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参考文献 1
王泽山,何卫东,徐复铭. 火药装药设计原理与技术[M]. 北京: 北京理工大学出版社, 2006: 219-221.
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参考文献 2
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参考文献 3
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参考文献 4
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参考文献 5
王锋,李梓超,刘国涛,等. 多孔环切杆状发射药的燃烧性能[J]. 火炸药学报. 2015, 23(2): 89-92.
WANGFeng, LIZi‑chao, LIUGuo‑tao, et al. Combustion performances of multi‑perforated curve‑cut stick gun propellants[J]. Chinese Journal of Explosives and Propellants,2015, 23(2): 89-92.
参考文献 6
CharJ M, KuoK. Study of combustion processes of single‑perforated stick propellants[J]. Journal of Propulsion and Power, 1987, 5(3): 262-268.
参考文献 7
HsiehW H, KUOK. Erosive and strand burning of stick propellants. II‑theoretical modeling of erosive‑burning processes[J]. Journal of Propulsion and Power, 1990, 6(4): 400-406.
参考文献 8
Char, Jir‑Ming. A study of flame spreading, combustion, and fracture of single‑perforated stick propellants[D]. Pennsylvania: The Pennsylvania State University,1987.
参考文献 9
张柏生. 炮药侵蚀燃烧的理论分析[J]. 华东工学院学报,1986, 10(2): 73-87.
ZHANGBai‑sheng. Theoretical analysis of erosive burning for gun propellants[J]. Journal of East China Institute of Technology, 1986, 10(2), 73-78.
参考文献 10
杨丰友. 太根发射药侵蚀燃烧效应研究[D]. 南京:南京理工大学, 2013.
YANGFeng‑you. The Research of the Erosive Burning Effect on TEGN Propellant[D]. Nanjing University of Science and Technology, 2012.
参考文献 11
XiaoZ, XuH, HeW. Influence of venting parameters on erosive burning of partially cut multi‑perforated stick propellants[J]. Science and Technology of Energetic Materials, 2015, 76(1): 42-46.
参考文献 12
徐汉涛,肖正刚,何卫东. 部分切口多孔杆状发射药的燃烧性能[J]. 含能材料. 2014, 22(2): 251-255.
XUHan‑tao, XIAOZheng‑gang,HEWei‑dong. Combustion characteristics of partially cut multi‑perforated stick propellant[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao), 2014, 22(2): 251-255.
参考文献 13
XiaoZ, XuF. Relationship between slivering point and gas generation rules of 19‑perforation TEGDN propellants with different length/outside diameter ratios and perforation diameters[J]. Journal of Energetic Materials, 2016, 36(2): 141-151.
参考文献 14
张小兵,金志明. 枪炮内弹道学[M]. 北京: 北京理工大学出版社, 2014: 14‑18.
ZHANGXiao‑bing, JINZhi‑ming. Interior ballistics of guns[M]. Beijing:Beijing Institute of Technology Press, 2014: 14-18.
参考文献 15
何洪庆. 固体火箭发动机气体动力学[M].西安: 西北工业大学出版社, 1988: 28-32.
HEHong‑qing. Aerodynamics of solid rocket motor[M]. Northwestern Polytechnical University Press, 1988: 28-32.
参考文献 16
MukundaS H, PaulJ P. Universal behaviour in erosive burning of solid propellants[J]. Combustion and Flame. 1997, 109(1-2): 224-236.
参考文献 17
王志健,杜佳佳. 动网格在固体火箭发动机非稳态工作过程中的应用[J]. 固体火箭技术. 2008, 31(4): 350-353.
WANGZhi‑jian, DUJia‑jia. Application of dynamic mesh to unsteady burning of solid rocket motor[J]. Journal of solid rocket technology, 2008, 31(4): 350-353.
目录 contents

    摘要

    为了研究管状发射药内孔侵蚀燃烧及气体流动的特性,建立了考虑管内气相区域、管外的气相区域和固体火药区域的密闭爆发器内弹道模型。通过数值模拟结果与文献实验数据比对,验证了该密闭爆发器内弹道模型与计算方法的准确性。在此基础上,分别讨论了不同火药长度、内径和装填密度对内孔侵蚀燃烧的影响,结果表明,内径d=0.56 mm、长度l=50 mm管状药、已燃百分比0.016≤ψ≤0.8范围内,孔内外最大压力差由1.23 MPa增加至2.00 MPa,端面最大气体速度由430 m·s-1减小至200 m·s-1,端面最大的侵蚀燃烧系数由1.98下降至1.10,内孔侵蚀燃烧临界点由距离对称面7 mm处移动到20 mm,侵蚀燃烧面积减小65%;燃通比是影响内孔侵蚀燃烧的重要因素,燃通比小于71.4时侵蚀燃烧不发生;随长度增加、内径减小即随燃通比增大,侵蚀燃烧强度变强,燃通比大于142.8时侵蚀燃烧非常明显;当装填密度增加时,端面气体最大速度和侵蚀燃烧系数有微弱减小,而管内外气体压差增加明显。

