Experimental investigation on enhanced damage to fuel tanks by reactive projectiles impact

Hai-fu Wang,Jian-wen Xie,Chao Ge,Huan-guo Guo,Yuan-feng Zheng

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

Keywords:Reactive material projectile Fuel tank Enhanced damage effect Enhanced ignition mechanism Impact behavior

ABSTRACT Enhanced damage to the full-filled fuel tank,impacted by the cold pressed and sintered PTFE/Al/W reactive material projectile(RMP)with a density of 7.8 g/cm3,is investigated experimentally and theoretically.The fuel tank is a rectangular structure,welded by six pieces of 2024 aluminum plate with a thickness of 6 mm,and filled with RP-3 aviation kerosene.Experimental results show that the kerosene is ignited by the RMP impact at a velocity above 1062 m/s,and a novel interior ignition phenomenon which is closely related to the rupture effect of the fuel tank is observed.However,the traditional steel projectile with the same mass and dimension requires a velocity up to 1649 m/s to ignite the kerosene.Based on the experimental results,the radial pressure field is considered to be the main reason for the shear failure of weld.For mechanism considerations,the chemical energy released by the RMP enhances the hydrodynamic ram(HRAM)effect and provides additional ignition sources inside the fuel tank,thereby enhancing both rupture and ignition effects.Moreover,to further understand the enhanced ignition effect of RMP,the reactive debris temperature inside the kerosene is analyzed theoretically.The initiated reactive debris with high temperature provides effective interior ignition sources to ignite the kerosene,resulting in the enhanced ignition of the kerosene.

1.Introduction

Fuel tank is identified as one of the important vulnerable components for aircraft since it represents the largest exposed area of all the vulnerable components.Current air defense weapons usually attack the fuel tanks by the inert metal(typically tungsten alloy and steel)projectiles,which damage the fuel tank mainly by impact kinetic energy(KE)induced hydrodynamic ram(HRAM)effect[1].To understand the HRAM effect caused by the inert metal projectiles,considerable effort has been devoted to relative researches.In order to evaluate the survivability of the fuel tank structure in military aircraft,the four evolution stages of HRAM(including shock,drag,cavitation and exit)had been investigated and demonstrated by both experimental and simulation approaches[2,3].Varas et al.performed a series of experiments of partially filled tubes subjected to high-velocity impact,both the projectile velocity and the KE of the layer of fluid had significant influences on the deformation and failure of tube upper wall,and the filling percentage affected the areas far from the impact,whereas the impact velocity mainly affected the areas near the impact[4].Artero-Guerrero et al.successfully reproduced the HRAM event in partially filled aircraft fuel tank by numerical simulation,the KE of the layer of fluid raised by the projectile movement was found to be the main reason of the upper wall failure[5].Huang et al.performed serial tests of water-filled tanks subjected to high-velocity projectiles impact,and decayed characteristics of the initial shock waves were investigated[6].Ren et al.investigated the failure modes of water-filled vessel under projectile impact by both experiments and numerical simulations[7,8].In addition to the water-filled tank impact experiments,Liu et al.also conducted experiments of inert tungsten projectiles impacting fuel-filled tanks,experimental results indicated that the inert tungsten projectile could hardly produce effective structural damage to the fuel tank and could hardly generate effective ignition source[9].The research results indicate that,due to the KE-only penetration mechanism,both the damage capacity and ignition capacity of inert metal projectile are greatly limited,which restricts the development of air defense weapons.

Reactive materials are a class of novel energetic materials,which remain inert and insensitive under normal conditions but will be initiated and release large amounts of chemical energy(CE)under highly dynamic loads.Significantly different from the traditional inert metal projectile,the reactive material projectile(RMP)provides a combined damage mechanism of KE impact and CE release due to the impact-induced initiation[10],which has great potential in the military application of both structural damage enhancement and ignition effect enhancement to the fuel tank.Generally,RMPs are formed by means of uniformly mixing active metal powders into a polymer matrix(typically polytetrafluoroethylene),then consolidated via pressed/sintered process[11].Over the past few decades,much progress has been achieved in reactive material application,such as the mechanical properties[12,13],microstructure[14,15],impact-induced initiation[16,17],and energy release characteristics[18,19],as well as the enhanced damage effects to the targets by RMPs[20,21].In addition,our research group has conducted experiments on RMPs impacting fuel tanks,demonstrating the enhanced ignition behavior of RMP against aviation kerosene[9].Moreover,ballistic experiments of RMP impacting partially/fully filled fuel tanks were also performed to investigate the influence of filling level,compared with a fully filled fuel tank,the existence of fuel-vapor air mixtures made it easier for RMP to ignite a partially filled fuel tank[22],and RMP was found to enhance its damage by incorporating the terminal defeat mechanisms of KE and CE[23].However,there is no serial study on the ignition and damage enhancement behavior,the penetration behavior and enhanced ignition mechanism of RMP impacting fuel tank have not been well known,which brings difficulties to the application of RMP in damaging fuel tank.

