performamance of transient tempertureature in hot spot
5 (State key Lab. of Explosion Science and Tech., Beijing Institute of Technology,
Abstract: This work presents a method to estimate probability initiating combustion and detonation by
temperature load in void in energetic material. When a void is compressed its volume decreases and the
temperature in the void increases. The local thermal source due to the void deformation in energetic 10 material forms a temperature load which may initiate combustion and detonation. The temperature-time
history in the void was called temperature load in this work. Its peak value and holding time are the
necessary and sufficient condition initiating combustion or detonation of energetic material
surrounding the void. Comparing with the energy acted on the unit area of hot spot, the performance of
transient temperature which can better serve to reflect the physical essence in ignition. The main object 15 of this work is to study transmitting process of temperature load from void to energetic material and
probability initiating combustion and detonation by temperature load in void.
Keywords: ignition; temperature load; energetic material
20 Voids within energetic material can generate “hot spots” that have the potential to start local
burning leading to partial reaction or detonation. Several thermomechanical mechanisms that have
been suggested as potential hot-spot sources include: friction between adjacent grains, jetting of
material fragments across voids, hydrodynamic pore collapse, viscous heating and internal shear,
and shock interactions at density discontinuities [1-2]. Much of the experimental data and 25 analytical modeling of hot spots indicates that the specific mechanisms responsible for hot spot
formation depend on the physical and thermodynamic properties of the heterogeneous materials,
as well as the means by which the energy is transmitted to the material from an external source. In
general, there are three kinds of mechanisms in the theory referring to hot spot formation to
transition to detonation in inner voids of energetic materials. The first is the compression of any 30 gaseous or vapour content in a void to produce high temperature [3-5].The second is the action of
the plastic flow and the high-speed jet in the collapse of a void . The third is the ignition energy
from viscoplastic heating of the condensed-phase material surrounding a collapsing cavity in the
process of void compression. Many works have investigated those conditions corresponding to
each one or two of three mechanisms. It is widely agreed that under the low loading rate the void 35 with large size prefers the first mechanism.
In analyzing the hot spot ignition, the energy per unit of area on the surface of hot spot is
often taken as the critical condition of ignition. It means that the critical ignition value is
determined by the total energy of the hot spot divided by its surface area of boundary. However, in
the experiment of hot spot ignition that the authors carried out, it was found that the hot spots with 40 the same dimension and energy, obviously having an identical energy per unit of area for each
other, caused different ignition phenomena in practice. When the holding time or the duration is
longer, the hot spots with an identical energy can lead to ignition, while when the holding time is
shorter they cannot. It showed that in the theory taking the energy per unit of area as the critical
condition of ignition is not complete and correct. In order to comprehensively understand this
45 phenomenon, it is necessary to study response of energetic material around a void to the
Foundations: Foundation for Doctor Dissertation of China？20111101110008？
Brief author introduction:Zhang Qi, (1956-), Prof. Explosion Mechnics. E-mail: firstname.lastname@example.org
temperature inside the void so as to obtain the knowledge of different modes initiating combustion
or detonation by local thermal source.
When a void is compressed its volume decreases and the temperature in the void increases.
The temperature-time history in the void was called temperature load in this work. The 50 temperature load is exerted on the surrounding energetic material around the void, and makes its
temperature rise and chemical reaction start. If the chemical reaction can release enough energy to
make shock wave to keep in self-sustained state, the ignition occurs. Whether the chemical
reaction can cause shock wave self-sustained is dependent on the reaction rate and the width of
reaction zone under the temperature load inside the void. Generally, the ignition is a process in 55 which the energy of reaction zone increases with distance and the width of reaction zone decreases
with distance gradually till the width of reaction zone tends to a constant in state of stable
detonation. Although a large number of reports dealt with the experimental results of the width of
reaction zone in the process of stable detonation, few works focused on its varying in the process
of ignition. By analysis above, it is known that when the width of reaction zone close to the void is 60 less than that in state of stable detonation, combustion or detonation can not be initiated.
Width of reaction zone is the span from start section to finish section of chemical reaction
along to propagation direction. Since the chemical reaction close to void originates from heat
transfer of the temperature load in void, the responding zone width to temperature in void caused
by heat transfer can be considered to be the critical parameter. By using numerical simulation, the 65 response characteristics of energetic materials around void to the temperature load was discussed
in this work, the probability initiating combustion or detonation by temperature load in void was
analyzed, and a method to estimate the critical parameter initiating combustion or detonation was
proposed and proved by the designed experiment.
