WENG Jidong, LI Yinglei, CHEN Hong, YE Xiangping, YE Suhua, TAN Hua, LIU Cangli. Application of an All-Fiber Displacement Interferometer on SHPB Experiment Measurements[J]. Chinese Journal of High Pressure Physics, 2018, 32(1): 013201. doi: 10.11858/gywlxb.20170533
Citation: TAO Peidong, ZHANG Hongping, ZHANG Zhiyou, LI Mu. Backward Integration Method for Multilayer Target Quasi-Isentropic Compression Experiments[J]. Chinese Journal of High Pressure Physics, 2023, 37(1): 012301. doi: 10.11858/gywlxb.20220640

Backward Integration Method for Multilayer Target Quasi-Isentropic Compression Experiments

doi: 10.11858/gywlxb.20220640
  • Received Date: 15 Aug 2022
  • Rev Recd Date: 28 Aug 2022
  • Available Online: 21 Feb 2023
  • Issue Publish Date: 05 Feb 2023
  • According to the requirements of target structure design and experimental data processing in multilayer target quasi-isentropic compression experiments, an interlayer transfer method for multilayer targets was proposed based on the backward integration method, the backward calculation of multilayer targets from the measuring surface to the loading surface or laser ablation surface was realized. Through the forward and backward integration numerical experiments and the application in laser driven experiment, the effectiveness of the backward integration method in multilayer targets was verified, and the backward integration processing accuracy of multilayer targets can reach within 1% in most of the calculation area. The waveform design of quasi-isentropic compression multilayer target experiments was carried out by backward integration method, and the influence of multilayer targets with different thicknesses of glue on quasi-isentropic compression experiments was analyzed.

     

  • 同轴内外层双元组合装药是一种工程中常见的装药方式,早期主要采用不敏感炸药包覆高能炸药的方式提高整体装药对各类危险刺激的不敏感性[1]。近年来,国内外一些研究人员尝试采用高爆速炸药包覆高爆热炸药的方式调节整体装药的能量释放特性[2],即利用内、外层装药的爆速差形成聚心爆轰波形,使内层装药产生超压爆轰[3-4],进而可能提升反应速率[4-6]。虽然这方面的机理研究目前仍较少,但工程上已进行了较多的应用,且爆炸作用效果在一些方面具有优势。如Arthur[7]、尹俊婷[8]等将该类组合装药应用于杀爆战斗部中,以兼顾破片速度和冲击波超压两方面的性能优势;牛余雷等[9]对该类组合装药进行水下爆炸实验,发现冲击波传播过程的能量损失比单一装药明显减小。

    这类组合装药常采用不同成型工艺或配方体系的炸药进行组合,为了确保制备过程的安全及便利,在内、外层装药之间增设较薄的金属隔层,如薄壁铝筒隔层等。由于金属隔层的冲击阻抗与炸药差异较大,可能会影响组合装药的爆轰波形,且一些金属的延展性较好,在爆轰过程中若不能马上破裂,则可能阻碍内、外层装药爆轰产物的快速混合,使铝粉在高温高压条件下不能获得更多的氧元素,从而不利于无氧燃烧阶段的充分释能。而对于这些问题,目前并未见到相关研究报道。因此,本研究制备了两种组分和尺寸均相同的同轴双元组合装药试样,其中一种试样含有薄壁铝隔层,通过爆轰波形扫描试验及圆筒试验分别对比两种试样的爆轰波形及圆筒比动能,并采用脉冲X射线观测爆轰过程中薄铝隔层的膨胀轨迹,从而系统分析铝隔层对组合装药爆轰性能的影响规律,以期为该装药的工艺设计及优化提供依据。

    实验样品为同轴内外层组合圆柱体(如图1所示),每节药柱的尺寸均为ø50 mm×100 mm,内、外层装药均采用熔铸成型工艺制备。外层装药采用高爆速炸药DOL制备,内层装药采用高爆热炸药DRLU制备(配方及参数见表1),内、外层装药的质量比约为1。实验样品包含A和B两种,样品A中不含有铝隔层,内层装药的直径为35 mm;样品B中含有铝隔层,内层装药的直径为34 mm,铝隔层的壁厚为0.5 mm;当两种样品的长度相同时,样品B中的有效装药量相当于样品A的97.2%。

    表  1  炸药配方及参数
    Table  1.  Formulation and parameters of explosives
    Explosive Mass fraction ρ/(g·cm–3 DCJ/(km·s–1 Q/(kJ·g–1
    DOL 30∶60∶5∶5 (DNTF∶HMX∶Al∶binder) 1.84 8.65 6.56
    DRLU 15∶35∶20∶30 (DNAN∶RDX∶AP∶Al) 1.88 6.84 8.19
    下载: 导出CSV 
    | 显示表格
    图  1  组合装药结构
    Figure  1.  Structure of composite charge

