The law of gas explosion and gas-liquid coupling in urban underground drainage pipelines
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摘要: 为研究城市地下排水管道中燃气爆炸传播特性和气-液两相耦合作用规律,基于气-液两相流理论和计算流体力学方法,对不同水深率下的天然气/空气混合物的爆炸-加速-衰减过程进行了数值模拟。研究结果表明:当水深率小于0.7时,随着水深率的增加,气相空间的长径比增大,燃料燃烧加剧,火焰的加速现象逐渐显著,导致峰值超压逐渐增大,超压峰值显现时间逐渐缩短,且峰值超压沿轴向的提升效果更加显著;当水深率达到0.7时,火焰在管道内的传播明显受阻,水震荡产生的波动及细水柱迅速占据了有限的气相空间,阻断了火焰的自维持传播,使得爆炸超压仅在点火源附近显现。不同水深率条件下,管道中相同区域内,同一时刻水面被扬起的高度和气相区域的速度场不同,被卷扬起的低温液体对其相邻区域的高温火焰形成降温和阻断,之后由于气体的宏观流动,与液面相邻的低温气体流动至管道内高温区域,进而造成管道内火焰温度降低,同时,水的震荡和细水柱的飞扬大大降低了爆炸超压风险。Abstract: There are frequent gas explosion accidents in urban rain and sewage drainage pipes, which pose a serious threat to people’s lives and property safety. To study the propagation characteristics of gas explosion and the law of gas-liquid two-phase coupling in urban underground drainage pipes, based on the gas-liquid two-phase flow theory and computational fluid dynamics method, a numerical simulation study of the explosion-acceleration-decay process of gas/air mixture under different water depth ratio was conducted. The results show that when the water depth ratio is less than 0.7, as the water depth ratio increases, the long-diameter ratio of the gas phase space increases, the fuel combustion intensifies, and the flame acceleration phenomenon gradually becomes significant, which leads to a gradual increase in peak overpressure, a gradual reduction in peak overpressure time, and a more significant effect of peak overpressure along the axial direction. When the water depth ratio reaches 0.7, the propagation of the flame in the pipeline is blocked, and the fluctuation caused by the water shock and the fine water column quickly occupy a small gas phase space, blocking the continuous propagation of the flame, which makes the explosion overpressure appear only near the ignition source. Under different water depth ratios, in the same zone of the pipeline and at the same moment, the height of the water being rolled up and the velocity field of the gas phase region is different, and the cryogenic liquid is rolled up to cool and block the high-temperature flame in the adjacent zone. Then, due to the macroscopic flow of the gas, the cryogenic gas adjacent to the liquid surface flows to the high-temperature region in the pipeline, resulting in a decrease in the flame temperature in the pipeline. The shock of water and the flying of fine water columns greatly reduce the risk of explosion overpressure. The research results provide a scientific basis for the explosion protection of urban gas lifelines.
