Effects of nano-sized aluminum on detonation characteristics and metal acceleration for RDX-based aluminized explosive

Dn-yng Liu ,Pin Zho ,Serene Hy-Yee Chn ,Huey Hoon Hng ,Lng Chen ,*

a State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology,Beijing,100081,China

b School of Materials Science and Engineering,Nanyang Technological University,639798,Singapore

Keywords:Nano-sized aluminum Detonation reaction zone Explosive metal acceleration Thermodynamic equilibrium calculation Laser interferometry

ABSTRACT Nano-sized aluminum(Nano-Al)powders hold promise in enhancing the total energy of explosives and the metal acceleration ability at the same time.However,the near-detonation zone effects of reaction between Nano-Al with detonation products remain unclear.In this study,the overall reaction process of 170 nm Al with RDX explosive and its effect on detonation characteristics,detonation reaction zone,and the metal acceleration ability were comprehensively investigated through a variety of experiments such as the detonation velocity test,detonation pressure test,explosive/window interface velocity test and confined plate push test using high-resolution laser interferometry.Lithium fluoride(LiF),which has an inert behavior during the explosion,was used as a control to compare the contribution of the reaction of aluminum.A thermochemical approach that took into account the reactivity of aluminum and ensuing detonation products was adopted to calculate the additional energy release by afterburn.Combining the numerical simulations based on the calculated afterburn energy and experimental results,the parameters in the detonation equation of state describing the Nano-Al reaction characteristics were calibrated.This study found that when the 170 nm Al content is from 0% to 15%,every 5% increase of aluminum resulted in about a 1.3%decrease in detonation velocity.Manganin pressure gauge measurement showed no significant enhancement in detonation pressure.The detonation reaction time and reaction zone length of RDX/Al/wax/80/15/5 explosive is 64 ns and 0.47 mm,which is respectively 14% and 8% higher than that of RDX/wax/95/5 explosive(57 ns and 0.39 mm).Explosive/window interface velocity curves show that 170 nm Al mainly reacted with the RDX detonation products after the detonation front.For the recording time of about 10μs throughout the plate push test duration,the maximum plate velocity and plate acceleration time accelerated by RDX/Al/wax/80/15/5 explosive is 12%and 2.9μs higher than that of RDX/LiF/wax/80/15/5,respectively,indicating that the aluminum reaction energy significantly increased the metal acceleration time and ability of the explosive.Numerical simulations with JWLM explosive equation of state show that when the detonation products expanded to 2 times the initial volume,over 80%of the aluminum had reacted,implying very high reactivity.These results are significant in attaining a clear understanding of the reaction mechanism of Nano-Al in the development of aluminized explosives.? 2021 China Ordnance Society.Production and hosting by Elsevier B.V.on behalf of KeAi Communications Co.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

