气相爆轰波起爆与传播机理研究进展

韩文虎; 张博; 王成

doi:10.11883/bzycj-2021-0398

气相爆轰波起爆与传播机理研究进展

doi: 10.11883/bzycj-2021-0398

韩文虎^1,,
张博²,
王成^1, ,

1.
北京理工大学爆炸科学与技术国家重点实验室，北京 100081
2.
上海交通大学航空航天学院，上海 200240

基金项目: 国家自然科学基金（11972090）

详细信息

作者简介:
韩文虎（1982－　），男，博士，副研究员，hanwenhu@bit.edu.cn

通讯作者:
王　成（1972－　），男，博士，教授，wangcheng@bit.edu.cn

中图分类号: O381
计量
- 文章访问数: 1240
- HTML全文浏览量: 767
- PDF下载量: 303
- 被引次数: 1
出版历程
- 收稿日期: 2021-09-22
- 修回日期: 2021-12-12
- 网络出版日期: 2021-12-14
- 刊出日期: 2021-12-05

Progress in studying mechanisms of initiation and propagation for gaseous detonations

HAN Wenhu^1
,,
ZHANG Bo²,
WANG Cheng^{1
, ,}

1.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
2.
School of Aeronautics and Astronautics, Shanghai Jiaotong University, Shanghai 200240, China

摘要

摘要: 对近年来气相爆轰起爆及传播在数值模拟和实验方面的研究工作进行了综述，结合作者近几年在这一领域开展的工作，评述了目前的研究热点和难点，简要指出了未来的研究方向。着重介绍了黏性扩散、详细化学反应机理、爆轰胞格不稳定性在爆轰起爆和传播理论和计算研究中的作用，以及爆轰波传播过程中实验技术和理论预测模型的进展。
- 气相爆轰 /
- 起爆与传播机理 /
- 黏性扩散 /
- 胞格不稳定性
Abstract: The numerical and experimental studies in recent years on the mechanisms of initiation and propagation for gas phase detonations are reviewed. Combined with the author’s works in recent years, the current hotspots and difficult issues are summarized, together with the proposed future research directions. The focus areas include viscous diffusion, detailed chemical reaction mechanism, the role of detonation instability in the theoretical and computational studies of detonation initiation and propagation, and the advances of experimental technology and theoretical prediction models on the propagation of detonation wave.
- gaseous detonations /
- mechanism of initiation and propagation /
- viscous diffusion /
- detonation instability

HTML全文

当前，随着海洋战略地位的日益突出，水下枪炮研究逐渐成为热点。膛口流场现象的复杂性和极高的时空演变特性会对弹丸的飞行产生初始扰动，进而影响到射击精度。因此，中间弹道学的研究受到了广泛关注。不同于空气中发射，水下发射时弹丸及火药燃气受到的水阻力更大，膛口流场现象更复杂。因此，有必要对水下枪炮发射膛口流场发展过程进行深入研究。

针对枪炮空气中发射时的膛口流场已经开展了大量的实验、理论分析和数值模拟研究。为了能够较清楚地认识膛口流场的结构，Steward等^[1]、Moumen等^[2]和郭则庆等^[3]对枪炮膛口流场进行了不同的可视化实验研究。随着计算机和动网格技术的发展，含初始流场和运动弹丸的膛口流场以及弹丸在膛口流场中的受力情况开始受到关注。膛口初始流场对火药燃气流场的发展及弹丸运动有一定的影响，李子杰等^[4]基于有限体积法，对有、无初始流场两种条件下的膛口流场进行了数值模拟，分析了初始流场对膛口流场的影响。陈川琳等^[5]利用实验和数值模拟相结合的方法分析了弹头在膛口流场中的受力和运动规律。

相较于空气中发射，枪炮水下发射时的情形更为复杂，因此学者们从不同的方面对枪炮水下发射过程进行了研究。水下发射时，燃气从炮口中喷出，在液体中高速扩展形成燃气射流。Harby等^[6]、甘晓松等^[7]和Xue等^[8]对水下燃气射流进行了实验和数值模拟研究，分析了射流气液边界的不稳定性及燃气扩展过程中出现的颈缩、断裂等现象。水下炮密封式发射内弹道特性虽与常规内弹道有许多相似之处，但仍存在一定的差异^[9]，通过对水下炮内弹道的研究，可以更好地掌握弹丸水下运动规律。超空泡射弹入水后形成超空泡，利用超空泡的水中减阻特性，降低了弹丸衰减速度，实现水中高速航行。易文俊等^[10]、施红辉等^[11]、刘富强等^[12]、黄海龙等^[13]及Gao等^[14]对水下超空泡射弹特性进行了数值模拟。针对水下膛口流场方面的研究，则主要体现在密封式发射和全淹没式发射方式。张欣尉等^[15]、张京辉等^[16]分别利用密封式发射和全淹没式发射方式对12.7 mm水下枪在不同水深条件下的膛口流场进行了数值模拟，发现水深与膛口流场特性存在一定的规律性。

前人所研究的重点多为空气中膛口流场、水下燃气射流场及水下枪膛口流场特性，对于水下火炮发射膛口流场特性的研究尚未见报道。本文中，利用30 mm口径火炮研究水下炮密封式发射膛口流场特性及演变规律，通过对火炮在空气中和水下发射时的膛口流场特性进行对比分析，讨论不同介质对火炮膛口流场演化特性的影响规律。

1. 数理模型

1.1 物理模型

水下发射膛口流场是一个较复杂的流场，为了能够对其进行有效的数值模拟，根据火炮水下密封式发射的特点，对所研究模型进行如下假设：

（1）火药颗粒膛内燃烧遵循几何燃烧定律，药粒具有均一的理化性质，形状和尺寸一致，且遵循燃烧速度定律。

（2）弹丸沿x轴正向移动，不考虑重力的影响，将膛口燃气射流与水的相互作用近似看作二维轴对称非稳态过程问题进行处理。

（3）膛口燃气射流视为可压缩理想气体，满足理想气体状态方程，且忽略膛口燃气多组分化学反应的影响；将水视为不可压缩相，密度取 998.2 kg/m³。

（4）因水下密封式发射时，身管内有少量气体，弹丸出膛后不会直接与水接触，且膛口流场作用时间短暂，因此不考虑膛口附近水的空化及相变。

1.2 数学模型^[15-16]

本文中，各模型方程式如下。

（1）连续性方程为：

$\frac{{\partial \left( {{\alpha _q}\,{\rho _q}} \right)}}{{\partial t}} + \nabla \cdot \left( {{\alpha _q}\,{\rho _q}\,{\boldsymbol{v}}} \right) = 0$

(1)

式中： $q = 1,2$ 分别表示气体相和液体相； ${\ \rho _q}$ 为对应气体相和液体相的密度； ${\alpha _q}$ 为对应气体相和液体相的体积分数，且 ${\alpha _1} + {\alpha _2} = 1$ ； $t$ 为时间；v为速度矢量。

（2）动量守恒方程为：

$\frac{\partial }{{\partial t}}(\rho {\boldsymbol{v}}) + \nabla \cdot (\rho {{\boldsymbol{v}}{\boldsymbol{v}} }) = - \nabla p + \nabla \cdot [\mu (\nabla {{\boldsymbol{v}}} + \nabla {{{\boldsymbol{v}}}^{\rm{T}}})]$

(2)

$\rho = \sum\limits_{{{q}} = 1}^{{n}} {{\alpha _{{q}}}} {\rho _{{q}}}$

(3)

式中： $\ \rho$ 为气液混合密度，且 $\ \rho = {\alpha _1}{\rho _1} + (1 - {\alpha _1}){\rho _2}$ ；p为流场中的流体压力； $\mu$ 为黏度系数。

（3）能量守恒方程为：

$\frac{\partial }{{\partial t}}(\rho E) + \nabla \cdot [{\boldsymbol{v}}(\rho E + p)] = \nabla \cdot ({k_{\rm{e}}}\nabla T)$

(4)

式中: E为平均能量，E=( ${\alpha _1}{\rho _1}{E_1} + {\alpha _2}{\rho _2}{E_2}$ )/( ${\alpha _1}{\rho _1} + {\alpha _2}{\rho _2}$ )；T为平均温度，T= ( ${\alpha _1}{\rho _1}{T_1} + {\alpha _2}{\rho _2}{T_2}$ )/( ${\alpha _1}{\rho _1} + {\alpha _2}{\rho _2}$ )； ${k_{\rm{e}}}$ 为有效热传导率。

（4）理想气体状态方程为：

$p = \rho RT$

(5)

式中：R为火药燃气常数。

（5）湍流方程：

采用的湍流模型为标准k- $\varepsilon$ 模型，该模型的优点是可以忽略分子黏性的影响，具有较高的稳定性、经济性和计算精度：

$\frac{\partial }{{\partial t}}\left( {\rho \kappa } \right) + \frac{\partial }{{\partial {x_i}}}\left( {\rho \kappa {{\boldsymbol{u}}_i}} \right) = \frac{\partial }{{\partial {x_j}}}\left[ \left( {\mu + \frac{{{\mu _{\rm{t}}}}}{{{\sigma _\kappa }}}} \right)\frac{{\partial \kappa }}{{\partial {x_j}}} \right] - \rho \overline {{\boldsymbol{u}}'_i\, {\boldsymbol{u}}'_j} \frac{{\partial {{\boldsymbol{u}}_j}}}{{\partial {x_i}}} - \rho \varepsilon$

(6)

$\frac{\partial }{{\partial t}}\left( {\rho \varepsilon } \right) + \frac{\partial }{{\partial {x_i}}}\left( {\rho \varepsilon {{\boldsymbol{u}}_i}} \right) = \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _{\rm{t}}}}}{{{\sigma _\varepsilon }}}} \right)\frac{{\partial \varepsilon }}{{\partial {x_j}}}} \right] - {C_{\varepsilon 2}}\rho \frac{{{\varepsilon ^2}}}{\kappa } + {C_{\varepsilon 1}}\frac{\varepsilon }{\kappa }\rho \overline {{\boldsymbol{u}}'_i\, {\boldsymbol{u}}'_j} \frac{{\partial {{\boldsymbol{u}}_j}}}{{\partial {x_i}}}$

(7)

${\mu _{\rm{t}}} = {C_\mu }{\kappa^2}/\varepsilon$

(8)

式中： $\kappa$ 为湍流脉动动能； $\varepsilon$ 为湍流耗散率；i和j为自由指标， ${{\boldsymbol{u}}_i}$ 和 ${{\boldsymbol{u}}_j}$ 为速度矢量； $\overline {{\boldsymbol{u}}'_i\,{\boldsymbol{u}}'_j}$ 为雷诺应力；常数 ${\sigma _\kappa }$ =1.0和 ${\sigma _\varepsilon }$ =1.3分别为湍流脉动动能和湍流耗散率对应的普朗特数； ${\mu _{\rm{t}}}$ 为湍流黏性系数；经验系数 ${C_{\varepsilon 1}}$ =1.44， ${C_{\varepsilon 2}}$ =1.92， ${C_\mu }$ =0.08。

本文中，数值模拟计算需要耦合以下内弹道方程组^[15]。

（1）火药形状函数为：

$\psi = \chi Z\left( {1 + \lambda Z + {\mu _{\rm{c}}}{Z^2}} \right)$

(9)

式中： $\psi$ 为药室内已燃火药的百分数， $\ \chi$ 、 $\lambda$ 和 ${\ \mu _{\rm{c}}}$ 分别为火药形状特征量， $Z$ 为已燃相对厚度。

