Spherical detonation

DETONATION (EXPLOSION AND COMBUSTION), SPHERICAL (Spherical Blast, Spherical Front and Spherical Wave). Spherical detonations (explosion and combustion) are those in which initiation in the center of a charge (preferably spherical in shape) will cause formation of spherical shock and detonation waves. These waves move radially away from the charge into the surrounding medium (gaseous, liquid or solid) in such a manner that particles of their outer boundary (front) are always equidistant from the center of the charge in the manner shown in Fig on p 183 of Vol 2 of Encycl 

The simplest method for producing a spherical combustion in gases is to place a combustible (but not explosive) gaseous mixture in a thin latex, rubber or plastic balloon and ignite it in the center by means of an electric spark 

Spherical combustion waves are described in the book of Lewis von Elbe (Ref 23) and recently investigated by Plickenbaum et al (Ref 25). It was found that such waves are not affected by flow interactions with solid surfaces, and therefore require longer run-ups for transition to detonation 

In the overdriven state, the observed propagation velocity of the combustion front was found to be much higher than the steady-state velocity of spherical detonation. The overdriven state exists for only a short time, and the combustion front velocity then drops rapidly to the steady-state value. The rate at which this exceedingly high velocity decreases was found by experiment to be inversely proportional to the induction distance 

The high flame front velocities prior to attainment of the steady state probably result from the transient conditions between the combustion front and shock front. Sufficient data were lacking to show whether the shock-heated gas ignited spontaneously, immediately behind the shock front, or whether the flame front overtook the shock front. In any event, the combustion wave finally moves along with the shock wave, thus forming a detonation wave 

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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. 

Phillips, H. 1980. Decay of spherical detonations and shocks. Health and Safety Laboratories Technical Paper No. 7. 

D. Desbordes, Correlation between shock wave predetonation zone size and cell spacing in critically initiated spherical detonations. Prog. Astron. Aeron., 106,166-180, 1986. 

Rarefaction waves are generated circumferentially at the tube as the detonation leaves then they propagate toward the tube axis, cool the shock-heated gases, and, consequently, increase the reaction induction time. This induced delay decouples the reaction zone from the shock and a deflagration persists. The tube diameter must be large enough so that a core near the tube axis is not quenched and this core can support the development of a spherical detonation wave. 

In initiation from a point source and subsequent expansion of a spherical detonation front , the quantity of explosive absorbing the energy at any time exceeds that in a layer of the same original thickness releasing the energy. In effect, the energy per unit mass available for propagating the wave is decreased by convexity of the wave front. 

N) C.L. Mader, "Detonation Properties of Condensed Explosives Using BeCker-Kistiakowsky-Wilson Equation of State , LASL Rept LA-2900(1963) O) M. Lutzky, "The Flow Field Behind a Spherical Detonation in TNT Using the Landau-Stanyukovich Equation of State for Detonation Products , USNavalOrdnanceLaboratory, White Oak, Md, NOLTR 64-40(1964) (The equation discussed in Rept is the one modified by Zel dovich Kompaneets and is referred to by Lutzky as "LSZK Equation of State ) Oi) M.L. Wilkins, Univ of Calif, LawrenceRadLab, Livermore, Calif, Rept UCRL-7797(1964) P) H. Hurwitz, "Calculation of the Detonation Parameters With... 

In contrast to the shock zone, the detonation zone includes the shock zone (10 5 cm) 8t the chem reaction zone (0.1 to 1.0 cm). These two zones together make up the deton zone. In the shock zone little or no chem reaction occurs, but the pressure reaches its peak due to the shock. At or near the forward boundary of the second zone, the high temp to which the expl has been raised by compression in the shock zone initiates chem reaction. As the material moves toward the rear boundary of the chem reaction zone, the resulting expansion lowers the pressure so that this falls thruout the zone. See also Detonation Head and Its Development Addnl info on these subjects may be found in the following Refs Refs 1) G.I. Taylor, The Dynamics of the Combustion Products Behind Plane and Spherical Detonation Fronts in Explosives , PrRoySoc 200A, 235-47(1950) 2) C.G. 

Motion of the Detonation Products Behind Plane and Spherical Detonation Waves in Solid Explosives , Penn State Uiiv, Dept of Engrg Mechanics Tech Rept 3 (30 Nov 1964) (Dept of Army Contract DA-36-034-ORD-3576RD) 9) M. Lutzky, "The Flow... 

Field Behind a Spherical Detonation in TNT Using the Landau-Stanyukovich Equation... 

The Three-Dimensional Wave System of Spinning Detonation , Ibid, pp 839-50 890 R. Cheret J. Brossard, "Cylindrical and Spherical Detonations in Gases , Ibid, Paper 84, p 149 (Abstracts only) 89g)... 

V.P. Karpov A.S. Sokolik, "On the Mechanism of Generation of Shock Waves, Their Amplification on Interaction with the Flame, and Transition to Detonation , Ibid, Paper 85, p 149 (Abstracts only) 89h) J.H. Lee et al, "Direct Initiation of Spherical Detonations in Gaseous Explosives , Ibid, Paper 86, p 150 (Abstracts only) 90)... 