Ideal explosives like RDX,HMX,CL-20,with high detonation velocities and pressures have strong metal accelerating abilities,but the shock energy declines rapidly in open air or water.It is well known that the addition of aluminum powders to these explosives can increase the total reaction energy and enhance the overall blast performance[1-3].Aluminum particles are widely used in the micrometer range sizes and were found to be able to enhance the late work output of explosives by combustion in explosive products turbulence(through calorimetric heat of detonation test or underwater test[4])or afterburn in the air(through air blast effect test[5]).However,for the detonation velocity,detonation pressure,and metal accelerating ability of explosives which are mainly determined by density,energy release rate and its efficiency on supporting detonation wave propagation,they are usually reduced in aluminized formulations.For example,the increase of 20μm aluminum content from 0%to 30%in RDX-based explosives resulted in about 5% decrease of detonation velocity[6].By comparing explosives containing aluminum and lithium fluoride(an inert substitute for aluminum),cylinder test showed that the detonation velocity of aluminized explosive HMX/Al(3.2μm)/GAP/FomblinD/Isonate/69/15/7.5/7.5/1 was similar to that of HMX/LiF(5μm)/69/15 explosive[7].Due to the extremely short detonation reaction zone(less than 200 ns for most of high energy explosives[8])of ideal explosives,it is widely presumed that most of the aluminum particles react with the ensuing detonation products only after the detonation front[9,10].For the last 20 years,there has been immense research interest in understanding if the aluminum reaction contributes to the early work output of explosives[11-13].By using submicron aluminum(Nano-Al)particles mixed with explosives,researchers aim to develop a new kind of aluminized explosive in which the metal acceleration ability and the late blast energy can be enhanced simultaneously by the aluminum reaction.It is inspired by findings that the smaller the particle size of aluminum,the earlier it begins to react and the faster its reaction rate[14,15].Through cylinder test and JAGUAR thermochemical equilibrium code calculation result,Stiel et al.[16]found that when the size of aluminum particles is over 50μm,the aluminum begins to react only if the expansion volume of the detonation products is 12 times the initial volume.Conversely,Baker et al.[17]found that when the size of aluminum particles is less than 10μm,the aluminum could be fully reacted within 7 times the product expansion volume,which may significantly increase the metal acceleration ability of the aluminized explosive.However,smaller particle sizes do not correlate to a stronger enhancement of metal acceleration ability.Works on detonation velocity test,plate push test and cylinder test for explosives containing Nano-Al from Gogulya et al.[18,19]and Balas et al.[20]suggest that the presence of the Al oxide layer on the surface of the particles needs to be considered.Nano-Al has a thicker oxide film,resulting in lower activity,for example,the active content of 40 nm aluminum may be only 70%.Hence,the presence of the oxide layer will limit the acceleration potential of aluminum.In addition,encouraged by the observation that the early reaction of nano-powders can increase the burning rate of propellants,whether the Nano-Al can participate in the detonation zone is of great interest.TNT explosive mixtures with Nano-Al have reportedly showed a slight increase in detonation velocity as compared to micron-size aluminum[14,21],indicating that Nano-Al may have reacted in the detonation reaction zone.Conversely,studies on explosives such as BTNEN[17],HMX[18]and CL-20[22]indicate that there is no obvious enhancement of detonation parameters when mixed with Nano-Al.Baker et al.[23]calculated the detonation velocities with different aluminum reaction degree using JAGUAR thermochemical equilibrium code and then compared the calculation results with experiments to determine the aluminum reaction in detonation reaction zone.In their calculations,because the aluminum reaction reduces the total moles of gas products,the higher Al reaction degree in detonation reaction zone may induce a lower detonation velocity[24].For most of the explosives they studied,including mixture with three kinds of 100 nm-500 nm aluminum,the measured detonation velocity is similar to the calculated result for inert Al,indicating that aluminum does not react at detonation zone[25].Liu et al.[22]studied the detonation reaction zone length of aluminized CL-20 by measurement of explosive/window interface particle velocity.The authors found that the 200 nmaluminum surprisingly resulted in a significant increase in CL-20’s detonation reaction length which could be explained by the aluminum reaction in the detonation reaction zone.However,the lower particle velocity indicates that the reaction degree is low.It can be seen that studies on the effect of Nano-Al on detonation parameters are still limited with conflicting results.Studies on HMX/Al/85/15 and BTNEN/Al/85/15[26]showed that the detonation velocity slightly decreased with the replacement of micro-size aluminum to Nano-Al,whereas that of TNT/Al/90/10 slightly increased.Gonthier et al.‘s[6]found that when the aluminum content is 10%,there is no significant effect on detonation velocity of RDX-based explosives comparing 50 nm and 100 nm aluminum with 20μm aluminum.However,when the content increased to 30%,50 nm aluminum significantly decreased the detonation velocity,which may result from the increasing importance of oxide passivation.The short reaction time scale of Nano-Al and its early behavior near detonation reaction zone makes it difficult to experimentally investigate its reaction characteristics.

This work seeks to study the effect of Nano-Al on detonation characteristics of RDX explosive and the metal acceleration ability at the early stages of detonation.Through high-resolution laser interferometry techniques and a series of small-scale tests including explosive/window interface-particle-velocity test and confined plate push test,the detonation velocity,detonation pressure,detonation reaction-zone-length,and metal acceleration ability were comprehensively investigated.A thermochemical approach taking into account the reactivity of aluminum and the resulting detonation intermediates and products was adopted to calculate the additional energy release by afterburn.Combined with the experimental results and thermochemical calculations,the Jones-Wikins-Lee-Miller(JWLM)[27,28]equation of state(EOS)of the detonation products were calibrated for aluminized RDX in which the Al particle size is circa 170 nm.The afterburn reaction of 170 nm aluminum in relation to the volume expansion of products was further analyzed.

2.Materials and experimental methods

RDX-based aluminized explosives mixed with 5 wt%,10 wt%and 15 wt% aluminum content were investigated.Because lithium fluoride(LiF)is inert during explosive detonation,and has similar physical properties to aluminum,it can be treated as inert aluminum[29].Thus,to isolate the effect and to analyze the time dependence of the reacting aluminum in the explosives,the aluminum was replaced by LiF in some of the explosives,which acts as control.The SEM image of the aluminum powder and its particle size distribution obtained by laser diffraction analyzer(Malvern Mastersizer 2000)are shown in Fig.1.It can be seen that the aluminum particles are spherical with particle sizes of about 170 nm(90%of the particles are less than 200 nm).This particle size is chosen prudently because if the size of aluminum particle is too small,it may have a thicker oxide layer which will lower the active Al content and effective reaction mass.The thickness of oxide layer here is about 3-4 nm detected by Transmission Electron Microscopy(TEM with a resolution of 0.17 nm)and the calculated active content of aluminum based on it is nearly 85%[30,31].The paraffin wax was used as a binder with a melting point of about 58°C.Solid RDX grains under 100μm,170 nm Al particles or LiF(particle size 11μm),and wax are mixed together and then pressed into cylinder charges under 1000 bars.The explosive formulations include RDX/Wax(95/5),RDX/Al/Wax(90/5/5),RDX/Al/Wax(85/10/5),RDX/Al/Wax(80/15/5)and RDX/LiF/Wax(85/10/5),RDX/LiF/Wax(80/15/5),in which the explosive with 15% aluminum was mainly studied.