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建筑玻璃的抗爆性能已成为人们日益关注的一个重要课题[1], 纯理论方法难以量化分析, 而实验研究又存在费用昂贵和具有一定危险性的问题。近年用数值模拟对玻璃抗爆性能的研究取得了一定进展。M.Larcher等[2]建立了分层壳单元的夹层玻璃模型, 定义了PVB胶的弹塑性失效准则, 并通过实验验证了模型的正确性。T.Krauthammer等[3]评估了爆炸冲击波负压阶段对玻璃板的影响。邓荣兵等[4]通过LS -DYNA软件, 采用多物质的ALE有限元法, 研究了玻璃幕墙在爆炸冲击波作用下的动态响应过程, 分析了玻璃幕墙的破坏情况。上述研究中, 玻璃模型只是通过线弹性材料模型来模拟, 并没有建立不同种类玻璃在爆炸冲击波作用下的计算模型, 对玻璃的失效准则也只是定义了拉应力失效。
本文中, 建立3种常用建筑玻璃在近场爆轰作用下的有限元分析模型, 以冲击波超压对玻璃面板作用产生的拉应力和剪切应变为失效判据, 并通过实验对模型进行对比验证。空气冲击波超压有自由场超压和壁面超压2种[5]。壁面超压是指初始冲击波到达壁面(主要是地面)产生反射后壁面所承受的压力, 该压力比自由场压力高。由于爆炸的破坏作用等原因, 要测定自由场超压很困难, 故本文中的超压值为壁面超压值。
1. 数值模拟
选用ANSYS/LS -DYNA作为计算工具。采用LSDYNA对空气冲击波传播规律的模拟包括TNT炸药的起爆、爆轰波及空气冲击波的形成及传播、冲击波的相互作用等复杂的物理化学过程, 几何模型如图 1所示。
1.1 几何模型和计算方法
建立的几何模型主要包括TNT炸药、空气和玻璃。考虑到问题的对称性, 为减少计算量, 取1/2实体进行建模。其中, 炸药采用柱形结构; 空气场为长1.2m、宽为0.25m与玻璃同宽的矩形结构。模型中对称面采用对称边界, 非对称面采用透射边界, 使用刚性壁面来模拟地面。模拟整个爆炸过程的数值方法主要包括Lagrange法、Euler法、ALE(arbitrary Lagrange -Euler)法、SPH(smoothed particle hydrodynamics)法[6]。本文中采用ALE法实现炸药与空气场的耦合作用。首先, 在结构边界运动的处理上, 引进了Lagrange法的特点, 能有效跟踪物质结构边界的运动; 其次, 在内部网格的划分上, 吸收了Euler法的长处, 使内部网格单元独立于物质实体, 可以根据定义的参数, 在求解过程中适当调整网格位置, 使网格不出现严重畸变。
1.2 有限元模型
模型中全部采用SOLID164八节点实体单元。为了模拟玻璃的裂纹扩展情况, 用Lagrange单元描述玻璃, 用多物质ALE单元描述空气和TNT炸药, 采用Van Leer(二阶精度)方法进行计算。空气场与玻璃相连接的一层网格为ALE网格到Lagrange网格的过度层网格, 实为Lagrange网格。当载荷过大时, 会发生网格畸变, 导致计算无法正常进行。本模拟中采用当过渡层网格变形在可控范围内并且冲击波正压段已作用到玻璃时, 通过重启动删除炸药和空气场网格的方法保证计算正常进行, 并且能提高计算效率, 计算结果也在可接受范围。模拟中, 通过命令*ALE_MUITI -MATERIAL_GROUP和*SECTION_SOLID_ALE定义空气和炸药的耦合及其算法; 通过命令*CONSTRAINED_LAGRANGE_IN_SOLID_TITLE定义空气与玻璃面板之间的耦合作用。
1.3 材料模型和状态方程
1.3.1炸药
炸药为60g TNT, 采用*HIGH_EXPLOSIVE_BURN模型作为炸药的材料模型, 采用JWL状态方程描述TNT炸药[7], 通过命令*INITIAL_DETONATION来控制炸药起爆的时间和爆心。JWL状态方程的表达式为:
p=A(1−ωR1V)e−R1V+B(1−ωR2V)e−R2V+ωe0V (1) 式中:p为爆轰压力; V为爆轰产物体积相对于初始体积的比值; e0为初始体积内能; ω、A、B、R1和R2均为方程系数。该状态方程通过反应爆炸气体压力-体积关系来描述炸药的爆轰过程。
具体参数值为:炸药密度ρ=1.631g/cm3, 爆速D=6.717km/s, 爆轰波阵面压力pCJ=18.5GPa, e0=7GPa, V0=1.0, A=540.9GPa, B=9.373GPa, R1=4.5, R2=1.1, ω=0.35。
1.3.2空气