    Abstract

    To study the characteristics of erosive burning and gas flow in internal perforation of a tubular propellant, an interior ballistic model of a closed bomb was established considering the gas phase region inside the tube, gas phase region outside the tube and solid propellant region. The accuracy of the interior ballistic model and calculation method of the closed bomb was verified through comparing the numerical simulation results with the experimental data in the literature. On this basis, the effects of different length, internal diameter and loading density of propellant on the erosive burning of internal perforation were discussed respectively. Results show that for the tubular propellant with d=0.56 mm, l=50 mm, when 0.016 ψ 0.80 (ψ is the burned percentage, the maximum pressure difference of internal and external perforation increases from 1.23 MPa to 2.00 MPa, the maximum gas velocity on the end face decreases from 430 m·s-1 to 200 m·s-1, the erosive burning coefficient on the end face decreases from 1.98 to 1.10, the erosive burning critical point of internal perforation moves from 7mm away from the symmetrical plane to 20 mm, the erosive burning area decreases by 65%. The ratio of burning surface to port area is an important factor affecting the erosive burning of internal perforation. The erosive burning does not occur when the ratio of burning surface to port area is less than 71.4. The erosive burning intensity becomes stronger with the increase of length and decrease of internal diameter, i.e. with the increase of the ratio of burning surface to port area, the erosive burning occurs evidently when the ratio of burning surface to port area is larger than 142.8. The maximum gas velocity on the end face and the erosive burning coefficient decrease slightly as the loading density increases, while the gas pressure difference of internal and external perforation increases obviously.

    Graphic Abstract

    图文摘要

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image018.png

    A single perforation stick propellant closed bomb model was established to study the internal perforation erosive burning and flow filed. The closed bomb is divided into three regions: the external gas region, solid propellant region and internal gas region. It′s a useful approach to reveal the erosive burning process in the combustion process.

  • 1 引 言

    1

    高装填密度和高渐增性燃烧装药技术是提高火炮弹道性能的有效途[1,2,3]。长杆状发射药具有点传火性能好,压力波小,装填密度高等优点,是提高火炮弹道性能的有效途径之一,美国使用部分切口多孔杆状药技[4],通过试验发现在保持最大膛压不变的情况下炮口初速增加6%。王琼[5]等通过对多孔环切杆状发射药在半密闭爆发器和模拟火炮中进行试验,发现该种药型点火通畅,压力波变小,示压效率高于粒状药。研究发[6,7,8],杆状药内孔直径越小、长度越长越有利于火药的增面燃烧;但是随着火药长度的增加,火药内孔的长径比将变大,火药孔内外的压力差将增大,端面气体速度将增大,极易导致火药破碎和侵蚀燃烧现象的发生。张柏[9]基于谢列伯梁列夫的窄孔理论,对侵蚀燃烧形成的双锥喇叭口形状的原因和机理进行了分析,提出管内气流效应是侵蚀燃烧的关键因素。杨丰[10]制备了不同尺寸管状药,通过密闭爆发器试验测试得到火药燃气生成猛度,发现当管状药燃通比大于某值后,其燃烧是一个非等面燃烧过程,燃烧前期燃气生成猛度增长较大,通过半密闭爆发器中止试验回收测得管状药的直径分布,发现由于侵蚀燃烧作用,管状药的喇叭口形状明显,靠近端面部分的内孔药由于侵蚀燃烧作用燃速增加非常明显。肖正刚[11,12,13]对多孔长杆状药进行了密闭爆发器中止试验,测试了内孔直径的分布情况,发现长杆状药侵蚀作用也非常明显,可通过合理的切口减小多孔长杆状药的侵蚀燃烧的影响。

    火药内孔气体的压力、密度和速度等是影响火药侵蚀燃烧的重要参数,而火药密闭爆发器试验是一个高温、高压密闭燃烧过程,内孔气体的压力、密度和速度参数不可能进行实时测量。因此,为了研究管状发射药(也称管状药)内孔侵蚀燃烧及流动特性,本研究建立了考虑管状药内孔侵蚀燃烧的密闭爆发器内弹道模型,通过数值模拟计算了管状药内孔的压力、气流速度及侵蚀燃烧等特性的变化规律,为管状发射药的试验研究及实际应用提供指导。

