Control Volume Alternative to the Theory of Diffusive Burning

9 Control Volume Alternative to the Theory of Diffusive Burning 

This chapter began by discussing the steady burning of liquids and then extended that theory to more complex conditions. As an alternative approach to the stagnant layer model, we can consider the more complex case from the start. The physical and chemical phenomena are delineated in macroscopic terms, and represented in detailed, but relatively simple, mathematics - mathematics that can yield algebraic solutions for the more general problem. 

The approach is to formulate the entire burning problem using conservation laws for a control volume. The condensed phase will use control volumes that move with the vaporization front. This front is the surface of a regressing liquid or solid without char, or it is the char front as it extends into the virgin material. The original thickness, l, does not change. While the condensed phase is unsteady, the gas phase, because of its lower density, is steady or quasi-steady in that its steady solution adjusts to the instantaneous input of the condensed phase. 

The condensed phase (solid or liquid) is considered as a general phase that will vaporize to a gaseous fuel with a mass fraction TFo, and can possibly form char with properties designated by ()c. The virgin fuel properties are designated without any subscript. 

The control volume relationships that are considered are based on a moving control volume surface with velocity, w, while the medium velocity is v. The conservation of mass is given as 

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CONTROL VOLUME ALTERNATIVE TO THE THEORY OF DIFFUSIVE BURNING... 

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