（2）火药燃速方程为：

$\frac{{{\rm{d}}Z}}{{{\rm{d}}t}} = \frac{{{u_1}{{p_{\rm{a}}^n}}}}{e}$

(10)

式中：u₁为燃速常数； n为燃速指数，由实验确定；e为药粒半厚度；p_a为膛内燃气平均压力。

（3）弹丸运动方程为：

$\int_0^A {({p_{\rm{b}}} - {p_{\rm{h}}}} ){\rm{d}}A = \varphi m\frac{{{\rm{d}}{{v_{\rm{p}}}}}}{{{\rm{d}}t}}$

(11)

式中： ${p_{\rm{b}}}$ 和 ${p_{\rm{h}}}$ 分别为弹丸底部压力和弹丸头部压力， $A$ 为弹丸的横截面积， $m$ 为弹丸的质量， $\varphi$ 为次要功系数，v_p为弹丸速度。

（4）内弹道基本方程组为：

$\frac{{Ap({l_\psi } + l)}}{\theta } = \frac{{f\omega \psi }}{\theta } - \frac{\varphi }{2}m{{{v_{\rm{p}}^2}}} - \int_0^x {\int_0^A {{p_{\text{h}}}}\, {\rm{d}}A} \,{\rm{d}}l$

(12)

${l_\psi } = {l_0}\left[1 - \frac{\varDelta }{{{\rho _{\rm{p}}}}}(1 - \psi ) - \alpha \varDelta \psi \right]$

(13)

式中： ${l_0}$ 为药室容积缩径长； ${l_\psi }$ 为药室自由容积缩径长； $\varDelta$ 为火药装填密度； $\omega$ 为火药装药质量； $\alpha$ 为火药气体的余容； ${\ \rho _{\rm{p}}}$ 为火药密度； $l$ 为弹丸运动距离；比热比 $\theta= {{k}} - 1$ ， $k$ 为绝热指数； $f$ 为火药力。

（5）弹丸速度与行程关系式为：

$\frac{{{\rm{d}}l}}{{{\rm{d}}t}} = v_{\rm{p}}$

(14)

将式(9)～(14)构成的内弹道方程组编写用户自定义函数（UDF）和FLUENT程序进行耦合计算。

1.3 数值模拟

数值模拟基于压力的隐式算法求解，多相流采用VOF模型，利用PRESTO!插值格式进行压力项离散，利用压力隐式算子分裂（PISO）算法求解压力-密度的耦合，动量和能量的离散均采用一阶迎风格式，为了保证计算的稳定性，计算过程中时间步长控制在0.1 μs以内。

2. 计算模型及边界条件

2.1 计算模型及网格划分

对膛口流场进行数值模拟时，很难生成单块高质量网格，因此采用网格分区划分进行处理。将整个计算域划分为3个区，即药室Ⅰ区、身管Ⅱ区和膛口流场Ⅲ区。炮膛身管内径为30 mm，弹丸内弹道行程为1.9 m，膛口流场计算域为长1.3 m、半径0.35 m的圆柱形区域。为了更好地捕捉膛口流场波系结构，对膛口流场区采用渐变网格的方式进行了局部加密，膛口附近计算域的网格比较密集，最小网格尺寸为0.5 mm×0.5 mm，流场边界域的网格比较稀疏；在弹头附近采用三角形网格以更好地捕捉其形状，药室区和身管区采用均匀大小的结构网格，计算网格总数为240 000。图1(a)为计算模型示意图，图1(b)为计算网格示意图。

图 1 计算模型

Figure 1. Calculation model

下载: 全尺寸图片幻灯片

2.2 初始及边界条件

设定药室为压力入口边界条件，身管、膛口为固壁边界条件，弹丸设定为刚体运动，从膛底开始按内弹道方程组计算弹丸运动速度；膛口流场区域外边界为压力出口边界。初始时刻，药室和身管充满气体，膛口外部区域中充满液体介质水，计算初值与环境参数相同，即初始压力为101 325 Pa，初始温度为300 K。

2.3 网格无关性验证

网格无关性验证的目的是验证网格密度变化对计算结果的影响，即通过不断改变网格疏密来观察计算结果的变化，当其波动幅度在允许范围内时，就可以认为计算值与网格无关。

为了保证数值模拟的效率与结果的精确性，对计算网格模型膛口周围流场区域进行了不同尺寸的网格加密，得到了3组不同密度的计算网格数，分别为200 000、240 000及270 000。以膛口到弹底轴向燃气压力分布为参考值，如图2所示，与采用240 000网格数计算时膛口到弹底轴向燃气压力分布相比，采用200 000和270 000网格数进行计算时的平均误差分别为12.5%和4.2%，其波动幅度在允许范围内，因此本文中采用240 000网格数进行数值模拟。

图 2 膛口到弹底压力沿轴向变化曲线

Figure 2. Variation of axial pressure from the muzzleto the projectile bottom

下载: 全尺寸图片幻灯片

3. 膛口流场数值模拟结果与分析

3.1 数值模型的实验验证

为了研究水下发射膛口流场演变特性并验证数值模型的有效性，通过搭建可视化水下发射实验测试系统，对弹道枪水下密封式发射进行了可视化实验，图3(a)为实验系统。密封式发射时，为了保证身管中充满空气，使用密封膜片将膛口密封，当膛内燃气达到一定压力时膜片打开。实验采用高速摄像机观察和记录多相流场的演化过程，得到了不同时刻的实验阴影图。通过采用与实验相同（弹体质量为45 g、水深0.5 m）的条件工况进行数值模拟，得到相应时刻的模拟相图与实验阴影图对比，如图3(b)所示。图3(b)中上半部分为实验阴影图，下半部分为采用本文中数值模拟方法得到的相图。由图3(b)可知，数值模拟相图中燃气的物质边界扩展尺度和位置与实验阴影图吻合较好。为了进一步说明数值模型的有效性，图4给出了不同时刻射流头部的最大轴向位移对比，由图4可知，数值模拟结果与实验测量结果吻合较好，最大偏差为4.2%。由此可知，利用本文中的数值模型和计算方法进行水下发射膛口流场模拟是可行的。

图 3 实验系统（a）和数值模拟得到相应时刻的模拟相图与实验阴影图对比（b）

Figure 3. Experimental system (a) and the comparison of experimental shadow diagram and simulation results (b)

下载: 全尺寸图片幻灯片

图 4 射流头部轴向最大位移对比

Figure 4. Comparison of maximum axial displacement of jet head

下载: 全尺寸图片幻灯片

3.2 计算结果与分析

对30 mm火炮在水下密封式发射时的膛口流场分布进行数值模拟，密封片破膛压力取0.2 MPa，并与在空气中发射时的膛口流场进行比较，将弹丸出膛口瞬间看作t=0时刻。表1为两种发射环境下的部分内弹道及膛口参数，通过内弹道方程组（式(9)～(14)）求解所得，表1中 $x$ 为身管长度， ${p_{\rm{m}}}$ 为膛内最大压力， ${v_0}$ 为弹丸出膛口时的速度（弹丸初速）， ${p_0}$ 为燃气在膛口处的压力， ${T_0}$ 为燃气在膛口处的温度。图5给出了两种发射环境下的燃气射流膛口压力在不同时刻的变化曲线。由表1中可以看出，由于两种发射环境下的膛内阻力基本相同，水下密封式发射时膛内最大压力较空气中发射只升高了7 MPa，而弹丸初速却比空气中发射降低了32 m/s，这是由于密封片使膛口处压力升高和弹丸出膛口时受到水的阻力共同使得弹丸初速降低，此时弹前燃气在炮口处聚集，导致膛口压力和温度显著升高，分别升高了54.8%和10.6%。由图5可知，弹丸出膛口后，两种发射环境下的燃气射流膛口压力均随时间呈衰减趋势，在50 μs内压力衰减迅速，然而由于水对燃气扩展的阻碍较大，气体在水中的膨胀速度比在空气中慢，燃气聚集使得炮口气体压力始终较高。

表 1 内弹道及膛口参数

Table 1. Interior ballistics and muzzle parameters

发射环境	x/m	v₀/（m·s⁻¹）	p_m/MPa	p₀/MPa	T₀/K
空气中	1.94	985	317	62	2 152
水下	1.94	953	324	96	2 380

下载: 导出CSV

| 显示表格

图 5 膛口燃气压力变化曲线

Figure 5. Variation of muzzle gas pressure

下载: 全尺寸图片幻灯片

为了研究膛口压力场的演变特性，图6、图7分别给出了两种环境下不同时刻的压力分布和纹影图，上半部为压力云图，下半部为纹影图。图8给出了200 μs时刻燃气压力沿轴向的分布曲线。弹丸出膛口后，高温高压的火药燃气迅速喷出扩展，当射流滞止压力与环境压力之比大于3～4时, 流场结构中会出现瓶状正激波结构, 称为马赫盘。由图6可知，当弹丸运动30 μs时，燃气还未追上弹丸，炮口处燃气呈球状扩展。当弹丸运动70 μs时，火药燃气轴向迅速膨胀且已经包围弹丸；弹丸运动240 μs时，弹丸追赶初始冲击波，初始冲击波是弹前激波在膛口外绕射形成的球形冲击波，火药燃气扩展受冲击波影响压力升高；随着弹丸运动350 μs，弹丸已完全摆脱火药燃气的包围，形成完整的膛口流场。由图7可以发现，水下发射膛口压力场与空气中有所不同。弹丸运动30 μs时，火药燃气主要向弹丸侧前方（径向）膨胀且激波核心区较小，这是由于燃气同时受到弹丸和水的阻力，扩展不够充分。随着弹丸在水下不断运动，燃气逐渐由径向转为轴向膨胀，膛口处的燃气压力衰减比空气中更迅速。在水下运动过程中，由于高密度的水，弹丸头部产生的压力远高于膛口核心区的燃气压力，在空气运动过程中，受初始燃气流场的影响，被压缩的低密度空气在弹丸头部产生的压力极低，尽管弹丸被燃气包围后弹前压力有所升高，但仍远低于膛口核心区的燃气压力，从纹影图中可以更加清晰地看出两种介质中的流场波系结构。结合图8可以看出，在200 μs时，水下发射时燃气压力先沿轴向快速下降，穿越马赫盘后有较大幅度的上升，然后波动变化。由于此时空气中发射时马赫盘尚未形成，燃气压力迅速下降，之后基本保持不变。可见，介质密度的巨大差异导致膛口压力场的时空分布存在显著差别。

图 6 空气中膛口压力分布及纹影图

Figure 6. Pressure distribution and schlieren diagram at muzzle in air

下载: 全尺寸图片幻灯片

图 7 水下膛口压力分布及纹影图

Figure 7. Pressure distribution and schlieren diagram at muzzle under water

下载: 全尺寸图片幻灯片

图 8 200 μs时轴向压力分布曲线

Figure 8. Axial pressure distribution curves at 200 μs

下载: 全尺寸图片幻灯片

为进一步了解水下发射膛口燃气压力变化，图9给出了水下不同时刻膛口的轴向压力分布曲线，由图9可知，70 μs时，由于燃气速度大于弹丸速度而形成的弹底激波所致，燃气压力会有突跃，此时马赫盘尚未形成；140 μs时，马赫盘开始形成，燃气压力上升幅度最大；随着弹丸不断运动，燃气压力波动逐渐减小，趋于平缓。由此可见，膛口激波结构是一个生长-衰减-稳定的过程。

