Jouguet Point Research Articles

Detonation parameters of the mixture of gelled nitromethane/microballoons at high porosity

The detonation properties of mixtures of gelled nitromethane (NM) with hollow glass microballoons (GMBs), the concentration of which varied from 16 to 30 wt. %, have been studied using an optical technique with high temporal and spatial resolution. It is shown that the addition of GMBs up to 30 wt. % does not qualitatively change the reaction zone structure of NM, which is in accordance with the classical detonation theory. However, the detonation parameters of the mixture decrease significantly with increasing GMB concentration—the pressure at the Chapman–Jouguet point drops by more than an order of magnitude at a porosity of 75%. The non-monotonic nature of the change in critical detonation diameter with decreasing mixture density is noted. The dependence of the critical diameter on the porosity of U-shape with the formation of two local minima at 8 and 18 wt. % GMB in the mixture and a local maximum at 13 wt. % GMB is obtained. At a concentration above 20 wt. % GMB, the critical detonation diameter increases dramatically, and at 30 wt. % GMB, the critical diameter becomes comparable to that of gelled NM.

Shock waves in (1 + 1-dimensional) curved space-time

ABSTRACT Shock jump conditions are widely used to solve various astrophysical problems. From the hydrodynamic equation, we derive the jump condition and the Taub adiabat equation in curve space-time for both time-like and space-like shocks. We find that the change in entropy for the weak shocks for curved space-time is small, similar to that for flat space-time. We also find that for general relativistic space-like shocks, the Chapman–Jouguet point does not necessarily correspond to the sonic point for downstream matter, unlike the special relativistic case. To analyse the shock wave solution for the curved space-time, one needs the information of metric potentials describing the space-time, which is assumed to be a neutron star for the present work. Assuming a shock wave is generated at the star’s centre, and as it propagates outward, it combusts nuclear matter to quark matter. We find that the general relativistic treatment of shock conditions is necessary to study shocks in neutron stars so that the results are consistent. We also find that with such general relativistic treatment, the combustion process in neutron stars is always a detonation.

Assessment of the Parameters of a Shock Wave on the Wall of an Explosion Cavity with the Refraction of a Detonation Wave of Emulsion Explosives

At present, studying the parameters of shock waves at pressures up to 20 GPa entails a number of practical difficulties. In order to describe the propagation of shock waves, their initial parameters on the wall of the explosion cavity need to be known. With the determination of initial parameters, pressures in the near zone of the explosion can be calculated, and the choice of explosives can be substantiated. Therefore, developing a method for estimating shock wave parameters on an explosion cavity wall during the refraction of a detonation wave is an important problem in blast mining. This article proposes a method based on the theory of breakdown of an arbitrary discontinuity (the Riemann problem) to determine the shock wave parameters on the wall of the explosion cavity. Two possible variants of detonation wave refraction on the explosion cavity wall are described. This manuscript compares the parameters on the explosion cavity wall when using emulsion explosives with those obtained using cheap granular ANFO explosives. The detonative decomposition of emulsion explosives is also considered, and an equation of state for gaseous explosion products is proposed, which enables the estimation of detonation parameters while accounting for the incompressible volume of molecules (covolume) at the Chapman–Jouguet point.

Estimation of pressure during steam explosion in the sub-reactor room of NPP with RBMK-1000

The article analyzes the scenario of a severe beyond the design basis accident with core melting at a nuclear power plant with RBMK-1000. Molten reactor core falls into the sub-reactor space filled with a steam-water mixture. The interaction of melt core and the coolant can lead to the creation of conditions for the occurrence of a steam explosion. Parameters of this steam explosion have been evaluated by Hugoniot adiabat method. Such approach considers the steam explosion as detonation phenomenon, where shock wave impacts initial multiphase mixture and initiates melt droplets fragmentation and high heat flux from melt to water. Mass, momentum and energy conservation equations for initial mixture and for equilibrium explosion products mixture lead to Hugoniot equation for the adiabat. The tangent from initial point (initial mixture) on the plane “mixture volume-mixture pressure” to the Hugoniot adiabat determines Chapman – Jouguet point, which characterizes steam explosion parameters. Our calculations have demonstrated that obtained values of steam explosions do not exceeds dangerous limits.

