Rankine-Hugoniot curve

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... 

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... 

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... 

A numerical evaluation of the condensation discontinuity is performed for several values of the critical saturation ratio x - State 1 is related isentropically to a fixed reference state 0. In Fig. 1. the Rankine-Hugoniot curves and the Ma2 Ma relations are shown for a mixture of water vapour and nitrogen gas. Only those parts of the curves are shown that correspond to entropy increase, to real massflux and to positive droplet mass fraction downstream the discontinuity. The Chapman-Jouguet points, defined by Ma2 = 1, separate the curves in four different regions ... 

The basic equations for describing the detonahon characteristics of condensed materials are fundamentally the same as those for gaseous materials described in Sections 3.2 and 3.3. The Rankine-Hugoniot equations used to determine the detonation velocities and pressures of gaseous materials are also used to determine these parameters for explosives. Referring to Sechon 3.2.3, the derivative of the Hugoniot curve is equal to the derivative of the isentropic curve at point J. Then, Eq. (3.13) be-... 

The mathematical treatment given by eqs 3.1.1 to 3.118 incl, is the same as is discussed under Rankine-Hugonoit Relations, p D 604 and Fig 6, -showing "Hugoniot Curve H ( ) = J 0f Reaction Products (Ref 66, p 13 is given under History of Detonation Theories, p D606... 

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... 

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. 

These equations relate the undisturbed explosive lying at rest with pressure Pq = 0 and specific volume Vq = to the state behind the detonation front, which is characterized by a pressure P, a specific volume V, and a particle flow velocity u. Both u and the detonation velocity, D, are measured in the reference frame of the undisturbed material. Because Pq and Vq are known, the Rankine-Hugoniot relations are a set of three equations for the four unknowns, u, D, P, and V. The first relation determines u in terms of D, P, and Vi, which leaves two equations with three unknowns. The first of the remaining equations, Eq. (4b) defines the Rayleigh line while Eq. (4c) defines the Hugoniot curve. The problem is formally determined by selecting the solution of Eqs. (4b) and (4c) that corresponds to the minimum value of D for an unsupported detonation. This additional condition is the Chapman—Jouguet hypothesis, which was put on a firmer foundation by Zel dovich. ... 

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. 

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