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Understanding the Effects of a Finite-Length Reaction Zone

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Understanding the Effects of a Finite-Length Reaction Zone High-Explosives Performance Understanding the effects of a finite-length reaction zone John B. Bdzil with Tariq D. Aslam, Rudolph Henninger, and James J. Quirk igh explosives—explosives such as that in a match head. Ordinary sure detonation wave streaks through with very high energy density combustion is a coupled physico- the material at supersonic speeds, H—are used to drive the implo- chemical process in which the inter- turning the material into high-pres- sion of the primary in a nuclear face separating fresh from burnt ener- sure, high-temperature gaseous prod- weapon. That circumstance demands getic material travels as a wave ucts that can do mechanical work at precision in the action of the high through the sample. Exothermic an awesome rate. Figure 1 shows the explosive. To predict with high accura- chemical reactions begin on the sur- initiation of a detonation wave from cy the course of energy release under face of the match head and burn the shock compression through the forma- various conditions is therefore an outer layer of material. The heat tion of a self-sustaining Zeldovich important problem that we face in cer- released is transferred through thermal –von Neumann–Doring (ZND) deto- tifying the safety, reliability, and per- conduction to an adjacent unreacted nation reaction zone behind the shock. formance of nuclear weapons in the layer until that second layer ignites, The power delivered by an explosive stockpile. Here we survey our progress and this layer-by-layer process contin- depends on its energy density and its on the problem of explosives perform- ues until the entire sample is con- ance: predicting the outcome of inten- sumed. The speed of the combustion The pressure plot on this opening page tional detonation of high explosives in wave is relatively low, depending on shows a steady-state detonation wave complex three-dimensional (3-D) both the rate of energy transport from propagating through a cylindrical explo- geometries. The problems of safety one layer to the next and the rate of sive (gray) confined by a low-density (accidental initiation) and reliability the local exothermic chemical reac- inert material (yellow). Red is the high- (reproducible response to a prescribed tions in each layer. est pressure; purple, the lowest. The stimulus) are also under investigation Explosives, in contrast, support reaction starts along the shock (red curve) and ends along the sonic surface but will be only briefly mentioned here. very high speed combustion known as (white curve). A large pressure drop at Explosives belong to the class of detonation. Like an ordinary combus- the edge of the explosive leads to a sig- combustibles known as energetic tion wave, a detonation wave derives nificant lengthening of the chemical materials, which means that they con- its energy from the chemical reactions reaction zone near the edges of the deto- tain both fuel and oxidizer premixed in the material, but the energy trans- nating explosive, a reduction in the on a molecular level. Such materials port occurs not by thermal conduction speed of the detonation wave, and the can support a whole range of combus- but rather by a high-speed compres- development of a curved detonation tion, including ordinary combustion sion, or shock, wave. The high-pres- shock front. 96 Los Alamos Science Number 28 2003 High-Explosives Performance (a) t0 t1 t2 t3 L1 L2 Distance (b) 0.3 0.2 ZND reaction 0.1 zone Pressure (Mbar) 0 –5 0 5 10 Distance (mm) (c) 0.4 PZND = 0.36 Mbar 0.3 PCJ = 0.27 Mbar Figure 1. Initiation and Propagation of a ZND Detonation Wave (a) A schematic 1-D (planar) experiment is shown at different times. In the 0.2 experiment, the impact of a plate thrown on one face of a cube of explosive (t = t0) produces a planar shock wave (t = t1) that gradually accelerates (t = 0.1 Pressure (Mbar) t2) to a steady-state detonation (t = t3) as the shock sweeps through the explosive and causes chemical energy to be released to the flow at a finite 0 rate. (b) The corresponding pressure-vs-distance snapshots show the evolu- 0.5 1.0 1.5 2.0 tion of an essentially inert shock wave at t = t growing into a classical 1-D 1 Time (µs) ZND detonation structure at t = t3, namely, a shock, or pressure, discontinu- ity at the ZND point followed by decreasing pressure through the reaction zone, ending at the CJ point, the pressure predicted by the simple CJ model (see text). (c) Pressure-vs-time plots for material particles originally at the shock front locations in (b) show the particle pres- sure (or velocity) histories in the form measured in actual experiments (see Figures 5, 6, and 7). Only at the location of the right- most particle has a ZND detonation fully formed. Note: The point of