  • 2 物理模型

    2

    在密闭爆发器测试中,点火药燃烧产生高温火药气体点燃发射药,发射药的燃烧过程分为两个阶段:管状药完整燃烧阶段和烧穿分裂后减面燃烧阶段。图1为密闭爆发器内单根管状药简化示意图,密闭爆发器内的空间可分为三个区域:管内气相区域、管外气相区域和固体火药区域。管状药着火后固体火药区域开始释放火药燃气,内外壁不断退移。在管状药内壁区域形成管内气相区域,管状药外部形成管外气相区域,同时内外区域不断进行质量、动量和能量的交换。管内气相区域由于燃烧及流动特性的影响,产生侵蚀燃烧。当固体火药区域达到破裂条件后,管状药燃烧将进入分裂后减面燃烧阶段。

    图1
                            管状药燃烧简化示意图

    图1 管状药燃烧简化示意图

    Fig.1 Sketch of the tubular propellant combustion

    注:l—火药长度, d—火药内径, D—火药外径

    NOTE: l—propellant length, d—internal diameter of propellant, D—external diameter of propellant

  • 3 数学模型及计算方法

    3
  • 3.1 基本假设

    3.1

    根据以上所描述物理模型,为了便于进一步数学建模与计算,需要进行一定的基本假设,具体如下:

    (1) 管状药具有相同尺寸,不考虑点火过程影响,所有表面同时着火;

    (2) 不考虑气体粘性影响,火药燃气服从诺贝尔‑阿贝尔方[14]

    (3) 管状药内孔表面考虑侵蚀燃烧,火药退移速率由当地火药燃烧速率决定;

    (4) 管状药外侧及端面服从平行层燃烧假设,在平均压力作用下燃烧;

    (5) 火药最大厚度小于0.1 mm即可以认为固体区域破裂,火药燃烧将进入分裂后减面燃烧阶段;

    (6) 忽略火药化学反应及火药气体向爆发器内壁的热散失。

  • 3.2 管内气相区域建模

    3.2
  • 3.2.1 管内气相控制方程

    3.2.1

    管内区域采用二维流体控制方程,包括连续方程、动量方程和能量方[15]

    Q t + E x + F y = 0
    (1)

    其中,

    Q = ρ , ρ u , ρ v , ρ T T
    E = [ ρ u , ρ u 2 + p , ρ u v , ( ρ E + p ) u ] T
    F = ρ v , ρ u v , ρ v 2 + p , ( ρ E + p ) v T

    式中, ρ 为流体密度,kg·m-3uv分别为流体xy向速度,m·s-1E为单位体积内能,J·m-3p为流体压强,Pa。

  • 3.2.2 边界条件

    3.2.2

    火药内孔中间对称面为镜面对称边界条件;中轴线为二维轴对称边界;右侧为压力出口边界条件,压力和温度值与管外气相区域压力和温度值耦合计算;管内燃烧表面为质量入口边界条件,温度为火药气体燃烧温度Tf

    m ˙ = ρ p r
    (2)

    式中, m ˙ 为单位面积质量流率,kg·m-2·s-1r为火药表面火药燃烧速率,m·s-1; ρ p 为火药密度,kg·m-3

  • 3.2.3 侵蚀燃烧模型

    3.2.3

    管内燃烧表面侵蚀燃烧采用Mukunda[15]基于实验拟合得到的通用侵蚀燃烧公式:

    r = ε r 0
    (3a)
    r 0 = u 1 p n
    (3b)
    ε = 1 + 0.023 g 0.8 - g t h 0.8 Η g - g t h
    (3c)
    g = G / ρ p r 0 ρ p r 0 d 0 / μ - 0.125
    (3d)

    式中,r0为基础燃速, u 1 为燃速系数,m·s-1·Pa-1n为燃速压力指数; ε 为侵蚀燃烧系数,是侵蚀燃烧强弱的标志;g为无量纲质量流率,gth为无量纲质量流率阀值,H为Heaviside阶跃函数; G 为通过截面的质量流率,kg·m-2·s-1 ρ p r 0 为无侵蚀燃烧表面燃烧流率,kg·m-2·s-1

  • 3.3 管外的气相区域建模

    3.3

    管外气体区域内弹道基本方[14]

    p o u t V 0 - V p - α ω g = f ω g
    (4)

    式中,pout为平均压强,Pa;V0为密闭爆发器容积,m3Vp为颗粒总体积; α 为火药余容,m3·kg-1 ω g 为火药外火药燃气的总质量,f为火药力,kJ·kg-1