图 9 水下不同时刻轴向压力分布曲线

Figure 9. Distribution curves of underwater axial pressureat different moments

下载: 全尺寸图片幻灯片

弹丸出膛口时，膛内燃气压力远高于外部环境压力，属于高度欠膨胀射流。为了更直观地了解膛口燃气高度欠膨胀射流的结构特征，图10给出了空气中发射和水下密封式发射时膛口燃气射流结构流谱图^[17]，并给出了气液边界线。其中A区为核心激波自由膨胀区，火药燃气主要在该区域内膨胀，压力剧降，速度激增，该区域为超音速气流，Ma＞1。B区为相交激波与反射边界之间的超音速区域。大部分燃气在扩展过程中穿过马赫盘进入亚声速区C，该区域燃气经过马赫盘后聚集，压力陡增，速度降为亚声速，Ma＜1。有少部分的燃气经过两次斜激波后（入射激波和反射激波）进入D区，D区的燃气压力虽与C区相同，但由于经过两次不同的压缩过程使得速度增高，为超音速气流。由图10可以看出，空气中发射时膛口马赫盘完全形成后呈圆弧状结构，而水下发射时马赫盘结构呈梯形状。由于火炮在水下发射时，燃气在扩展过程中受到高密度水（约为空气密度的800倍）的挤压，射流前端高压区的存在使气体产生回流现象，该回流对射流主通道具有剪切作用，挤压与回流导致气流在垂直于炮口轴线方向上产生不稳定性，使得燃气射流扩展过程中出现颈缩现象，激波核心区受颈缩作用，马赫盘形状结构呈梯形状，导致空气中发射和水中发射时的马赫盘结构不同。

图 10 两种环境下膛口流场流谱

Figure 10. Flow spectrum of muzzle flow field in two environments

下载: 全尺寸图片幻灯片

为了更好地了解马赫盘的形成过程及特性，图11～12分别给出了水下发射和空气中发射时不同时刻的马赫数分布和纹影图，其中上半部为马赫数云图，下半部为纹影图。图13给出了70与200 μs时刻马赫数沿轴线的分布曲线。由图11可以看出，70 μs时，由于受到弹丸和水的阻力作用，燃气主要为径向膨胀，炮口两侧马赫数较高。随着燃气的喷射和膨胀，气体射流形成主轴激波结构，直到140 μs时马赫盘初步生成。随着弹丸不断运动，燃气射流充分发展，激波面积增大，马赫盘向垂直轴线方向变化，直径逐渐增大，在240 μs时，入射激波、反射激波及马赫盘在接触面交汇于一点，形成三波点结构。由图12可知，70 μs时，火药燃气流场逐步吞没初始流场，在炮口后形成球状激波结构；随着弹丸运动和燃气不断喷出，在320 μs时马赫盘开始初步生成，三波点结构也已形成。当弹丸运动到480 μs，激波结构完全生成，马赫盘呈碗状结构。由图13（a）可知，两种环境发射时马赫数均先沿轴线增大后减小，由图13（b）可知，200 μs、水下发射时，马赫数沿轴线增大后呈断崖式衰减，结合图10的膛口流场流谱图可知，燃气在穿越马赫盘后进入亚声速区，速度骤降，与水下发射不同，空气中发射时的马赫盘还未形成。

图 11 水下发射时膛口马赫数分布及纹影图

Figure 11. Mach number distribution and schlieren diagram at muzzle under water

下载: 全尺寸图片幻灯片

图 12 空气中发射时膛口马赫数及纹影图

Figure 12. Mach number distribution and schlieren diagram at muzzle in air

下载: 全尺寸图片幻灯片

图 13 马赫数轴向分布曲线

Figure 13. Axial distribution of Mach number

下载: 全尺寸图片幻灯片

对比可知：水下发射时膛口附近会有气液夹带，而空气中发射时低密度的空气对射流尾翼没有大的影响；水下发射时火药燃气射流受气液界面的相互作用影响，更快形成马赫盘结构，而在空气中，火药燃气膨胀过程中受阻较小，燃气射流较长时间与弹底作用形成弹底激波，阻碍马赫盘的形成；水下发射时的激波核心区面积明显小于空气中发射时的激波核心区面积，且弹丸头部不存在冠状冲击波。

两种环境下的马赫盘轴向位移随时间变化曲线如图14所示，为了直观地看出马赫盘距离膛口位置随时间变化的规律，经过计算得出，马赫盘距离膛口位置随时间变化呈指数增长，拟合公式为：

图 14 两种环境下的马赫盘轴向位移随时间变化曲线

Figure 14. Mach disc’s axial displacement with time in two environments

下载: 全尺寸图片幻灯片

$x\left(t\right)={x}_{0}+{x}_{1}{{\rm{e}}}^{-t/{t}_{1}}$

(15)

式中： $x\left(t\right)$ 为马赫盘距膛口位移（mm），膛口为坐标原点； ${x}_{0}$ 为初始系数， ${x}_{0}=113\;\mathrm{m}\mathrm{m}$ ； ${x}_{1}$ 为增速系数， ${x}_{1}=-80\;\mathrm{m}\mathrm{m}$ ； ${t}_{1}$ 为时间增长因子， ${t}_{1}=180$ 。

而空气中发射时马赫盘距离膛口位置随时间的变化呈线性增长，拟合公式为：

$x\left(t\right)={{x}_{{0}}'}+{{x}_{1}'}t$

(16)

式中： $x\left(t\right)$ 为马赫盘距膛口位移（mm）；膛口为坐标原点； ${{x}_{0}'}=152.2\;\mathrm{m}\mathrm{m}$ ； ${{x}_{1}'}$ 为线性增长因子， ${{x}_{1}'}=$ $0.35\;\mathrm{m}/\mathrm{s}$ 。

为了进一步研究不同介质中的弹丸速度衰减规律，图15给出了两种介质中弹丸速度随时间变化的曲线，弹头出膛口记为零时刻，从图15中可以看出，水下发射时，当弹头与水接触后，弹丸速度开始迅速衰减，直到弹丸全部出膛后一直呈线性衰减，而在空气中发射时，弹丸刚飞出膛口后，弹丸在火药燃气作用下先加速运动，当弹丸摆脱燃气流作用后，在空气阻力作用下，弹丸速度又开始缓慢衰减。

图 15 不同介质中弹丸速度随时间变化曲线

Figure 15. Variation of projectile velocitywith time in different media

下载: 全尺寸图片幻灯片

4. 结　论

利用30 mm火炮建立了水下密封式发射数值模型，模拟了火炮水下发射时的膛口流场演变过程，通过对火炮在空气中和水下发射时的膛口流场特性进行对比分析，发现两种不同介质环境下的膛口流场特性存在较大的不同。

（1）水下密封式发射时，弹丸在膛内所受的阻力与空气中发射时基本相同，水下发射时的膛内最大压力只比空气中发射时高7 MPa，弹丸出膛口时受到水的阻力较大，弹丸初速比空气中发射时降低了32 m/s，弹丸初速的降低使得膛口压力和温度比空气中发射时分别升高54.8%和10.6%。

（2）弹丸出膛口后，两种发射环境下的燃气射流膛口压力均随时间呈衰减趋势，水下发射时燃气膨胀受水的阻碍，燃气压力始终高于空气中发射；弹丸入水后，弹丸头部产生的压力远高于膛口核心区的燃气压力，而弹丸在空气中飞行时，弹丸头部产生的压力却远低于膛口核心区的燃气压力。

（3）水下密封式发射时，膛口附近会有气液夹带，而空气中发射时，低密度的空气对射流尾翼没有较大的影响；火药燃气射流受气液界面的相互作用影响，在140 μs时初步形成马赫盘结构，而空气中发射时马赫盘结构形成较晚，约在320 μs时形成；水下发射时的激波核心区面积明显小于空气中发射时的激波核心区面积。水下密封式发射时，马赫盘距离膛口轴向位移随时间变化呈指数增长；而空气中发射时，马赫盘距离膛口位置随时间变化呈线性增长。

本文中在计算和分析时暂未考虑弹体高速运动在水中的冲击波效应及空穴效应，在后续的工作中将会进一步研究冲击波效应及空穴效应对膛口流场演化过程的影响规律。

图 1 自发起爆过程中压力和温度分布^[30]

Figure 1. Pressure and temperature profile in spontaneous initiation^[30]

下载: 全尺寸图片幻灯片

图 2 自发波速度与传播距离的关系

Figure 2. Speed of spontaneous wave as a function of distance

下载: 全尺寸图片幻灯片

图 3 反应波速度与传播距离的关系

Figure 3. Speed of reaction wave as function of distance

下载: 全尺寸图片幻灯片

图 4 宏观通道中爆燃到爆轰的转变和胞格爆轰

Figure 4. Transition from deflagration to detonation and cellular detonation in macro-scale cannel

下载: 全尺寸图片幻灯片

图 5 边界层火焰结构与局部爆炸的形成

Figure 5. Flame structures of boundary layer and formation of local explosion

下载: 全尺寸图片幻灯片

图 6 当量甲烷-空气混合气体的诱导时间与温度的关系^[27]

Figure 6. Induction time vs. temperature for stoichiometric methane-air mixture^[27]

下载: 全尺寸图片幻灯片

图 7 层流火焰速度与压力函数关系^[27]

Figure 7. Laminar flame speed as a function of pressure^[27]

下载: 全尺寸图片幻灯片

图 8 爆轰形成过程中温度、压力波演化^[27]

Figure 8. Temperature and pressure profiles in initiation process^[27]

下载: 全尺寸图片幻灯片

图 9 温度、压力波演化^[27]

Figure 9. Temperature and pressure frofiles in initiation process^[27]

下载: 全尺寸图片幻灯片

图 10 温度、压力波演化^[27]

Figure 10. Temperature and pressure frofiles in initiation process^[27]

下载: 全尺寸图片幻灯片

图 11 温度、压力波演化： DRM-19机理^[27]

Figure 11. Temperature and pressure frofiles in initiationprocess: DRM-19 mechanism^[27]

下载: 全尺寸图片幻灯片

图 12(a) 胞状柱爆轰的最大压力历程^[114]

Figure 12(a). Maximum pressure history of cellular cylindrical detonation ^[114]

下载: 全尺寸图片幻灯片

12(b) 圆柱形爆轰平均速度^[114]

12(b). Average velocity of cylindrical detonation^[114]

下载: 全尺寸图片幻灯片

图 13 圆柱爆轰的最大压力历程^[114]

Figure 13. Maximun pressure history of cylindrical detonation^[114]

下载: 全尺寸图片幻灯片

图 14 圆柱形爆轰的平均速度^[114]

Figure 14. Average velocity of cylindrical detonation^[114]

下载: 全尺寸图片幻灯片

图 15 胞状圆柱爆轰的锋面结构^[114]

Figure 15. Frontal structure of celluar cylindrical detonation^[114]

下载: 全尺寸图片幻灯片

图 16 欧拉和NS方程求得的爆轰平均速度^[114]

Figure 16. Average velocity of detonation obtained by Euler and NS equations^[114]

下载: 全尺寸图片幻灯片

图 17 自由空间和约束空间中爆轰平均速度^[114]

Figure 17. Average velocity of detonation in free and confined spaces^[114]

下载: 全尺寸图片幻灯片

图 18 不同氩稀释度的最大压力随距离的变化趋势

Figure 18. Maximum pressure history of detonation for different Ar dilutions

下载: 全尺寸图片幻灯片

图 19 壁面上的最大压力历程和主螺旋轨迹（爆轰波沿着 $x$ 正向传播）

Figure 19. Maximum pressure history and main spinning track of detonation (detonation wave propagates along x direction)

