Chapter 4: Overdriven Detonation from Interactions of Common Detonation Waves

5/13/2018 Chapter 4: Overdriven Detonation from Interactions of Common Detonation Waves

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CHAPTER 4: OVERDRIVEN DETONATION FROM INTERACTIONS OFCOMMON DETONATION WAVES

4.1 INTRODUCTIONIn gas dynamics, it has been well-known that when a shock encounters another shock

or an obstacle, a third strong shock will be formed. This phenomenon is called Machreflection of shock wave and has been documented elsewhere [1]. A usual detonationwave, according to Zeldovich-von Neumann-Doring's explanation (see Chapter 2),consists of a heading shock wave with the following chemical reaction zone. Therefore,when the interactions occur between the usual detonation waves, it is expectable toacquire the similar reflection configuration to the one by the shock waves in gases. Onthis circumstance, it is the strong detonation wave that is formed instead of the strongshock appeared in the cases of gaseous shocks. This strong detonation is, in reality, whatis referred to as the overdriven detonation. Some scholars [2] also called it as Machdetonation due to its origination from Mach refection of detonation wave. Theinteractions of detonation waves in plane geometry [3] or in cylindrical geometry [4,5]were investigated by several researchers. In plane geometry, the detonation waves aregenerated by two plane-wave generators or explosive lens with a specific apex angle,while, in cylindrical geometry, the detonation wave interactions arise from anarrangement of two layer of explosives in which the low velocity explosive is put intothe inside cylinder and the high explosive wraps around it. For the understanding offormation mechanism of Mach detonation as well as its propagation, the plane geometryis of the superiority to the cylindrical geometry because the detonation waves in planegeometry avoids the effect due to the geometrical condition. So, in this chapter, theattention is primarily paid to the plane detonation wave interactions. First, the theory onthe determination of the critical angle of Mach detonation is presented. Then, anexperimental design developed from the idea of plane-wave generator is proposed toimprove the conventional experimental set-up. The detonation wave interactions areobserved by the high speed camera in the form of framing mode. Finally the numericalsimulation is performed for the aim of reproducing some important features in the

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experiments as well as of providing the detailed understanding toward this subject.

4.2 CRITICAL ANGLE FOR MACH DETONATIONIn the study of the formation and propagation of Mach detonation of explosives, it is

necessarily important to learn under what conditions the Mach detonation is available.The occurrence of Mach detonation often accompanies the process of collision of twodetonation waves of the reflection of detonation wave off 'hard' surface (high-impedance solid). Let us consider the situation that a detonation wave obliquelyincidences onto a rigid surface. As shown in Fig. 4.I(a), when the incidence angle, a, issmall, the reflection configuration is of the regular refection type that only involves anincidence detonation wave and a reflected shock wave starting from the incident point.While, if a moving reference coordinate system is used, i.e., the origin of the coordinatesystem is attached at the incident point, 0, the flow will be changed into such a steadyconfiguration as shown in Fig. 4 1(b). Only is the one streamline expressed forrepresentation. It is known from the detonation property that no matter where theincident detonation wave locates, the pressure and particle velocity in the regionimmediately behind the oblique incident detonation wave possesses unchangeableChapman-Jouguet (C-J) detonation properties or simply C-J values. A s can be seenfrom Fig. 4.1 (b), the incoming stream is forced to turn toward the solid surface after itpasses over the incident detonation wave. The reflected shock inversely deflects thestreamline again from the solid surface. As long as the streamline passed through thereflected shock is able to be parallel to the solid surface, the regular reflection is alwayspresentable. However, when this condition is broken, i.e., no matter what position of thereflected shock wave is located, the flow passed through the reflected shock isimpossible to become parallel to the solid surface but incidences onto the rigid surface,the Mach detonation front should be introduced as Fig. l(c) shown. The occurrence ofthis circumstance corresponds to the incidence of the oblique detonation wave with alarger incident angle a into the solid surface. With the aid of Fig. 1, the condition for thetransition from regular reflection to Mach detonation is given by employing the shock-polar method.

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Reflected shock wave (R) Incident detonation wave (I)C-J state

Rigid wall(a) In static reference frame.

R I

Rigid wall(b) In moving reference frame.

