(568e) Intra-Bubble Combustion: the Thin Flame Limit

The present work considers the an idealized mathematical model motivated by the application of chemically processing crude oils using submerged oxygen bubble jets [1 ]. In this theoretical analysis we examine a fully transient, spherically symmetric oxidizer gas bubble immersed in an unconfined, otherwise quiescent, single-component constant density viscous liquid fuel. At the bubble surface the liquid vaporizes supplying fuel vapor which then diffuses inside the bubble, reacting finally with the oxygen initially in the bubble in a spherical diffusion flame. The present paper focuses in the dynamics of this diffusion flame inside the oscillating bubble, coupled with the consequences of momentum-, mass- and heat- transport across the bubble (gas/liquid) interface. To gain insight into these complex interactions, the combustion process itself is approximated by means of the 'thin-flame' (Burke-Schumann) limit. Hence, flame ignition or extinction phenomena are not dealt with here. Three zones are considered ---two inside the bubble (where the heat and mass diffusivities are taken to be equal) and one outside (the thermal boundary layer in the liquid)---using a Chebyshev-based orthogonal collocation method [2].

Our theoretical analysis reveals that the dynamics of this single bubble heterogeneous combustion system depends on the square of the ratio of the characteristic liquid inertial time (proportional to the initial bubble radius and the square root of the liquid density) to the characteristic diffusion time within the bubble. This dimensionless parameter plays the role of the (dimensionless) effective inertia of the two-phase dynamical system.

As applications of the present theoretical model, the 'conversion' of such a bubble reactor (amount of fuel processed per bubble oscillation) is computed as a function of the dimensionless effective inertia, along with the total time to complete the consumption of the initial O2(g) inventory[3]. In our future work this mathematical model will be broadened to incorporate the formation and survival of important reaction intermediates (such as acetylene) on the fuel-rich side of the gaseous diffusion flame.

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Prepared for presentation at AIChE '05, Cincinnati OH, November 2005

[1] Bauer, K.G. (1969), ?Acetylene From Crude Oil Makes Debut in Italy', Chem. Eng., Feb 10, pp 82-84, (1969)

[2] Arias-Zugasti, M. and Rosner, D.E., "Intra-Bubble Combustion: Diffusion Limit", Paper presented at III International Workshop on Combustion Modeling, Mexico City, March 20-22(2005)

[3] Paper in preparation for Combustion Theory and Modeling; see also: CTM 7, 269-300(2003)