下载: 全尺寸图片幻灯片

图 20 壁面上最大压力历程

Figure 20. Maximum pressure history on walls

下载: 全尺寸图片幻灯片

图 21 不同时刻的爆轰阵面结构

Figure 21. Detonation frontal structures at different times

下载: 全尺寸图片幻灯片

图 22 不同时刻的阵面结构演化

Figure 22. Detonation frontal structures at different times

下载: 全尺寸图片幻灯片

图 23 不同时刻的阵面结构

Figure 23. Detonation frontal structures at different times

下载: 全尺寸图片幻灯片

图 24 2H₂-O₂-80%Ar的爆轰胞格（p₀=20 kPa）

Figure 24. Detonation cell for 2H₂-O₂-80%Ar mixture (p₀=20 kPa)

下载: 全尺寸图片幻灯片

图 25 2H₂-O₂-80%Ar的爆轰结构^[150]

Figure 25. Detonation cellular structure in 2H₂-O₂-85%Ar mixture^[150]

下载: 全尺寸图片幻灯片

图 26 2H₂-O₂-85%Ar爆轰胞格^[151]（p₀=20 kPa）

Figure 26. Detonation cells in 2H₂-O₂-85%Ar mixture^[151] (p₀=20 kPa)

下载: 全尺寸图片幻灯片

图 27 2H₂-O₂-85%Ar爆轰结构^[150]

Figure 27. Detonation cellular structure in 2H₂-O₂-85%Ar mixture^[150]

下载: 全尺寸图片幻灯片

图 28 2H₂-O₂-72%N₂混合气体^[151]

Figure 28. Detonation cellular structure in 2H₂-O₂-72%N₂ mixture^[151]

下载: 全尺寸图片幻灯片

图 29 H₂-N₂O-60%N₂混合气体^[151]

Figure 29. Detonation cellular structure in H₂-N₂O-60%N₂ mixture^[151]

下载: 全尺寸图片幻灯片

图 30 不同初始压力下CH₄-2O₂的胞格结构^[156]

Figure 30. Detonation cell size of CH₄-2O₂ mixture under different initial pressures^[156]

下载: 全尺寸图片幻灯片

图 31 爆轰波接近极限状态的多种传播模式

Figure 31. Typical propagation modes near the detonation limits

下载: 全尺寸图片幻灯片

图 32 爆轰极限Fay模型与改进模型的对比

Figure 32. Theoretical prediction models (Fay model and modified model)

下载: 全尺寸图片幻灯片

表 1 CH₄-2O₂爆轰极限预测模型中的参数

Table 1. Parameters of prediction model for CH₄-2O₂

p₀/kPa	Δ_I/cm	Δ_R/cm	α	x/mm	μ_e/(Pa·s)	ρ/（kg·m⁻³）	γ	δ^*	ξ	ν	(D_CJ−ū)/（m·s⁻¹）	ū/D_CJ
5	0.4942	0.0839	5.892	0.0850	6.02×10⁻⁵	0.0595	1.178	1.64×10⁻³	0.183 0	0.070 9	0.09465	0.905
10	0.2227	0.0402	5.535	0.0383	6.09×10⁻⁵	0.1191	1.177	7.57×10⁻⁴	0.084 1	0.035 6	0.04836	0.952
20	0.1013	0.0262	5.211	0.0174	6.16×10⁻⁵	0.2381	1.176	3.51×10⁻⁴	0.039 0	0.017 2	0.02360	0.976
40	0.0464	0.0095	4.882	0.0080	6.24×10⁻⁵	0.4762	1.175	1.63×10⁻⁴	0.018 2	0.082 0	0.01127	0.989

下载: 导出CSV

参考文献(198)