Ignition process was considered in the model. A void exists in energetic material and a 70 temperature load acts on the interface between void and energetic material. The temperature load
is ignition source. The ignition source in the void is called hot spot in the model. It is different
from traditional thermal explosion theory in which hot spot refers to a small volume of energetic
material with high temperature.
Two stages existing in the process initiating combustion or detonation were assumed in the 75 model. The first is transmitting of temperature load from void to energetic material. This is base
initiating combustion or detonation. The second is chemical reaction in energetic material
surrounding the void. The effect of chemical reaction surrounding the void on temperature inside
void was ignored in the model. That chemical reaction surrounding void occurs in a span of delay
time was assumed in the model.
80 1 Computational model of temperature response
Governing equation of heat transfer is given by 2? ?? 2 ? T T ?T & ? ? ++ q= ρ c λ2?r r ?r ?t ? ?
Where T is the temperature; ρ is the density of energetic material which is equal to 3 1470kg/mfor given energetic material in this work; c is the specific heat of energetic material
& 85 which is equal to 300 Jkg?; qis the heat produced by chemical reaction in unite mass of
energetic material in unite time. From the supposition of the model the effect of chemical reaction
in process of transmitting of temperature load from void to surrounding region was ignored, hence, 豆丁网地址！/msn369
?1?1?1& q= 0; λ is the heat conductivity which is equal to 0.21 JmsK. Boundary and initial conditions for Equations (1) are
90 r = aT , =f (t)
t = 0,T = T 0 Where a is the radius of spherical void, f(t) is a function of t, shown in Fig.1,Tis the initial0 temperature in energetic material. onsideration. The temperature In calculating, a spherical void of diameter 1mm is taken into c
load is exerted on the boundary of void. The aim is to clarify the responding regularity of 95 energetic material to temperature load in the void and probability initiating combustion or
detonation by the temperature load. 2 Response of energetic material around void to temperature The temperature acted on the boundary of void varying with time was shown in Fig. 1. Under
this boundary condition, the response process of energetic material around the void to temperature 100
was analyzed, and the temperature variations in energetic material around the void were given as shown in Fig. 2. From Fig. 2, it can be obtained that the maximum width of temperature distribution in the near region of void is about 10μm if the flash point for energetic material is equal to 230?C. Fig.1 Temperature load on boundary of void 105
110 s103μs 164μ 207μs 400μs Fig.2 Temperature distribution in energetic material around void
115 In the process of ignition the chemical reaction in energetic material close to the void is
driven by the temperature load in void. To reach a self-sustained state, the leading wave must rely on sufficient energy from the chemical reaction. The reaction zone supplies energy for the leading
wave. When chemical rate is given, amount of energy released in reaction zone increases with its width. If the temperature in the void is not high enough to cause an appropriate width of chemical
reaction zone in the surrounding energetic material through the heat transfer, ignition will not 120
occur. The zone width of response to temperature in energetic material around the void has relation to the temperature load inside the void. Performance of the temperature load includes peak
and duration of temperature load. When the duration is too short, it is impossible to form temperature response zone with width enough to initiate combustion or detonation. Therefore the
temperature response zone is the basis of the chemical reaction zone existing. 125
In Ref. , the reaction zone width of TNT, 0.135mm, was obtained by using velocity interferometer system (VISAR) technique. The width of detonation reaction zone was 1.75mm
and the duration of reaction process was 0.31μs for the JB-9014 explosive. The average width of reaction zone for the ultrafine TATB was 0.3mm.