This paper begins with a series of ballistic impact experiments of RMPs impacting fuel tanks.The enhanced ignition behavior of RMP is demonstrated by the contrast experiments,and the enhanced rupture and ignition mechanisms are analyzed and discussed,which may provide a useful guide for the improvement of RMP damage potential and the development of air defense weapons.

2.Experimental details

2.1.Preparation of projectiles

The PTFE/Al/W RMPs were fabricated from reactive granular mixture by cold isostatic pressing and vacuum sintering.The composition of reactive granular mixture was 11.3% PTFE,7.5% Al,and 81.2%W,by weight.The original average particle sizes of each component were as follows:100 nm PTFE,44μm Al,and 44μm W.The mixed granular mixture was pressed at 200 MPa using cold isostatic pressing,then consolidated by vacuum sintering.The vacuum oven temperature was firstly risen to 380°C at a rate of 50°C/h and maintained for 6 h.Then,the temperature was reduced to 310°C at a rate of 50°C/h and maintained for 4 h.Finally,the specimen was further cooled to ambient temperature at an average rate of 50°C/h.The density of pressed/sintered cylindrical RMP was about 7.8 g/cm3,and the samples used in the experiments had a maximum porosity of 5.14%in the present study.All the projectiles used in the experiments had the same size(diameter×height):10 mm×10 mm.In consideration of the contrast,the experiments of inert steel projectiles impacting fuel tanks were also conducted,and the steel projectile was designed to be the same mass and dimension as that of the RMP,as shown in Fig.1.

Fig.1.Photographs of projectiles:(a)the PTFE/Al/W RMP;(b)the steel projectile.

2.2.Fuel tank structure

The fuel tanks used in the experiment were fabricated by welding six pieces of 2024-T3 aluminum plate with a thickness of 6 mm together.The photograph and schematic of fuel tank are shown in Fig.2.The fuel tank had the following interior dimension:188 mm×188 mm×100 mm,and the fuel amount stored was 3.53 L of RP-3 aviation kerosene at each test.The RP-3 aviation kerosene used in the experiment was refueled through the refuel hole in the top of fuel tank,and its density was 0.8 g/cm3.During the manufacture of the fuel tanks,the equivalent width of the weld was strictly kept at 6 mm to ensure that the failure criteria of each fuel tank was almost the same.The fuel tank was fixed on the target stand during the impact.

2.3.Experimental setup

The schematic and photographs of experimental setup are shown in Fig.3.The projectile was fixed in the sabot and launched by a 14.5 mm caliber ballistic gun.By controlling the mass of black powder inside the cartridge,the impact velocity ranged from 855 m/s to 1649 m/s.During the flight process,the projectile and sabot would automatically separate before impacting the fuel tank due to the difference in mass.Two velocity probes and the electronic timer were used to measure the impact velocities of projectiles,the distance between two probes was 500 mm.The entire impact and ignition process were recorded by a high-speed video camera,and the distance between the muzzle and the front plate of fuel tank was 8 m.In addition,during the whole test,the ambient temperature ranged from 22°C to 25°C and the ambient pressure was 1 atm.

3.Experimental results

Table 1 gives the experimental results of RMPs and inert steel projectiles impacting fuel tanks at different velocities,in which the‘√’means‘Yes’and‘×’means‘No’.The damage to the fuel tank consists of four degrees:intact,weld torn,fuel tank ruptured and fire,in which“intact”means all welds keep well and the fuel only ejects from the refuel hole or the penetration hole,“weld torn”means the weld is torn partially and the fuel also ejects from weld cracks,“fuel tank ruptured”means all welds are torn and the fuel tank is ruptured completely,and“fire”means the kerosene is successfully ignited.In addition,the ignition time and burning duration of kerosene are also obtained based on the high-speed video data.