    组合装药爆轰波形演变至稳定状态需要较长的距离,这不仅与内、外层装药的爆速差有关,还受结构尺寸等因素的影响。本研究中仅需对比两种试样爆轰波形演变过程中的差异,其所获波形并不一定为稳态波形,因此只要求样品A和样品B的尺寸相同。采用一节ø50 mm×100 mm的药柱为实验主装药,药柱的起爆端粘接ø50 mm的平面透镜,使内、外层装药的起始波形相同,并通过SJZ-15型转镜式高速扫描相机获取药柱尾部端面的爆轰波形,实验布局如图2所示。扫描爆轰波形时,相机的光学狭缝通过高清晰反射镜对准主装药端面的直径,相机扫描速度设定为6 km/s。

    图  2  爆轰波形扫描实验装置示意图
    Figure  2.  Schematic of scanning test of detonation wave shape

    图3为样品B的爆轰波形,其中虚线标识为铝隔层所对应的位置,不含有铝隔层的样品A的爆轰波形与样品B极为相似。结合图像放大比及相机的扫描速度可获得图3中波形的具体曲线数据。由于波形关于装药轴线对称,为了便于表示,图4中仅列出了轴心至装药半径R处的波形曲线(判读时,相邻数据点纵坐标的差值恒定)。图4t = 0时刻为爆轰波最早到达药柱端面的时刻,该位置处于外层装药 R21.4 mm处。从图4可以看出:样品A和样品B的爆轰波形曲线整体偏差较小,主要差异仅局限于内层装药 R<7.5 mm区域;而铝隔层附近( R17.5 mm)两条曲线吻合较好,说明冲击波穿越铝隔层时未产生较强的反射效应,可能是铝的冲击阻抗(即铝的密度与声速的乘积,约为 1.44×106g/(cm2s) [10])与炸药爆轰阻抗(即炸药密度与爆速的乘积,DOL炸药的爆轰阻抗约为 1.55×106g/(cm2s) )较为接近所致。此外,从图4中还可看出,爆轰波到达装药中心处( R=0 )的时刻较外层装药滞后约1μs,结合试样长度及DOL炸药的爆速可估算出,装药中心附近爆轰波的传播速度约为7.9 km/s,而在7.5 mm < R < 17.5 mm区域爆轰波的传播速度更高。这表明内层装药的爆速较DRLU炸药的CJ爆速具有较大幅度的提升,呈现出明显的超压爆轰特征,从而显著提升爆轰反应区内的能量释放速率 [6]

    图  3  样品B的爆轰波形扫描底片
    Figure  3.  Photographs of detonation wave shape of sample B
    图  4  爆轰波形曲线
    Figure  4.  Detonation wave shape

    图3所示的聚心爆轰波不仅能为内层装药中的铝粉提供更高压力和温度的无氧燃烧环境,还能促使外层装药的爆轰产物向内聚集,为铝粉提供更多的氧元素,使其释放出更多的能量[11],从而提升整体装药的驱动能力。因此,铝隔层是否会对内、外层装药爆轰产物造成隔离便显得尤为关键。本研究将通过脉冲X射线摄影技术对组合装药爆轰过程中铝隔层的运动状态进行观测。图5为该实验的布局示意。

    图  5  脉冲X射线摄影实验布局
    Figure  5.  Experiment layout of pulsed X-ray photography

    图6为脉冲X射线观测样品B爆轰过程时所获底片,从中可以看出,此时该装药的爆轰波还未传播完毕,且铝隔层的轮廓较为光滑,未见明显碎渣(底片左侧边缘的竖向条纹为洗相过程中意外刮擦所致,且离铝隔层较远,故认为这不是铝隔层的碎片),因此可认为铝隔层此时破裂的可能性较小。为便于定量描述铝隔层的运动轨迹,设定装药轴向为x轴,原点为装药的起爆端,半径方向为y轴,则可获得铝隔层的膨胀轨迹,如图7所示。从图7中可以看出: 18mm<x<50 mm区域近似为直线段,可计算出其斜率的绝对值 k=dy/dx0.257 x>62 mm时,铝隔层仍位于初始位置 y0=17.5 mm,表明爆轰波未到达该区域;设爆轰波到达的位置为 x0 ,则不同位置处铝隔层已膨胀的时间 t=(x0x)/D ,因此,可计算出铝隔层的径向膨胀速度 v

    图  6  脉冲X射线摄影所获底片
    Figure  6.  Experimental film obtained by pulsed X-ray photography
    v=dydt=dyd(x0xD)=dydxD=Dk
    (1)

    式中:D可近似取DOL炸药的爆速,即D ≈ 8.65 km/s,则v ≈ 2.2 km/s。此外,图7 x<18 mm区域的斜率明显偏低,则该区域铝隔层的径向膨胀速度 v 也偏低,可能是装药端部的稀疏波所致。