Pertinent detonation parameters such as detonation velocity and pressure were first experimentally determined to investigate the effect of aluminum on the propagation of the detonation wave.Detonation velocity was measured by ionization pins[32]and the detonation pressure was measured by manganin pressure gauges[33].The schematic and experimental apparatus for the measurement of detonation velocity is shown in Fig.2.In the experiment,the RDX-based explosives were pressed to cylindrical charges with a diameter of 20 mm and a thickness of 20 mm.These test charges were initiated by a booster charge made of JO-9159(95 wt%HMX,5 wt%binder)explosive with a diameter of 20 mm and a thickness of 20 mm.The booster was initiated by an electrical detonator and was found to provide over 30 GPa of initiating pressure to the RDXbased explosive.This high input pressure led to a reliable detonation of our experimental samples.The embedded pins were used to record the arrival time of the detonation wave during propagation so as to determine the detonation velocity.The uncertainty on attained detonation velocity is about 0.2% with a charge surface irregularity of 0.02 mm[32].Similarly,in detonation pressure tests,the setup of booster and RDX-based explosive charges are described in Fig.3.The H-shape foil-like manganin piezoresistive gauges were used to measure pressure during detonation,in which the measuring range is 2-53.5 Gpa and the thickness is 10μm[33].The manganin gauge was embedded at 80 mm away from the interface of the booster and the tested charge so as to capture the steady detonation pressure history.During the test,the relative changes of the resistance R/R0can be obtained from the voltage output of the manganin gauges asΔU/U0.The relationships between the pressure(P)and the relative resistance change of the gauge were:

Fig.1.SEM image of the aluminum powder(Left)and Aluminum particle size distribution(Right).

Fig.2.Schematic of detonation velocity test(a)and experimental apparatus photograph(b).

Typical voltage output signal of manganin gauge is shown in Fig.3b.Invalid signal peaks after 7.7μs were removed.The reference voltage(U0)was determined as the average value before the sharp increase in voltage.Based on Eq.(1),the voltage change can be converted to pressure change.The peak pressure(voltage)attained was considered as the detonation pressure.The maximum relative deviation of the peak pressure value is less than 3%[33].

To investigate the effect of aluminum on the detonation wave structure and detonation reaction zone characteristics,interfacial particle velocities at the explosive/window interface were measured via interferometric measurements.This method has been proven to be successfully used to detect the reaction zone length of explosive[22,34].The schematic diagram of the experimental setup is shown in Fig.4.The RDX-based charges under test was with 20-mm-diameter and 20-mm-thickness which were initiated by JO-9159 charges,as reported in the earlier section.A 20-mm-diameter,10-mm-thick transparent LiF window was placed next to the explosive charge.A 600-nm-thick aluminum film vacuum-coated on the window surface was connected to the explosive to provide a reflective surface for the laser light.A DISAR(Displacement Interferometer System for Any Reflector)laser interferometer[35]was used to measure the explosive/window interfacial particle velocity history by converting the laser interferometer signal into velocity based on the Doppler-shift principle.The DISAR was triggered by an electric probe sandwiched between the booster and the explosive.The time resolution of the measurement system was 5 ns

To investigate the contribution of aluminum reaction to metal acceleration and the reaction characteristics,a unique confinedplate push test,as proposed in our earlier work[36],was used to investigate the metal acceleration ability for aluminized explosive.The sectional view of the apparatus is shown in Fig.5.The cylindrical test explosive with 40 mm diameter and 40 mm thickness was placed in a half-closed steel cylinder with thickness of 10 mm.One end of the explosive was glued to the closed end of the cylinder and the other end was adjacent to a copper plate with thickness of 1.5 mm.A plane-wave lens and a booster explosive were used to initiate the tested explosive.When ignited,the detonation products were confined in a space enclosed by the cylinder and the plate,then accelerated the plate during expansion.The DISAR was deployed to measure the velocity of the metal plate using a time resolution of 10 ns to continuously record the changes in the metal plate velocity.The digital storage oscilloscope was triggered by an electronic probe sandwiched between the plane wave lens and the booster explosive.This design has been successfully used in the investigation of CL-20-based aluminized explosives.The calculated high-pressure maintaining time of the detonation products by the strong confinement is about two times that of the conventional cylinder test[36].Because the reaction between aluminum particles and detonation products correlates positively with expansion pressure,and as a result of strong confinement,the reaction of aluminum was enhanced and the reaction characteristics could be better observed.

