Polytropic equation of state

Simulations of this scenario have been performed by Lee (Lee 2001 and references therein) using Newtonian gravity and polytropic equations of state of varying stiffness. Ruffert, Janka and Eberl performed similar simulations but with a detailed microphysics input (nuclear equation of state and neutrino leakage ). In our own simulations of NS-BH mergers we used a relativistic mean field equation of state together with three-dimensional smoothed particle hydrodynamics and a detailed, multiflavour neutrino treatment. [Pg.325]

The polytropic equation of state, also known as gamma law equation of state can be expressed as ... [Pg.290]

Wj) Vj/ilkins Equation of State and Its Modi-f ications. The polytropic equation of state written in the form ... [Pg.294]

Among the experiments which were reported, there were several pertaining to measurements of the C-J (Chapman-Jouguet) particle velocity and sound speed and one experiment concerned with an examination of the polytropic equation of state for reaction products of condensed explosives... [Pg.343]

Detonation (and Explosion), Polytropic Curve, and Polytropic Law. Dunkle (Ref 2, p 184), under the heading "Polytropic Law , explained that a simplified form very useful in expls calcns is obtd by assuming that the expin products behave as a polytropic gas, i.e., an ideal gas having constant specific heats and hence a constant value of specific heat ratio y. He gives also the polytropic equation of state, which we included under "Detonation (and Explosion), Equations of State ... [Pg.474]

A semi-infinite explosive slab of thickness h, -bounded on both free faces by vacuum (or air), is initiated instantaneously at one free face. We wish to compute the impulse delivered at the other free face. From the polytropic equation of state assumption it follows that ... [Pg.321]

For detonation products that obey a polytropic equation of state (probably also true for other equations of state), pulse duration is t = nh/D, where 1 < n < °°. Thus, for a triangular pressure pulse... [Pg.326]

Lamboum (Ref 14) used the polytropic equation of state in a hydro-code called McCoy to examine energy partition of underwater expls. [Pg.93]

To gain some insight into these phenomena, without getting toe involved in m a them ati ca 1 complexities, let us first examine some limiting cases of impulse delivered to a) a rigid wall b) air (for HE detonations there is very little difference in the final results in the explosive impulse delivered to air or to a vacuum) a) The rigid wall problem has been treated in detail by Baum et al (Ref 2), on the basis of a polytropic equation of state for the detor laticii products atid a poly tropic coefficient 1-3. They find that... [Pg.321]

For a gas that obeys the so-called polytropic equation of state (EOS) p/p = const and... [Pg.702]

The work in a compressor under ideal conditions as previously shown occurs at constant entropy. The actual process is a polytropic process as shown in Fig. 10-65 and given by the equation of state Pv = constant. [Pg.917]

Detonation pressure may be computed theoretically or measured exptly. Both approaches are beset with formidable obstacles. Theoretical computations depend strongly on the choice of the equation of state (EOS) for the detonation products. Many forms of the EOS have been proposed (see Vol 4, D269—98). So.far none has proved to be unequivocally acceptable. Probably the EOS most commonly, used for pressure calcns are the polytropic EOS (Vol 4, D290-91) and the BKW EOS (Vol 4, D272-74 Ref 1). A modern variant of the Lennard Jones-Devonshire EOS, called JCZ-3, is now gaining some popularity (Refs -11. 14). Since there is uncertainty about the correct form of the detonation product EOS there is obviously uncertainty in the pressures computed via the various types of EOS ... [Pg.844]

A useful insight into the structure of nearly homogeneous stars or parts thereof can be gained from the study of so-called polytropic stellar models which depend on a combination of the principle of hydrostatic equilibrium with an assumed equation of state of the form... [Pg.413]

For steady flow of an ideal gas between points 1 and 2, distance L apart, in a pipe of constant cross-sectional area in which no shaft work is done, the energy equation is given by equation 6.19. For the general case of polytropic flow, from equation 6.27, the equation of state can be written as... [Pg.199]

From the theory of polytropic gravitating gas spheres with the equation of state P = Kp1 it was known (Emden, 1907), that at 7 = 4/3 the equilibrium mass has a unique value... [Pg.6]

The polytropic exponent y is the exponent in the polytropic or "gamma-law equation of state, PV =a constant (See item (w) under Detonation, Equations of State) (Dunkle s letter of April 16, 1968)... [Pg.231]

Unfortunately, the extensive work on gas detonations has had little impact on the development of the theory for condensed phas es. The reason is the lack of a reliable equation of state for these. While fundamental significance must be achieved eventually, an empirical fit to actual performance would be helpful at present. A sophisticated general equation for the isentrope, which is a C-J isentrope, is called for. Above 150-200 kbar, the polytropic (gamma-law) equation of state is valid (Skidmore Hart, in Ref 19, p 47). [Pg.239]

Rankine-Hugoniot equations 181-87 (Equations of state which include among others the following Jones Miller, Lennard-Jones Devonshire, Halford-Kistiakowsky-Wilson, Joffe its modification by Su Chang, Taylor, Kihara Hikita, Travers, Cook, Kistiakowsky-Wilson-Brinkley and Polytropic equations) 194 (Landau-Stanyukovich and Hirschfelder et al equations of state 11) J.F. Roth, Explosiv-stoffe 1958, 50 (Abel sche Zustandsgleichung fur die Detonation) 12) Cook (1958), 37 (General equation of state) 62-3 [Halford-Kistiakowsky-W ilson-Brinkley equation of state, (listed as K-H-W-B equation of state)] ... [Pg.297]

Dunkle also discussed in Ref 3, p 15e some modifications of the polytropic equation, some of which are included under Detonation (and Explosion), Equations of State... [Pg.474]

Reynolds number, p 46), etc 61-72 (Shock relationships and formulas) 73-98 (Shock wave interactions formulas) 99-102 (The Rayleigh and Fanno lines) Ibid (1958) 159-6l(Thermal theory of initiation) 168-69 (One-dimensional steady-state process) 169-72 (The Chapman-Jouguet condition) 172-76 (The von Neumann spike) 181-84 (Equations of state and covolume) 184-87 (Polytropic law) 188, 210 212 (Curved front theory of Eyring) 191-94 (The Rayleigh transformation in deton) 210-12 (Nozzle thepry of H. Jones) 285-88 (The deton head model) ... [Pg.617]

To determine how the numerical factors in Eqs (1), (8) (9) vary with T (the other terms are unchanged by variation in T as long as the equation of state is still of the polytropic form) we have re-computed Eq (1) in its generalized form,... [Pg.322]

Deal polytropic (detonation) equation of state 4D276... [Pg.536]

Work in polytropic compression of a gas with equation of state PV = zRT is entirely analogous to Eq. (7.26). The hydrodynamic work or the work absorbed by the gas during the compression is... [Pg.156]

When adiabatic conditions are not attained, the process is called a polytropic change of state. Such a change of state is described by the Equation 5.15. [Pg.224]

Suppose the equation of state takes the polytropic form... [Pg.53]

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