Hugoniot adiabatic curve

K. Troshin, "The Generalized Hugoniot Adiabatic Curve Ibid, p 789 (Overcompressed detonation waves) 56) F.J. Martin D.R. White Formation and Structure of Gaseous Detonatio n Waves, Ibid, 856—65 56a) F.H. 

The subscript H is used to emphasize that derivatives are along the Hugoniot curve. Now, somewhere along the Hugoniot curve, the adiabatic curve passing through the same point has the same slope as the Hugoniot curve. There, ds2 must be zero and Eq. (5.18) becomes... 

The p(V) diagram shows the shock adiabat of the explosive, which is also called the Hugoniot curve or Hugoniot adiabat (see Fig. 1.22). The shock adiabat can be calculated for both the non-reacted explosive as well as for the reaction products (see Fig. 1.22). The C-J point, which represents the point where the C-J conditions are fulfilled, is therefore the point where the shock adiabat of the reaction products touches the Raleigh line (tangent), which is described by the following equation ... 

The crosspoints of these two lines are S and W. But in normal detonation, Rayleigh line is tangential to Hugoniot curve (the detonation adiabatic curve). And the contact point is P. Figure 2.6 gives the relative positions of Rayleigh line and Hugoniot curve. 

Figure 2.14 shows that the detonation with propagation velocity D = D starts from the crosspoint N of the Hugoniot curve and shock adiabatic curve. Only after passing point P is under pressure detonation point (or weak detonation point) is reached. Von Neumann named the detonation velocity as eigenvalue detonation... 

The Rankine-Hugoniot curve is sometimes referred to as the shock adiabat (especially in the Soviet literature). This terminology reflects the fact that the shock process is so fast that there is insufficient time for heat... 

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,... 

When q = 0, the Hugoniot curve represents an adiabatic shock. Point 1 (Pi, p ) is then on the curve and Y and J are 1. Then [(l/pt) - (Ilp2) = 0, and the classical result of the shock theory is found that is, the shock Hugoniot curve osculates the adiabat at the point representing the conditions before the shock. 

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. 

Tables of the Properties of Air along the Hugoniot Curve and the Adiabatics Terminating in the Hugoniot Curve , OSRD Rept 3550 (1944) 36) L.H. Thomas, "Theory of the... 

The book includes among other topics Definition of expln and classification of expln processes, pp 9-l6 Theory of shock waves, which includes "shock adiabat on p 190 (pp 182-224) Theory of deton waves (pp 225-27) Hugoniot curve for detonation waves (p 228) Hydrodynamic Theory of deton (p 226) Explosion in air. (pp 555-663) Theory of point initiation of deton, called in Rus "Teoriya tochechnago vzryva (pp 598-624) Theory of spherical expln (pp 624-40) Explosion in condensed medium (pp 664-81) Propagation of shock waves in water (pp 681-90) Some problems of theory of deton in liquids (pp 690-98) Propagation of waves in solids (pp 708-18) and Theory of deton in earth. (pp 718-44)... 

Fio 7 Hugoniot curve H[Pg.706]

This means that at the Chapman Jouguet points the Hugoniot curve and the adiabat are both tangent to the Rayleigh-Mikhel son line... 

Fig 6 The Rankine-Hugoniot curve defines states that can be induced in substance by shock compression in terms of pressure (p), specific volume (V), and internal energy (E). Shock compression from initial state B to shocked state C follows the R-H curve and dissipates energy shown by the hatched area. Thus shock compression is not a reversible process—unlike adiabatic compression, which is, at least ideally reversible... 

Figure 12. Comparison of (a) shock Hugoniot data (b) static cold compression, and (c) ISLS adiabatic sound velocities, and corresponding calculated curves. The respective summation of average errors between experiment and calculations are 4.0%, 0.5% and 6.5%.

In Figure 9 we present a calculated melt curve that compares favorably with our experimental results. This melt curve is the result of a minimized two-phase Gibbs free energy equation of state made to match accepted thermodynamic parameters and all available high-pressure experimental data including shock Hugoniot data [126], static cold compression volumes and compressibility from x-ray [128], and adiabatic ISLS sound velocity measiu-ements [127]. Comparisons of these data are provided in Figure 12a,b, and c. 

Fig.c-3 PV plots of Hugoniot, reversible adiabatic, and isothermal functions for an ideal monatomic gas (y = 1.67). The dashed line is the asymptote of the Hugoniot curve. 

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