Fig.3.Schematic of detonation velocity test(a)and voltage signal outputted by manganin gauge from RDX/Al/wax/80/15/5 explosive(b).

Fig.4.Schematic of the experimental arrangement for measurement of explosive/window interfacial velocity.

Fig.5.Sectional view of the experimental apparatus for confined plate push test.

3.Experimental results

3.1.Detonation velocity and pressure of RDX-based explosive containing Nano-Al

The measured detonation velocities(D)and detonation pressures(PCJ)of RDX-based explosives containing different content of Nano-Al particles as well as that with LiF are listed in Table 1.The calculated detonation parameters by thermochemical equilibrium code,EXPLO5[37]were also given in the table.

From Table 1,it can be seen that the%TMD of different explosive formulations are around 97% which suggests that their detonation parameters could be comparable.However,as the density of the aluminized explosives increased due to the addition of more aluminum powder,the detonation velocity consequently decreased.The relationship between detonation velocity and 170 nm nano al content is shown in Fig.6,which can be described by the linear function given by Eq.(2):

where D is detonation velocity(m/s),cAlis the content of the Nano-Al(%).It can be shown from Fig.6 that a 5% increase of Nano-Al content resulted in about 1.3% decrease in detonation velocity.

The detonation pressures of aluminized explosive decreased with an increase in aluminum content.When the aluminum content is 15 wt %,the detonation pressure was measured to be 26.94 GPa,which is only slightly lower(about 0.7%)than that of the non-aluminized explosive(27.21 GPa).This could be attributed to the higher density of the aluminized explosive.When LiF,which is inert,was used in place of aluminum,the measured detonation velocities and pressures of RDX/Al explosives were found to be a slightly lower to that of the RDX/LiF explosives.These results indicate that the Nano-Al powder was essentially inert and not contributing to the propagation of the detonation wave.Similar results were also found in Gogulya’s[26]and Gonthier’s[6]work where detonation velocity of explosives containing Nano-Al was lower than that of explosives containing micron-sized aluminum or LiF.It may attribute to the higher thickness of the oxide layer of Nano-Al.The calculated detonation velocity and pressure and their variation with aluminum content are similar to the experimental results.The maximum error is less than 3%.The main difference lies in LiF-containing explosives,which may be because the inert behavior of aluminum or LiF has not been accurately described in theory so far.

3.2.Detonation reaction zone characteristics of RDX-based explosive containing Nano-Al

The detonation reaction zone of explosives such as(i)RDX without aluminum(ii)RDX-based explosives containing 15 wt%Nano-Al,and(iii)RDX-based explosives containing 15 wt%inert LiF were investigated through the explosive/window interfacial particle velocities test.Fig.7 shows the interfacial particle velocity profile obtained for the non-aluminized explosive(RDX 95 wt%Wax 5 wt%).The DISAR successfully recorded the interfacial particle velocity between explosive and window.The observed profile structure is consistent with the features of the Zel’dovich-Neumann-D¨oring(ZND)model,which comprises of an initial spike caused by shock front,followed by a rapidly decreasing phase corresponding to the detonation reaction zone.Then the interface velocity slowly declined,indicating the expansion phase of detonation reaction products(influenced by Taylor wave).The Chapman-Jouget(CJ)point,an indicator of the end of detonation and the beginning of product expansion,is key to analyze the structure of the detonation wave.However,the absence of a distinct transition point on the velocity curve,corresponding to the CJ point,makes it difficult to distinguish the detonation reaction zone directly.Much work has been reported to identify the CJ point,but most of them require a large amount of tests[38]or complicated calculations with a well-known equation of state of detonation products[39].Here,we used a simple two-function fitting method proposed in our previous study on aluminized explosive to estimate the CJ point based on only one velocity profile[22].Its accuracy has been verified by comparing with other commonly used methods[22].

Table 1Detonation parameters of RDX-based explosives containing different 170 nm nano al content or LiF content.

Fig.6.Detonation velocity of RDX-based explosives at different aluminum content.

Fig.7.Interfacial velocity profile for 1.675 g/cm3 RDX/Wax/95/5 explosive.

In this method,the interfacial particle velocity profile up(t)before the CJ point(tCJ)was fitted by the exponential function,for t≤tCJ:

After the CJ point,up(t)was fitted by the polynomial function to describe the expansion of detonation products,for t≥tCJ:

where u1,u2,u3,u4,u5,andτare fitting parameters at the point tCJ.