对空气采用*MAT_NULL材料模型以及线性多项式*EOS_LINEAR_POLYNOMIAL状态方程加以描述[8]。线性多项式状态方程为:
p=C0+C1μ+C2μ2+C3μ3+(C4+C5μ+C6μ2)e (2) 式中:C0~C6为常量, e为初始体积内能, μ=1/V0-1, V0为相对体积。具体参数值为:空气密度ρ=0.001 3g/cm3, C0=-0.1MPa, C1=C2=C3=0, C4=C5=0.4, C6=0, E=0.25MPa, μ=1。
1.3.3玻璃
对玻璃面板采用框支约束, 对玻璃材料四周采用固端约束。通过命令*MAT_ADD_EROSION实现对玻璃材料失效准则的定义。由于是近场的爆轰作用, 玻璃除了拉应力失效, 应该还会有冲切破坏, 因此采用拉应力和切应变来控制玻璃材料的破坏。玻璃单元达到破坏后, 即从模型中删除, 从而得到玻璃的裂纹扩展情况。
对普通玻璃和钢化玻璃采用线弹性材料模型*MAT_ELASTIC[9]。具体参数值为:密度ρ=2.56g/cm3, 弹性模量E=72GPa, 泊松比ν=0.2。
对浮法玻璃采用*MAT_JOHNSON_HOLMQUIST_CERAMICS(JH -2)模型[10]。材料未发生损伤时, JH -2本构模型中材料的状态方程可表示为:
p=K1μ+K2μ2+K3μ3 (3) 式中:K1为材料的体积模量, K2、K3为材料常数, p为静水压力, μ为体应变。
JH -2强度模型是将材料的等效应力表示成静水压力的幂函数形式并且与应变率和损伤因子δ相关, 其中定义的量纲一材料强度模型表示为:
σ∗=σ∗i−δ(σ∗i−σ∗f) (4) 当材料未发生损伤(δ=0)时, 量纲一等效应力表示为:
σ∗i=A(p∗+σ∗t, m)N[1+Cln(˙ε/˙ε0)] (5) 当材料完全破碎(δ=1)时, 量纲一等效应力表示为:
σ⋆i=Bp⋆M[1+Cln(˙ε/˙ε0)] (6) 同时等效破碎强度应小于材料的最大破碎强度
。强度模型中引入的材料常数为A、B、C、M、N、σt, m以及
。p*为量纲一静水压力, p*=p/pHEL,
=σt, m/pHEL, 其中pHEL为材料处于Hugoniot弹性极限时的压力分量, σt, m为材料能承受的最大静水拉应力,
为真实应变率,
为参考应变率。
具体参数值为:密度ρ=2.53g/cm3, 剪切模量G=30.4GPa, 相对应变率
/
=1.0, 抗拉强度T=0.15GPa, 最大裂缝强度
=0.5, Hugoniot弹性极限σHEL=5.95GPa, 作用在Hugoniot弹性极限上压力pHEL=2.92GPa, 损伤因子D1=0.053, 损伤因子D2=0.85, 体积模量K1=45.4GPa, A=0.93, B=0.088, C=0.003, M=0.35, N=0.77, β=1.0, K2=-138GPa, K3=290GPa。
1.3.4 PVB胶
对玻璃夹层的PVB胶采用线性黏弹性模型*MAT_VISCOELASTIC。通过定义玻璃与PVB胶之间的自动面-面接触来实现相互的粘结作用[4]。PVB胶的具体参数为:密度ρ=1.1g/cm3, 弹性体积模量K=20GPa, 短期剪切模量G0=0.33GPa, 长期剪切模量G∞=0.69MPa, 衰减常数β=12.6s-1。
2. 模型验证
为了验证计算模型的合理性, 对建筑玻璃的抗爆性能进行了实验研究, 实验的工况条件与数值模型相同。在半径为4m的爆轰实验塔内对3种框支玻璃开展爆轰实验。利用压力传感器测得不同爆距处的冲击波超压值, 通过高速摄影机捕捉3种不同建筑玻璃在爆炸冲击波作用下的破坏情况, 并通过反复计算得到符合本实验所用炸药的冲击波超压公式:
Δpf=0.013√WR+0.084(3√WR)2+0.21(3√WR)3 (7) 对计算模型进行校验和调试。式中:W为炸药质量; R为爆距。
通过实验不仅验证了计算模型, 还与数值模拟结果进行了对比, 并得到了建筑玻璃在爆炸冲击波作用下破坏的一些认识。
空气中爆炸冲击波超压峰值会受炸药和空气网格尺寸的影响, 不同尺寸的网格会导致计算结果差异较大[11], 所以网格划分和网格数量的合理性对模拟结果至关重要。为观察玻璃的破坏形态, 必须保证玻璃的网格数量, 本文中玻璃1/2边长(25cm)网格数量为70, 即玻璃全边(50cm)网格数量为140。
沿模型x方向(冲击波传播方向)网格数量对超压峰值的结果会有很大的影响, 因此模型沿x方向网格数量的选择也尤为重要。模型沿x方向网格数量分别取为150、180、200、220进行计算。结果表明, 沿模型x方向网格数量取220时, 超压峰值最接近实验值, 如图 2(a)所示。通过反复的调试发现, 爆距小于0.5m时, 超压峰值对网格尺寸的敏感度很高。, 离爆源越近, 单元越小时, 冲击波超压峰值的计算值与实验值的偏差也越小, 但相应会增加计算时间。为了更好地提高计算效率, 在爆距R小于0.5m的范围内采用渐进的网格划法[12], 以期计算所得冲击波超压峰值的衰减规律更符合常理。分别取渐进比例系数1.02、1.05、1.08和1.10进行计算。通过计算发现, 当爆距小于0.4m、渐进比例系数为1.08时, 计算得到的冲击波超压峰值最接近于实验值, 如图 2(b)所示。
3. 数值模拟与实验结果的对比
