Hugoniot function

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

By plotting Hugoniot curves in the pressure-particle velocity plane (P-u diagrams), a number of interactions between surfaces, shocks, and rarefactions were solved graphically. Also, the equation for entropy on the Hugoniot was expanded in terms of specific volume to show that the Hugoniot and isentrope for a material is the same in the limit of small strains. Finally, the Riemann function was derived and used to define the Riemann Invarient. 

Figure 4.23. Elastic wave velocities as a function of pressure along the Hugoniot of iron. The solid curve is the calculated bulk sound velocity. (From Brown and McQueen (1982).)...

For a transmitted shock wave advancing into any gas at an initial pressure pe of 1 atm, the RH (Rankine-Hugoniot) equation defines a functional relationship between pressure p and particle velocity w behind the wave S3, involving initial pressure, initial specific volume v, and equations of state of the target medium. Similarly, the conditions behind the reflected wave S2 and close to the product-target interface are expressible by means either of the shock wave equations or the Rie-mann adiabatic wave equations in terms of any one such variable and the conditions... 

In Appendix B is described on p 45, the "Measurement of Shock Velocity" on p 46 is given "Shock Velocity as a Function of Distance", when the shock has travelled in PMMA for SSGT (Table Bl) on p 47, Fig B, a curve representing "Shock Velocity vs Distance in PMMA for the SSGT and on p 48 is a curve showing "PMMA Hugoniot Data Obtained in Calibration of SSGT"]... 

The Rankine-Hugoniot relationship expressed by Eq. (3.10) or Eq. (3.9) is shown in Eig. 3.2 as a function of 1/p andp, and such a plot is called the Hugoniot curve. The Hugoniot curve for q = 0,i.e, no chemical reaction, passes through the initial point... 

Attenuation of shock waves in air as a function of distance was detd by R.G.Stoner W.Bleakney, JApplPhys 19, 670-8(1948) CA 42, 8475(1948). They measured the velocity of propagation produced on expin in air of chges TNT or 50/50 Pentolite 1.45 to 8 lb (either spherical or cylindrical in shape) and then caled peak pressures by applying the velocity-pressure relation derived from the Rankine-Hugoniot equations... 

Strong detonations can be discussed qualitatively on Hugoniot or (M) curves but an additional classification is necessary if one is to analyze these waves quantitatively. A convenient means is provided by the introduction into the conservation equations of the function (I),... 

To put gap test results on a more absolute basis (so that comparisons can hopefully be made between various forms of the gap test as weil as with other shock sensitivity tests) it is necessary to calibrate the donor-gap system so that shock strengths are known as a function of barrier thickness. Details of calibration procedures are found in Refs 4 20a. If the shock Hugoniot of the unreacted test expl is known, the input shock in the test sample at the sample/barrier interface can be determined as discussed in Section II (Figs 1 2)... 

From equation (23) an explicit algebraic expression for as a function of along the Hugoniot curve may be obtained. Equations (8) and (23) therefore determine the complete solution for the simplified system. 

The isentrope, the path function that describes a continuity and not a jump, is different from the Hugoniot. Remember that a relief wave is a continuous... 

Figure 7. Schematic illustrating how regions on the Flugoniot where M +c = v (which lead to the formation of a second shock wave) can be detected. If a plot of the final pressure (or particle velocity or volume) as a function of shock speed for multiple single wave simulations at various shock speeds is discontinuous in some pressure region, a state exists on the shock Hugoniot where +c = v and a second shock wave can form. States B and D in this plot correspond to those shown in Figure 2. The first wave shock speed for double wave simulations is chosen to the smallest shock speed that takes the material to state D.

Calculated , pressure O, shock velocity , bulk particle velocity as a function of pulse energy in aluminum films, determined with the aluminum Hugoniot [22] and the free surface velocities from the slopes in (a) at times >100 ps. 

The Rankine-Hugoniot equation given by Eq. (3.10) or Eq. (3.9) is shown in Fig. 3-2 as a function of 1 /p and p called the Hugoniot curve. The Hugoniot curve for q= 0, i.e., no chemical reactions, passes the initial point (1/pi, Pi) and is exactly equivalent to the shock wave described in Chapter 1. When heat q is produced in the combustion wave, the Hugoniot curve shifts to the position shown in Fig. 3-2. It is evident that two different types of combustion are possible on the Hugoniot curve (1) a detonation, in which pressure and density increase, and (2) a deflagration, in which pressure and density decrease. 

The JCZ3 EOS was the first successful model based on a pair potential that was applied to detonation [11]. This EOS was based on fitting Monte Carlo simulation data to an analytic functional form. Hobbs and Baer [12] have recently reported a JCZ3 parameter set called JCZS. JCZS employs some of the parametrization techniques used in the construction of BKWC. It achieves better accuracy for the detonation of common high explosives than BKW equations of state. Since it is extensively parametrized to detonation, it has difficulty in reproducing reactive shock Hugoniots of hydrocarbons and other liquids [13]. 

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