The intersection of the two fitting curves are determined as the CJ point,where Eqs.(3)and(4)can be equated and have equal values at the CJ point.A fit to the experimental data for the 1.675 g/cm3RDX/Wax/95/5 explosive is shown in Fig.8.The two functions provide a good fit to the velocity history.

After locating the CJ point on the velocity profile,the reaction zone length x0could be calculated according to the ZND model assumption that the shock wave front and the reaction zone propagate along the detonated explosive at detonation velocity D:

Fig.8.Functional fits to the experimental data for the 1.675 g/cm3 RDX/Wax/95/5 explosive.

The CJ pressure PCJcan be calculated from the particle velocity upCJat the CJ point according to the Hugoniot of LiF window[40]:

whereρm0is the initial density of the LiF window(2.638 g/cm3).The uncertainty for obtained reaction time is about±5 ns as shown in reference[22],resulting in uncertainties for reaction zone length and CJ pressure of±0.02 mm and±0.05 Gpa,respectively.

Table 2 lists the deduced reaction zone parameters for both the aluminized and non-aluminized RDX-based explosives.It can be seen that the reaction time for RDX/Wax/95/5 explosive is about 57 ns with a reaction zone length of about 0.39 mm,which is in good agreement with the 60 ns reaction time reported by Loboiko et al.[8]The addition of 15 wt% of 170 nm aluminum powders slightly increased the reaction time to about 64 ns as well as the reaction zone length to about 0.42 mm,implying 14%and 8%increase in the reaction delay and zone length,respectively.In contrast with micron-sized aluminum powder which may significantly increase the reaction time and reaction zone length of explosive,the effect of 170 nm aluminum powders was found to be insignificant when present in small amounts.The calculated CJ pressure using this method is slightly lower than that obtained by the pressure gauge.This could be due to the fact that the pressure curve measured by the manganin gauge could not clearly distinguish the reaction structure of the explosive,and hence the pressure peak was assumed to be the detonation pressure.However,because of the nanosecond resolution of the manganin gauge,the pressure peaks are likely to be between the von Neumann and CJ point,so the detonation pressure obtained by the manganin gauge is higher than the calculated pressure.

Table 2Reaction zone parameters for RDX-based explosives.

Fig.9 plots the interfacial particle velocity profiles for both aluminized and non-aluminized RDX/Al explosives as well as RDX/LiF explosive.It can be seen that the three velocity curves are very close to each other.The interface velocities are ranked as follows:RDX/Wax/95/5 explosive＞RDX/Al/80/15 explosive＞RDX/LiF/80/15 explosive.The overlapping of the three profiles indicates that the aluminum may react in 1μs after the CJ point,but the extent of reaction is low[22].

Fig.9.Interfacial velocity profiles for RDX/Al and RDX/LiF explosive.

3.3.Metal acceleration ability and aluminum reaction of RDXbased explosive containing Nano-Al

The metal acceleration ability of explosives(i)RDX-based explosives containing 15 wt% Nano-Al particles and(ii)RDX-based explosives containing 15 wt% inert LiF were investigated through the confined plate push test.The velocity profiles of the copper plate accelerated by the 1.681 g/cm3and 1.683 g/cm3RDX/LiF/wax/80/15/5 explosives are plotted in Fig.10.The DISAR recorded the velocity changes clearly and continuously.The two history profiles are practically overlapping,indicating good repeatability of the experiments.The velocity of the copper plate rapidly accelerated to 1430 m/s and then increased with oscillations,indicating a shock wave reflected inside the copper plate.As the oscillation amplitude decreased,the velocity reached its maximum value of 2414 m/s at about 8μs after the plate was accelerated.

Fig.10.The velocity profiles of the copper plate accelerated by the 1.681 g/cm3 and 1.683 g/cm3 RDX/LiF/wax/80/15/5 explosives.

Fig.11 plots the plate velocities for the RDX/Al explosives and the RDX/LiF explosive.Table 3 shows the maximum velocity of the plate accelerated by the different RDX-based explosives.Comparing the curves,the effect of the reaction energy from the aluminum powder on the acceleration ability of the explosive can be clearly observed.Obviously,the velocities of the aluminized explosives increased beyond that of RDX/LiF.The measured maximum velocity of 1.746 g/cm3RDX/Al/wax/80/15/5 is about 12%higher than that of RDX/LiF/wax/80/15/5 explosive.The difference maybe higher because the velocity of RDX/Al/wax/80/15/5 was still increasing.For the RDX/LiF/wax/80/15/5 explosive,the plate reaches 99% of the maximum velocity at about 6μs,whereas the plate velocity of RDX/Al/wax/80/15/5 kept increasing until the end of recording time(8.9 μs for 1.746 g/cm3),indicating at least 2.9μs(48%)increase of acceleration time for aluminized explosive compared to nonaluminum explosive.It implies that the reaction energy of Nano-Al could be used to enhance the metal acceleration ability of explosives at microsecond timescale.Higher plate velocity could be correlated with higher degrees of aluminum reaction.In addition,the velocity profiles of the two aluminum-containing explosives implies that the higher density explosives show a higher acceleration ability.