The order of reaction zone width for the most condensed composite energetic materials is 130
?110mm. Fig.2 showed that the width of temperature response zone to the boundary condition -1shown in Fig.1 is far less than the order of 10mm. Therefore, it is impossible to initiate
combustion or detonation in energetic material around the void by temperature load shown in
135 3 Attenuation of temperature in energetic material Under boundary condition of action time 10μs and peak temperature 500?C, the temperature in energetic material changes with distance, as shown in Fig. 3(a). In this figure, curve 1 is the
emperature load on the boundary of void(a= 0.5mm), and curve 2 and curve 3 are temperature t responses in energetic material at the radii r = 0.503mm and r = 0.5061mm respectively. The
140 temperatures at the positions r = 0.503mm and r = 0.5061mm are far less than 230?C. According to flash point 230?C for the given energetic material in this paper, it can be estimated that rapid chemical reaction does not occur. The calculation result showed that the width of response zone to -1 high temperature, less than 3μm, was far less than the order of 10mm. therefore, the temperature load acted on the boundary of void in Fig. 3(a) can not initiate combustion or detonation in
energetic material. Similar conclusion can be drawn for Fig. 3(b) by use of analysis mentioned 145
Time/μs Time/μs (a) (b)
Fig. 3 Temperature load and its attenuation in energetic material
155 In Fig. 3(a) the temperature load acted on the boundary of void has peak value of temperature 500?C and holding time 10μs; In Fig. 3 (b) the temperature load acted on the boundary of void has peak value of temperature 1000?C and holding time 10μs; In Fig. 3 (c) the temperature load acted on the boundary of void has peak value of temperature 500?C and holding time 100μs; In Fig. 3 (d) the temperature load acted on the boundary of void has peak value of temperature 1000?C and holding time 100μs. In these Figures, curve 1 represents the temperature load on the boundary of void, and curves 2 to 6 are the temperature responses at positions r =0.503, 0.5061, 0.5091, 0.5122
and 0.5153mm respectively.
Furthermore, according to Fig.3, attenuation rule of peak value of temperature in energetic
material with distance was obtained:
a α = A(? r ?0.5153mm) T(0.5mm ) max r 165(2) is the peak where a denotes the radius of void; r is the distance to the center of void; T max
value of temperature response at position r; A and α are the constants depending on the peak value of temperature and the holding time of temperature load acted on the boundary of void; α is called attenuation component of temperature load with distance.
170 For Fig.3(c), A = 493 and α = 100 in equation (2) were obtained from fitting of peak values vs distance. For Fig.3(d), A = 493 and α = 67 in equation (2) were obtained from fitting of peak values vs distance. Similarly, when the peak value of temperature load is equal to1000?C, more results can be 175 obtained as follows. (i) the holding time 100μs, A = 965, α = 94; (ii) the holding time 200μs, A = 992, α = 71; (iii) the holding time 400μs, A = 973, α = 48; (iv) the holding time 600μs, A = 973, α = 39. In comparing above results with each other, it was found that the attenuation component α strongly depends on the holding time of temperature load. For given temperature load whose is
1000?C, the attenuation component varying with the holding time was list as shown in Table 1. 180 Table 1 Attenuation exponent varying with the holding time 100 200 400 600 Holding time, sμ 94 71 48 39 α
185 Attenuation components in Table 1 obey the following relationship. ?β (3) α = Bt h
is the holding time of temperature load in μs. In this equation, B = 95 and β = 0.498where th were obtained by least square fitting.
190 In an experiment to operate the physical simulation of thermal ignition, the peak temperature
depends on the method of ignition, such as spark. Otherwise, the holding time of temperature load can be controlled in some cases. In view of this, the temperature load with special physical
characteristics can be generated. It is the basic idea of physical simulation experiment for ignition, in which it is key to estimate the holding time of temperature. In equation (2), r = a +δ, where a is the radius of void and δ is the width of the chemical reaction zone in the energetic material. When a, δ and the holding time A are known, parameter α 195 can be determined if T is taken as the flash point of energetic material. Then, the holding time of temperature load in void can be obtained by using equation (2). For example, let δ = 0.1mm, a = 0.5mm, A =1000? and T= 230? (flash point), from max equation (2), there is α = 8.06. From equation (3) in which B = 95 and β = 0.498, there is t h =142μs. This example showed that the holding time of temperature load in void should be 142μs
δ = 0.1mmcorresponding to response zone width . In fact, the flash point is the ignition temperature when an temperature load holds several seconds. Generally the hot spot holds only a
hundredth of a second or even less. Therefore, the actual holding time of temperature load should 205 be larger than 142μs to initiate combustion or detonation for given energetic material in this example. In other words, when the holding time of temperature in void is less than 142μs, the combustion or detonation can not be initiated by the temperature load for given energetic material
in this example. Thereby, it provides an approach to estimate probability initiating combustion or detonation in energetic material by temperature load in void.