    ω g = ω f l o w + ω o u t + ω i g n
    (5)

    式中, ω g ω f l o w ω i g n ω o u t 分别为管外气相区域火药气体总质量、管内外交换的质量、点火药的质量和火药外侧燃烧质量,kg。

    d ω o u t d t = ρ p S p r 0
    (6)

    式中,Sp分别为火药颗粒外侧表面面积和端面的面积,m2r0外表面火药燃烧速度,方程同式(3b)。

  • 3.4 管状药分裂后减面燃烧阶段建模

    3.4

    管状药分裂后燃烧过程是一个减面燃烧过程,内弹道方程、形状函数和燃速方[16]如下:

    p o u t V 0 ω - 1 - ψ ρ p - α ψ = f ψ ψ = χ s 1 + λ s Z d Z d t = u 1 p n e 1
    (7)

    式中, ψ 为已燃百分比;Z为相对已燃厚度;e1为火药半弧厚,m; χ s λ s 为火药形状特征量。

  • 3.5 数值计算方法

    3.5

    管内气相计算区域用FLUENT软件进行求解,管外气相区域利用User‑Defined Function(UDF)进行计[17]。管内气相区域采用轴对称结构和镜面对称结构,取火药内孔四分之一气相区域为流体计算的区域。管内气相区域采用Roe_FDS有限体积法进行离散,采用二阶迎风格式离散控制方程,常微分方程组采用四阶精度的Runge‑Kutta法进行数值求解。

    管内气相区域与管外区域进行质量、动量和能量进行交换,管外气相区域计算所得参数作为下一时刻的管内区域端面的边界条件。管内区域采用非结构网格,火药燃烧面为动网格区域,网格退移速度由火药燃烧速率决定。当网格移动后内孔变大后,网格尺寸或者畸变率超过某一值后,网格将分裂产生新的网格来提高网格质量,保证计算的精度。

  • 4 计算方法验证及数值结果分析

    4
  • 4.1 数值方法验证

    4.1

    为了验证本文提出的模型及计算方法对内孔侵蚀燃烧描述的准确性,选取文献[10]200 cm3半密闭爆发器燃烧中止试验为验证对象,通过与中止燃烧测试结果进行比较验证模型及计算方法的准确性。管状药的具体尺寸及参数如下:管状药长l=50 mm,内径d=0.560 mm,外径D=1.820 mm,爆温T0=3362 K,装填密度Δ=140 kg·m-3,孔内外初始压力为点火压力p=10 MPa,气体速度为零。

    本文计算的内孔半径分布和试验结[10]对比如图2所示。从图2中可以看出,计算结果与文献中止燃烧测试的半径沿轴向分布两者基本吻合,说明本文提出的模型及计算方法能够准确描述管状药内孔侵蚀燃烧过程;管状药端面处和中间部分的火药燃烧厚度分别为1.094 mm和0.072 mm,这主要是由于侵蚀燃烧的作用使得靠近端面部分的火药燃烧速度增加。

    图2
                            模拟计算的内孔半径分布与试验结果[10]比较

    图2 模拟计算的内孔半径分布与试验结[10]比较

    Fig.2 Comparison of the radius distribution of internal perforation obtained by simulated calculation(this work) and the experimental results[10]

    管状发射药管内与管外两区域是耦合计算的过程,为了验证该耦合计算的准确性,对管外气相区域压力与理论值进行比较,具体结果如表1。由表1中可见, ψ = 0.3 ψ = 0.5 ψ = 0.9 三个时刻,压力理论解和本研究结果的绝对误差小于2.5 MPa,相对误差小于2.5%,说明该模型能够准确地模拟管状药的燃烧过程。 ψ = 0.9 时,对称面和端面处的管状药壁厚分别为0.07 mm、0.04 mm,根据前文假设,火药壁厚小于0.10 mm即认为此时管状药分裂,进入减面燃烧阶段。

    表1 管外气体压力理论值和数值计算值的比较及火药厚度

    Table 1 Comparison of the theoretical values and the numerical calculation ones of gas pressure outside the tube and the thickness of propellant

    Ψp/MPa((D‑d)/2)/mm
    theory value[10]this paperabsolute difference

    relative

    difference/%

    symmetryend face
    01010000.6300.630
    0.365.564.41.11.70.4500.416
    0.5103.6101.91.71.60.3250.290
    0.9183.3180.82.51.40.0700.040
    表1
                    管外气体压力理论值和数值计算值的比较及火药厚度
  • 4.2 计算结果分析