[1]	LEE J H S. The detonation phenomenon [M]. Cambridge: Cambridge University Press, 2008.
[2]	范玮, 李建玲. 爆震组合循环发动机研究导论 [M]. 北京: 科学出版社, 2014.
[3]	ZHOU R, WANG J P. Numerical investigation of flow particle paths and thermodynamic performance of continuously rotating detonation engines [J]. Combustion and Flame, 2012, 159(12): 3632–3645. DOI: 10.1016/j.combustflame.2012.07.007.
[4]	TENG H H, JIANG Z L, NG H D. Numerical study on unstable surfaces of oblique detonations [J]. Journal of Fluid Mechanics, 2014, 744: 111–128. DOI: 10.1017/jfm.2014.78.
[5]	POLUDNENKO A Y, CHAMBERS J, AHMED K, et al. A unified mechanism for unconfined deflagration-to-detonation transition in terrestrial chemical systems and type Ia supernovae [J]. Science, 2019, 366(6465): eaau7365. DOI: 10.1126/science.aau7365.
[6]	SHEPHERD J E. Detonation in gases [J]. Proceedings of the Combustion Institute, 2009, 32(1): 83–98. DOI: 10.1016/j.proci.2008.08.006.
[7]	CICCARELLI G, DOROFEEV S. Flame acceleration and transition to detonation in ducts [J]. Progress in Energy and Combustion Science, 2008, 34(4): 499–550. DOI: 10.1016/j.pecs.2007.11.002.
[8]	ROY G D, FROLOV S M, BORISOV A A, et al. Pulse detonation propulsion: challenges, current status, and future perspective [J]. Progress in Energy and Combustion Science, 2004, 30(6): 545–672. DOI: 10.1016/j.pecs.2004.05.001.
[9]	ORAN E S, GAMEZO V N. Origins of the deflagration-to-detonation transition in gas-phase combustion [J]. Combustion and Flame, 2007, 148(1): 4–47. DOI: 10.1016/j.combustflame.2006.07.010.
[10]	姜宗林, 滕宏辉. 气相规则胞格爆轰波起爆与传播统一框架的几个关键基础问题研究 [J]. 中国科学: 物理学力学天文学, 2012, 42(4): 421−435. DOI: 10.1360/132011-945. JIANG Z L, TENG H H. Research on some fundamental problems of the universal framework for regular gaseous detonation initiation and propagation [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2012, 42: 421–435. DOI: 10.1360/132011-945.
[11]	姜宗林, 滕宏辉, 刘云峰. 气相爆轰物理的若干研究进展 [J]. 力学进展, 2012, 42(2): 129–140. DOI: 10.6052/1000-0992-2012-2-20120202. JIANG Z L, TENG H H, LIU Y F. Some research progress on gaseous detonation physics [J]. Advances in Mechanics, 2012, 42(2): 129–140. DOI: 10.6052/1000-0992-2012-2-20120202.
[12]	ZHANG B, BAI C H. Methods to predict the critical energy of direct detonation initiation in gaseous hydrocarbon fuels–an overview [J]. Fuel, 2014, 117: 294–308. DOI: 10.1016/j.fuel.2013.09.042.
[13]	张博, 白春华. 气相爆轰动力学特征研究进展 [J]. 中国科学: 物理学力学天文学, 2014, 44(7): 665−681. DOI: 10.1360/N132013-00028. ZHANG B, BAI C H. Research progress on the dynamic characteristics of gaseous detonation [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2014, 44: 665–681. DOI: 10.1360/N132013-00028.
[14]	范宝春, 张旭东, 潘振华, 等. 用于推进的三种爆轰波的结构特征 [J]. 力学进展, 2021, 42(2): 162–169. DOI: 10.6052/1000-0992-2012-2-20120204. FAN B C, ZHANG X D, PAN Z H, et al. Fundamental characteristics of three types of detonation waves utilized in propulsion [J]. Advances in Mechanics, 2021, 42(2): 162–169. DOI: 10.6052/1000-0992-2012-2-20120204.
[15]	王健平, 周蕊, 武丹. 连续旋转爆轰发动机的研究进展 [J]. 实验流体力学, 2015, 29(4): 12–25. DOI: 10.11729/syltlx20150048. WANG J P, ZHOU R, WU D. Progress of continuously rotating detonation engine research [J]. Journal of Experiments in Fluid Mechanics, 2015, 29(4): 12–25. DOI: 10.11729/syltlx20150048.
[16]	王兵, 谢峤峰, 闻浩诚, 等. 爆震发动机研究进展 [J]. 推进技术, 2021, 42(4): 721–737. DOI: 10.13675/j.cnki.tjjs.210109. WANG B, XIE Q F, WEN H C, et al. Reseach progress of detonation engine [J]. Jounal of Propusion Technology, 2021, 42(4): 721–737. DOI: 10.13675/j.cnki.tjjs.210109.
[17]	WOLAŃSKI P. Detonative propulsion [J]. Proceedings of the Combustion Institute, 2013, 34(1): 125–158. DOI: 10.1016/j.proci.2012.10.005.
[18]	OPPENHEIM A K. A contribution to the theory of the development and stability of detonation in gases [J]. Journal of Applied Mechanics, 1952, 19(1): 63–71. DOI: 10.1115/1.4010408.
[19]	OPPENHEIM A K, STERN R A. On the development of gaseous detonation—analysis of wave phenomena [J]. Symposium (International) on Combustion, 1958, 7(1): 837–850. DOI: 10.1016/S0082-0784(58)80127-7.
[20]	URTIEW P A, OPPENHEIM A K. Experimental observations of the transition to detonation in an explosive gas [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1966, 295(1440): 13–28. DOI: 10.1098/rspa.1966.0223.
[21]	DAI P, QI C, CHEN Z. Effects of initial temperature on autoignition and detonation development in dimethyl ether/air mixtures with temperature gradient [J]. Proceedings of the Combustion Institute, 2017, 36: 3643–3650. DOI: 10.1016/j.proci.2016.08.014.
[22]	MEYER J W, OPPENHEIM A K. On the shock-induced ignition of explosive gases [J]. Symposium (International) on Combustion, 1971, 13(1): 1153–1164. DOI: 10.1016/S0082-0784(71)80112-1.
[23]	VALIEV D M, BYCHKOV V, AKKERMAN V, et al. Different stages of flame acceleration from slow burning to Chapman-Jouguet deflagration [J]. Physical Review E, 2009, 80(3): 036317. DOI: 10.1103/PhysRevE.80.036317.
[24]	LIBERMAN M A, IVANOV M F, PEIL O E, et al. Self-acceleration and fractal structure of outward freely propagating flames [J]. Physics of Fluids, 2004, 16(7): 2476–2482. DOI: 10.1063/1.1729852.
[25]	HE L T, CLAVIN P. Critical conditions for detonation initiation in cold gaseous mixtures by nonuniform hot pockets of reactive gases [J]. Symposium (International) on Combustion, 1992, 24(1): 1861–1867. DOI: 10.1016/S0082-0784(06)80218-3.
[26]	BRADLEY D, CRESSWELL T M, PUTTOCK J S. Flame acceleration due to flame-induced instabilities in large-scale explosions [J]. Combustion and Flame, 2001, 124(4): 551–559. DOI: 10.1016/S0010-2180(00)00208-X.
[27]	WANG C, QIAN C G, LIU J N, et al. Influence of chemical kinetics on detonation initiating by temperature gradients in methane/air [J]. Combustion and Flame, 2018, 197: 400–415. DOI: 10.1016/j.combustflame.2018.08.017.
[28]	LIBERMAN M, WANG C, QIAN C G, et al. Influence of chemical kinetics on spontaneous waves and detonation initiation in highly reactive and low reactive mixtures [J]. Combustion Theory and Modelling, 2019, 23(3): 467–495. DOI: 10.1080/13647830.2018.1551578.
[29]	PAN J Y, DONG S, WEI H Q, et al. Temperature gradient induced detonation development inside and outside a hotspot for different fuels [J]. Combustion and Flame, 2019, 205: 269–277. DOI: 10.1016/j.combustflame.2019.04.003.
[30]	HAN W H, LIANG W K, WANG C, et al. Spontaneous initiation and development of hydrogen-oxygen detonation with ozone sensitization [J]. Proceedings of the Combustion Institute, 2021, 38(3): 3575–3583. DOI: 10.1016/j.proci.2020.06.239.
[31]	BURKE M P, CHAOS M, JU Y G, et al. Comprehensive H₂/O₂ kinetic model for high-pressure combustion [J]. International Journal of Chemical Kinetics, 2012, 44(7): 444–474. DOI: 10.1002/kin.20603.
[32]	KIVERIN A D, KASSOY D R, IVANOV M F, et al. Mechanisms of ignition by transient energy deposition: regimes of combustion wave propagation [J]. Physical Review E, 2013, 87(3): 033015. DOI: 10.1103/PhysRevE.87.033015.
[33]	DAI P , CHEN Z, GAN X H, et al. Autoignition and detonation development from a hot spot inside a closed chamber: Effect of end wall reflection [J]. Proceedings of the Combustion Institute, 2021, 4: 5905–5913. DOI: 10.1016/j.proci.2020.09.025.
[34]	HE L T, CLAVIN P. Theoretical and numerical analysis of the photochemical initiation of detonations in hydrogen-oxygen mixtures [J]. Symposium (International) on Combustion, 1994, 25(1): 45–51.
[35]	RADULESCU M I, SHARPE G J, BRADLEY D. A universal parameter for quantifying explosion hazards, detonability and hot spot formation, the χ number [C] // Proceedings of the Seventh International Seminar on Fire and Explosion Hazards. Singapore: Research Publishing, 2013: 617−626.
[36]	NG H D, RADULESCU M I, HIGGINS A J, et al. Numerical investigation of the instability for one-dimensional Chapman-Jouguet detonations with chain-branching kinetics [J]. Combustion Theory and Modelling, 2005, 9(3): 385–401. DOI: 10.1080/13647830500307758.
[37]	RADULESCU M I, NG H D, LEE J H S, et al. The effect of argon dilution on the stability of acetylene/oxygen detonations [J]. Proceedings of the Combustion Institute, 2002, 29(2): 2825–2831. DOI: 10.1016/S1540-7489(02)80345-5.
[38]	SHCHELKIN K I. Influence of tube roughness on the formation and detonation propagation in gas [J]. Journal of Experimental and Theoretical Physics, 1940, 10: 823–827.
[39]	MALLARD E, LE CHATELIER H. Thermal model for flame propagation [J]. Annales des Mines, 1883, 4: 379–568.
[40]	HAN W H, GAO Y, LAW C K. Flame acceleration and deflagration-to-detonation transition in micro-and macro-channels: an integrated mechanistic study [J]. Combustion and Flame, 2017, 176: 285–298. DOI: 10.1016/j.combustflame.2016.10.010.
[41]	LIBERMAN M A, IVANOV M F, KIVERIN A D, et al. Deflagration-to-detonation transition in highly reactive combustible mixtures [J]. Acta Astronautica, 2010, 67(7–8): 688–701. DOI: 10.1016/j.actaastro.2010.05.024.
[42]	GAMEZO V N, KHOKHLOV A M, ORAN E S. The influence of shock bifurcations on shock-flame interactions and DDT [J]. Combustion and Flame, 2001, 126(4): 1810–1826. DOI: 10.1016/S0010-2180(01)00291-7.
[43]	LEE J H S. Initiation of gaseous detonation [J]. Annual Review of Physical Chemistry, 1977, 28: 75–104. DOI: 10.1146/annurev.pc.28.100177.000451.
[44]	LEE J H S. Dynamic parameters of gaseous detonations [J]. Annual Review of Fluid Mechanics, 1984, 16: 311–336. DOI: 10.1146/annurev.fl.16.010184.001523.
[45]	LAFITTE P. Sur la propagation de l'onde explosive [J]. Comptes Rendus de l'Académie des Sciences, 1923, 177: 178–180.
[46]	ZHANG B, NG H D, LEE J H S. Measurement of effective blast energy for direct initiation of spherical gaseous detonations from high-voltage spark discharge [J]. Shock Waves, 2012,22: 1–7.
[47]	ZELDOVICH Y B, KOGARKO S M, SIMONOV N N. An experimental investigation of spherical detonation of gases [J]. Soviet Physics–Technical Physics, 1956, 1(8): 1689–1713.
[48]	BULL D C, ELSWORTH J E, QUINN C P, et al. A study of spherical detonation in mixtures of methane and oxygen diluted by nitrogen [J]. Journal of Physics D: Applied Physics, 1976, 9(14): 1991–2000. DOI: 10.1088/0022-3727/9/14/009.
[49]	BULL D C, ELSWORTH J E, HOOPER G. Concentration limits to unconfined detonation of ethane-air [J]. Combustion and Flame, 1979, 35: 27–40. DOI: 10.1016/0010-2180(79)90004-X.
[50]	ALEKSEEV V I, DOROFEEV S B, SIDOROV V P. Direct initiation of detonations in unconfined gasoline sprays [J]. Shock Waves, 1996, 6(2): 67–71. DOI: 10.1007/BF02515189.
[51]	KNYSTAUTAS R, LEE J H. On the effective energy for direct initiation of gaseous detonations [J]. Combustion and Flame, 1976, 27: 221–228. DOI: 10.1016/0010-2180(76)90025-0.
[52]	LEE J H, MATSUI H. A comparison of the critical energies for direct initiation of spherical detonations in acetylene-oxygen mixtures [J]. Combustion and Flame, 1977, 28: 61–66. DOI: 10.1016/0010-2180(77)90008-6.
[53]	ZHANG B, LIU H, WANG C. Detonation propagation limits in highly argon diluted acetylene-oxygen mixtures in channels [J]. Experimental Thermal and Fluid Science, 2018, 90: 125–131.
[54]	MATSUI H, LEE J H. Influence of electrode geometry and spacing on the critical energy for direct initiation of spherical gaseous detonations [J]. Combustion and Flame, 1976, 27: 217–220. DOI: 10.1016/0010-2180(76)90024-9.
[55]	MATSUI H, LEE J H. On the measure of the relative detonation hazards of gaseous fuel-oxygen and air mixtures [J]. Symposium (International) on Combustion, 1979, 17(1): 1269–1280. DOI: 10.1016/S0082-0784(79)80120-4.
[56]	BERETS D J, GREENE E F, KISTIAKOWSKY G B. Gaseous detonations. I. stationary waves in hydrogen-oxygen mixtures [J]. Journal of the American Chemical Society, 1950, 72(3): 1080–1086. DOI: 10.1021/ja01159a008.
[57]	MOORADIAN A J, GORDON W E. Gaseous detonation. I. Initiation of detonation [J]. Journal of Chemical Physics, 1951, 19(9): 1166–1172. DOI: 10.1063/1.1748497.
[58]	NORRISH R G W. The study of combustion by photochemical methods [J]. Symposium (International) on Combustion, 1965,10(1): 1−18.
[59]	NORRISH R G W, PORTER G, THRUSH B A. Studies of the explosive combustion of hydrocarbons by kinetic spectroscopy—Ⅱ. comparative investigations of hydrocarbons and a study of the continuous absorption spectra [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1955, 227(1171): 423–433. DOI: 10.1098/rspa.1955.0021.
[60]	THRUSH B A. The homogeneity of explosions initiated by flash photolysis [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1955, 233(1192): 147–151. DOI: 10.1098/rspa.1955.0251.
[61]	KLIMKIN V F, SOLOUKHIN R I, WOLANSKY P. Initial stages of a spherical detonation directly initiated by a laser spark [J]. Combustion and Flame, 1973, 21(1): 111–117. DOI: 10.1016/0010-2180(73)90012-6.
[62]	KATAOKA H, KATO H, ISHII K. Direct initiation of acetylene-oxygen mixture using laser ablation [C] // Proceedings of the 22nd International Colloqium on the Dynamics of Explosions and Reactive Systems. Belarus, 2009.
[63]	LEE J H, KNYSTAUTAS R, YOSHIKAWA N. Photochemical initiation of gaseous detonations [J]. Acta Astronautica, 1978, 5(11–12): 971–982. DOI: 10.1016/0094-5765(78)90003-6.
[64]	解立峰, 郭学永, 果宏, 等. 燃料-空气云雾爆轰的直接引爆实验研究 [J]. 爆炸与冲击, 2003, 23(1): 78–80. DOI: 10.3321/j.issn:1001-1455.2003.01.015. XIE L F, GUO X Y, GUO H. Experimental study on the direct initiation of detonation in fuel-air sprays [J]. Explosion and Shock Waves, 2003, 23(1): 78–80. DOI: 10.3321/j.issn:1001-1455.2003.01.015.
[65]	姚干兵, 解立峰, 刘家骢. 碳氢燃料云雾直接起爆感度的实验研究 [J]. 弹道学报, 2006, 18(3): 9–13. DOI: 10.3969/j.issn.1004-499X.2006.03.003. YAO G B, XIE L F, LIU J C. Experimental study on the direction initiation sensitivity of hydrocarbon-air cloud [J]. Journal of Ballistics, 2006, 18(3): 9–13. DOI: 10.3969/j.issn.1004-499X.2006.03.003.