Fig.11.Plate velocity vs.time for the RDX/Al and RDX/LiF explosives.

Table 3Maximum velocity of the plate accelerated by different RDX-based explosives.

There is a simple but classical theoretical method reported in Ref.[41]to calculate the aluminum reaction fraction based on metal acceleration results of aluminized and LiF-containing explosives.For RDX/LiF explosive,LiF did not participate in the plate acceleration,so the plate was driven only by the explosive energy of RDX.However,in the RDX/Al explosives,other than the detonation energy of RDX,the aluminum reaction clearly contributed to the plate acceleration.Thus,by comparing the velocity history of the RDX/Al explosives with that of the RDX/LiF explosive,the extent of the aluminum reaction with time could be inferred and analyzed.The energy that the aluminum reaction contributes to theplate acceleration(ΔE)can be given by:

where mpis the mass of the copper plate,and uAland uLiFare the velocity contributions of the metal plate driven by the RDX/Al explosives and RDX/LiF explosives.

ΔE can also be described as[41]:

where QAlis the heat of aluminum oxidation(20.126 MJ/kg,the heat of reaction between aluminum and CO2with products of Al2O3and solid carbon),meis the quality of RDX/Al explosives(around 85 g),αis the mass fraction of aluminum in the RDX/Al explosives,andλ(t)is the mass fraction of the reacted aluminum.ηis the efficiency of the plate acceleration,describing how much energy can be converted to kinetic energy of the plate as described in Eq.(9).It is the ratio of maximum kinetic energy of the plate Ekand the entire energy that an explosive could release after a full reaction(heat of explosive)Qexp.

Based on the RDX/LiF/80/15 explosive result,the maximum plate velocity was 2414 m/s and the corresponding Ekis 49.2 kJ.Since the heat of detonation of RDX is 5600 kJ/kg[41]and effective mass percentage is 80%,the Qexpshould be 378.768 kJ.Therefore,η was estimated to be 0.13.

According to Eqs.(7)and(8),the reaction fraction of aluminum can be calculated by:

Using this method,the derived time evolution of the mass fraction of reacted aluminum for 170 nm aluminum in 1.746 g/cm3RDX/Al/80/15 explosive is plotted in Fig.12.The degree of reaction started from about 5 wt% and then increased.This is in good agreement with the above observation in the explosive/window particle velocity test,verifying the 170 nm aluminum started to react with detonation products within 1μs after detonation.The difference is that the aluminum reacted earlier in the plate push test,which we think may be attributed to the stronger reflection of the copper plate than that of the LiF window.The aluminum reaction rate gradually decreased with time and the expansion of detonation products.After 5μs,the mass fraction of reacted 170 nm aluminum was about 35%.The result was compared with that of 200 nm and 16-18μm aluminum in CL-20/Al/80/15 explosives from our previous study[36]using the same experimental setup and analysis method.It can be seen that as compared to micronsized aluminum,Nano-Al advanced the aluminum reaction start time and improved the degree of aluminum reaction.The reaction extent of 170 nm aluminum in RDX/Al explosive is higher than that of 200 nm aluminum in CL-20/Al explosive,which may be attributed to the smaller particle size and longer reaction time of RDX(about 60 ns)than that of CL-20(about 40 ns).The aluminum particles may absorb more energy in a longer detonation period,which facilitates the subsequent reaction between aluminum and the detonation products.

Fig.12.Mass fraction of reacted aluminum for 170 nm aluminum in RDX/Al explosive and 200 nm and 16-18μm aluminum in CL-20/Al explosive[36].

4.Afterburn energy release calculation for Nano-Al and RDX explosive

A 2D confined plate push test model was constructed to simulate the afterburn reaction between 170 nm aluminum and RDX explosive.The JWLM EOS[27,28]considering the time-dependent aluminum reaction was used to describe the detonation products.The reaction characteristics parameters of 170 nm aluminum could be calibrated by comparing simulated results with experiments.

The JWLM EOS is given by:

JWLM is a modification of the standard Jones-Wikins-Lee(JWL)EOS for ideal explosives.In the equation,excluding energy from the detonation of the explosive E0,λQ is added to describe the additional energy released by aluminum reaction,whereλrepresents the extent of Al reaction and Q represents the additional energy of the aluminum reaction.The reaction rate was taken to be dependent on pressure and reaction fraction according to Equation(12):

In Eq.(12),a,m and n are aluminum reaction parameters.

