreversible reaction is assumed between the fuel vapor and the oxygen of the air. Most of the computations consider the thermochemical, vaporization, and transport properties of dodecane, with additional results for the properties of methanol used to assess effects of higher fuel volatility. The analysis considers moderately small values of the liquid mass loading ratio at the injection plane, consistent with the stoichiometric value of the fuel-to-air mass ratio of the global oxidation reaction of typical hydrocarbon and alcohol fuels. Attention is mainly focused on inertial droplets with associated Stokes numbers St of order unity or larger, for which the droplets penetrate far into the oxidizer stream, vaporizing over distances of order z_l and leading to combustion occurring outside the mixing layer. In this inertial regime, besides solutions involving a diffusion flame separating the fuel and oxygen with a well-defined peak temperature of the order of the adiabatic flame temperature, the analysis reveals, for the first time, the existence of flameless solutions with distributed combustion and small temperature increments from the air-side value. The two solutions are found to exist for the same sets of boundary conditions. Integrations for increasing values of St identify a value of the Stokes number St₂ above which the vaporization rate is too small to support a diffusion-flame solution, while integrations for decreasing St lead to the identification of another value of the Stokes number St₁ < St₂ below which a distributed reaction cannot occur. In the intermediate hysteretic range St₁ ≤ St ≤ St₂ where two different steady solutions may exist, the type of solution encountered depends on the initial conditions imposed. The preliminary results suggest that future efforts targeting quantification of the flameless regime, which is found to be relevant in applications with larger droplets, would benefit from consideration of different possible gas-phase chemical kinetics, including cool-flame chemistry.

KEYWORDS:

• Counterflow spray flames
• flameless combustion
• S-shape curve
• inertial droplets

Additional information

Funding

This work was supported by the US AFOSR Grant No. FA9550-16-1-0443 and by the Spanish Ministerio de Ciencia, Innovación y Universidades through project MTM2015-67030-P.