    4.2

    建立管状发射药密闭爆发器模型并进行数值计算,可以得到管内外压力、管内气体速度及侵蚀燃烧系数随燃烧过程的变化情况,管内外压力差Δp和端面气体最大速度vd与已燃百分比ψ关系如图3所示。由图3可以看出,在燃烧初期,ψ<0.016时,管内外压力差和气体速度急剧增加,这主要是在火药所有表面同时着火的假设下,内孔燃烧释放的火药气体不能及时通过端面孔流出而导致这一反常现象。当ψ≥0.016时,管内燃烧释放和通过端面流出的气体的速度达到动态平衡状态;当ψ=0.016时Δp=1.23 MPa、vd=456.8 m·s-1,随着燃烧进行,管内外的压力差增加,端面的气体速度减小,到ψ=0.80时Δp=2.00 MPa、vd=200.0 m·s-1

    图3
                            端面气体最大速度vd‑ψ和管内外压差Δp‑ψ关系

    图3 端面气体最大速度vdψ和管内外压差Δpψ关系

    Fig.3 The relationship of the maximum gas velocity on the end face v d and pressure difference inside and outside the tube Δ p vs. the burned percentage ψ

    对管内二维轴对称的气体区域进行计算可得,在 ψ = 0.05 时,管内气体压力和速度分布见图4。从图4可见,沿轴向方向,从管状药中间对称面到端面,气体压力逐渐减小、速度逐渐增加;压力最大点在中间对称面,速度的最大点在端面轴线处。

    图4
                            ψ=0.05时管内气体速度和压力分布图

    图4 ψ = 0.05 时管内气体速度和压力分布图

    Fig.4 Internal perforation gas velocity and pressure distribution when ψ = 0.05

    不同已燃百分比下管内轴线上气体速度分布如图5。图5可见,气体速度从中间对称面到两端出口端面几乎呈线性增加,且在端面处达到最大速度值,气体速度随着已燃百分比增加而减小。

    侵蚀燃烧系数ε是侵蚀燃烧强弱的标志,ε=1表示没有侵蚀燃烧的作用;ε≥1的转折点为侵蚀燃烧临界点,ε越大侵蚀燃烧作用越明[9]。端面侵蚀燃烧系数εd和管外气相区域压力pout与已燃百分比的关系如图6。由图6可见,初始状态压力为点火压力p=10 MPa,管外区域的压力与已燃百分比近似呈线性增加; ψ = 0.016 时,侵蚀燃烧系数 ε = 1.98 即火药的燃烧速度是基础燃烧速度的1.98倍;随着燃烧的进行,侵蚀燃烧系数减小,侵蚀燃烧减弱;当 ψ = 0.90 时,端面最大侵蚀燃烧系数减小到1即没有侵蚀燃烧作用。

    图6
                            端面侵蚀燃烧系数和管外气相区域压力与已燃百分比关系

    图6 端面侵蚀燃烧系数和管外气相区域压力与已燃百分比关系

    Fig.6 The relationship of the end face erosive burning coefficient ε and gas phase region pressure outside the tube pout vs. the burned percentage ψ

    图5
                            不同已燃百分比轴线上气体速度分布

    图5 不同已燃百分比轴线上气体速度分布

    Fig.5 The gas velocity distribution on axis at different the burned percentage

    不同的已燃百分比管内侵蚀燃烧系数沿轴向的分布如图7。由图7可见, ψ = 0.10 时,侵蚀燃烧临界点在l=8mm处, l 8 m m 区域内 ε = 1 ,侵蚀燃烧没有发生;当 l > 8 m m 时, ε > 1 ,且越靠近端面侵蚀燃烧系数越大,侵蚀燃烧作用越明显。在 0.10 ψ 0.70 范围内,侵蚀燃烧临界点从8 mm处逐渐向端面方向移至22 mm位置,侵蚀燃烧影响的面积减小50%;端面最大侵蚀燃烧系数从1.63减小至1.05。侵蚀燃烧面积逐渐减小、强度减弱,两者共同作用下侵蚀燃烧对火药燃烧的影响将逐渐减弱。

    图7
                            不同已燃百分比侵蚀燃烧系数沿轴向分布

    图7 不同已燃百分比侵蚀燃烧系数沿轴向分布

    Fig.7 Erosive burning distribution along the axis direction at different burned percentage

  • 5 不同因素对管状药侵蚀燃烧的影响分析

    5

    管状药的长度、内孔直径和装填密度是影响火药侵蚀燃烧的重要因素,本部分计算了这几个因素对管状药管内气体速度、侵蚀燃烧系数和管内外压力差等参数的影响。由4.2计算可知侵蚀燃烧主要发生在燃烧初期,同时为了节约计算资源只计算 ψ 0.20 的燃烧过程。