4.1.Thermochemical approach to model additional energy release(Q)

Knowledge of the additional energy release from aluminum reactions,Q,is the first step in understanding and calibrating the EOS of aluminized explosives.Usually,the energy is simplified by the heat of aluminum oxidation from Eq.(13):

In reality,the afterburn process involves much more complex chemistry,such as the reactions between reactant intermediates,detonation products and aluminum,such as:

Here,to more accurately describe the afterburn energy,a twostep thermochemical approach is taken.Firstly,an ideal detonation calculation of the main explosive RDX is performed to predict the composition of the detonation products.Then,the combustion characteristics of aluminum and explosive detonation products are determined assuming thermochemical equilibrium in a constant volume.Since heat losses are not accounted for,the combustion energy can be taken to be the afterburn energy.EXPLO5[37]is employed to perform the above calculation.The loading density for the combustion calculation is taken to be low at 0.001 g/cm3since the reactants are mostly gaseous products from the detonation of RDX.An ideal detonation run for RDX/wax/95/5(by wt.%,1.675 g/cm3)was first conducted to yield the detonation energy released solely from the explosive and to determine the reactants for further reaction with aluminum.Theoretically,explosions in a confined geometry do not appear to remain in chemical equilibrium throughout their entire expansion.The reaction between aluminum and explosive is also affected by the detonation product species,pressure,and subsequent interaction with reflection waves.It can be concluded from the above test that the aluminum starts to react with the RDX detonation products as soon as the end of detonation reaction.Thus,the composition of the products at CJ point was considered as the initial reactants which the aluminum powders react with.In fact,due to the lower impedance of the explosive,in the interfacial velocity test and plate push test,the interface between the explosive and the window or cooper plate reflects a shock wave,which induces a higher pressure environment than CJ detonation and may affect the reaction pathways between aluminum and detonation products.Since the overall aluminum afterburn energy is required and the high pressure will decrease during the expansion process,the reflection effect was not considered here.Following the ideal detonation calculation,the next step is to determine the species and amount(percent composition)of products that may react with aluminum.Table 4 gives the detonation product composition of RDX/wax explosive at CJ point and the mass% of the dominant species per mass of explosive.The products mainly comprise N2,H2O,carbon and so on.Not all of the products will react with aluminum.For example,the C(d)and C(gr)refer to carbon with diamond and graphite structures respectively,which were considered stable and would not react with aluminum.Thus,to simplify the calculation,eight dominant product species(CH2O2,CH4,CO,CO2,H2,H2O,N2and NH3)that are more likely to react with aluminum were chosen to calculate the aluminum reaction energy.The last column shows the mass percentage of these dominant species with respect to the explosive formulation RDX/Al/wax/80/15/5.In addition,for 170-nm Nano-Al,the reactivity of the aluminum was considered as about 85%,which means the mass percentage of the aluminum that can react with the detonation products is about 12.75%for RDX/Al/wax/80/15/5 explosive.It can be seen that after detonation,76.93%of the product mix arising from the detonation of RDX is likely to react with 12.75% of reactive aluminum.These product species and corresponding ratios were then considered as inputs to an isochoric combustion run in EXPLO5.

In the ideal situation,we want the products to be fully oxidized and in thermal equilibrium.Hence,stable products such as CO2,N2,H2O,and C(gr)should be included,in order to achieve convergence and minimize numerical errors.The products database also include possible aluminum-based products such as Al(l,liquid),Al(s,solid),AlO,Al2O,Al2O2,Al2O3(l,liquid),Al2O3(s,solid),AlOH,AlH,AlN,AlN(s,solid),Al4C3(s,solid).The heat of combustion from the isochoric combustion of the 8 dominant detonation product species with the aluminum(equals to Q)was found to be 2133.42 kJ/kg of RDX/Al/wax/80/15/5 after normalization.This value is equal to the heat of reaction per kilogram of aluminum of 17.785 MJ,which is lower than the energy used in Eq.(8)(20.126 MJ/kg).It may be because,in the EXPLO5 prediction,aluminum mainly reacts with explosive products such as CH2O2,CO2and H2O,among which CH2O2is completely consumed,CO2consumes 45%,H2O consumes 32%,and the main products are Al2O3,CO and H2.The abovementioned reaction heat is lower than that of the reaction used in Eq.(8):aluminum and CO2to produce alumina and solid carbon.The above described a methodology for calculating the additional energy release,Q,in Eq.(11).It is important to note that the above thermochemical calculations are based on the following assumptions:

(a)Only the initial and final states of the reaction(detonation+afterburn)are considered without detailed reaction chemistry of the intermediates.