Fast Ignition by a Proton Beam and Burning of a DT Cylindrical Shell Target

Edge ignition of a cylindrical shell target by a proton beam with a small mass heating depth of about 0.5 g/cm2 is analyzed for two values of the initial mass density of the DT fuel, $${{\rho }_{0}} \approx 110$$ and 22 g/cm3, and given beam parameters (the intensity $$J \propto {{\rho }_{0}}$$ and impact time $$\Delta {{t}_{{{\text{pr}}}}} \propto \rho _{0}^{{ - 1}}$$ ). By comparing results obtained using different models of heat transfer through the fuel–shell interface, it is shown that application of a strong magnetic field that suppresses heat transfer but does not affect the trajectories of the α-particles produced in the DT reaction reduces the ignition energy by only about 10%. The unsteady detonation wave generated in the course of ignition transforms into a steady-state fast shockless burning wave, in which the cold fuel is heated by α-particles. The wave parameters depend on the deposited energy. As the wave propagates through the fuel, the α-particles escaping from the fuel volume carry away about one-half of their initial power. For one of the simulation versions, the target length H is determined ( $${{\rho }_{0}}H \approx 10$$ g/cm2) at which the gain reaches a value of $$G = 1250$$ . An approximate formula is derived that relates the slope of the pressure profile in a steady-state wave to the wave velocity and the heating power per unit mass of the fuel near the wave front. The applicability of the formulas relating the pressure and velocity at the Chapman–Jouguet point to the propagation velocity of a strong detonation wave is demonstrated.

Simulation of Double-Front Detonation of Suspended Mixed Cyclotrimethylenetrinitramine and Aluminum Dust in Air

The two-phase detonation of suspended mixed cyclotrimethylenetrinitramine (i.e., RDX) and aluminum dust in air is simulated with a two-phase flow model. The parameters of the mixed RDX-Al dust detonation wave are obtained. The double-front detonation and steady state of detonation wave of the mixed dust are analyzed. For the dust mixed RDX with density of 0.565 kg/m3 and radius of 10 μm as well as aluminum with density of 0.145 kg/m3 and radius of 4 μm, the detonation wave will reach a steady state at 23 m. The effects of the size of aluminum on the detonation are analyzed. For constant radius of RDX particles with radius of 10 μm, as the radius of aluminum particles is larger than 2.0 μm, the double-front detonation can be observed due to the different ignition distances and reaction rates of RDX and aluminum particles. As the radius of aluminum particles is larger, the velocity, pressure and temperature of detonation wave will be slower. The pressure at the Chapman–Jouguet (CJ) point also becomes lower. Comparing the detonation with single RDX dust, the pressure and temperature in the flow field of detonation of mixed dust are higher.

Correlation of electrical conductivity in the detonation of condensed explosives with their carbon content

This paper presents the comparative analysis of the results of more than fifty experiments on measuring the electrical conductivity of detonation products of RDX, HMX, PETN, TNT, and TATB-based explosives. It is revealed that there is a correlation between the electrical conductivity and the mass fraction of carbon both in the chemical spike and at the Chapman–Jouguet point.

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

A shock wave structure problem, like the one which can be formulated for the planar detonation wave, is analyzed here for a binary mixture of ideal gases undergoing the symmetric reaction . The problem is studied at the hydrodynamic Euler limit of a kinetic model of the reactive Boltzmann equation. The chemical rate law is deduced in this frame with a second-order reaction rate, in a chemical regime such that the gas flow is not far away from the chemical equilibrium. The caloric and the thermal equations of state for the specific internal energy and temperature are employed to close the system of balance laws. With respect to other approaches known in the kinetic literature for detonation problems with a reversible reaction, this paper aims to improve some aspects of the wave solution. Within the mathematical analysis of the detonation model, the equation of the equilibrium Hugoniot curve of the final states is explicitly derived for the first time and used to define the correct location of the equilibrium Chapman–Jouguet point in the Hugoniot diagram. The parametric space is widened to investigate the response of the detonation solution to the activation energy of the chemical reaction. Finally, the mathematical formulation of the linear stability problem is given for the wave detonation structure via a normal-mode approach, when bidimensional disturbances perturb the steady solution. The stability equations with their boundary conditions and the radiation condition of the considered model are explicitly derived for small transversal deviations of the shock wave location. The paper shows how a second-order chemical kinetics description, derived at the microscopic level, and an analytic deduction of the equilibrium Hugoniot curve, lead to an accurate picture of the steady detonation with reversible reaction, as well as to a proper bidimensional linear stability analysis.

Stability of cosmological detonation fronts

The steady-state propagation of a phase-transition front is classified, according to hydrodynamics, as a deflagration or a detonation, depending on its velocity with respect to the fluid. These propagation modes are further divided into three types, namely, weak, Jouguet, and strong solutions, according to their disturbance of the fluid. However, some of these hydrodynamic modes will not be realized in a phase transition. One particular cause is the presence of instabilities. In this work we study the linear stability of weak detonations, which are generally believed to be stable. After discussing in detail the weak detonation solution, we consider small perturbations of the interface and the fluid configuration. When the balance between the driving and friction forces is taken into account, it turns out that there are actually two different kinds of weak detonations, which behave very differently as functions of the parameters. We show that the branch of stronger weak detonations are unstable, except very close to the Jouguet point, where our approach breaks down.