In the experiment carried out, the temperature load was at the order of a thousand degree.
210 Theoretically, the ignition should be an inevitable result, but it was actually not so. It failed in ignition. It is this phenomenon that urged us into doing further study for relevant issues to avoid not correct design for experiments. In the experiment, a system with a transient ignition device as shown in Fig. 4 was used. Its
block diagram was given as shown in Fig. 5. 215
Fig. 4 Transient ignition device
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for Measuring PC Measure d Hi gh Voltage DPO4054 Pri nter Object Probe Oscillograph Computer
220 Fig. 5 Block diagram of experimental system
In the process of ignition test, the voltage at both end of the wire and the electric current through the wire were controllable and measurable. The recordings of voltage and current in the
experiment were shown in Fig. 6. The energy released by the wire satisfies the following relation. 225
t0 E = U (t )i(t )dt ?0 (4) where E is the energy released by the wire, J; t is the time, s; U is the voltage at both end of
the wire, V; i is the electric current through the wire, A; and tis the holding time of energy 0 released by the wire, s.
In the experiment, the spark energy ranged from 0.00128J to 0.00357J, and the duration of 230 spark from 21μs to 27μs. The wire, made up of nichrome alloy of melting point 1455?C, with a circle cross section, is 60μm in diameter and 4mm in length. If the volume that the wire possesses ?143is regarded as that of hot spot, it is easy to calculate the volume of hot spot equal to 3.8×10?143m. The energy which acts on unit area of the hot spot (the volume of hot spot equal to 3.8×10m)is 豆丁网地址！/msn369
882235 ×10?9.39×10J/m. Although this experiment was repeated several times, no ignition was3.37 observed for the given energetic material. Fig. 6 Recordings of voltage and current in the experiment When the temperature reached 230?C, for the chosen energetic material combustion and detonation was initiated in slowly heating experiment. If this temperature, 230?C, is taken as the 240 critical parameter to the ignition, the energetic material should be ignited when the wire was fused.
However, no ignition happened in each of the experiments. It showed that in addition to the peak of temperature load, the holding time of temperature load is also an important parameter. One the
other hand, it also proved that the theoretical analysis to estimate probability initiating combustion
or detonation in energetic material around void was coincided with the experimental results. 245 4 Conclusion The local thermal source due to the void deformation in energetic material forms a
temperature load which may initiate combustion and detonation. The temperature-time history in the void was called temperature load in this work. Its peak value and holding time are the
necessary and sufficient condition initiating combustion or detonation of energetic material 250 surrounding the void. Compared with the energy acted on the unit area of the hot spot, performance of temperature load directly relates to the temperature distribution in surrounding region of void which can better serve to reflect the physical essence of ignition. The result derived from the energy acted on the unit area of the hot spot was not consistent with experimental results
in some case. This work presents a method to estimate probability initiating combustion and 255 detonation by temperature load in void.
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Materials, Combst. Flame89(1992)117-139  D.L.Bonnett,P.B.Butler. Hot spot ignition of condensed phase energetic materials[J],J. Propul. 260 Power,1996,12:680-690  J.E.Field,G.M. Swallowe,S.N. Heavens.Ignition mechanism ofexplosion during mechanical deformation[J],Proc. R. Sco.London Ser. A.,1982,382:231-244  M.M.Chaudhri,J.E.Field.The role of rapidly compressed gas pockets in the initiation of condensed explosives[J],Proc. R.Sco.London Ser.A.,1974,340:113-128. 265  N.K.Bourne, J.E.Field.Shock indued collase of single cavities inliquids[J].J. Fluid Mch., 1992,244:225-240
275 张奇 ？北京理工大学爆炸科学与技术国家重点实验室，北京 100081？ 摘要！发射 过程中，物理作用在战斗部装药内形成局部高温“热点”，“热点”是引起早炸或膛 炸的危险 源。研究“热点”引发早炸或膛炸事故的物理机制，是战斗部发射安全性研究中核心 问题。本 文通过理论分析和数值模拟，研究“热点”瞬态温度载荷在近区内的温度响应，研究 “热点”瞬
态温度载荷特性对近区温度响应的影响规律。研究表明“热点”边界单位面积上的能 量及其280 瞬态温度载荷的作用时间是“热点”起爆两个不可缺少的指标。给出“热点”起爆临界参 数的估