  • 5.1 管状药长度对内孔燃烧影响

    5.1

    为了研究管状药长度对内孔侵蚀燃烧的影响,计算了长度分别为l=10 mm、20 mm、40 mm、50 mm和60 mm的5种尺寸火药的燃烧情况。不同长度火药的端面最大气体速度vd、端面侵蚀燃烧系数εd和管内外压力差 Δ p 与已燃百分比的关系如图8。由图8a、8b可见,火药长度越大,端面最大气体速度、端面侵蚀燃烧系数和管内外压差的值越大; l 40 m m ε d > 1.35 ,侵蚀燃烧作用明显; l 20 m m 时,端面侵蚀燃烧系数 ε d 接近于1,侵蚀燃烧影响非常微弱。由图8c可见,随着火药长度增加,管内外压差有明显增加, l = 60 m m 管状药管内外压差大于2.0 MPa。

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image008.png

    a. end face max gas velocity distribution

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image009.png

    b. end face erosive burning distribution

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image010.png

    c. internal and external max pressure difference

    图8 管状药长度对气体速度、侵蚀燃烧和压力差的影响

    Fig.8 Effect of length of tubular propellant on gas velocity, erosive burning and pressure difference

    已燃百分比 ψ = 0.2 时不同长度管状药侵蚀燃烧系数沿轴向的分布如图9。由图9可见,不同长度火药侵蚀燃烧发生临界点在距离对称面x=10 mm处;x>10 mm区域为侵蚀燃烧影响区域,火药越长侵蚀燃烧的面积越大;同时侵蚀燃烧系数越大,两者共同作用下,侵蚀燃烧作用越明显。

    图9
                            ψ=0.20时不同火药长度侵蚀燃烧系数沿轴向分布

    图9 ψ = 0.20 时不同火药长度侵蚀燃烧系数沿轴向分布

    Fig.9 Distribution along the axis direction for erosive burning coefficient with different propellant length when ψ = 0.20

  • 5.2 管状药内径对内孔燃烧的影响

    5.2

    为了研究管状药内径对内孔侵蚀燃烧的影响,计算了内径d=2.800 mm、1.400 mm、0.700 mm、0.560 mm和0.467 mm的5种火药燃烧情况。不同内径的火药端面最大气体速度vd、端面侵蚀燃烧系数εd和管内外压力差 Δ p 与已燃百分比的关系如图10。由图10a、10b可见,d<0.700 mm时,vd>300 m·s-1 ε > 1.40 ,且内径越小,端面气体最大速度及端面侵蚀燃烧系数越大;d>1.400 mm, ε < 1.27 此时侵蚀燃烧作用不明显。由图10.c可见,内径越小,管内外最大压差越大,且内径d=0.560 mm和d=0.700 mm两种火药的管内外压差随着燃烧进行增加更为明显。

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image012.png

    a. end face max gas velocity distribution

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image013.png

    b. end face erosive burning distribution

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image014.png

    c. the internal and external max pressure difference

    图10 管状药内径对气体速度、侵蚀燃烧和压力差的影响

    Fig.10 Effect of internal perforation diameter of tubular propellant on gas velocity, erosive burning and pressure difference

  • 5.3 装填密度对内孔燃烧的影响

    5.3

    为了研究装填密度对管状药内孔侵蚀燃烧的影响,计算了126 kg·m-3、140 kg·m-3和154 kg·m-3三种装填密度下的燃烧情况。不同装填密度端面气体最大速度vd、端面侵蚀燃烧系数εd和管内外压力差 Δ p 与已燃百分比关系如图11所示。由图11a和图11b可见,装填密度增加,端面气体最大速度、侵蚀燃烧系数将越小,但影响非常小;由图11c可见,装填密度增加管内外压差明显增加; ψ = 0.20 时,管内外压力差分别增加了0.34 MPa、0.49 MPa和0.56 MPa,这可能是由于装填密度增加,火药外部气体压力变大,火药气体在内孔不容易排出,致使孔内外压差增加。

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image015.png

    a. end face max gas velocity distribution

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image016.png

    b. end face erosive burning distribution

    html/hncl/CJEM2018080/media/3900802a-3d88-482d-9d2d-1ae758047f9b-image017.png

    c. internal and external max pressure difference

    图11 装填密度对气体速度、侵蚀燃烧和压力差的影响

    Fig.11 Effect of loading density on gas velocity, erosive burning and pressure difference

  • 5.4 燃通比对管状药侵蚀燃烧现象的影响

    5.4

    燃通比 χ 为内孔火药燃烧面积与端面通道面积的比[10],其定义如下,

    χ = S A p = π d l 2 π d 2 4 = 2 l d
    (11)