[66]	ZHANG B, KAMENSKIHS V, NG H D, et al. Direct blast initiation of spherical gaseous detonations in highly argon diluted mixtures [J]. Proceedings of the Combustion Institute, 2011, 33(2): 2265–2271. DOI: 10.1016/j.proci.2010.06.165.
[67]	ZHANG B, NG H D, MÉVEL R, et al. Critical energy for direct initiation of spherical detonations in H2/N2O/Ar mixtures [J]. International Journal of Hydrogen Energy, 2011, 36(9): 5707–5716. DOI: 10.1016/j.ijhydene.2011.01.175.
[68]	KAMENSKIHS V, NG H D, LEE J H S. Measurement of critical energy for direct initiation of spherical detonations in stoichiometric high-pressure H₂-O₂ mixtures [J]. Combustion and Flame, 2010, 157(9): 1795–1799. DOI: 10.1016/j.combustflame.2010.02.014.
[69]	宋述忠, 彭金华, 陈网桦, 等. 几种燃料云雾爆轰临界起爆能的研究 [J]. 爆炸与冲击, 2002, 22(4): 373–376. DOI: 10.3321/j.issn:1001-1455.2002.04.016. SONG S Z, PENG J H, CHEN W H, et al. Study on critical initiation energy of several fuel-air mixture [J]. Explosion and Shock Waves, 2002, 22(4): 373–376. DOI: 10.3321/j.issn:1001-1455.2002.04.016.
[70]	LEE J H S, HIGGINS A J. Comments on criteria for direct initiation of detonation [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1999, 357(1764): 3503–3521. DOI: 10.1098/rsta.1999.0506.
[71]	KUNDU S, ZANGANEH J, MOGHTADERI B. A review on understanding explosions from methane-air mixture [J]. Journal of Loss Prevention in the Process Industries, 2016, 40: 507–523. DOI: 10.1016/j.jlp.2016.02.004.
[72]	KESSLER D A, GAMEZO V N, ORAN E S. Simulations of flame acceleration and deflagration-to-detonation transitions in methane-air systems [J]. Combustion and Flame, 2010, 157(11): 2063–2077. DOI: 10.1016/j.combustflame.2010.04.011.
[73]	ZELDOVICH Y B. Regime classification of an exothermic reaction with nonuniform initial conditions [J]. Combustion and Flame, 1980, 39(2): 211–214. DOI: 10.1016/0010-2180(80)90017-6.
[74]	ZEL’DOVICH Y B, LIBROVICH V B, MAKHVILADZE G M, et al. On the development of detonation in a non-uniformly preheated gas [J]. Astronautica Acta, 1970, 15(5): 313–321.
[75]	LIBERMAN M A, KIVERIN A D, IVANOV M F. On detonation initiation by a temperature gradient for a detailed chemical reaction models [J]. Physics Letters A, 2011, 375(17): 1803–1808. DOI: 10.1016/j.physleta.2011.03.026.
[76]	LIBERMAN M A, KIVERIN A D, IVANOV M F. Regimes of chemical reaction waves initiated by nonuniform initial conditions for detailed chemical reaction models [J]. Physical Review E, 2012, 85(5): 056312. DOI: 10.1103/PhysRevE.85.056312.
[77]	GU X J, EMERSON D R, BRADLEY D. Modes of reaction front propagation from hot spots [J]. Combustion and Flame, 2003, 133(1–2): 63–74. DOI: 10.1016/S0010-2180(02)00541-2.
[78]	KUZNETSOV M, LIBERMAN M, MATSUKOV I. Experimental study of the preheat zone formation and deflagration to detonation transition [J]. Combustion Science and Technology, 2010, 182(11–12): 1628–1644. DOI: 10.1080/00102202.2010.497327.
[79]	IVANOV M F, KIVERIN A D, LIBERMAN M A. Flame acceleration and DDT of hydrogen-oxygen gaseous mixtures in channels with no-slip walls [J]. International Journal of Hydrogen Energy, 2011, 36(13): 7714–7727. DOI: 10.1016/j.ijhydene.2011.03.134.
[80]	IVANOV M F, KIVERIN A D, LIBERMAN M A. Hydrogen-oxygen flame acceleration and transition to detonation in channels with no-slip walls for a detailed chemical reaction model [J]. Physical Review E, 2011, 83(5): 056313. DOI: 10.1103/PhysRevE.83.056313.
[81]	IVANOV M F, KIVERIN A D, YAKOVENKO I S, et al. Hydrogen-oxygen flame acceleration and deflagration-to-detonation transition in three-dimensional rectangular channels with no-slip walls [J]. International Journal of Hydrogen Energy, 2013, 38(36): 16427–16440. DOI: 10.1016/j.ijhydene.2013.08.124.
[82]	SEPULVEDA J, ROUSSO A, HA H, et al. Kinetic enhancement of microchannel detonation transition by ozone addition to acetylene mixtures [J]. AIAA Journal, 2019, 57(2): 476–481. DOI: 10.2514/1.J057773.
[83]	WESTBROOK C K, DRYER F L. Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames [J]. Combustion Science and Technology, 1981, 27(1–2): 31–43. DOI: 10.1080/00102208108946970.
[84]	FRANZELLI B, RIBER E, SANJOSÉ M, et al. A two-step chemical scheme for kerosene-air premixed flames [J]. Combustion and Flame, 2010, 157(7): 1364–1373. DOI: 10.1016/j.combustflame.2010.03.014.
[85]	JONES W P, LINDSTEDT R P. Global reaction schemes for hydrocarbon combustion [J]. Combustion and Flame, 1988, 73(3): 233–249. DOI: 10.1016/0010-2180(88)90021-1.
[86]	ZAMBON A C, CHELLIAH H K. Explicit reduced reaction models for ignition, flame propagation, and extinction of C₂H₄/CH₄/H₂ and air systems [J]. Combustion and Flame, 2007, 150(1): 71–91. DOI: 10.1016/j.combustflame.2007.03.003.
[87]	KAZAKOV A, FRENKLACH M. Reduced reaction sets based on GRI-Mech 1.2: 19-species reaction set [EB/OL]. University of California, USA: Berkeley, 1994. http://combustion.berkeley.edu/drm/.
[88]	SMOOKE M D. Reduced kinetic mechanisms and asymptotic approximations for methane-air flames [M]. Berlin: Springer, 1991.
[89]	GOSWAMI M, DERKS S C R, COUMANS K, et al. The effect of elevated pressures on the laminar burning velocity of methane + air mixtures [J]. Combustion and Flame, 2013, 160(9): 1627–1635. DOI: 10.1016/j.combustflame.2013.03.032.
[90]	GOSWAMI M, COUMANS K, BASTIAANS R J M, et al. Numerical simulations of flat laminar premixed methane-air flames at elevated pressure [J]. Combustion Science and Technology, 2014, 186(10): 1447–1459. DOI: 10.1080/00102202.2014.934619.
[91]	HU E J, LI X T, MENG X, et al. Laminar flame speeds and ignition delay times of methane-air mixtures at elevated temperatures and pressures [J]. Fuel, 2015, 158: 1–10. DOI: 10.1016/j.fuel.2015.05.010.
[92]	FRENKLACH M, MORIARTY N W, EITENEER B, et al. Gri-Mech 3.0 [EB/OL]. 1995. http://combustion.berkeley.edu/gri-mech/version30/text30.html.
[93]	ZENG W, MA H A, LIANG Y T, et al. Experimental and modeling study on effects of N₂ and CO₂ on ignition characteristics of methane/air mixture [J]. Journal of Advanced Research, 2015, 6(2): 189–201. DOI: 10.1016/j.jare.2014.01.003.
[94]	ROZENCHAN G, ZHU D L, LAW C K, et al. Outward propagation, burning velocities, and chemical effects of methane flames up to 60 atm [J]. Proceedings of the Combustion Institute, 2002, 29(2): 1461–1470. DOI: 10.1016/S1540-7489(02)80179-1.
[95]	GU X J, HAQ M Z, LAWES M, et al. Laminar burning velocity and Markstein lengths of methane-air mixtures [J]. Combustion and Flame, 2000, 121(1): 41–58. DOI: 10.1016/S0010-2180(99)00142-X.
[96]	KOBAYASHI H, NAKASHIMA T, TAMURA T, et al. Turbulence measurements and observations of turbulent premixed flames at elevated pressures up to 3.0 MPa [J]. Combustion and Flame, 1997, 108(1): 111–117. DOI: 10.1016/S0010-2180(96)00103-4.
[97]	HASSAN M I, AUNG K T, FAETH G M. Measured and predicted properties of laminar premixed methane/air flames at various pressures [J]. Combustion and Flame, 1998, 115(4): 539–550. DOI: 10.1016/S0010-2180(98)00025-X.
[98]	PARK O, VELOO P S, LIU N, et al. Combustion characteristics of alternative gaseous fuels [J]. Proceedings of the Combustion Institute, 2011, 33(1): 887–894. DOI: 10.1016/j.proci.2010.06.116.
[99]	EGOLFOPOULOS F N, LAW C K. Chain mechanisms in the overall reaction orders in laminar flame propagation [J]. Combustion and Flame, 1990, 80(1): 7–16. DOI: 10.1016/0010-2180(90)90049-W.
[100]	EGOLFOPOULOS F N, CHO P, LAW C K. Laminar flame speeds of methane-air mixtures under reduced and elevated pressures [J]. Combustion and Flame, 1989, 76(3): 375–391. DOI: 10.1016/0010-2180(89)90119-3.
[101]	NG H D, HIGGINS A J, KIYANDA C B, et al. Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations [J]. Combustion Theory and Modelling, 2005, 9(1): 159–170. DOI: 10.1080/13647830500098357.
[102]	WATT S D, SHARPE G J. Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves [J]. Journal of Fluid Mechanics, 2005, 522: 329–356. DOI: 10.1017/S0022112004001946.
[103]	ECKETT C A, QUIRK J J, SHEPHERD J E. The role of unsteadiness in direct initiation of gaseous detonations [J]. Journal of Fluid Mechanics, 2000, 421: 147–183. DOI: 10.1017/S0022112000001555.
[104]	SHORT M, STEWART D S. Cellular detonation stability. Part 1. a normal-mode linear analysis [J]. Journal of Fluid Mechanics, 1998, 368: 229–262. DOI: 10.1017/S0022112098001682.
[105]	SHORT M. A nonlinear evolution equation for pulsating Chapman−Jouguet detonations with chain-branching kinetics [J]. Journal of Fluid Mechanics, 2001, 430: 381–400. DOI: 10.1017/S0022112000003116.
[106]	PINTGEN F, ECKETT C A, AUSTIN J M, et al. Direct observations of reaction zone structure in propagating detonations [J]. Combustion and Flame, 2003, 133(3): 211–229. DOI: 10.1016/S0010-2180(02)00458-3.
[107]	EDWARDS D H, JONES A T. The variation in strength of transverse shocks in detonation waves [J]. Journal of Physics D: Applied Physics, 1978, 11(2): 155–166. DOI: 10.1088/0022-3727/11/2/013.
[108]	DORMAL M, LIBOUTON J C, VAN TIGGELEN P J. Etude expérimentale des paramètres à l’intérieur d’une maille de detonation [J]. Explosifs, 1983, 36: 76–94.
[109]	SHARPE G J. Transverse waves in numerical simulations of cellular detonations [J]. Journal of Fluid Mechanics, 2001, 447: 31–51. DOI: 10.1017/S0022112001005535.
[110]	TAKAI R, YONEDA K, HIKITA T. Study of detonation wave structure [J]. Symposium (International) on Combustion, 1975, 15(1): 69–78. DOI: 10.1016/S0082-0784(75)80285-2.
[111]	RADULESCU M I, LEE J H S. The failure mechanism of gaseous detonations: experiments in porous wall tubes [J]. Combustion and Flame, 2002, 131(1): 29–46. DOI: 10.1016/S0010-2180(02)00390-5.
[112]	SUBBOTIN V A. Two kinds of transverse wave structures in multifront detonation [J]. Combustion, Explosion and Shock Waves, 1975, 11(1): 83–88. DOI: 10.1007/BF00742862.
[113]	STREHLOW R A. Gas pase detonations: recent developments [J]. Combustion and Flame, 1968, 12(2): 81–101. DOI: 10.1016/0010-2180(68)90083-7.
[114]	HAN W H, KONG W J, LAW C K. Propagation and failure mechanism of cylindrical detonation in free space [J]. Combustion and Flame, 2018, 192: 295–313. DOI: 10.1016/j.combustflame.2018.01.049.
[115]	SÁNCHEZ A L, WILLIAMS F A. Recent advances in understanding of flammability characteristics of hydrogen [J]. Progress in Energy and Combustion Science, 2014, 41: 1–55. DOI: 10.1016/j.pecs.2013.10.002.
[116]	MAZAHERI K, MAHMOUD Y, SABZPOOSHANI M, et al. Experimental and numerical investigation of propagation mechanism of gaseous detonations in channels with porous walls [J]. Combustion and Flame, 2015, 162(6): 2638–2659. DOI: 10.1016/j.combustflame.2015.03.015.
[117]	RADULESCU M I, SHARPE G J, LAW C K, et al. The hydrodynamic structure of unstable cellular detonations [J]. Journal of Fluid Mechanics, 2007, 580: 31–81. DOI: 10.1017/S0022112007005046.
[118]	RADULESCU M I, SHARPE G J, LEE J H S, et al. The ignition mechanism in irregular structure gaseous detonations [J]. Proceedings of the Combustion Institute, 2005, 30(2): 1859–1867. DOI: 10.1016/j.proci.2004.08.047.
[119]	MAXWELL B M, BHATTACHARJEE R R, LAU-CHAPDELAINE S S M, et al. Influence of turbulent fluctuations on detonation propagation [J]. Journal of Fluid Mechanics, 2017, 818: 646–696. DOI: 10.1017/jfm.2017.145.
[120]	FARIA L M, KASIMOV A R. Qualitative modeling of the dynamics of detonations with losses [J]. Proceedings of the Combustion Institute, 2015, 35(2): 2015–2023. DOI: 10.1016/j.proci.2014.07.006.
[121]	WATT S D, SHARPE G J. One-dimensional linear stability of curved detonations [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2004, 460(2049): 2551–2568. DOI: 10.1098/rspa.2004.1290.
[122]	SOW A, CHINNAYYA A, HADJADJ A. Mean structure of one-dimensional unstable detonations with friction [J]. Journal of Fluid Mechanics, 2014, 743: 503–533. DOI: 10.1017/jfm.2014.49.
[123]	CLAVIN P, WILLIAMS F A. Dynamics of planar gaseous detonations near Chapman-Jouguet conditions for small heat release [J]. Combustion Theory and Modelling, 2002, 6(1): 127–139. DOI: 10.1088/1364-7830/6/1/307.
[124]	HE L T, LEE J H S. The dynamical limit of one-dimensional detonations [J]. Physics of Fluids, 1995, 7(5): 1151–1158. DOI: 10.1063/1.868556.
[125]	SHORT M, KAPILA A K, QUIRK J J. The chemical-gas dynamic mechanisms of pulsating detonation wave instability [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1999, 357(1764): 3621–3637. DOI: 10.1098/rsta.1999.0513.
[126]	SHARPE G J, FALLE S A E G. One-dimensional numerical simulations of idealized detonations [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1999, 455(1983): 1203–1214. DOI: 10.1098/rspa.1999.0355.
[127]	MEYER J W, URTIEW P A, OPPENHEIM A K. On the inadequacy of gasdynamic processes for triggering the transition to detonation [J]. Combustion and Flame, 1970, 14(1): 13–20. DOI: 10.1016/S0010-2180(70)80005-0.
[128]	CLAVIN P. Nonlinear dynamics of shock and detonation waves in gases [J]. Combustion Science and Technology, 2017, 189(5): 747–775. DOI: 10.1080/00102202.2016.1260562.
[129]	WHITE D R, CARY K H. Structure of gaseous detonation. Ⅱ. generation of laminar detonation [J]. The Physics of Fluids, 1963, 6(5): 749–750. DOI: 10.1063/1.1706806.
[130]	STREHLOW R A. Multi-dimensional detonation wave structure [J]. Astronautica Acta, 1970, 15: 345–357.
[131]	CAMPBELL C, WOODHEAD D W. CCCCI—The ignition of gases by an explosion-wave. Part Ⅰ. carbon monoxide and hydrogen mixtures [J]. Journal of the Chemical Society, 1926, 129: 3010–3021. DOI: 10.1039/JR9262903010.
[132]	LEE J H S, SOLOUKHIN R I, OPPENHEIM A K. Current views on gaseous detonation [J]. Astronautica Acta, 1969, 14: 565–584.
[133]	SCHOTT G L. Observations of the structure of spinning detonation [J]. The Physics of Fluids, 1965, 8(5): 850–865. DOI: 10.1063/1.1761328.
[134]	HANANA M, LEFEBVRE M H. Pressure profiles in detonation cells with rectangular and diagonal structures [J]. Shock Waves, 2001, 11(2): 77–88. DOI: 10.1007/PL00004068.
