Shock Hugoniots

Marsh, S.P. (1980), EASE Shock Hugoniot Data, University of California Press, Berkeley, pp. 1-327. 

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. 

Figure 3 The shock Hugoniot of PETN as calculated with exp-6 (solid line) and the JCZS library (dotted line) vs. experiment (error bars).

FIGURE 5.2 Hugoniot relationship with energy release divided into five regions (I-V) and the shock Hugoniot. 

From Eq. (5.13), it can be considered that the pressure differential generated is proportional to the heat release q. If there is no heat release (q = 0), Px = I 2 and the Hugoniot curve would pass through the initial point A. As implied before, the shock Hugoniot curve must pass through A. For different values of q, one obtains a whole family of Hugoniot curves. 

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. 

The element may enter the wave in the state corresponding to the initial point and move directly to the C-J point. However, this path demands that this reaction occur everywhere along the path. Since there is little compression along this path, there cannot be sufficient temperature to initiate any reaction. Thus, there is no energy release to sustain the wave. If on another path a jump is made to the upper point (1 ), the pressure and temperature conditions for initiation of reaction are met. In proceeding from 1 to 1, the pressure does not follow the points along the shock Hugoniot curve. 

Addnl Refs A) Collective, "Air Burst in Blast Bombs . A Compilation of Papers Presented at NDRC Div 2 Symposium, OSRD 4923 (1945) B) Collective, "Underground Explosion Test Program , Final Rept, Vol II, "Rock , Engineering Research Associates, Division of Remington Rand Inc, 30 April 1953 (Conf) (Not used as a source of information) C) G.R. Pickett, "Seismic Wave Propagation and Pressure Measurements Near Explosions , Quarterly of the Colorado School of Mines 50(4) (Oct 1955) D) W.E. Deal, "Shock Hugoniot in Air , JApplPhys 28, 782-84(1957) E) Dunkle s Syllabus, Session 26, 23 Apr 1958, pp 313-18 F) Dunkle s Syllabus, Suppl to Section 26 (1961) G) Dunkle, private communication,... 

To these add the paper entitled "Determination of Shock Hugoniots for Several Condensed Phase Explosives , by V.M. Boyle et al, in 4thONRSympDeton(1965), pp 241-47... 

Detonation Reflected Shock Hugoniot and Isentrope for Explosion Reaction Products, Measurements of. This subject was discussed by W.E. Deal in Physics of Fluids 1(6), 523(1958)... 

T.P. Liddiard Jr, "The Unreacted Shock Hugoniots for TNT and Composition B , InterntlConfer on Sensitivity and Hazards of Explosives, London, Oct (1963)... 

Physics of Fluids 1 (6), 523(1958) (Measurement of the Reflected Shock Hugoniot and Isentrope for Explosive Reaction Products) 4) D. Price, ChemRevs 59(5), 801-25 (Oct 1959) (Measurement of the Reflected Shock Hugoniot and Isentrope for Explosive Reaction Products) 5) M. Lutzky, "The Spherical Taylor Wave for the Gaseous Products of Solid Explosives , NavWeps Rept 6848(1960)... 

An excellent compendium of shock Hugoniot data has been prepared by LRL (Ref 14). It includes some of the earlier Hugoniot data for explosives. These data as well as more recent data are summarized in Table 1 in the form of least square fits to the empirical equation in Fig 2a... 

Here the TNT sample is compressed at very low pressures from V=1 cc/g to V X).62 cc/g (crystal density). Further compression (increase in pressure) then causes the sample to expand This can only mean that some heat effect is overcoming this compression. Since it can be shown that uniform shock heating at pressures of the order of a few kbars is very small, this heat effect must be produced by exothermic chemical reaction at or very near the shock front. Thus shock Hugoniots for reactive materials can provide information on the presence or absence of chemical reaction at the shock front... 

Considerable effort has been devoted to the determination of the shock Hugoniot data which were recently published (Ref 30). These are reproduced for both U and several of its alloys in Table 4... 

Shock Hugoniot Data , Univ of Calif Press, Berkeley (1980) 31) C.E. Ragan H, Ultra... 

The booster-and-attenuator system is selected to provide about the desired shock pressure in the sample wedge. In all but a few of the experiments on which data are presented here, the booster-and-attenuator systems consisted of a plane-wave lens, a booster expl, and an inert metal or plastic shock attenuator. In some instances, the attenuator is composed of several materials, The pressure and particle velocity are assumed to be the same on both sides of the attenuator-and-sample interface. However, because initiation is not a steady state, this boundary condition is not precisely correct. The free-surface velocity of the attenuator is measured, and the particle velocity is assumed to be about half that. The shock Hugoniot of the attenuator can be evaluated using the free-surface velocity measurement. Then, the pressure (P) and particle velocity (Up) in the expl sample are found by determining graphically the intersection of the attenuator rarefaction locus and the explosives-state locus given by the conservation-of-mom-entum relation for the expl, P = p0UpUs where Us = shock velocity and p0 = initial density. The attenuator rarefaction locus is approximated... 

Density (g/cc) Shock Hugoniot (mm/jLts) Particle Velocity (mm/jLts)... 

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