Rigid wall(c) Occasion of Mach detonation.

Fig. 4.1 Conceptual diagrams for the reflection of detonation wave off a rigid surface.

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The shock polar for the incident detonation wave can be expressed by the followingequation in the form of the incidence angle aand the flow deflection angle 8.

(4.1)

where,qo=Dlsina (4.2)

and PC]and VC]is pressure and volume at C-J state, Vo is the initial volume of explosive.For a specific explosive, these values are known. The shock polar for the reflectedshock is given by the following relation in the form of the angle of the reflected shockwith the rigid surface, 1 3 , and the flow deflection angle, 82, behind the reflected shock,

(4.3)

sinj3=_1 ~(P-PCJ).Vb/(VCJ-V)qiCombining Eq. (4.3) with the equation of state of explosive. the shock polar can bereadily acquired. For instance, when the explosive is assumed to be SEP and theequation of state chooses the simple polytropic y-Iaw equation. i.e .. PVY=const., thecalculated shock polars for the incident detonation wave and the reflected shock aredrawn in Fig. 4.2. All the reflected shock polars start on the incident shock polarbecause the reflected shocks appear in the region behind the incident detonation wave.If the reflected shock polar has an interception with the vertical axis. it means that theflow passed through the reflected shock can be converted into its original incomingdirection towards the incident detonation front. The solution for the reflected shock ispossible and the reflection is accordingly the regular reflection. If it is not the case, thereflection falls into the range of Mach reflection. From Fig. 2, it is known that thecritical angle, a, for Mach detonation is within the range of 40 to 46 degrees.

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.. _o~

e or ~(degrees)Fig. 4.2 Shock polars for incident detonation wave and the reflected shock wave.

4.3 EXPERIMENTAL STUDIES4.3.1 Experimental Device for Mach Detonation.

In the study, the following experimental device was developed to use for thegeneration of the interactions of plane detonation waves. As shown in Fig. 4.3, thegenerators for plane detonation are composed of two kinds of explosives in which thehigh velocity explosive is arranged at the slant sides of the right triangles. Two suchtriangles that are put into a specific apex angle forms two plane detonation waves inanother piece of pentagon-shaped explosive that has an obtuse sides completelycoincide with the apex angle of the generators. In practice, the generators may beregarded as two parts of one commonly used plane-wave generator that is divided fromthe central symmetric line. The open space between the generators is filled with sand toeliminate the possible effect from the air jet due to the initiation. The high and lowexplosives are, respectively, SEP (PETN 65 wt.% and paraffin 35 wt.%) and HABW(PETN 35 wt.% and binders 35 wt.%) mixture explosives that have detonationvelocities of6.97 kmls and 4.86 kmls. The pentagon-shaped explosive piece is made upof SEP with height of about 70mm and 55 mm length at the sides coinciding with the

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I P : rvnv1A plate

Fig. 4.3 Device of Mach detonation by collision of planar detonation waves.

generators. The two sides of pentagon-shaped explosive neighboring the generators areset to be perpendicular to the corresponding plane-wave generator. The shapedexplosives have the identical thickness of 5mm by considering that the amount ofexplosives is allowed to be performed at the experimental facility as well as thedetonation properties of explosives. The shaped explosives are fixed on a PMMA plate.Three apex angles (Zcc), 100, 120 and 140 degrees, are selected to be studied in theexperiments so that the incident angle, e x , of plane detonation wave is 50, 60, and 70degrees, respectively. According to the theory described in previous section, theseincident angles all make the Mach detonation possible to occur.

4.3.2 High-Speed Photographic Observation and ResultsThe experiments on the interaction of plane detonation waves was conducted at the

explosion chamber facility of Shock Wave and Condensed Matter Center, KumamotoUniversity, where the high-speed camera systems is equipped for the observation. The

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camera is IMACON 790 (Hadland Photonics) capable of taking both framing and streakphotographs with maximum framing mode of 20 mil1ion frames in a second and fasteststreak writing speed of 1mm per nanosecond. During the experiments, the framingmode was selected. The time interval between each frame was set to be 21ls so that inone Polaroid film paper (l07mm long by 85 mm wide) 8 frames might be attainable.The auxiliary equipment include an Xenon-flash-light generator (HL 20/50 type Flash-light) and a delay generator (THREE-DELAY GENERATOR TYPE JH-3CDG). Thestart of the photography was controlled by ionization wire probes inserting into theexperimental device, which could be connected from the cut-off state by the explosionaction and sent back a signal to the camera shutter. The experimental device was placedinto water contained by a PMMA-made aquarium for the considerations of preventingthe projection of the fragments and degrading the explosion noise. The schematicphotographic system is shown in Fig. 4.4.

