Properties of the Hugoniot curve

FIGURE 2.2. The determination of downstream flow properties from the Hugoniot curve. 

Constitutive relation An equation that relates the initial state to the final state of a material undergoing shock compression. This equation is a property of the material and distinguishes one material from another. In general it can be rate-dependent. It is combined with the jump conditions to yield the Hugoniot curve which is also material-dependent. The equation of state of a material is a constitutive equation for which the initial and final states are in thermodynamic equilibrium, and there are no rate-dependent variables. 

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... 

Since the equations of continuity, momentum, energy, and state do not suffice to determine the five unknowns, it. is necessary to inquire into the conditions under which solutions exist and whether solns are unique. The information which has thus far been omitted is a specification of the flow field of die reaction products, that is to say, since this section is restricted to one--dimensional flow, of the rear boundary condition. Before discussing the question of determinancy it is necessary to deduce from the equations of Section II of Ref 66, the general properties of flow ahead and behind reaction waves. To do this the Hugoniot curve for the products... 

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. 

The properties of reflected waves in the deton products were detd by a similar impedance match at the explosive-backing plate interface using the measured transmitted shock velocity in the backing plate whose Hugoniot curve was known. This technique was described by Al tschuler et al (Addnl Ref Fj) for detg the shock properties of inert solids... 

Table 2.1 summarizes many of the properties of Hugoniot curves. In the table, quantities identified by the subscripts -h, —, 1, max, and min are fixed constants, determined by the initial state of the mixture. The quantities... 

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,... 

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