Von Neumann spike

Fig. 3.6 Detonation wave formation from shock wave to von Neumann spike, and then to the Chapman-Jouguet point.

Detonation, NDZ (Neumann-DSring-Zel dovich) Theory called by Cook and by Evans Ablow The Zel dovich-von Neumann-Doring Model and the Von Neumann Spike. Accdg to Evans Ablow (Ref 9), it was postulated independently by Zel dovich (Ref 1), von Neumann (Ref 2)and Doring (Ref 3), that detonation is a reaction initiated by a shock. This... 

The shock part of the detonation wave is often called the von Neumann spike (Ref 9, pp 147-48)... 

Dunkle (Ref 7) stated that accdg to the NDZ theory the first part of the deton wave, sometimes called the von Neumann spike, is an almost ideal shock wave in which very little chem reaction takes place. While the pressure at the spike is ca twice the C-J pressure, the temperature is ca half the C-J temp. This initial pressure and temp rise occurs entirely within ca 10 5cm thickness of the deton front. The 2nd phase of the deton wave is a gradual decrease in the pressure and an increase in the temp concurrent with the completion of the chem reactions. The length of the reaction zone can be detd experimentally from the minimum diam of a rod of explosive which propagates a steady-state detonation also from the changes in the deton velocity when this rod is surrounded by an inert casing material of varying thickness or from the decrease in the deton velocity when the deton wave is made to go around a bend of known radius of curvature... 

C(v,P). It is seen that the temp of the spike N is somewhat lower than half of the C-J temp. Since the temp is low, it is not expected that the chem reactions could occur to any appreciable extent in the short time required for the gas to pass thru the initial shock. Actually the temp at Njis so low that in many practical cases one would expect a time lag or a quenching zone before the reaction sets in. Hirschfelder inferred that accdg to NDZ theory some chem reaction can take place within the detonation front (in cases of unusually high reaction rates), and blunt the von Neumann spike, as can be seen in Fig 4 (Ref 7, pp 172-74)... 

The pressure obtd from equation in dynes/cm was divided by 10 to express it in kbars. It varied for Comp B from 62 to 173 kbar. A single point at 388 kbar was obtd from shock-velocity measurements on a thin aluminum foil placed in contact with the explosive. This point corresponds to the von Neumann "spike pressure ... 

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) ... 

Picture this as the shock state that brings on reaction, but the reaction zone is so short, and the reaction so fast that the energy involved in this pressure spike is negligible compared to the energy in the fully reacted products. This point, by the way, is referred to as the Von Neumann spike, and is seen more clearly if we view the detonation wave in the P-x plane. Figure 20.3. 

For the purpose of the simple model, the Von Neumann spike is ignored and the reaction zone thickness is assumed to be zero. The gas expansion or rar-... 

Since the main use of detonating solid explosives is to accelerate metals and other materials to high velocities, accurate measurements of the unreacted shock state (the von Neumann spike ), the pressure profile of the reaction zone, and the subsequent expansion of the reaction products as they deliver their momentum are essential. Currently these properties are known to within a few percent with nanosecond resolution [67]. Improved accuracy and time resolution are future experimental and computational goals. 

Fig. 6. Detonation in a slab of energetic material, (a) The detonation shock front runs at a constant velocity, driven by fast expansion of chemical reaction products. The highest pressure is in the von Neuman spike region just behind the front. At the Chapman Jouguet (C-J) plane the reaction is Just complete, (b) Shock compression follows the indicated Rayleigh line to where it intersects the unreacted Hugoniot at the von Neumann spike. The point where this Rayleigh line is tangent to the reacted Hugoniot is the C-J state of stable detonation velocity.

As a result of these simplifications, the computed induction times and lengths define characteristic time and length scales rather than the precise history of a gas element through the detonation front. The evolution of the reacted gas subsequent to the induction period considered here is dominated by the fluid mechanics of the post-induction expansion of the reaction products. This expansion reduces the pressure and density of these products and alters the kinetic equilibrium, leading eventually to the CJ state. Since virtually all of the reactants have been consumed by this time, the kinetics of this final expansion phase are controlled by relatively slow radical recombination processes. The present model does not attempt to follow that entire relaxation phase, concentrating on the details of the induction kinetics in the von Neumann spike. 

The heterogeneous explosive reaction zone that has been the most studied is PBX-9404 (94/3/3 HMX/Nitrocellulose/Tris-/3-Chloroethyl phosphate). A summary of the estimated reaction zone thickness and Von Neumann spike pressure is given in Table 1.4 along with the calculated reaction zone parameters using the solid Arrhenius HMX constants of... 

Thus, any experimental study of a reaction region in a heterogeneous explosive is actually measuring some mean value of an irregular, complicated multi-dimensional flow. It is not surprising that different experimental techniques may give quite different reaction zone thicknesses, Von Neumann spike pressures and profiles. 

The measured Von Neumann spike pressure can also vary with the experimental technique as shown in Table 1.6, where the reported Composition B Von Neumann spike pressure varies from 374 to 420 kilobars, and in Table 1.4, where it varies from 485 to 550 kilobars for PBX-9404. 

The reactive region has bounds which approach a steady-state condition, but the flow inside those bounds is multi-dimensional and time-dependent. The reaction zone thickness at various locations across the zone may vary by an order of magnitude. The Von Neumann spike pressure and the pressure at the end of the reaction zone also vary with location by 25 percent or more. The reaction zone is highly variable with time but has bounds within which it varies. 

In the present treatment, in which we solve the set of differential equations, some of the solutions are shown to come close to, but not pass through, the von Neumann spike. 

If is greater than N> there is a lower hmit of i initial conditions. If, on the other hand, 6f is less than 6n, the curve d = cuts the line x = within the h = 0 parabola. The point of intersection corresponds to = 0. The solution curve for... 

Fig. 13a. A schematic illustration of the behavior of the solutions near the von Neumann spike.

Figure 16 shows a set of solution curves plotted upon a Hugoniot diagram. Here > Sjy, so that there is a lower limit to This lower limit corresponds to a shock wave with x = I followed by the reaction zone starting at the von Neumann spike, N. The... 

Fig. 7.3 Pressure distribution through the duct in the one-dimensional ZND model of a detonation wave for stoichiometric HAM at Tq = 300 K i - von-Neumann spike ...

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