Hugoniot relation

Conservation equations Expressions that equate the mass, momentum, and energy across a steady wave or shock discontinuity ((2.1)-(2.3)). Also known as the jump conditions or the Rankine-Hugoniot relations. 

From the R-H (Rankine-Hugoniot) relations at the shock, there was obtd ... 

Theory. If p is pressure, v - specific volume, e - specific internal energy, D detonation velocity, u - particle velocity, C - sound velocity, y - adiabatic exponent and q -specific.detonation energy, the velocity of propagation and particle velocity immediately behind any plane detonation wave in an explosive, defined by initial conditions, pD, v0, eQ, and uQ, are given by the first two Rankine-Hugoniot relations ... 

Detonation Hugoniot Curves (or Hugoniots), Huganiot Equation and Hugoniot Relation in. See under DETONATION (AND EXPLOSION), THEORIES OF and also paper of M.W. Evans C.M. Ablow, ChemRevs 61, 138 (Fig 6),... 

Dunkle s Syllabus (1957 58), 1-36 (Detonation phenomena, mathematical background) 37-60 (Initiation of shock waves formulas equations including Riemann equation, p 43 Hugoniot relations in gases, p 44 Rankine-Hugoniot equation, p 45 ... 

Evaluation of the density at the front, together with the Rankine-Hugoniot relations and the measured front velocity, determines the pressure and particle velocity there. In practice, this requires an additional assumption, which will be made throughout. Since the reaction zone is much smaller than the foil spacing, the reaction is treated as instantaneously complete within the shock transition, and the final state to which the Rankine-Hugoniot equations apply is taken to be the equilibrium state at the end of the reaction zone. No evidence of a reaction zone can be detected either in the analysis of the foil data or on the radiographs. 

It is immediately apparent that the energy equation (the Rankine-Hugoniot relation) is expressed entirely in terms of thermodynamic quantities. 

The conservation equations are frequently referred to as the Hugoniot relations. 

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. 

C. Hugoniot Relations and the Hydrodynamic Theory of Detonations are developed and substituted in... 

---