Detonation Hugoniots

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),... 

Detonation, Hugoniot Function. Properties of Hugoniot Function are described by R.D. Cowan in JFIuidMech 3(5), 531-45 (1957)... 

In Sec. 3.1, we reviewed results that established that Model I supports detonations with properties consistent with ZDN theory. In this section we make more detailed comparisons between the results of our simulations of detonations and the predictions of the continuum theory. In Sec. 4.1, we define the detonation Hugoniot curve, a concept central to continuum theory,... 

This result, when written in terms of PoolPo Po/Poo is the usual detonation Hugoniot,... 

The Rayleigh line can cross the detonation Hugoniot at two points. The upper crossing point, 1, corresponds to < 1, whereas the lower crossing point, /, corresponds to > 1. The lowest... 

The major difficulty in applying this hydrodynamic theory of detonation to practical cases lies in the calculation of E2, the specific internal energy of the explosion products immediately behind the detonation front, without which the Rankine-Hugoniot curve cannot be drawn. The calculations require a knowledge of the equation of state of the detonation products and also a full knowledge of the chemical equilibria involved, both at very high temperatures and pressures. The first equation of state used was the Abel equation... 

Extension of the hydrodynamic theory to explain the variation of detonation velocity with cartridge diameter takes place in two stages. First, the structure of the reaction zone is studied to allow for the fact that the chemical reaction takes place in a finite time secondly, the effect of lateral losses on these reactions is studied. A simplified case neglecting the effects of heat conduction or diffusion and of viscosity is shown in Fig. 2.5. The Rankine-Hugoniot curves for the unreacted explosive and for the detonation products are shown, together with the Raleigh line. In the reaction zone the explosive is suddenly compressed from its initial state at... 

Figure 2 Allowed thermodynamic states in detonation are constrained to the shock Hugoniot. Steady-state shock waves follow the Rayleigh line.

Exp-6 potential models can be validated through several independent means. Fried and Howard33 have considered the shock Hugoniots of liquids and solids in the decomposition regime where thermochemical equilibrium is established. As an example of a typical thermochemical implementation, consider the Cheetah thermochemical code.32 Cheetah is used to predict detonation performance for solid and liquid explosives. Cheetah solves thermodynamic equations between product species to find chemical equilibrium for a given pressure and temperature. From these properties and elementary detonation theory, the detonation velocity and other performance indicators are computed. 

As will be shown, the steady solution for the detonation velocity does not involve any knowledge of the structure of the wave. The Hugoniot plot discussed in Chapter 4 established that detonation is a large Mach number phenomenon. It is apparent, then, that the integrated momentum equation is included in obtaining a solution for the detonation velocity. However, it was also noted that there are four integrated conservation and state equations and five unknowns. Thus, other... 

This relationship, of course, will hold for a shock wave when q is set equal to zero. The Hugoniot equation is also written in terms of the enthalpy and internal energy changes. The expression with internal energies is particularly useful in the actual solution for the detonation velocity tq. If a total enthalpy (sensible plus chemical) in unit mass terms is defined such that... 

Thus far in the development, the deflagration, and detonation branches of the Hugoniot curve have been characterized and region V has been eliminated. There are some specific characteristics of the tangency point J that were initially postulated by Chapman [7] in 1889. Chapman established that the slope of the adiabat is exactly the slope through J, that is,... 

Along the detonation branch of the Hugoniot curve, the variation of the entropy is as given in Fig. 5.4. For the adiabatic shock, the entropy variation is as shown in Fig. 5.5. 

FIGURE 5.14 Effect of chemical reaction rates on detonation structures as viewed on Hugoniot... 

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