G.G. Bach et al, "Direct Initiation of Spherical Detonations in Gaseous Explosions , Ibid, 853-64... 

Flow Field Behind a Spherical Detonation in TNT, Using the Landau-Stanyukovich Equation of State , USNavalOrdnanceLa-boratory, White Oak, NOLTR 64-40, Dec 1964 5) C.G. Dunkle, private communi-... 

B) M. Lutzky, "The Flow Field Behind a Spherical Detonation in TNT Using the Landau-Stanyukovicb Equation of State for Detonation Products , USNOL - White... 

The mixtures were placed in transparent round latex flasks. Initiation was in the center. With their method, it was possible to record spherical detonation waves whose velocities were the same as when these mixtures were detonated in tubes. The waves usually originated very near the ignition source (electric spark or electric primer), but in some cases there was a brief predetonation period... 

In another paper Freiwald Koch described (Ref 24) investigation of spherical detonations of acetylene-oxygen-nitrogen mixtures as a function of nature and strength of initiation... 

Baum, Stanyukovich 8c Shekhter (Ref 20) gave a rather comprehensive discussion on spherical detonations and following are some high points of this discussion ... 

Spherical detonation waves can also be produced by condensed expls (solid ot liquid), especially if the charges are spherical in shape and they are initiated in the center. The above discussion of Baum et al applies to both gaseous and condensed expls. Addnl information on spherical detonation of solid explosives can be obtd from the works of Landau 8c Stanyukovich (Ref 2), Jones Miller (Ref 3), Wecken Sc Muecke (Ref 4a), Lutzky (Ref 26), Rudlin (Ref 26a) and Green James (Ref 27)... 

Discussing the analysis of spherical detonation in TNT, Lutzky (Ref 26) noted that, as described in Cole (Ref 3a), H. 

AnnPhys 10(IV), 645(1925) (Spherical detonations of CS2+3O2 mixture) 2) L.D. Landau K.P. Stanyukovich, DoklAkadN 46, 399(1945) (On the study of detonation in condensed explosives) 3) H. Jones Sc A.R. Miller, PrRoySoc 194A, 480-507(1948) (The detonation of solid explosives The equilibrium conditions in the detonation wave-front and the adiabatic expansion of the products of detonation) 3a) Cole, Underwater (1948), pp 81-83 4) J. 

G.I. Taylor, PrRoySoc 200A, 235-47(1950) (The dynamics of combustion products behind plane and spherical detonation fronts)... 

N. Manson F. Ferrie, "Spherical Detonation Waves , 4thSympCombstn(1952)... 

Andreev 8c Belyaev (I960) (Nothing on spherical detonations) 23) Lewis von... 

Detonation, TDBP Wave (Taylor- Doring-Burkhardt-Pfriem Wave). Accdg to discussion given by Cook in Chapter 5, under "Theoretical Wave Profiles (Ref 4, pp 92ff), Taylor (Ref 3) studied theoretically the p(x) and W (x) distributions behind plane and spherical detonation waves for gaseous expls and TNT, using the hydrodynamic equation ... 

Taylor (Ref 23) stated that ignition of TNT chge at some point inside the expl, results in a very rapid drop in pressure velocity behind the deton front. A fixed proportion of the whole vol of burnt gas is at rest and the radial rat e of change of the variables velocity, pressure density become finite at the deton front. The fact that the velocity drops to ze ro at some point between the deton surface the center shows that a spherical deton wave can maintain itself in the case of TNT. It is not known whether this is true in all cases Lutzky (Ref 86) determined the "Flow ... 

Eyring et al (Refs 9 22a) postulated that the curved shock front is made up of spherical segmen ts and that behind each segment is the radially divergent flow which occurs behind a spherical deton wave initiated at a point inside an explosive (Taylor, Ref... 

The flow lines in a coordinate system at rest in the unreacted expl are shown in Fig 32a. A spherical deton is not steady, since the radius of curvature increases with time. For an instantaneously steady spherical segment of shock front moving in the direction of axis of a cylindrical chge, the flow lines betw the front and the C-J plane in a coordinate system at rest in the shock front will diverge, as shown in Fig 32b... 

The question considered is a description of the conditions which must be met by a localized initiator if a spherical detonation wave is to be formed. The first problem is a determination of the possibility of the existence of such a wave. Taylor analyzed the dynamics of spherical deton from a point, assuming a wave of zero-reaction zone thickness at which the Chapman-Jouguet condition applies. He inquired into the hydrodynamic conditions which permit the existence of a flow for which u2 +c2 = U at a sphere which expands with radial velocity U (Here U = vel of wave with respect to observer u2 = material velocity in X direction and c -= sound vel subscript 2 signifies state where fraction of reaction completed e = 1). Taylor demonstrated theoretically the existence of a spherical deton wave with constant U and pressure p2equal to the values for the plane wave, but with radial distribution of material velocity and pressure behind the wave different from plane wave... 

An Approximate Solution of the Flow Within the Reaction Zone Behind a Spherical Detonation Wave in TNT, NavWepsRept 7364... 

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