Taylor wave

The flux-corrected-transport technique was also used by Phillips (1980), who successfully simulated the process of propagation of a detonation wave by a very simple mechanism. The reactive mixture was modeled to release its complete heat of combustion instantaneously after some prescribed temperature was attained by compression. A spherical detonation wave, simulated in this way, showed a correct propagation velocity and Taylor wave shape. 

Detonation, Spherical Taylor Wave for the Gaseous Products of Solid Explosives in. 

Using the methods of Taylor s analysis as the basis of machine computation, Lutzky has computed "Spherical Taylor Wave for several high explosives (TNT, Pentolite, 65/35 60/40-Cyclotols, TNEtB, RDX, Tetryl and NGu) with the equation of state ... 

In Appendix I, Lutzky stated that it is instructive to display the Taylor Wave in the form of a space-time diagram (See Fig 1). Since all of the dependent variables are functions only of the quantity r/t, as was shown by Taylor (where r is distance and t is time), constant values of these variables are propagated along straight lines in the (r-t) plane, fanning out from the origin. 

Physics of Fluids 1 (6), 523(1958) (Measurement of the Reflected Shock Hugoniot and Isentrope for Explosive Reaction Products) 4) D. Price, ChemRevs 59(5), 801-25 (Oct 1959) (Measurement of the Reflected Shock Hugoniot and Isentrope for Explosive Reaction Products) 5) M. Lutzky, "The Spherical Taylor Wave for the Gaseous Products of Solid Explosives , NavWeps Rept 6848(1960)... 

FIGJ SPACE - TIME DIAGRAM OF THE SPHERICAL TAYLOR WAVE... 

Based on the above, as well as data on PETN/ polyurethane compns, a tentative model of binder-expl reaction is presented, which ascribes some reaction to the CJ state, and additional reaction in the Taylor wave... 

Detonation, spherical Taylor wave for the gaseous products of solid expls during 4 D554... 

For the explosives that exhibit a narrow chemical reaction zone, the CJ point is not clearly marked (Figure 4.51). In such a case, the CJ point may be obtained by the extrapolation of the Taylor wave, whereas for the explosives that exhibit a broad chemical reaction zone, the CJ point may be easily obtained as the point of marked change of curve slope (Figure 4.52). 

The flowfield produced by an ideal detonation within a closed vessel consists of a constant-velocity, infinitely-thin reactive shock wave (the detonation wave itself) followed by a self similar isentropic wave (Taylor wave) that brings the fluid set in motion back to rest. Solutions to this problem were obtained independently by Taylor and Zel dovich for the planar and spherical cases. Pressure, density, and temperature distributions behind such an ideal wave are illustrated in... 

Fig. 1. Nondimensional temperature, pressure, and density profiles for a CJ detonation followed by a self-similar isentropic flow (Taylor wave) in (a) planar and (b) cylindrical geometries.

When the detonation first reflects as a shock wave from the end of the tube opposite the ignition point, the highest pressures will be obtained. That pressure will be immediately followed by a decay due to the interaction of the shock with the expansion (Taylor) wave following behind the detonation. The initial interaction and pressure-time history near the end-wall immediately following reflection are discussed in this section. 

The interaction of the reflected-detonation shock with the following expansion wave is of some interest. The shock will propagate back through the Taylor wave, moving into regions of lower density as it moves away from the wall. This effect will tend to steepen the wave. However, an expansion also follows the reflected shock, which will attenuate the shock. The net effect is attenuation as shown in computed pressure waveforms presented in Fig. 3. Times are nondimensional t = CrtjL and relative to the initiation of detonation at the opposite end... 

Edwards et al. have observed that proper accounting for losses is needed to obtain correct description of the pressure in the Taylor wave prior to reflection. In that case, they were able to account for their observations by using quasi-one-dimensional computations... 

The basic Pilch model describes primary breakup of a drop via penetration of the drop by Rayleigh-Taylor waves, and it is expressed as... 

Such shock matching is useful for plane, one-dimensional systems with flat-topped detonation waves. The CD-ROM has a shock matching code called MATCH. Numerical studies are necessary to determine the effect of multidimensional geometries and of explosives with steep Taylor waves. 

To further test the weak detonation model, S. Goldstein measured the water shock velocity in the aquarium test after the detonation wave interacted with the water above the top of the X0233 cylinder. Her experimental water shock velocities, as a function of distance above the top of the explosive cylinder, are shown in Figure 2.28 along with the calculated water shock velocities. They are consistent with a flat top Taylor wave characteristic of a weak detonation and a detonation front pressure of 160 kbars. The initial water shock velocities exhibit behavior characteristic of irregular decomposition of the explosive near the shock front. The 2DL calculated aquarium pressure contours are shown in Figure 2.29. 

Figure 2.27 The Taylor waves for X0233 assuming a C-J and a weak detonation.

Characterization of the explosive requires experimental determination of the detonation pressure and velocity. If the experimental state is near the ideal BKW detonation product Hugoniot, the isentrope of the detonation products can be determined by displacing the isentrope through the experimental state. Otherwise, the ideal detonation product Hugoniot must be displaced so that it intersects the observed detonation pressure and velocity by decreasing the energy available to the detonation products. This results in a weak detonation with a flat top Taylor wave. 

The addition of inert metal (or other inerts) particles to explosives results in weak detonations with flat topped Taylor waves. The nonideal behavior is caused by failure of some of the individual detonation wavelets between the metal particles. Subsequent decomposition of the partially decomposed explosive occurs behind the detonation front. 

The methods of burning the explosive were studied to determine whether the numerical results were independent of the burn technique. The gamma-law Taylor wave burn technique for slabs, the Arrhenius rate law, the C-J volume burn technique, and the sharp-shock burn technique are described in Appendix A. Another method in common use is the programmed burn, which assumes that the time required to burn an explosive cell can be predetermined from the detonation velocity. Any of the methods is satisfactory for plane geometry, but the gamma-law Taylor wave method is faster and requires fewer cells in the numerical calculation. 

Figure 2.33 Calculated Taylor waves for 1.27 and 2.54 cm of 9404 with constant gammas of 3.77 and 3.227, respectively, and with a variable gamma.

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