As listed in Table 1,the damage to the fuel tank by the projectile impact is significantly influenced by the projectile type and the impact velocity.For the RMP,it fails to damage the weld at an impact velocity of 855 m/s.When the impact velocity of RMP increases to 949 m/s,the kerosene is successfully ignited,whereas the burning lasts only 76.4 ms.With the impact velocity further increasing to 1062 m/s,the kerosene is also successfully ignited,and the ignition finally develops into sustained burning.Moreover,with the impact velocity of RMP increasing from 949 m/s to 1251 m/s,the ignition time first increases and then decreases.While for the steel projectile,it cannot ignite the kerosene even at an impact velocity of 1326 m/s until the velocity increases to 1649 m/s.

Fig.2.Photograph and schematic of the fuel tank.

Fig.3.Schematic and photographs of experimental setup.

Table 1Experimental results of ballistic impact tests.

Fig.4 shows the typical high-speed video frames of the RMP impacting the fuel tank at velocities of 855-1251 m/s.The impact firstly leads to fracture and initiation of the RMP,the impactinduced deflagration flame expands in front of the fuel tank with high brightness,and some reacted debris ejects rearward,which is observed clearly in each impact.With the impact velocity increasing from 855 m/s to 1251 m/s,the deflagration flame becomes brighter and the expansion region becomes larger,which means more reactive materials are initiated.After perforating the front plate of the fuel tank,the residual projectile and most of the initiated reactive debris travel through the liquid kerosene.Then the projectile transfers its KE to the surrounding kerosene during penetration,meanwhile,the initiated debris releases its CE inside the penetration trajectory.Thus,the kerosene begins to expand radially from the penetration trajectory,creating a radial pressure field inside the fuel tank.However,as shown in Fig.4(a),the pressure caused by the HRAM effect in this case is not enough to damage the weld,thus the kerosene only ejects from the refuel hole or the penetration hole with a poor atomization effect.As such,the impact at 855 m/s only leads to the leakage of kerosene without ignition eventually.

As Fig.4(b)shows,both rupture and ignition effects of the fuel tank change significantly when the impact velocity increases to 949 m/s.Due to the increase in both KE and CE,the HRAM effect is significantly enhanced,and welds are torn partially under the higher pressure.As such,the kerosene ejects from both refuel hole and weld cracks,and then mixes with the surrounding air,forming a large area of fuel/air mixture with a better atomization effect.At approximately 6.0 ms after impact,before the deflagration flame extinguishes,the fuel/air mixture which contacts with the flame is ignited,while the rest is not.However,since the fuel tank is still not completely ruptured in this case,no more kerosene ejects outward over time.As a result,the burning cannot be sustained and gradually extinguishes at approximately 82.0 ms.

Fig.4.Typical high-speed video frames of RMP impacting fuel tank.

As the impact velocity further increases to 1062 m/s,the damage behavior becomes more complex.As Fig.4(c)shows,due to the further increase in both KE and CE,all the welds fail at approximately 2.0 ms.The kerosene ejects outward at a high velocity in the direction parallel to the rear plate,however,it results in the consequence that the fuel/air mixture fails to contact with the deflagration flame.Interestingly,a novel ignition phenomenon ensues.Within the time scale of 8.0-23.0 ms,the kerosene is gradually ignited from the central area of the fuel/air mixture.In fact,the high temperature initiated reactive debris may ignite the kerosene inside the penetration trajectory.However,this ignition is most likely to extinguish rapidly due to the lack of oxygen inside the penetration trajectory.In the situation shown in Fig.4(c),the fuel tank is completely ruptured,thus all the kerosene ejects outward at a high velocity,forming an ideal fuel/air mixture around the initiated debris.As such,the fuel/air mixture in the central area is firstly ignited by the initiated reactive debris,and the ignition finally develops into sustained burning at approximately 40.0 ms after impact.Similar interior ignition phenomena also occur at velocities of 1153 m/s and 1251 m/s,except that the ignition time varies,as shown in Fig.4(d)and 4(e).Moreover,the interior ignition mode of the fuel tank impacted by high-velocity RMP is further demonstrated.