P M M Aaquar ium

Image Lightconverter flashercamera Observationwindows

Wall WallObservation Explosion Light sourceroomroom chamber

Fig. 4.4 The photographic arrangement for observing the detonation of explosives.

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The framing photographs for the three incident angle conditions are shown in Fig. 4.5.The results are sequentially arranged for the angles of a=50, 60 and 70 degrees. Thetwo intersected white lines are the detonation wave front in the pentagon-shapedexplosive piece except the snapshot #1 in Fig. 4.5(b) that gives the detonation wavefront in plane-wave generators. Because HABW is a low-velocity mixture explosive, itsself-luminosity is relatively weak compared to the high velocity SEP explosive. Fromthe detonation wave configurations shown in the photographs, it is seen that theexperimental device for the generation of plane detonation wave is successful and theconfiguration of detonation front generally holds a planarity. It can be thought to muchextent that the two plane detonation waves collides on the symmetric plane in thedesigned explosive piece. On the occasion of 50 degrees incident angle, the Machdetonation is not obviously visible since the cusp of intersection of two detonationwaves keeps remained until the detonation ends. Itmay be due to this incident anglealmost approaching the critical condition of Mach detonation occurrence. As theincident angle increases, as shown in the cases of 60 and 70 degrees incident angles, thesituations are greatly changed. It is clearly seen that as the propagation of detonationwaves runs down., the cusp of intersection of two detonation waves becomes graduallyinvisible and instead a curved connection appears even though it is still relatively short.This curved connection is the Mach detonation front. The spreading width of Machdetonation front is approximately 7 mm for the case of 60 degrees incident angle and 9mm for the case of 70 degrees incident angle. The trajectory angle of the triple point.according to Mach reflection theory, falls into the range of 5 to 6 degrees. Of course, thephotographic experiments took only the pictures of the detonation waves near thesurface on which the propagation of detonation wave may much or less be weakened [6].Itis naturally envisioned that the detonation in the middle section of explosive piece canmore appropriately represent the plane detonation wave circumstance. Theimprovement on the experiments is going to be continued in the later work.

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#1 #2 #3(a) a=50 degrees (interframe time: Zus)

#1

#4

#2

" .. ~ .... ~ ...{~ r~,C'I I'. ~

,

#3

#5(b) a=60 degrees (interframe time: 2J.ls)

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#32(c) a=70 degrees (interframe time: 2J..ls)

Fig. 4.5 Sequential framing photographs of the collisions of detonation waves at three

#1

incident angles.

SEPx

Fig. 4.6 Calculation model for Mach reflection of plane detonation waves.

4.4 NUMERICAL INVESTIGATIONFor the Mach detonation of explosive from the collision of two plane detonation

waves, a numerical analysis on this phenomenon was performed. In the calculation, theinitiation for the generation of plane detonation wave was omitted and the considerationwas only involved the detonation wave interaction in the explosive block. Fig. 4.5illustrates the calculation model. Here, the quadrilateral was used to replace the

