Basic Modeling Equations
Equations describing the conservation of mass, momentum, and energy of a flowing gas—particle suspension or gas—droplet suspension can be found in various books, papers, and reports (Bird et al.,1960; Trusdell and Toupin, 1960; Soo, 1967; Drew, 1971; Smoot and Pratt, 1979). The presentation of these equations in the various sources are often very different among authors. Some equations have included too many assumptions to be of practical use for predicting combustion or gasification of coal and coal slurries. Others are in a form which are too complex to be of utility for practical systems. Although the equations are presented in many sources, very few sources present analytic or numerical solutions for the two-phase flow equations. The fundamental equations are very complex and formulating a solution requires many numerical approximations, large-scale computers, and a significant dedication of time on the part of the user. This book introduces calculational procedures for combustion and gasification of coal and coal slurries which include sufficient detail to describe the important features of the reacting flow field, but which have incorporated adequate engineering approximations to render the solution algorithm tractable. In this chapter we have focused upon the basic conservation equations for the multiphase field.
KeywordsControl Volume Conservation Equation Extensive Property Continuum Hypothesis Fluid Element
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