(b)Enough time is available for reactions and full oxidation to take place(CO is not considered in the combustion products).

Table 4Products from detonation of RDX/wax(inputs to EXPLO5 for afterburn calculation).Last column shows the mass percentage of the dominant species that more likely to react with aluminum.

4.2.Calibration of Nano-Al reaction parameters

After obtaining the additional energy of afterburn Q,the other parameters describing aluminum reaction rate a,m and n of Eq.(12)can be calibrated according to the plate push test results.During calibration,the plate velocity history of the RDX/LiF/wax/80/15/5 explosive was first used to determine the parameters of the JWL part in the JWLM EOS to describe the detonation of RDX.Based on that,the parameters of additional energy release termλQ were calibrated from the velocity curve of the RDX/Al/wax/80/15/5 explosive.Table 5 lists the calibrated parameters of the aluminum reaction.Fig.13 plots the calculated and experimental plate velocity profiles for RDX/Al/wax/80/15/5 and RDX/LiF/wax/80/15/5 explosives.It can be shown that the calculated velocity histories based on the calibrated JWLM parameters are in good agreement of both RDX/LiF/wax/80/15/5 and RDX/Al/wax/80/15/5 explosives,indicating that parameters in Table 5 can accurately describe the aluminum reaction and its contribution to metal acceleration.Fig.14 shows the calculated reaction fraction of 170 nm aluminum(λ)with expansion of detonation products(V/V0).It can be seen that when the explosive has expanded to about 2 times of the initial volume,more than 80 wt % of the aluminum have reacted,indicating a very high reactivity of 170 nm aluminum powder.

Table 5170 nm aluminum reaction parameters of JWLM EOS for RDX/Al/wax/80/15/5 explosives.

Fig.13.Calculated and experimental plate velocity profiles for RDX/Al/80/15 and RDX/LiF/80/15 explosives.

Fig.14.Calculated reaction fraction of 170 nm aluminum vs.time.

5.Conclusions

To investigate the effect of an non-ideal,late-burning component such as Nano-Al in explosives,a large number of small scale experiments for RDX-based explosives containing 170 nm aluminum have been conducted and results compared with that from a theoretical approach based on thermochemical equilibrium calculations and numerical methods with experimental calibration.Lithium fluoride(LiF)was used as a control to compare the contribution of the reaction of aluminum.Detonation velocity and pressure were measured,showing no enhancement of 170 nm aluminum on the detonation parameters.Every 5% increase of 170 nm aluminum resulted in about a 1.3% decrease in detonation velocity The particle velocities of aluminized and non-aluminized explosives were measured via interferometric measurements at the explosive/window interface,which is an effective way to investigate the detonation wave structure and early detonation energy release.The detonation reaction time and reaction zone length of RDX/Al/wax/80/15/5 explosive is 64 ns and 0.47 mm respectively.In contrast with micron-sized aluminum powder which may significantly increase the reaction time and reaction zone length,the addition of 15 wt % 170 nm aluminum powders induced a respectively 14% and 8% increase of reaction time and zone length compared to RDX/wax/95/5 explosive.Showing insignificant effects.The 170 nm aluminum may begin to react with the explosive products in the first 1μs after detonation but the extent of reaction and its effect on product particle velocity is negligible.A confined plate push plate test was conducted in which the confinement was stronger than that in standard cylinder tests in order to maintain pressure and promote the afterburning reactions of aluminum with detonation products.Plate velocities obtained by laser interferometry techniques showed that the 170 nm aluminum mainly reacted with detonation products after the CJ point.The maximum plate velocity of RDX/Al/wax/80/15/5 explosive is 12%higher than that of RDX/LiF/wax/80/15/5 explosive,indicating that the aluminum reaction energy can be used to accelerate the metal.In addition,in the recording time of about 10μs,the plate acceleration duration of RDX/Al/wax/80/15/5 explosive is 2.9μs longer,showing a significant enhancement of the explosive acceleration time.The parameters of the JWLM EOS was calibrated both theoretically and experimentally.The thermochemical combustion energy of aluminum and predicted detonation products were calculated to estimate the potential afterburn energy of aluminum that could be harnessed from the afterburn.It was found that when the detonation products expanded to 2 times of the initial volume,more than 80% of the 170 nm aluminum powder has reacted,indicating very high reactivity.In this work,we have presented a combined theoretical-experimental strategy which may be applied,improved and extended for other non-ideal explosive formulations.Efforts are on-going to improvise the experimental test setups,and minimize computational assumptions so as to better understand the true underlying physical phenomena.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge National Natural Science Foundation of China(Grant No.11832006)and Open Project of State Key Laboratory of Explosion Science and Technology in Beijing Institute of Technology(Grant No.KFJJ20-04 M)to provide fund for conducting experiments.