Energy release behind the Jouguet point during detonation of plasticized PETN from the results of experiments by the T-20 method

The trajectory of motion of a copper shell, the velocity of its flight, and the pressure of the explosion products on the inside of the copper shell were simulated. It was found that there is a significant difference in pressure behavior between experiments and calculations performed using the standard equations of state of explosives and explosion products. Most likely, there is a significant contribution of kinetic processes to the energy release behind the Jouguet point. In this case, the conversion of explosives to explosion products apparently include not only exothermic reactions but also endothermic processes.

Investigation of the evolutionarity of discontinuities in binary mixture flows through a porous medium

The discontinuity surfaces (shock waves) that arise in nonisothermal carbon dioxide-water binary mixture flows through a porous medium are considered. In the plane of determining parameters the discontinuity adiabats are investigated and their evolutionarity diagrams are plotted. It is shown that one of the adiabat branches corresponds to the displacement fronts at which there are no temperature jumps and phase transitions and the other branch to temperature jumps and phase transition fronts. The adiabat branches may intersect at a point that corresponds to the Jouguet point for the parameters both ahead of and behind the finite-amplitude jump. It is shown that in the neighborhood of this double Jouguet point the adiabat behavior differs from the classical adiabat behavior at single Jouguet points.

Experience of using synchrotron radiation for studying detonation processes

Results of studying detonation processes in condensed high explosives, which are obtained by methods based on using synchrotron radiation, are summarized. Beam parameters are given, and elements of the station and measurement system are described. Data on the density distribution in the detonation front for several high explosives are presented, and values of parameters in the Neumann spike and at the Jouguet point are determined. A method used to reconstruct a complete set of gasdynamic characteristics (density fields, particle velocity vector, and pressure) from the experimentally measured dynamics of the x-ray shadow of the examined flow is described. Results of using this method for studying detonation of a charge of plastic-bonded TATB are presented. A method of measuring small-angle x-ray scattering in the course of detonation conversion is described. Based on results obtained by this method for a number of high explosives with an excess content of carbon, kinetics of condensation of free carbon and dynamics of the mean size of nanoparticles being formed thereby are analyzed.

Principles of the radiative ablation modeling

Indirectly driven inertial confinement fusion (ICF) rests on the setting up of a radiation temperature within a laser cavity and on the optimization of the capsule implosion ablated by this radiation. In both circumstances, the ablation of an optically thick medium is at work. The nonlinear radiation conduction equations that describe this phenomenon admit different kinds of solutions called generically Marshak waves. In this paper, a completely analytic model is proposed to describe the ablation in the subsonic regime relevant to ICF experiments. This model approximates the flow by a deflagrationlike structure where Hugoniot relations are used in the stationary part from the ablation front up to the isothermal sonic Chapman–Jouguet point and where the unstationary expansion from the sonic point up to the external boundary is assumed quasi-isothermal. It uses power law matter properties. It can also accommodate arbitrary boundary conditions provided the ablation wave stays very subsonic and the surface temperature does not vary too quickly. These requirements are often met in realistic situations. Interestingly, the ablated mass rate, the ablation pressure, and the absorbed radiative energy depend on the time history of the surface temperature, not only on the instantaneous temperature values. The results compare very well with self-similar solutions and with numerical simulations obtained by hydrodynamic code. This analytic model gives insight into the physical processes involved in the ablation and is helpful for optimization and sensitivity studies in many situations of interest: radiation temperature within a laser cavity, acceleration of finite size medium, and ICF capsule implosion, for instance.

Steady-State Detonation Wave Parameters in a FEFO/Nitrobenzene Solution

This paper gives the results of experimental studies of the reaction zone structure during steady detonation in bis-(2-fluoro-2,2-dinitroethyl)-formal (FEFO, C5H6N4O10F2) and its mixtures with nitrobenzene (NB). For pure FEFO, the pressure and particle velocity at the Chapman—Jouguet point and the characteristic reaction time were measured. For FEFO/NB, the dependence of the detonation parameters of the mixture on the NB concentration was determined, and the detonation front was shown to be unstable in pure and in mixtures containing more than 30% NB.

