The dynamics and thermodynamics of a chemically reacting flow are governed by the conservation laws of mass, momentum, energy, and the concentration of the individual species. In this chapter, we shall first present a derivation of these conservation equations based on control volume considerations. We shall then derive a simplified form of these equations describing only those effects which are of predominant importance in most of the subsonic combustion phenomena to be studied later. Some useful concepts and analytical techniques for combustion modeling will be discussed and several important nondimensional numbers will be introduced. Whenever possible, we will adhere to the nomenclature of Williams (1985) for consistency and ease of referencing. A summary of the symbols is given at the end of this chapter.

Further discussions emphasizing on the mathematical aspects of combustion theory can be found in Buckmaster and Ludford (1982) and Williams (1985).

CONTROL VOLUME DERIVATION

To derive the various conservation equations, we first take a control volume that is at rest with respect to an inertia reference frame. It has a volume V and a control surface S, with a unit normal vector n, as shown in Figure 5.1.1. Within this control volume a flow element of velocity v passes through. This bulk, mass-weighted velocity v is the resultant of the individual velocities vi of the various species.