[135]	TSUBOI N, ASAHARA M, ETO K, et al. Numerical simulation of spinning detonation in square tube [J]. Shock Waves, 2008, 18(4): 329–344. DOI: 10.1007/s00193-008-0153-y.
[136]	TSUBOI N, HAYASHI A K. Numerical study on spinning detonations [J]. Proceedings of the Combustion Institute, 2007, 31(2): 2389–2396. DOI: 10.1016/j.proci.2006.07.262.
[137]	TSUBOI N, KATOH S, HAYASHI A K. Three-dimensional numerical simulation for hydrogen/air detonation: rectangular and diagonal structures [J]. Proceedings of the Combustion Institute, 2002, 29(2): 2783–2788. DOI: 10.1016/S1540-7489(02)80339-X.
[138]	WILLIAMS D N, BAUWENS L, ORAN E S. Detailed structure and propagation of three-dimensional detonations [J]. Symposium (International) on Combustion, 1996, 26(2): 2991–2998. DOI: 10.1016/S0082-0784(96)80142-1.
[139]	DELEDICQUE V, PAPALEXANDRIS M V. Computational study of three-dimensional gaseous detonation structures [J]. Combustion and Flame, 2006, 144(4): 821–837. DOI: 10.1016/j.combustflame.2005.09.009.
[140]	TEODORCZYK A, LEE J H S, KNYSTAUTAS R. Photographic study of the structure and propagation mechanisms of quasidetonations in rough tubes [M] // LEYER J C, BORISOV A A, KUHL A L, et al. Dynamics of Detonations and Explosions: Detonations. Washington: American Institute of Aeronautics and Astronautics, 1991: 233−240.
[141]	TEODORCZYK A. Fast deflagrations and detonations in obstacle-filled channels [J]. Journal of Power Technologies, 1995, 79: 145–178.
[142]	TEODORCZYK A, DROBNIAK P, DABKOWSK A. Fast turbulent deflagration and DDT of hydrogen-air mixtures in small obstructed channel [J]. International Journal of Hydrogen Energy, 2009, 34(14): 5887–5893. DOI: 10.1016/j.ijhydene.2008.11.120.
[143]	FAY J A. A mechanical theory of spinning detonation [J]. The Journal of Chemical Physics, 1952, 20(6): 942–950. DOI: 10.1063/1.1700655.
[144]	LEE J H, KNYSTAUTAS R, CHAN C K. Turbulent flame propagation in obstacle-filled tubes [J]. Symposium (International) on Combustion, 1985, 20(1): 1663–1672. DOI: 10.1016/S0082-0784(85)80662-7.
[145]	DOROFEEV S B, KUZNETSOV M S, ALEKSEEV V I, et al. Evaluation of limits for effective flame acceleration in hydrogen mixtures [J]. Journal of Loss Prevention in the Process Industries, 2001, 14(6): 583–589. DOI: 10.1016/S0950-4230(01)00050-X.
[146]	WOLANSKI P, LIU J C, KAUFFMAN C W, et al. On the mechanism of influence of obstacles on the flame propagation [J]. Archivum Combustionis, 1988, 8: 15.
[147]	RADULESCU M I. The propagation and failure mechanism of gaseous detonations: experiments in porous-walled tubes [D]. Montreal: McGill University, 2003.
[148]	NG H D, JU Y G, LEE J H S. Assessment of detonation hazards in high-pressure hydrogen storage from chemical sensitivity analysis [J]. International Journal of Hydrogen Energy, 2007, 32(1): 93–99. DOI: 10.1016/j.ijhydene.2006.03.012.
[149]	ZHANG B, LIU H, LI Y C. The effect of instability of detonation on the propagation modes near the limits in typical combustible mixtures [J]. Fuel, 2019, 253: 305–310. DOI: 10.1016/j.fuel.2019.05.006.
[150]	AUSTIN J M. The role of instability in gaseous detonation [D]. Pasadena: California Institute of Technology, 2003.
[151]	PINTGEN F, AUSTIN J M, SHEPHERD J E. Detonation front structure: variety and characterization [C] // Confined Detonations and Pulse Detonation Engines. Moscow: Torus-Press, 2003: 105−116.
[152]	ZHANG B, LIU H, YAN B J, et al. Experimental study of detonation limits in methane-oxygen mixtures: determining tube scale and initial pressure effects [J]. Fuel, 2020, 259: 116220. DOI: 10.1016/j.fuel.2019.116220.
[153]	GAO Y, ZHANG B, NG H D, et al. An experimental investigation of detonation limits in hydrogen-oxygen-argon mixtures [J]. International Journal of Hydrogen Energy, 2016, 41(14): 6076–6083. DOI: 10.1016/j.ijhydene.2016.02.130.
[154]	FAY J A. Two-dimensional gaseous detonations: velocity deficit [J]. The Physics of Fluids, 1959, 2(3): 283–289. DOI: 10.1063/1.1705924.
[155]	KOMATSU M, TAKAYAMA K, OHTANI K, et al. Effect of debris fragments on direct initiation of spherical detonation waves in stoichiometric oxygen/hydrogen mixtures [J]. Proceedings of the Combustion Institute, 2007, 31(2): 2437–2443. DOI: 10.1016/j.proci.2006.08.111.
[156]	ZHANG B, SHEN X B, PANG L, et al. Methane-oxygen detonation characteristics near their propagation limits in ducts [J]. Fuel, 2016, 177: 1–7. DOI: 10.1016/j.fuel.2016.02.089.
[157]	张超, 唐豪, 李明, 等. 当量比和间隙尺寸对爆震波传播过程的影响 [J]. 航空动力学报, 2012, 27(9): 1948–1957. DOI: 10.13224/j.cnki.jasp.2012.09.013. ZHANG C, TANG H, LI M, et al. Effects of equivalence ratio and gap size on the propagation behavior of detonations [J]. Journal of Aeerospace Power, 2012, 27(9): 1948–1957. DOI: 10.13224/j.cnki.jasp.2012.09.013.
[158]	WU M H, BURKE M P, SON S F, et al. Flame acceleration and the transition to detonation of stoichiometric ethylene/oxygen in microscale tubes [J]. Proceedings of the Combustion Institute, 2007, 31(2): 2429–2436. DOI: 10.1016/j.proci.2006.08.098.
[159]	WU M H, KUO W C. Accelerative expansion and DDT of stoichiometric ethylene/oxygen flame rings in micro-gaps [J]. Proceedings of the Combustion Institute, 2013, 34(2): 2017–2024. DOI: 10.1016/j.proci.2012.07.008.
[160]	WU M H, WANG C Y. Reaction propagation modes in millimeter-scale tubes for ethylene/oxygen mixtures [J]. Proceedings of the Combustion Institute, 2011, 33(2): 2287–2293. DOI: 10.1016/j.proci.2010.07.081.
[161]	CAMARGO A, NG H D, CHAO J, et al. Propagation of near-limit gaseous detonations in small diameter tubes [J]. Shock Waves, 2010, 20(6): 499–508. DOI: 10.1007/s00193-010-0253-3.
[162]	HUANG Y, JI H, LIEN F, et al. Numerical study of three-dimensional detonation structure transformations in a narrow square tube: from rectangular and diagonal modes into spinning modes [J]. Shock Waves, 2014, 24(4): 375–392. DOI: 10.1007/s00193-014-0499-2.
[163]	WU Y W, LEE J H S. Stability of spinning detonation waves [J]. Combustion and Flame, 2015, 162(6): 2660–2669. DOI: 10.1016/j.combustflame.2015.03.021.
[164]	GAO Y, NG H D, LEE J H S. Experimental characterization of galloping detonations in unstable mixtures [J]. Combustion and Flame, 2015, 162(6): 2405–2413. DOI: 10.1016/j.combustflame.2015.02.007.
[165]	WANG C, ZHAO Y Y, ZHANG B. Numerical simulation of flame acceleration and deflagration-to-detonation transition of ethylene in channels [J]. Journal of Loss Prevention in the Process Industries, 2016, 43: 120–126. DOI: 10.1016/j.jlp.2016.05.008.
[166]	喻健良, 高远, 闫兴清, 等. 高浓度氩气稀释气体爆轰波临界管径和临界间距关系 [J]. 爆炸与冲击, 2015, 35(4): 603–608. DOI: 10.11883/1001-1455(2015)04-0603-06. YU J L, GAO Y, YAN X Q, et al. Correation between the critical tube diameter and annular interval for detonation wave in high-concentration argon diluted mixtures [J]. Explosion and Shock Waves, 2015, 35(4): 603–608. DOI: 10.11883/1001-1455(2015)04-0603-06.
[167]	喻健良, 高远, 闫兴清, 等. 初始压力对爆轰波在管道内传播的影响 [J]. 大连理工大学学报, 2014, 54(4): 413–417. DOI: 10.7511/dllgxb201404007. YU J L, GAO Y, YAN X Q, et al. Effect of initial ressure on propagation of detonation wave in round tube [J]. Journal of Dalian University of Technology, 2014, 54(4): 413–417. DOI: 10.7511/dllgxb201404007.
[168]	夏昌敬, 周凯元. 气相爆轰波在90°矩形弯管中传播时胞格结构的演化 [J]. 爆炸与冲击, 2005, 25(2): 151–156. DOI: 10.11883/1001-1455(2005)02-0151-06. XIA C J, ZHOU K Y. Cellular structure evolution of gaseous detonation in a 90° rectangular bend [J]. Explosion and Shock Waves, 2005, 25(2): 151–156. DOI: 10.11883/1001-1455(2005)02-0151-06.
[169]	夏昌敬, 周凯元, 沈兆武. 初始条件影响气体非稳定爆轰波在弯管中传播特性的实验研究 [J]. 中国科学技术大学学报, 2004, 34(1): 92−97. DOI: 10.3969/j.issn.0253-2778.2004.01.014. XIA C J, ZHOU K Y, SHEN Z W. Experimental study on effects of initial conditions for propagation characteristics of unsteady gaseous detonation in channels with a bend [J]. Journal of University of Science and Technology of China, 2004, 34(1): 92−97. DOI: 10.3969/j.issn.0253-2778.2004.01.014.
[170]	YOSHIDA K, HAYASHI K, MORII Y, et al. Study on behavior of methane/oxygen gas detonation near propagation limit in small diameter tube: effect of tube diameter [J]. Combustion Science and Technology, 2016, 188(11): 2012–2025. DOI: 10.1080/00102202.2016.1213989.
[171]	ZHANG B, LIU H. The effects of large scale perturbation-generating obstacles on the propagation of detonation filled with methane-oxygen mixture [J]. Combustion and Flame, 2017, 182: 279–287. DOI: 10.1016/j.combustflame.2017.04.025.
[172]	ZHANG B, PANG L, GAO Y. Detonation limits in binary fuel blends of methane/hydrogen mixtures [J]. Fuel, 2016, 168: 27–33. DOI: 10.1016/j.fuel.2015.11.073.
[173]	LEE J H S, JESUTHASAN A, NG H D. Near limit behavior of the detonation velocity [J]. Proceedings of the Combustion Institute, 2013, 34(2): 1957–1963. DOI: 10.1016/j.proci.2012.05.036.
[174]	JACKSON S, LEE B J, SHEPHERD J E. Detonation mode and frequency analysis under high loss conditions for stoichiometric propane-oxygen [J]. Combustion and Flame, 2016, 167: 24–38. DOI: 10.1016/j.combustflame.2016.02.030.
[175]	ISHII K, MONWAR M. Detonation propagation with velocity deficits in narrow channels [J]. Proceedings of the Combustion Institute, 2011, 33(2): 2359–2366. DOI: 10.1016/j.proci.2010.07.051.
[176]	ISHII K, KATAOKA H, KOJIMA T. Initiation and propagation of detonation waves in combustible high speed flows [J]. Proceedings of the Combustion Institute, 2009, 32(2): 2323–2330. DOI: 10.1016/j.proci.2008.05.029.
[177]	GAO Y, NG H D, LEE J H S. Near-limit propagation of gaseous detonations in narrow annular channels [J]. Shock Waves, 2017, 27(2): 199–207. DOI: 10.1007/s00193-016-0639-y.
[178]	HALOUA F, BROUILLETTE M, LIENHART V, et al. Characteristics of unstable detonations near extinction limits [J]. Combustion and Flame, 2000, 122(4): 422–438. DOI: 10.1016/S0010-2180(00)00134-6.
[179]	颜秉健, 张博, 高远, 等. 气相爆轰波近失效状态的传播模式 [J]. 爆炸与冲击, 2018, 38(6): 1435–1440. DOI: 10.11883/bzycj-2017-0167. YAN B J, ZHANG B, GAO Y, et al. Investigation of the propagation modes for gaseous detonation at near-limit condition [J]. Explosion and Shock Waves, 2018, 38(6): 1435–1440. DOI: 10.11883/bzycj-2017-0167.
[180]	GOODERUM P B. An experimental study of the turbulent boundary layer on a shock-tube wall: NACA-TN-4243 [R]. Washington: Langley Aeronautical Laboratory, 1958.
[181]	LIU L J, ZHANG Q. Numerical study of cellular structure in detonation of a stoichiometric mixture of vapor JP-10 in air using a quasi-detailed chemical kinetic model [J]. Aerospace Science and Technology, 2019, 91: 669–678. DOI: 10.1016/j.ast.2019.07.017.
[182]	WANG L Q, MA H H, SHEN Z W, et al. Detonation behaviors of syngas-oxygen in round and square tubes [J]. International Journal of Hydrogen Energy, 2018, 43(31): 14775–14786. DOI: 10.1016/j.ijhydene.2018.05.163.
[183]	CRANE J, SHI X, SINGH A V, et al. Isolating the effect of induction length on detonation structure: hydrogen-oxygen detonation promoted by ozone [J]. Combustion and Flame, 2019, 200: 44–52. DOI: 10.1016/j.combustflame.2018.11.008.
[184]	ZHANG B, LIU H. Theoretical prediction model and experimental investigation of detonation limits in combustible gaseous mixtures [J]. Fuel, 2019, 258: 116132. DOI: 10.1016/j.fuel.2019.116132.
[185]	MORLEY C. Gaseq: A Chemical equilibrium program for windows [EB/OL]. 2007. http://www.gaseq.co.uk/.
[186]	BOECK L R, MÉVEL R, FIALA T, et al. High-speed OH-PLIF imaging of deflagration-to-detonation transition in H₂-air mixtures [J]. Experiments in Fluids, 2016, 57(6): 105. DOI: 10.1007/s00348-016-2191-z.
[187]	HAN W H, KONG W J, GAO Y, et al. The role of global curvature on the structure and propagation of weakly unstable cylindrical detonations [J]. Journal of Fluid Mechanics, 2017, 813: 458–481. DOI: 10.1017/jfm.2016.873.
[188]	MAHMOUDI Y, MAZAHERI K. Triple point collision and hot spots in detonations with regular structure [J]. Combustion Science and Technology, 2012, 184(7): 1135–1151. DOI: 10.1080/00102202.2012.664004.
[189]	MAHMOUDI Y, MAZAHERI K. High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations [J]. Acta Astronautica, 2015, 115: 40–51. DOI: 10.1016/j.actaastro.2015.05.014.
[190]	EINFELDT B, MUNZ C D, ROE P L, et al. On Godunov-type methods near low densities [J]. Journal of Computational Physics, 1991, 92: 273−295. DOI: 10.1016/0021-9991(91)90211-3.
[191]	LINDE T, ROE P L. Robust Euler codes [C] // Proceedings of the 13th Computational Fluid Dynamics Conference. USA: Snowmass Village, 1997.
[192]	张涵信. 差分计算中激波上、下游出现波动的探讨 [J]. 空气动力学学报, 1984, 1: 12–19. ZHANG H X. The exploration of the spatial oscillations in finite difference solutions for navier-stokes shocks [J]. Acta Aerodyn Sin, 1984, 1: 12−19.
[193]	张涵信. 无波动、无自由参数的耗散差分格式 [J]. 空气动力学学报, 1988, 6: 143–165. ZHANG H X. Non-oscillatory dissipation and non-free-parameter difference scheme [J]. Acta Aerodynamica Sinica, 1988, 6: 143–165.
[194]	沈孟育, 李海东, 刘秋生. 用解析离散法构造WENO-FCT格式 [J]. 空气动力学报, 1998, 16: 56−63. SHEN M Y, LI H D, LIU Q S. Analytic discrete WENO-FCT scheme [J]. Acta Aerodynamica Sinica, 1998, 16: 56–63.
[195]	ZHANG X X, SHU C W. On positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes [J]. Journal of Computational Physics, 2010, 229(23): 8918–8934. DOI: 10.1016/j.jcp.2010.08.016.
[196]	ZHANG X X, SHU C W. Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms [J]. Journal of Computational Physics, 2011, 230: 1238−1248. DOI: 10.1016/j.jcp.2010.10.036.
[197]	SHEN Y, SHEN H, LIU K X, et al. Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme [J]. Chinese Physics B, 2016, 25(11): 114702. DOI: 10.1088/1674-1056/25/11/114702.
[198]	韦伟, 翁春生. 基于三维两相CE/SE方法的点火位置对固体燃料PDE的影响研究 [J]. 弹道学报, 2016, 28(3): 65–70. DOI: 10.3969/j.issn.1004-499X.2016.03.012. WEI W, WENG C S. Analysis of the influence of different ignition location on pulse detonation engine with solid fuel based on three-dimensional two-phase CE/SE method [J]. Journal of Ballistics, 2016, 28(3): 65–70. DOI: 10.3969/j.issn.1004-499X.2016.03.012.