Compared with the RMP,the rupture and ignition behavior of fuel tanks impacted by steel projectiles are quite different.Fig.5 shows the typical high-speed video frames of steel projectile impacting fuel tank at velocities of 1326 m/s and 1649 m/s.As shown in Fig.5,the steel projectile also fractures with partial KE transferring to heat during the impact,causing a flame with low brightness and small expansion region.However,as shown in Fig.5(a),due to the KE-only damage mechanism,the weld is only torn partially even at 1326 m/s,and the kerosene ejects from weld cracks at a low velocity.Meanwhile,the impact-induced flame extinguishes rapidly,thus the kerosene with a poor atomization effect is not ignited,only resulting in the leakage of kerosene.As shown in Fig.5(b),the kerosene is successfully ignited by the inert steel projectile at 1649 m/s.At approximately 0.6 ms after impact,due to the weld failure between the front plate and the side plate,the kerosene ejecting from weld cracks successfully contacts with the flame before it extinguishes.Significantly different from the situation of RMP at 1062 m/s,with more kerosene ejecting outward,the ignition first occurs in the fuel/air mixture around the fuel tank in this case,then spreading to the central area and finally developing into sustained burning at approximately 37.0 ms.

Fig.5.Typical high-speed video frames of steel projectile impacting fuel tank.

From the high-speed video frames and the data in Table 1,it is observed that a completely ruptured fuel tank may be the necessary condition for the sustained burning of kerosene.If the fuel tank keeps intact or the weld is only torn partially,the kerosene cannot be ignited due to lack of ignition sources as shown in Figs.4(a)and Fig.5(a),or the burning only lasts for a while due to the insufficient kerosene as shown in Fig.4(b).It should be noted that after the fuel tanks being completely ruptured by both RMP and steel projectile,the ignition mechanisms for these two types of projectiles are quite different.Due to the KE-only damage mechanism,the ignition effect of the inert steel projectile strongly depends on the impactinduced flame which only lasts for a while.While for the RMP,even in the case that the fuel/air mixture fails to contact with the deflagration flame,it can ignite the kerosene from the central area of the fuel/air mixture by its initiated debris.In other words,the addition of CE not only enhances the damage to the fuel tank but also provides a more reliable ignition mode.It should be noted that the actual aircraft fuel tank may have excellent performance in protecting the aircraft from the damage caused by inert metal projectiles,which have little chance to rupture the fuel tank due to the limited KE.However,once perforating the fuel tank,the RMP will occur violent deflagration even without oxygen,and the CE released by deflagration may improve the rupture probability of the actual aircraft fuel tank.Then combined with the novel interior ignition mode,RMP is most likely to enhance the damage to the actual aircraft fuel tank.In the present analysis,since the ignition when the fuel tank is not completely ruptured is random to some extent and cannot be sustained,the focus will be on the impact behavior of RMP which has sufficient velocity to completely rupture the fuel tank.

4.Discussion

4.1.Enhanced rupture and ignition behavior

The experimental results show that compared with the inert steel projectile,both the rupture and ignition behavior of RMP are enhanced.For mechanism consideration,on the one hand,the reactive material will be initiated under the high-velocity impact load,and the CE released will enhance the HRAM effect,thereby enhancing the rupture damage to the fuel tank.On the other hand,the initiated reactive debris inside the fuel tank may be effective ignition sources in addition to the impact-induced deflagration flame,which provides another ignition mode.Therefore,as shown in Fig.6(in which the‘～’means‘a(chǎn)bout’),based on the impactinitiated characteristics of RMP,the impact process of RMP impacting fuel tank is divided into the following four principal phases:shock and initiation,drag and deflagration,enhanced rupture,interior ignition.

As shown in Fig.6(a),after the initial impact of the front plate,two initial impact-induced shock waves propagate forward into the front plate and backward into the RMP,causing high strain rate plastic deformation of the projectile.Since the ultimate strength for fragmentation of RMP is relatively low,some reactive debris is generated under impact load.As the penetration continues,tiny reactive debris with a high specific surface area is initiated firstly due to the low surface ignition energy,resulting in a local deflagration,then the impact-induced deflagration flame is formed.Meanwhile,the initial impact-induced shock wave propagates forward through the fuel,although its peak pressure is high,the pressure field weakens rapidly due to the geometric expansion of shock wave in the fuel.In this phase of shock and initiation,the shock wave results in damage primarily near the impact region.