A New Method for Evaluating the Energy Characteristics of CHNO Energetic Compounds

AbstractFrom the law of conversation of energy, the release energy from the initiation to the Chapman–Jouguet point during the detonation of an energetic compound has been deduced as a function of initial density, detonation velocity, and detonation pressure. For CHNO energetic compounds the relative release energy per unit volume (Iv) approaches the relative specific wall kinetic energy (Ecyl/EHMX) at 19 mm wall displacement from the cylinder test with HMX as reference. A good linear relationship between Iv and Ecyl/EHMX has been regressed, implying that Ecyl/EHMX is also a function of initial density, detonation velocity, and detonation pressure. It has been concluded that Iv can reflect the driving force of detonation products of energetic compounds and is appropriate to be used for the evaluation of energy characteristics. The assessment of the energy for a series of synthesized and theoretically designed high‐energy compounds reveals that the future of CHNO energetic compounds is promising after CL‐20 and ONC.

Microscopic Approaches to Liquid Nitromethane Detonation Properties

In this paper, thermodynamic and chemical properties of nitromethane are investigated using microscopic simulations. The Hugoniot curve of the inert explosive is computed using Monte Carlo simulations with a modified version of the adaptative Erpenbeck equation of state and a recently developed intermolecular potential. Molecular dynamic simulations of nitromethane decomposition have been performed using a reactive potential, allowing the calculation of kinetic rate constants and activation energies. Finally, the Crussard curve of detonation products as well as thermodynamic properties at the Chapman-Jouguet (CJ) point are computed using reactive ensemble Monte Carlo simulations. Results are in good agreement with both thermochemical calculations and experimental measurements.

A double-front structure of detonation wave as the result of phase transitions

Using thermochemical code calculations, we show that the nanographite–nanodiamond phase transition, which may occur in the detonation products of a number of carbon containing explosives, can affect the detonation properties and can cause a specific detonation regime with some unusual peculiarities. Among them, we first note the failure of the Chapman–Jouguet condition and the presence of the sonic plane, where the Mach number is equal to unity, in a detonation product expansion wave at a lower pressure than that at the Chapman–Jouguet point. The peculiarities of this detonation regime are demonstrated by the example of TNT, HNS, and RDX. The computed detonation velocities are in excellent agreement with experiments over a wide range of initial charge densities for all of the investigated explosives. The results of this work allow one to explain, e.g., contradictory experimental data on the detonation pressure and on the length of the reaction zone for TNT. We believe that some other solid–solid, solid–liquid, and liquid–liquid phase transformations in the detonation products may also cause a detonation regime with the same features as shown here for the nanographite–nanodiamond transition. We suggest a computational study that should facilitate proposing detonation experiments strongly arguing in favor of the model presented.

Molecular-dynamic study of detonation in a diatomic molecular crystal

The molecular-dynamics method was used to examine the effect of cross-sectional sample size on detonation processes in molecular crystals. It was shown that, in the molecular crystal model considered, an increase in cross-sectional size has no noticeable effect on the propagation velocity of detonation waves, on the delay time of the chemical reaction, and on the energy macrocharacteristics of the disturbed region. Also, the results of the present molecular-dynamic modeling were compared with the predictions of the continuum theory of detonation. Good agreement between the detonation velocities and between the values of thermodynamic parameters at the Chapman–Jouguet point was obtained.

Dependence of the Time-Space Structure of the Chemical-Reaction Zone on the Initial Density of the Explosive

The results of a study of the chemical‐reaction zone structure for a number of high explosives (HEs) are discussed. It is found that an increase in the initial density of the HEs leads to a structural change in the chemical‐reaction zone involving elimination of the Von Neumann spike at the critical density point. Conversely, as the initial density of the explosive decreases, the ratios of the gas‐dynamic parameters (in particular, mass velocities) at the Von Neumann point to the same parameters at the Jouguet point increase. It is shown that to explain the indicated regularities, one does not need to invoke the assumption of an increasing contribution of the exothermic decomposition of the HE the shock. The results can be explained within the framework of classical Zel‐dovich–Von Neumann–Doring theory with an ordinary shock at the detonation‐wave front and, hence, with a nearly zero contribution to the total energy release in the chemical reaction zone.

Structure of the Reaction Zone of a Steady Detonation Wave in Dinitrodiazapentane

The mass‐velocity profiles in 2,4‐dinitro‐2,4‐diazapentane samples of different densities were registered by a laser interferometer and the electromagnetic technique. The reaction time was shown to reach ≈ 300 nsec and weakly depend on density, while the pressure in the chemical spike can be twice as high as that at the Chapman–Jouguet point. No special features due to diamond formation were observed in the mass‐velocity profiles registered in the chemical reaction zone.