    式中,S为内孔燃面的面积,Ap是端面孔的面积,l、d分别是火药长度、内径。由于密闭爆发器尺寸限制,通常使用小孔径的短管状药密闭爆发器试验来研究具有相同燃通比的长管状药的侵蚀燃烧情[10],为了研究燃通比对管状药侵蚀燃烧现象的影响规律,计算得到的4组燃通比管状药端面侵蚀燃烧结果见表2。从表2中可见, ψ = 0.05 ψ = 0.10 ψ = 0.20 三种情况下,端面侵蚀燃烧系数的绝对误差不大于0.03,且相对误差不大于2.3%。 ψ = 0.05 时, χ 71.4 ε 1 ,侵蚀燃烧作用几乎不发生; χ 142.8 ε 1.57 ,侵蚀燃烧明显;燃通比越大,侵蚀燃烧作用越明显。由此可见,燃通比是影响火药侵蚀燃烧的重要因素,可以利用小尺寸管状药来预测相同燃通比的大尺寸火药的侵蚀燃烧作用。

    表2 不同燃通比端面侵蚀燃烧系数 ε d 比较

    Table 2 Comparison of the end face erosive burning coefficient ε d at the different ratio of burning surface to port area

    χ l/mmd/mmψ=0.05ψ=0.10ψ=0.20
    ε d ADRD/% ε d ADRD/% ε d ADRD/%
    214.3

    60

    50

    0.560

    0.467

    2.04

    2.06

    0.020.97

    1.80

    1.79

    0.010.56

    1.53

    1.51

    0.020.13
    35.8

    10

    50

    0.560

    2.800

    1.00

    1.00

    00

    1.00

    1.00

    00

    1.00

    1.00

    00
    71.4

    20

    50

    0.560

    1.400

    1.11

    1.12

    0.010.89

    1.05

    1.03

    0.021.90

    1.00

    1.00

    00
    142.8

    40

    50

    0.560

    0.700

    1.58

    1.57

    0.010.64

    1.44

    1.45

    0.010.69

    1.27

    1.30

    0.032.30

    NOTE: AD represents for absolute difference; RD represents for relative difference

  • 6 结 论

    6

    针对管状发射药内孔侵蚀燃烧问题,建立了考虑管状药内孔侵蚀燃烧的密闭爆发器内弹道模型,通过Fluent二次开发,计算了管状药内孔侵蚀燃烧及流动特性,主要结论如下:

    (1)侵蚀燃烧主要发生在火药燃烧初期,越靠近管状药端面侵蚀燃烧强度越大;0.016≤ψ≤0.8范围内侵蚀燃烧系数由1.98下降至1.10,侵蚀燃烧临界点由距离对称面7 mm处移动到20 mm,侵蚀燃烧面积减小65%,侵蚀燃烧强度及侵蚀燃烧面积均随着燃烧的不断进行而逐渐减小。

    (2)燃通比是影响火药侵蚀燃烧的因素,燃通比 χ 71.4 时,侵蚀燃烧不发生,同一燃通比下的不同尺寸火药的侵蚀燃烧系数基本相同; χ 142.8 侵蚀燃烧明显,燃通比越大,侵蚀燃烧越明显。

    (3)火药侵蚀燃烧系数和气流速度随着装填密度增加略有降低,管内外压力差增加明显,因此在高装填密度下需要特别考虑管内外压力差的影响。

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赵小亮

机 构:南京理工大学 能源与动力工程学院, 江苏 南京 210094

Affiliation:School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

邮 箱:xiaoliang2007@126.com

作者简介:赵小亮(1987-),男,博士研究生,主要从事火炮内弹道方向研究。e‑mail:xiaoliang2007@126.com

张小兵

机 构:南京理工大学 能源与动力工程学院, 江苏 南京 210094

Affiliation:School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

角 色:通讯作者

Role:Corresponding author

邮 箱:zhangxb680504@163.com

作者简介:张小兵(1968-),男,教授,主要从事内弹道两相流、新概念发射理论研究。e‑mail:zhangxb680504@163.com

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Ψp/MPa((D‑d)/2)/mm
theory value[10]this paperabsolute difference

relative

difference/%

symmetryend face
01010000.6300.630
0.365.564.41.11.70.4500.416
0.5103.6101.91.71.60.3250.290
0.9183.3180.82.51.40.0700.040
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χ l/mmd/mmψ=0.05ψ=0.10ψ=0.20
ε d ADRD/% ε d ADRD/% ε d ADRD/%
214.3