The second phase of drag and deflagration is shown in Fig.6(b).After perforating the front plate,on the one hand,the projectile transfers its KE to the surrounding fuel as the projectile is gradually slowed by viscous drag,then the fuel begins to flow radially,forming a cavity and producing a radial pressure field inside the fuel tank.On the other hand,the fragmented projectile further separates into much debris when travels through the fuel,in which the initiated reactive debris continues to deflagrate inside the cavity,releasing a large amount of CE and gaseous products,which further promotes the growth of the cavity.Meanwhile,after the reflected shock wave from the tank walls reaches the cavity surface in the liquid fuel(on the order of 100μs),the liquid fuel will be driven back onto the axis and cavitated,then generating vapor and fuel droplets.Compared with the liquid fuel,the vapor and droplet will be more readily able to ignite and burn.

The third phase of enhanced rupture is shown in Fig.6(c).As time progresses,most of the initiated reactive debris has been reacted,and the radial flow of fuel will be enhanced significantly due to the combined effect of KE and CE.As the radial flow of fuel expands to the side plate,the fuel will impact the side plate at a certain velocity.The side plate will undergo warp and plastic deformation under the impact pressure,leading to the failure of weld.In this case,the fuel will eject from weld cracks at a high velocity,and then mixes with the surrounding air to form a fuel/air mixture.

The fourth phase of interior ignition is shown in Fig.6(d).In fact,the high temperature initiated debris inside the cavity will heat the surrounding fuel to the temperature required for ignition,which means the initiated debris may be the interior ignition sources.When the fuel tank is ruptured completely,the fuel will be exposed to ambient oxygen,thus forming fuel/air mixture around these interior ignition sources.As such,the fuel/air mixture in the central area is firstly ignited by these interior ignition sources.As time progresses,the fire begins to spreads outward and eventually develops into sustained burning.It’s worth noting that some oxygen may flow into the penetration trajectory during penetration,however,the oxygen inside the penetration trajectory is most likely to be insufficient.Thus,if the fuel tank is not ruptured completely,these interior ignition sources will extinguish due to the lack of oxygen.

Fig.6.Enhanced rupture and ignition behavior of RMP impacting fuel tank.

In addition,both the projectile type and the impact velocity have significant influence on the damage to the fuel tank.The experimental results illustrate that the addition of CE not only enhances the rupture effect of the fuel tank but also provides a more reliable ignition mode.Moreover,the ignition effect is closely related to the rupture effect of the fuel tank,sustained burning only occurs when fuel tank is completely ruptured.To reveal the influence of projectile type and impact velocity on the damage to fuel tank,both the enhanced rupture and ignition effects are discussed in the following section.

4.2.Enhanced rupture effect analysis

The typical photographs of damaged fuel tanks impacted by RMPs are shown in Fig.7.It is shown that the rupture effect of the fuel tank impacted by RMP is significantly influenced by the impact velocity.When the RMP impacts the fuel tank at 855 m/s,the fuel tank remains intact without obvious deformation,only forming a penetration hole in the front plate.When the impact velocity of RMP further increases to 1062 m/s,the rear plate is detached from the fuel tank,and all the welds between the side plate and the rear plate fail.Moreover,the side plate is slightly warped and deformed,and the welds between the side plate and the front plate are cracked.With the impact velocity further increasing to 1251 m/s,one of the side plates is almost detached from the fuel tank,and the warp pattern of the side plate indicates that the failure of the fuel tank is mainly caused by the radial pressure field which is induced by the HRAM effect.Moreover,several severely cracked welds can be seen clearly in Fig.7(c),the cracked welds indicate that the main failure mode of the weld is the shear failure.The various rupture effects of the fuel tank also indicate that the structure damage to the fuel tank caused by the RMP strongly depends on the impact velocity.

Fig.7.Typical photographs of damaged fuel tanks impacted by:(a)RMP at 855 m/s(b)RMP at 1062 m/s(c)RMP at 1251 m/s.