maximum acceleration of the shock, called the point of deto- nation formation, coincides with the shape change in the pressure profile and the first appearance of a choked flow condition (sonic condition). Refer to Figure 3. detonation wave speed. Solid high the United States! This very rapid rate of the initiating shock strength and explosives, like those used in nuclear of energy liberation is what makes depend on only certain properties of weapons, have a detonation speed of solid explosives unique and useful. the explosive before and after passage about 8000 meters per second (m/s), The legacy weapons codes have of the detonation front, namely, the or three times the speed of sound in long used the simple Chapman- initial density of the unreacted materi- the explosive, a high liberated energy Jouguet (CJ) model to compute the al, the liberated energy density of the density of about 5 megajoules per performance of high explosives. In explosive, and the pressure–volume kilogram (MJ/kg), and an initial mate- this classical, one-dimensional (1-D) (P-v) response function of the reacted rial density of about 2000 kilograms model of detonation, it is assumed material (called the mechanical equa- per cubic meter (kg/m3). The product that the chemical reaction rate is infi- tion of state, or EOS). In this CJ limit, of these three quantities yields the nite (and therefore the length of the the explosive performance problem is enormous power density of reaction zone is zero rather than finite, reduced to providing an accurate 80,000,000 MJ/m2/s or 8 × 109 watts as in the opening figure and Figure 1). mechanical EOS for the gaseous prod- 2 per centimeter squared (W/cm ). By That assumption leads to the predic- ucts of detonation, Eg (P,v)—see comparison, a detonation with a sur- tion that the detonation speed is con- Figure 2. face area of 100 centimeters squared stant. Moreover, the values of the det- In this article, we focus on another operates at a power level equal to the onation speed, DCJ, as well as the det- aspect of the performance problem: total electric generating capacity of onation pressure, PCJ,are independent creating accurate 3-D detonation mod- Number 28 2003 Los Alamos Science 97 High-Explosives Performance 0.3 state of the art for modeling 3-D deto- nation flows, our models predict deto- CJ detonation state nation propagation only in homoge- 0.25 neous explosives under standard con- ditions. That is, they do not fully account for the effects that the hetero- 0.20 geneity of the real explosives we use today have on detonation. We there- 0.15 fore conclude this article with our vision for the future of detonation CJ detonation process (Rayleigh line) propagation modeling—one that Pressure (Mbar) 0.10 accounts for that heterogeneity yet EOS of detonation products remains practical for weapons per- (PSCJ(v) isentrope) formance studies. 0.05 Fully expanded state Initial of detonation products state The Detonation Process 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Volume (v/v0) How does a detonation wave reach and then maintain such enormous Figure 2. Maximum Work Obtainable from a CJ Detonation The E (P, v) mechanical equation of state (EOS) is required to model explosive per- power levels as it sweeps through the g explosive? The enormous pressures (a formance. Most often, it is measured along a restricted curve—an isentrope, PS(v), few hundred thousand atmospheres, or or a shock Hugoniot curve, PH(v)—in the state space defined by the thermodynamic variables Eg, P, and v.To characterize the maximum work that a detonation can per- a few hundred kilobars) and tempera- form (shaded area above), we need determine only the principal or CJ expansion tures (2000 to 4000 kelvins) behind isentrope of the detonation products, PSCJ(v), given that we know DCJ, and PCJ. The the detonation front originate from the two curves shown above are the detonation Rayleigh line, shown in red (detonation very rapid release of chemical energy. process), and the detonation products expansion isentrope, PSCJ(v). The area under Reactions are 90 percent complete in the isentrope (to some cut-off pressure) minus the area under the Rayleigh line less than a millionth of a second. As a (work done by the shock in compressing the explosive) is the maximum mechanical work that can be obtained from the explosive. For our high-performance, mono- result of this rapid release, the reac- molecular explosives, such as HMX, this work compared with the available explo- tion zone is very short. But how are sive energy can be very high (more than 90%). We perform experiments to measure the pressures sustained? this isentrope and then construct the Eg(P, v) mechanical EOS for the products of As shown in Figure 3, the reaction detonation, which is an essential ingredient in every model of how detonations do zone is bounded by two surfaces that work on their surroundings.
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