60

50

0.560

0.467

2.04

2.06

0.020.97

1.80

1.79

0.010.56

1.53

1.51

0.020.13
35.8

10

50

0.560

2.800

1.00

1.00

00

1.00

1.00

00

1.00

1.00

00
71.4

20

50

0.560

1.400

1.11

1.12

0.010.89

1.05

1.03

0.021.90

1.00

1.00

00
142.8

40

50

0.560

0.700

1.58

1.57

0.010.64

1.44

1.45

0.010.69

1.27

1.30

0.032.30

图1 管状药燃烧简化示意图

Fig.1 Sketch of the tubular propellant combustion

图2 模拟计算的内孔半径分布与试验结[10]比较

Fig.2 Comparison of the radius distribution of internal perforation obtained by simulated calculation(this work) and the experimental results[10]

表1 管外气体压力理论值和数值计算值的比较及火药厚度

Table 1 Comparison of the theoretical values and the numerical calculation ones of gas pressure outside the tube and the thickness of propellant

图3 端面气体最大速度vdψ和管内外压差Δpψ关系

Fig.3 The relationship of the maximum gas velocity on the end face v d and pressure difference inside and outside the tube Δ p vs. the burned percentage ψ

图4 ψ = 0.05 时管内气体速度和压力分布图

Fig.4 Internal perforation gas velocity and pressure distribution when ψ = 0.05

图6 端面侵蚀燃烧系数和管外气相区域压力与已燃百分比关系

Fig.6 The relationship of the end face erosive burning coefficient ε and gas phase region pressure outside the tube pout vs. the burned percentage ψ

图5 不同已燃百分比轴线上气体速度分布

Fig.5 The gas velocity distribution on axis at different the burned percentage

图7 不同已燃百分比侵蚀燃烧系数沿轴向分布

Fig.7 Erosive burning distribution along the axis direction at different burned percentage

图8 管状药长度对气体速度、侵蚀燃烧和压力差的影响 -- a. end face max gas velocity distribution

Fig.8 Effect of length of tubular propellant on gas velocity, erosive burning and pressure difference -- a. end face max gas velocity distribution

图8 管状药长度对气体速度、侵蚀燃烧和压力差的影响 -- b. end face erosive burning distribution

Fig.8 Effect of length of tubular propellant on gas velocity, erosive burning and pressure difference -- b. end face erosive burning distribution

图8 管状药长度对气体速度、侵蚀燃烧和压力差的影响 -- c. internal and external max pressure difference

Fig.8 Effect of length of tubular propellant on gas velocity, erosive burning and pressure difference -- c. internal and external max pressure difference

图9 ψ = 0.20 时不同火药长度侵蚀燃烧系数沿轴向分布

Fig.9 Distribution along the axis direction for erosive burning coefficient with different propellant length when ψ = 0.20

图10 管状药内径对气体速度、侵蚀燃烧和压力差的影响 -- a. end face max gas velocity distribution

Fig.10 Effect of internal perforation diameter of tubular propellant on gas velocity, erosive burning and pressure difference -- a. end face max gas velocity distribution

图10 管状药内径对气体速度、侵蚀燃烧和压力差的影响 -- b. end face erosive burning distribution

Fig.10 Effect of internal perforation diameter of tubular propellant on gas velocity, erosive burning and pressure difference -- b. end face erosive burning distribution

图10 管状药内径对气体速度、侵蚀燃烧和压力差的影响 -- c. the internal and external max pressure difference

Fig.10 Effect of internal perforation diameter of tubular propellant on gas velocity, erosive burning and pressure difference -- c. the internal and external max pressure difference

图11 装填密度对气体速度、侵蚀燃烧和压力差的影响 -- a. end face max gas velocity distribution

Fig.11 Effect of loading density on gas velocity, erosive burning and pressure difference -- a. end face max gas velocity distribution

图11 装填密度对气体速度、侵蚀燃烧和压力差的影响 -- b. end face erosive burning distribution

Fig.11 Effect of loading density on gas velocity, erosive burning and pressure difference -- b. end face erosive burning distribution

图11 装填密度对气体速度、侵蚀燃烧和压力差的影响 -- c. internal and external max pressure difference

Fig.11 Effect of loading density on gas velocity, erosive burning and pressure difference -- c. internal and external max pressure difference

表2 不同燃通比端面侵蚀燃烧系数 ε d 比较

Table 2 Comparison of the end face erosive burning coefficient ε d at the different ratio of burning surface to port area

image /

l—火药长度, d—火药内径, D—火药外径

l—propellant length, d—internal diameter of propellant, D—external diameter of propellant

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AD represents for absolute difference; RD represents for relative difference

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