Fig.8 shows the typical photographs of damaged fuel tanks impacted by steel projectiles.When the steel projectile impacts the fuel tank at 1326 m/s,the weld is only partially torn,and the weld cracks between the side plate and the rear plate can be clearly observed in Fig.8(a).As the impact velocity of steel projectile increases to 1649 m/s,the rear plate is detached from the fuel tank,and obvious burning marks are left on the surface of the front plate,as shown in Fig.8(b).Moreover,the dispersed crater is clearly observed on the rear plate,which indicates that the steel projectile fragments into several parts during the impact.Except for the rear plate,the rest of the fuel tank is still not obviously deformed.It can be seen that,the HRAM effect induced by the inert steel projectile is much weaker than that of the RMP.

Fig.8.Typical photographs of damaged fuel tanks impacted by:(a)steel projectile at 1326 m/s(b)steel projectile at 1649 m/s.

The experimental results show that the RMP significantly enhances the rupture damage to the fuel tank,and one of the reasons for this enhanced rupture effect is the impact-induced chemical reaction of the reactive materials,which is significantly influenced by the impact velocity.Different from the KE-only penetration behavior of the inert steel projectile,the penetration behavior of the RMP is much more complex due to its unique chemical response.In general,for the PTFE/Al/W reactive materials,PTFE acts as a binder for bonding the metal particles together during the fabrication process.When the reactive materials undergo high strain rate plastic deformation under impact conditions,Al will be oxidized by the fluoride generated by the decomposition of PTFE.The reaction process of PTFE/Al/W reactive materials under impact conditions may include the following reactions:

The above reactions will generate a large number of gaseous products,mainly including AlF3,AlF2,and AlF.Therefore,when penetrating the liquid fuel,the RMP not only transfers its KE to the surrounding kerosene,but also deflagrates inside the cavity to release its KE and a large number of gaseous products.As a result,the rapid expansion of gaseous products and the CE released will further promote the growth of the cavity,resulting in a stronger radial pressure field inside the fuel tank.In addition to the additional CE released by the RMP,the KE transferred by the RMP to the liquid fuel is the other reason for the enhanced rupture effect.Due to the lower strength of the RMP,it will deform and fragment more easily during the impact process than the steel projectile,leading to a larger viscous drag.Thus,more KE will be transferred to the liquid fuel by the RMP.Compared with the KE-only mechanism of the steel projectile,the RMP not only transfers more KE to the liquid fuel,but also releases additional CE inside the fuel tank.Therefore,the coupled response of KE and CE of RMP will significantly enhance the structure damage to the fuel tank.In fact,this is also demonstrated by the experimental results.Except for the detached rear plate,the fuel tank impacted by steel projectile at 1649 m/s is slightly deformed.While,the fuel tank impacted by RMP at 1251 m/s is severely deformed and ruptured,which indicates that the fuel tank undergoes more violently impact load in this case.For mechanism consideration,the KE transferred by the RMP will form a cavity inside the liquid fuel,and the rapid expansion of gaseous products and the CE released will further promote the growth of the cavity,resulting in a stronger radial pressure field,thereby enhancing the rupture effect.Since the transferred KE and the initiation efficiency of the reactive materials are both closely related to the impact velocity,the enhanced rupture effect also depends on the impact velocity,as shown in Fig.7.

It should be noted that,since the atomization effect of the kerosene is closely related to the rupture effect of the fuel tank,the impact velocity also has significant influence on the atomization effect of the kerosene.As shown in Fig.4,with the impact velocity of the RMP increasing from 855 m/s to 1251 m/s,the ejecting velocity of the kerosene increases significantly,and the atomization effect of the kerosene also improves rapidly.In other words,with increasing the impact velocity of the RMP,both KE and CE increase,resulting in more severely damaged weld and a higher ejecting velocity of kerosene,thereby enhancing the rupture effect of fuel tank and also improving the atomization effect of kerosene,which also creates a necessary condition for the subsequent ignition.

4.3.Enhanced ignition effect analysis

As the experimental results show,compared with the steel projectile,the ignition effect of the fuel is also enhanced significantly under the impact of the RMP.Based on the ignition conditions of aviation kerosene,the enhanced ignition effect can be analyzed as follows.On the one hand,the atomization effect of kerosene is significantly improved by RMP,which is a necessary condition for the subsequent ignition.On the other hand,the high temperature reactive debris produced during penetration may be effective interior ignition sources,which provides another more reliable ignition mode.In order to reveal the interior ignition mechanism of RMP,the temperature history of debris is analyzed theoretically.And the following assumptions are made for the analysis.Firstly,all the behind-plate debris is considered as spheres with the same size and initial velocity[23,24].Secondly,due to the high temperature field generated by the reactive reaction of RMP,the initial temperature of the initiated reactive debris is considered as the same as the temperature of the reactive reaction[23],and for the inert steel debris,it is assumed that all the KE loss during penetrating the front plate is converted to the heat of the debris[25].

