W. Fickett

Flow Calculations for Pulsating One‐Dimensional Detonations

The nature of the long‐time flow in an idealized one‐dimensional, piston‐supported detonation is investigated by numerical solution of the time‐dependent hydrodynamic equations. The method of characteristics is used, with shocks treated as jump discontinuities. The fluid is an ideal gas of constant heat capacity undergoing an exothermic, irreversible, unimolecular reaction A → B obeying an Arrhenius rate law. The results are consistent with Erpenbecks linearized analysis of the stability of the steady detonation, which revealed some cases in which the usual steady‐state solution is unstable to infinitesimal longitudinal perturbations. In a typical flow of this type, the shock pressure is found to oscillate about the steady‐solution value with a peak pressure nearly 50% higher and with a period of about 9 steady‐solution half‐reaction times.

Application of the Monte Carlo Method to the Lattice‐Gas Model. I. Two‐Dimensional Triangular Lattice

The Monte Carlo numerical method for obtaining statistical mechanical averages in the petite canonical ensemble has been applied to the two‐dimensional triangular lattice‐gas model. The Monte Carlo procedure described by Rosenbluth et al. and by Wood and Parker has been extended slightly to include the calculation of the partition function. The results are compared with the exact solutions for the two‐dimensional lattice and the agreement is well within the fluctuation displayed by the numerical method. The calculations are found to be relatively insensitive to a change in the pseudo‐random number sequence and to display no exceptional behavior in the region of the first‐order phase transition for small lattices.

Calculation of the Detonation Properties of Solid Explosives with the Kistiakowsky‐Wilson Equation of State

The Kistiakowsky‐Wilson equation of state, pVg = RT(1+xeβx), where x = k/Vg(T+θ)α, for the gaseous detonation products of solid explosives has been re‐examined in the light of new experimental data on detonation pressure and on the variation of detonation velocity D with loading density ρ0 for several RDX/TNT mixtures. The value β = 0.30 used in the past is too high to match the observed slopes of the D—ρ0 curves. The old value α = 0.25 is too small to match the experimental Chapman‐Jouguet pressure of most of these explosives, but too large to match the pressure of pure TNT. A suitable compromise for the explosives considered is α = 0.5, β = 0.09, θ = 400°K.

The Absolute Configuration of Optically Active Molecules

The problem of the absolute configuration of optically active molecules is investigated with the aid of the Kirkwood theory of optical rotatory power. Absolute configurations are assigned to the enantiomorphs of 2,3‐epoxybutane and 1,2‐dichloropropane. The assignments are consistent with the established experimental configurational relationships between these compounds. The Fischer convention is confirmed as a structurally correct representation of absolute configuration. The magnitudes of the calculated rotations of the compounds are in reasonably good agreement with experiment. The theory accounts satisfactorily for the effect of temperature and solvent on the optical rotation of 1,2‐dichloropropane.

The polymorphic detonation

A simple thermodynamic system, having a single first‐order phase transformation, is examined as an elementary explosive. The energy needed to support self‐sustaining waves is stored in the volume change of the phase transformation. It is shown that this system can support the conventional viscous detonations as well as a set of unsteady eigenvalue detonations. Eigenvalue detonations have been discussed previously with respect to conventional explosives, but the very large reaction rates required to produce them are not thought to exist in nature. The occurrence of eigenvalue detonations in our system, for arbitrarily small reaction rates, is due entirely to the presence of an equilibrium coexistence surface connecting the two phases of the material, allowing mixed phase equilibrium states to be attained in a single shock process.

Shock Hugoniots for Liquid Argon

Shock Hugoniots for liquid argon are calculated using equations‐of‐state obtained from the Monte Carlo method and the Lennard‐Jones‐Devonshire cell theory, using an experimentally determined pair potential. Agreement with presently available experimental data is poor.

Stability of the square-wave detonation in a model system

Abstract Using a set of model equations for reactive flow, we study the stability of a “square-wave” detonation, in which each particle of the fluid reacts instantaneously after an induction time which depends on how hard it was shocked. We obtain a differential-difference equation for the shock velocity, valid for small perturbations about the steady solution. This equation is of so-called “advanced” type, in which the velocity at a given time depends on both velocity and acceleration at an earlier time.

A Detonation‐Product Equation of State Obtained from Hydrodynamic Data

A recent experimental measurement of the Chapman‐Jouguet isentrope of the solid explosive Composition B, together with the experimental detonation velocity vs initial density curve, give considerable information about the equation of state of the detonation products. With the aid of some thermodynamic assumptions, a simple explicit form is obtained for the energy as a function of pressure and volume.

Shock initiation of detonation in a dilute explosive

The plane‐shock initiation of detonation in the limiting case of small heat release is studied by a linear perturbation analysis, with a small parameter which is roughly the ratio of chemical to mechanical energy. The solution consists of three waves traveling at different velocities. One of these is a steady wave and two are transients. The wave shapes are simply related to the composition dependence of the reaction rate.

Approach to the steady solution for a plane Chapman–Jouguet detonation

In the context of the author’s mathematical analog for reactive flow, the late‐time approach to the steady solution for a plane Chapman–Jouguet (CJ) detonation is studied. The reaction kinetics are those of the ‘‘small resolved heat release’’ model, in which the bulk of the chemical energy is released instantaneously in the shock and the remainder is released at a finite rate in the following reaction zone. Calculated shock histories and particle histories (Lagrangian gauge records) are presented for two driver prescriptions that initiate the detonation close to the steady solution. The implications of these results for the interpretation of CJ pressure measurements is discussed.