施引文献

期刊类型引用(1)
1. 张世文，陈艳，但加坤，李英雷，刘明涛，汤铁钢. 爆轰驱动下45钢半球壳膨胀断裂破片回收研究. 高压物理学报. 2023(02): 159-168 . 百度学术
其他类型引用(0)

资源附件(0)

访问统计

图(33) / 表(1)

计量

文章访问数: 1240
HTML全文浏览量: 767
PDF下载量: 303
被引次数: 1

1. 数理模型
1.1 物理模型
1.2 数学模型[15-16]
1.3 数值模拟
2. 计算模型及边界条件
2.1 计算模型及网格划分
2.2 初始及边界条件
2.3 网格无关性验证
3. 膛口流场数值模拟结果与分析
3.1 数值模型的实验验证
3.2 计算结果与分析
4. 结　论

气相爆轰波起爆与传播机理研究进展

doi: 10.11883/bzycj-2021-0398

作者简介: 韩文虎（1982－ ），男，博士，副研究员，hanwenhu@bit.edu.cn

通讯作者: 王 成（1972－ ），男，博士，教授，wangcheng@bit.edu.cn

计量

出版历程

Progress in studying mechanisms of initiation and propagation for gaseous detonations

1. 数理模型

1.1 物理模型

1.2 数学模型[15-16]

1.3 数值模拟

2. 计算模型及边界条件

2.1 计算模型及网格划分

2.2 初始及边界条件

2.3 网格无关性验证

3. 膛口流场数值模拟结果与分析

3.1 数值模型的实验验证

3.2 计算结果与分析

4. 结 论

期刊类型引用(1)

其他类型引用(0)

计量

出版历程

目录

1. 数理模型

1.1 物理模型

1.2 数学模型[15-16]

1.3 数值模拟

2. 计算模型及边界条件

2.1 计算模型及网格划分

2.2 初始及边界条件

2.3 网格无关性验证

3. 膛口流场数值模拟结果与分析

3.1 数值模型的实验验证

3.2 计算结果与分析

4. 结 论

作者简介:
韩文虎（1982－　），男，博士，副研究员，hanwenhu@bit.edu.cn

通讯作者:
王　成（1972－　），男，博士，教授，wangcheng@bit.edu.cn

1.2 数学模型^[15-16]

4. 结　论

1.2 数学模型^[15-16]

4. 结　论