For igniting the kerosene,it not only needs enough temperature required for ignition,but also needs to maintain that temperature for the duration of the ignition delay time.By combining the ignition criterion of fuel/air mixture with the Arrhenius equation,the ignition delay time tican be described as[25]:

Where:f is the pre-exponential factor,Eais the activation energy,Rgis the universal gas constant,T is the absolute temperature,n is the order of the reaction,P0is the atmospheric pressure.For the RP-3 aviation kerosene,f is 1.68×10-8ms/atm2,Eais 158.2 kJ/mol,and n is 2[25].

Consider a debris that travels through the aviation kerosene,the convective heat transfer occurs between the debris and kerosene.The average radius of the debris riis given by Ref.[10]:

Where:ρpis the projectile density.cpis the sound speed in the projectile,the value for reactive material and steel are 1350 m/s and 4569 m/s,respectively[20].KIcis the fracture toughness,the value for reactive material and steel are 1.2×107Pa·m1/2and 1.9×108Pa·m1/2,respectively[10,26].˙εis the average strain rate.

Due to the high thermal conductivity of the debris,the temperature gradients within the debris can be neglected.The temperature of the debris when travels through the kerosene is a function of time t,which can be derived as:

Where:Tsis the debris temperature,Tais the atmospheric temperature,T0is the initial temperature of the debris,h is the heat transfer coefficient,c is the specific heat.For reactive material and steel,c are 291.7 J/(kg k)and 460 J/(kg k),respectively[27].Based on the REAL/ASTD chemical thermodynamics software,the temperature of the reactive reaction(formulation:11.3% PTFE,7.5% Al,and 81.2% W,by weight)is about 2524 K,which is also assumed to be the initial temperature of reactive debris.And for the inert steel debris,T0is given by Ref.[25]:

Where:ΔEkis the KE loss of the projectile during penetrating the front plate,Dpis the projectile diameter,htis the front plate thickness.For the convective heat transfer,the heat transfer coefficient h is given by:

Where:k is the thermal conductivity of the kerosene,Pr is the Prandtl number,Re is the Reynolds number.For the RP-3 aviation kerosene,k is 0.145 W/(m K),Pr is 17[25].The Reynolds number is given by:

Where:νis the kinematic viscosity of the fuel,and the value for the RP-3 aviation kerosene is 2.37×10-6m2/s vf（t）is the penetration velocity of the debris inside the fuel,which can be expressed as:

Where:ρlis the kerosene density,CDis the drag coefficient,and CDis 0.42 for the spherical debris[28].vris the residual velocity of projectile after perforating the front plate,which is also considered to be the initial velocity of the debris.vris described as:

Where:Mpis the projectile mass(g),m is the plug mass(g),v0is the initial impact velocity(m/s),htis the front plate thickness(cm),Apis the sectional area of projectile(cm2).α,βandγare experimental coefficients for estimating the ballistic limit velocity,in the case of the steel projectile penetrating aluminum plate,the values of them are 2852,0.903 and-0.941,respectively.In the case of the RMP penetrating aluminum plate,the values of them are 1855.7,0.4143 and-0.5549,respectively[20].

The debris temperature versus duration time for both RMP and inert steel projectile have been shown in Fig.9.After perforating the front plate,within the time scale from 3×10-8s to 6×10-1s,with the impact velocity ranging from 855 m/s to 1251 m/s,all the reactive debris is hot enough to heat the kerosene to the temperature required for ignition and maintain it at that temperature for the duration of the ignition delay time.While for the inert steel projectile,due to the low initial temperature,its debris at both 1326 m/s and 1649 m/s cannot meet the ignition criterion,as shown in Fig.9.In addition,the analysis also shows that the impact velocity has a significant influence on the debris temperature.With the impact velocity of the RMP increasing from 855 m/s to 1251 m/s,the debris temperature drops earlier and faster.The main reason is that the average size of debris gradually decreases as the impact velocity increases,which means the specific surface area of the debris increases,thereby accelerating the heat transfer,resulting in an earlier and faster decrease of the debris temperature.While for the steel projectile,its debris size is much larger due to its higher strength,so its debris temperature drops later and more slowly.However,compared with the high temperature reactive debris,the steel debris can hardly meet the ignition criterion due to its low initial temperature.Thus,after perforating the front plate,the RMP provides additional interior ignition sources inside the cavity due to its high temperature debris,which provides an enhanced ignition mechanism.While the steel debris cannot be new ignition sources,thus the ignition effect of the steel projectile strongly depends on the impact-induced flame,as shown in Fig.5.

