General Rankine-Hugoniot equations

Zone involving heat conduction, diffusion, reaction, and viscous effects 

FIGURE 2.1. Schematic diagram of a deflagration or detonation wave. 

In future work it will be convenient to employ modified forms of equations (2) and (3). Since equation (1) implies that 

The species-conservation equations require further discussion because equations (4) and (5) may not all be independent, and all of the information that can be obtained from equation (1-29) is not contained in equations (4) and (5). From equation (1-8) we see that the mass rate of production of species i by chemical reactions may be expressed as 

However, when M N it is possible to derive additional (atom-conservation) conditions from equation (1-29). If denotes the number of atoms of kind j in a molecule of kind , then the fact that atoms are neither created nor destroyed by chemical reactions is expressed by the equation 

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The Rankine-Hugoniot relations are the equations relating the properties on the upstream and downstream sides of these combustion waves. In this chapter, general Rankine-Hugoniot equations are derived and discussed first then the Hugoniot curve for a simplified system is studied in detail in order to delineate explicitly the various burning regimes. 

Rankine-Hugoniot equations 181-87 (Equations of state which include among others the following Jones Miller, Lennard-Jones Devonshire, Halford-Kistiakowsky-Wilson, Joffe its modification by Su Chang, Taylor, Kihara Hikita, Travers, Cook, Kistiakowsky-Wilson-Brinkley and Polytropic equations) 194 (Landau-Stanyukovich and Hirschfelder et al equations of state 11) J.F. Roth, Explosiv-stoffe 1958, 50 (Abel sche Zustandsgleichung fur die Detonation) 12) Cook (1958), 37 (General equation of state) 62-3 [Halford-Kistiakowsky-W ilson-Brinkley equation of state, (listed as K-H-W-B equation of state)] ... 

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