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pentagon shape explosive piece In the experiments for simplicity of computationalprocedures. The numerical technique used here was a 20 Lagrange program codewhose computational procedures are described in detail in appendix II. The physicalmodel for the reaction of explosive was approximated by the 'C-J volume burn'technique. The equation of state of explosive still used the general JWL equation sincewe can not presently employ the new form EOS introduced in Chapter 3 because of thedeficiency on the data of state variables above the C-J region for SEP explosive. Thecalculated configurations of the collision of the detonation waves are expressed by thetechnique so called computer shadowgraph [7] that uses the values of the second-orderdifferentiation of density as a variable in space, i.e., S= ~ p. When density has aremarkable change, such as at detonation front or reflected shock, the differentiation ofthe density is also changed greatly so that such fronts are able to be vividly displayed.The calculated results corresponding to the three incident angles are shown in Fig. 4.6.Similar to experimental results, when the collision angle is equal to 50 degrees, it isfound that the Mach reflection of detonation wave is almost invisible. Then, with theincrease of the collision angle, for instance, being 70 degrees, the Mach reflectionbecomes clear. It can be known from the last snapshot in Fig. 4.6(c) that the reflectedshock locates on the incident detonation wave, being away from the symmetric plane.Nevertheless, the Mach detonation wave area (Mach stem) is relatively narrow,qualitatively agreeing with the experimental results.

4.5 DISCUSSIONFrom the experimental and numerical results, it is known that the Mach detonationarea is small in our plane detonation wave interactions. Except that it is related to the

dimensions of explosive specimens we used in the experiments were small-size, it ismore due to the characteristic of Mach detonation itself The feature can be furtherexplained by the following theoretical consideration. Please refer to Fig. 4. L when aplane detonation wave strikes on a rigid wall, the moving velocity of the colliding point

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(a) cx=50 degrees (interval of snapshot: 2 ) . l s )

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(b) a=60 d eg re es ( in te rv al of s na ps ho t: 2 J..l.s)

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D.S.100755025o-25-50-75-100

(a) u=70 degrees (interval of snapshot: 2f. ls)Fig. 4.7 Computer shadowgraphs of the collision of detonation waves at three differentincident angles.

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..-..r oc,


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the effect of Taylor wave so that the spreading of the Mach detonation area ISobstructed.

4.6 CONCLUSIONSAs one type of overdriven detonation, Mach detonation from the interactions of

plane detonation waves was experimentally observed by high-speed camera. Theexplosion device was newly improved on the basis of the conventionally used set-up forthe expectation of giving the better experimental consequences. The results show thatthe detonation waves generated from this device held a satisfactory planarity and welllocated on the two sides of the symmetrical plane. Through optical technique theinteraction process of detonation waves was sequentially taken for the survey of theMach detonation width obtained from experiments. For three incident angles of 50, 6070 degrees of the plane detonation waves, the Mach detonation area is limited to arelatively narrow range although it becomes greater as the incident angle increases. Thenumerical simulation on this process also gave the similarly consistent results. Finally, atheoretical explanation on this phenomenon is given, but the full understanding towardsthe formation mechanism of Mach detonation and its propagation should be furtherstudied. Nevertheless, one point is very certain that the Mach detonation exists in theinteractions of detonation waves. It directs the possibility of Mach detonation in theapplications to the generation of higher pressures utilized in some fields.

REFERENCES

1. Ben-Dor, G., Shock Wave Reflection Phenomena, Springer-Verlag, New York, 19922. Argous, 1. P., Peyre, C. and Thouvenin, 1., "Observation and Study of the Conditions

for Formation of Mach Detonation Waves, Fourth Symposium (International) onDetonation, Oct. 12-15,1965, White Oak, MD, pp.135-141.

3. Lambourn, B. D. and Writght, P. W., "Mach Interaction of Two Plane Detonation

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Waves," Fourth Symposium (International) on Detonation, White Oak, MD, Oct. 12-15,1965, pp. 142-152.

4. Muller, E, "Mach Reflection of Detonation Waves in Condensed High Explosives,"Propellants, Explosives and Pyrotechnics. Vol. 6, 1980. pp. 170-172.

5. Krishnan, S., Brochet, C. and Cheret, R., "Mach Reflection in CondensedExplosives," Propellants, Explosives and Pyrotechnics, Vol. 6, 1981, pp. 170-172.

6. Bdzil, J. B., "Steady-State Two-Dimensional Detonation," J. of Fluid Mechanics,Vol. 108, 1981, pp. 195-226.

7. Minota, T ., Nishita, M., Lee, M. G., Shock Waves (Eds. Sturtevant, B., Shepherd.lE. and Hornung, H.G.), World Scientific Press, Singapore, Vol. I, 1996, pp. 545-550.

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Chapter 4: Overdriven Detonation from Interactions of Common Detonation Waves