Fig.9.Debris temperature versus duration time.

However,the generation of interior ignition source does not mean that the ignition occurs.The theoretical analysis shows that,with the impact velocity of the RMP ranging from 855 m/s to 1251 m/s,all the initiated debris is hot enough to ignite the kerosene within a large time scale.Nevertheless,even under the combined effect of KE and CE,the oxygen inside the kerosene cavity is still insufficient to maintain the growth of the interior ignition source.If the interior ignition source cannot contact the ambient air,it will gradually extinguish.As shown in Fig.4(a)and 4(b),when the impact velocity is insufficient to completely rupture the fuel tank,eventually the kerosene only leaks from the penetration hole or burns briefly.When the impact velocity is high enough to rupture the fuel tank,these interior ignition sources grow gradually after contacting with sufficient ambient air,and the ignition finally develops into sustained burning,as shown in Fig.4(c)-4(e).It should be noted that,with the impact velocity of RMP increasing from 949 m/s to 1251 m/s,the ignition time,which is an experimental value starting from the moment when the projectile impacts the front plate,first increases and then decreases.When the impact velocity increases from 949 m/s to 1062 m/s,the ignition mode changes from exterior ignition to interior ignition,while the interior ignition only occurs after the fuel tank has been completely ruptured.Since the interior ignition requires a rupture process,the ignition time increases after the ignition mode changes.When the impact velocity further increases from 1062 m/s to 1251 m/s,since all the reactive debris in this impact velocity range has sufficient temperature,the ignition time mainly depends on how quickly the fuel tank ruptures.As shown in the high-speed video frames,with increasing the impact velocity,the fuel tank ruptures more quickly due to the increase in both KE and CE,therefore the ignition time gradually decreases.In other words,the rupture effect of the fuel tank is another key factor for the ignition.For mechanism consideration,the debris temperature determines the generation of interior ignition sources,and the rupture effect of fuel tank determines the growth of interior ignition sources and the final ignition,both of which are indispensable for the interior ignition mode.For the RMP which has enough impact velocity to completely rupture the fuel tank,both the debris temperature and the rupture effect are satisfied,thereby achieving the enhanced ignition effect.

Moreover,it is demonstrated by the current experiments that the RMP will fragment into a large number of debris and occur violent deflagration under the impact dynamic loads.The fragmentation and deflagration effects of the RMP may play different roles in the damage to the fuel tank,while the experiments presented in this paper may have some limitations in performing the detailed damage investigation regarding the separation between fragmentation and deflagration.In the future,this will be studied in detail.

5.Conclusions

The enhanced damage to fuel tanks by RMPs impact is investigated by ballistic impact experiments and theoretical analysis combined.

(1)The experiments demonstrate the enhanced ignition effect of RMP impacting fuel tank.For a given mass projectile,the RMP ignites the kerosene at a velocity above 1062 m/s,whereas the inert steel projectile requires a velocity up to 1649 m/s.

(2)The RMP provides an additional interior ignition mechanism by the CE released within the cavity,significantly enhancing its ignition capability.But the enhanced ignition effect strongly depends on the rupture effect,and the completely ruptured fuel tank is most likely to be primary determinant for the enhanced ignition effect.

(3)Compared with the steel projectile,due to the difference in fragmentation characteristic and the novel impact-induced deflagration,more KE and additional CE are transferred by the RMP to kerosene,thereby enhancing the rupture effect.Moreover,the rupture effect is significantly enhanced with increasing the impact velocity.

(4)The enhanced ignition performance of RMP is closely related to the initiated debris produced by penetration process.Due to the high reaction temperature and sufficient duration time,the initiated reactive debris provides enough energy required to ignite the kerosene,thereby enhancing the ignition effects.

Declaration of interests

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.