目前基于有限元方法还没有能够准确描述玻璃材料破坏的损伤模型, 通常只能通过删除失效材料单元来实现玻璃裂纹扩展, 并通过失效节点的分离实现玻璃碎片飞溅, 所以数值模拟中玻璃的破坏形态与实验结果有一定差别。
3.1 钢化夹胶玻璃
R=0.4m时, 数值模拟得到的6mm+6mm钢化夹胶玻璃的破坏特征与实验结果如图 3和表 1所示。钢化玻璃本身的性质决定其裂纹呈规则的放射状, 碎块较均匀, 且无明显棱角。实验中, 钢化夹胶玻璃由于自身材料强度和PVB胶的作用, 在爆距为0.4m处才由于冲切作用, 玻璃面板中部发生了局部飞溅, 其余部分呈放射状开裂。数值模拟中正面破坏特征图表明, 玻璃面板中部也明显出现了由冲切作用造成的裂纹。其余正面的四周和背面的裂纹均是由于玻璃面板受拉造成的。
表 1 钢化夹胶玻璃的冲击波超压Table 1. Shock overpressure of toughened PVB -laminated glassR/m Δpf/MPa 破坏情况 数值模拟 实验 数值模拟 实验 0.6 0.098 6 0.100 6 未破坏 未破坏 0.5 0.247 0 0.160 1 破坏 破坏 0.4 0.419 0 0.287 1 破坏 局部飞溅 3.2 普通夹胶玻璃
R=0.6m时, 数值模拟得到的6mm+6mm普通夹胶玻璃的破坏特征和实验结果的比较如图 4和表 2所示。普通玻璃本身的性质决定其裂纹呈不规则状, 破坏后大小不均, 且有明显棱角。实验中, 普通夹胶玻璃由于PVB胶的作用未发生飞溅, 破坏后玻璃面板呈不规则状开裂, 且由于壁面的反射作用面板下部开裂较严重。数值模拟中, 玻璃面板正面四周和背面下部由于受拉作用开裂较严重, 与实验吻合。
表 2 普通夹胶玻璃的冲击波超压Table 2. Shock overpressure of common PVB -laminated glassR/m Δpf/MPa 破坏情况 数值模拟 实验 数值模拟 实验 0.8 0.048 3 0.049 6 未破坏 未破坏 0.7 0.067 4 0.068 6 破坏 破坏 0.6 0.098 6 0.100 6 破坏 破坏 3.3 单层浮法玻璃
R=0.6m时, 数值模拟得到的12mm单层浮法玻璃的破坏特征与实验结果的比较如图 5和表 3所示。由于没有PVB胶的保护, 单层的浮法玻璃破坏后就发生了飞溅, 玻璃碎块大小不均, 且有明显的棱角。数值模拟结果展示了玻璃面板在破坏时的受力状态, 并且反映玻璃面板纵向的变形和破坏状况较其他2种玻璃严重。
表 3 浮法玻璃的冲击波超压Table 3. Shock overpressure of float glassR/m Δpf/MPa 破坏情况 数值模拟 实验 数值模拟 实验 0.8 0.048 3 0.049 6 未破坏 未破坏 0.7 0.067 4 0.068 6 破坏 整体飞溅 0.6 0.098 6 0.100 6 破坏 整体飞溅坏 4. 结论
借助LS -DYNA软件建立了3种建筑玻璃在近场爆轰冲击波作用下的数值模型, 通过数值模拟和实验研究得到了以下结论:
(1) 数值模拟结果与实验结果基本吻合, 说明本文中所建立的计算模型和方法符合实际情况;
(2) 爆距越大, 计算得到的冲击波超压峰值越接近实验值;
(3) 通过对3种建筑玻璃破坏结果的比较可知, 同种玻璃材料在厚度相同的情况下, 夹胶玻璃的抗爆性能优于单层玻璃的抗爆性能, 钢化玻璃的抗爆性能优于其他2种玻璃的抗爆性能;
(4) 模拟得到的玻璃破坏特征与实验结果有一定的差距, 因为对玻璃材料这种脆性材料的破坏过程还没有一个较准确的数值描述方法, 需在今后的工作中继续研究。
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表 1 水深率不同时管道内不同测点处的温度峰值
Table 1. Temperature peak at different measuring points in the pipeline under different water depth ratios
水深率 不同测点的温度峰值/K 0.4 m 0.7 m 1.0 m 1.3 m 1.6 m 1.9 m 2.2 m 2.5 m 2.8 m 0.2 3 117.6 3 082.4 3 336.6 3 216.4 2 760.8 2 778.5 2 757.1 490.8 510.9 0.3 3 029.9 3 128.6 3 190.2 3 086.7 2 622.4 2 664.6 2 717.9 2 801.7 536.2 0.4 2 832.4 3 102.3 3 062.2 3 126.8 2 657.6 2 745.1 2 856.3 2 892.2 557.7 0.5 2 800.9 3 102.2 3 077.3 2 925.4 2 652.6 2 641.6 2 552.3 2 860.3 556.1 0.6 2 650.7 2 777.9 2 395.2 2 983.2 2 883.8 2 978.6 2 770.4 2 552.8 547.0 0.7 1 978.3 469.3 316.2 312.3 313.2 313.8 314.9 310.9 310.7 -
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