    图  7  铝隔层的膨胀轨迹
    Figure  7.  Expansion track of aluminum interlay

    综合该实验的分析可以看出,铝隔层的径向膨胀速度为2.2 km/s时,其半径y由17.5 mm膨胀至30.0 mm时,未发现明显破裂。若根据爆轰产物相对比容 υ=(y/y0)2 进行估算,则可认为在内层装药爆轰产物的相对比容 υ >3.0之前,铝隔层能有效隔离内、外层装药的爆轰产物。

    本研究采用圆筒试验表征装药的驱动性能,其装置如图8所示。圆筒壁的材料为TU1无氧铜,密度为8.93 g/cm3,内、外直径分别为50.0和60.2 mm;狭缝扫描位置距圆筒尾端约200 mm,相机扫描速度设定为1.5 km/s;电探针粘贴在装药截面的边缘处,可获得该组合装药的外层装药在圆筒内的平均爆速 D 。根据GJB 8381―2015[12]中的实验数据处理方法,可获得圆筒壁质量中心面的半径 rm 随时间t的变化曲线,并按照(2)式对该曲线进行拟合

    图  8  圆筒试验装置示意
    Figure  8.  Schematic diagram of the cylinder test
    rmrm0=2j=1aj{(t+t0)1bj[1ebj(t+t0)]}
    (2)

    式中: rm0=(r2e0+r2i0)/2 rm 的初始值, ri0 re0 分别圆筒壁的初始内、外半径; aj bj t0 均为拟合参数。曲线拟合参数的具体值及 D 的测量值均列于表2中。

    表  2  圆筒壁膨胀位移曲线拟合参数
    Table  2.  Curve-fitting parameters of the expansion displacement of cylinder wall
    Sample D*/(km·s–1 a1/(km·s–1 b1/μs–1 a2/(km·s–1 b2/μs–1 t0/μs
    A 8.610 1.211 04 0.110 96 0.506 19 0.382 02 1.628 99
    B 8.624 1.119 78 0.111 27 0.570 49 0.421 29 1.441 05
    下载: 导出CSV 
    | 显示表格

    根据表2中的数据可计算出圆筒质量中心面的质点速度 us

    us=2Dsin[arctan(um/D)2]
    (3)

    式中: um=2j=1aj[1ebj(t+t0)] 。从而可获得圆筒的比动能 E=u2s/2 。爆轰产物的相对比容 υ 的计算公式为[13]

    υ=(riri0)2=r2m(r2e0r2i0)/2r2i0
    (4)

    则可获得 E-υ 曲线,如图9所示。

    图  9  Eυ曲线
    Figure  9.  Eυ curves

    图9中可以看出,随着爆轰产物相对比容 υ 的增大,两种试样的圆筒比动能差距逐渐增大,然后趋于稳定。为了进行更详细的对比分析,可由 υ =2.2,4.4,7.0三个位置描述爆轰产物在高压、中压、低压作用阶段的特征[14]。当 υ < 2.2,即爆轰产物处于高压阶段时,两种试样的圆筒比动能曲线几乎重合,表明在该阶段铝隔层对装药的驱动性能几乎没有影响,这可能是由于此时圆筒壁的加速主要依靠冲击波的驱动力 [14](取决于外层装药的性能)。随着 υ 的增大,爆轰产物进入中压驱动阶段,虽然样品B中的铝隔层可在 υ < 3.0时有效隔离内、外层装药的爆轰产物,但其圆筒比动能相对于样品A并没有呈现出明显的差异;当 υ =4.4时,其圆筒比动能约为样品A的97.7%,仍略大于两种试样有效装药量的比值。这表明在该阶段,内、外层装药爆轰产物的快速混合并不能显著提升能量的释放速率。当 υ =7.0时,样品B的圆筒比动能约为样品A的97.3%,与两种试样有效装药量的比值基本一致,由于此时一般认为爆轰产物的驱动能量已达到最大值[15],因此,可认为本研究中的铝隔层对同轴双元组合装药的驱动性能没有产生明显影响,但是否与装药的尺寸以及两种炸药的选择有关,还需要后续进一步深入研究。

    (1)在该同轴双元组合装药中,内、外层装药间增设薄壁铝隔层后,装药的爆轰波形未发生明显改变,这可能是由于铝的冲击阻抗与炸药爆轰阻抗较为接近,使冲击波穿越铝隔层时未发生较强的反射效应所致。

    (2)根据脉冲X射线摄影实验结果,该组合装药在爆轰过程中,铝隔层的径向膨胀速度为2.2 km/s时,其半径由17.5 mm膨胀至30.0 mm,未发现明显破裂,故可认为内层装药爆轰产物的相对比容小于3.0时,铝隔层能有效隔离内、外层装药的爆轰产物。

    (3)当 υ <2.2,即爆轰产物处于高压阶段时,两种试样的圆筒比动能曲线几乎重合;当 υ =4.4和7.0时,增设铝隔层的组合装药的圆筒比动能分别约为无铝隔层时的97.7%和97.3%,接近两种试样有效装药量的比值。因此,增设薄壁铝隔层以提升组合装药制备工艺的效率及安全性时,不会对装药的驱动性能产生明显影响。

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