• ISSN 1001-1455  CN 51-1148/O3
  • EI Compendex、CA收录
  • 力学类中文核心期刊
  • 中国科技核心期刊、CSCD统计源期刊
Volume 36 Issue 2
Oct.  2018
Article Contents

Citation:

Simulation on dynamic pressure of premixed methane/air explosion in open-end pipes

  • Received Date: 2014-08-18
    Accepted Date: 2014-10-24
  • In order to study the evolution of dynamic overpressure of deflagration, a simulation was carried out in an open end pipe. It was found that the dynamic pressure was closely correlated with the gas velocity so that they always arrive at the peak value at the same time. In addition, the first positive peak of the dynamic pressure was almost several times greater than that of the second. This may indicate that the blast wave has a greater influence on the dynamic pressure than the flame does. An empirical prediction equation was given to calculate the first and second positive peaks based on the propagation time. Maximum dynamic pressures were increased with the propagation distance in all the three directions (x, y and z), and so was with time. The maximum dynamic pressure value in the x direction was almost several thousand times greater than those in the other two directions. Compared with the explosive overpressure, the influence on the explosive damage by the dynamic pressure in the y and z direction was quite small. Three empirical formulas were given to calculate the maximum dynamic pressures in different directions. The relationship between the dynamic pressure and the square of the gas velocity was verified. An empirical formula of the dynamic overpressure was also given based on the length-diameter ratio and the gas velocity. The results may provide a reference for the study on the gas explosion in the limited spaces.
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Simulation on dynamic pressure of premixed methane/air explosion in open-end pipes

  • State Key Laboratory of Coal Resources and Safe Mining, Faculty of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Abstract: In order to study the evolution of dynamic overpressure of deflagration, a simulation was carried out in an open end pipe. It was found that the dynamic pressure was closely correlated with the gas velocity so that they always arrive at the peak value at the same time. In addition, the first positive peak of the dynamic pressure was almost several times greater than that of the second. This may indicate that the blast wave has a greater influence on the dynamic pressure than the flame does. An empirical prediction equation was given to calculate the first and second positive peaks based on the propagation time. Maximum dynamic pressures were increased with the propagation distance in all the three directions (x, y and z), and so was with time. The maximum dynamic pressure value in the x direction was almost several thousand times greater than those in the other two directions. Compared with the explosive overpressure, the influence on the explosive damage by the dynamic pressure in the y and z direction was quite small. Three empirical formulas were given to calculate the maximum dynamic pressures in different directions. The relationship between the dynamic pressure and the square of the gas velocity was verified. An empirical formula of the dynamic overpressure was also given based on the length-diameter ratio and the gas velocity. The results may provide a reference for the study on the gas explosion in the limited spaces.

    HTML

  • 煤炭作为主要能源,在国民经济的发展中占据着至关重要的地位。在众多的煤矿安全事故中,瓦斯爆炸事故无论是死亡人数、经济损失还是发生次数,都一直占据较大比重[1-5]。因此,煤矿瓦斯爆炸事故防治仍将是未来很长一段时间煤矿安全的重点。当前,对瓦斯爆炸的研究主要集中于对冲击波超压,波前瞬态流速和火焰传播速度的研究,而对动压缺乏足够的研究[6-10]。过去通常只考虑冲击波超压造成的爆炸伤害,而忽略了动压所造成的伤害。在此前的研究中,发现动压事实上和冲击波超压具有同等数量级的危害效果。因此,本文想要就动压的演化规律进行一些有益的探讨。应该说明的是,本文中研究的动压是指流体在流动过程中受阻时,由于动能转变为压力能而引起的超过流体静压力部分的压力[11]。S.Glasstone[12],G.F.Kinney等[13],L.D.Landau等[14]和M.J.Zucrow等[15]通过研究得到了动压的计算公式以及动压变化规律的主要影响因素。这些公式均基于爆炸冲击波的质量、动量和能量守恒假设,并依据Rankine-Hugoniot条件为基础而得出。朱传杰[16]通过数值模拟的方法研究瓦斯爆炸,得到了动压在管道系统内的一些基本演化特征。这些研究或仅基于理论推导,或爆炸环境只考虑了不受限环境,或对动压只进行了定性的描述,而且在煤矿井下,其巷道系统类似于开口型管道系统。因而,有必要完善动压的研究,观察其在受限空间内的变化规律,并给出相应的定量描述。

    针对瓦斯爆炸的研究中主要是矿井实验、管道实验和数值模拟。矿井实验由于准备繁复,耗资巨大,无法反复进行;而利用管道进行实验时,由于目前测量手段的局限性,测点的设置无形中改变了管壁粗糙度,对气体的流动状态有很大的影响,进而改变了瓦斯爆炸参数的变化规律;但是用数值模拟的方法可以避免以上情况的出现。目前应用较多的计算软件主要是AutoReaGas和FLACS,这2种软件广泛应用于石油、化工和天然气的危险评估当中,而且有些学者也将其应用于煤矿瓦斯爆炸研究中,并取得一些很好的成果[17-21]。AutoReaGas和FLACS相比较而言,AutoReaGas的预测值稍微偏高,但是设计煤矿瓦斯爆炸的保护措施应该保留一定的安全余量,因此选用AutoReaGas进行数值模拟。

    本文中拟通过AutoReaGas软件模拟开口型巷道系统内爆燃波的传播过程,得到动压的传播演化规律,以期为全面了解瓦斯爆炸参数的演化规律提供参考。

1.   数值模型及其验证

    1.1.   数值模型

  • AutoReaGas是三维计算流体分析软件,主要用来模拟气体爆炸与由此引发的冲击波效应。专门设计用在那些非常拥塞(如管道工程管和设备)和限制(由于建筑物/结构,包括通风口等)的场所,这些场所对燃烧加速有很重要的影响,从而引起超压。AutoReaGas软件在模拟气体爆炸方面,其可靠性得到了多方的验证和认可[22-24]。数值模型中的气体动力学过程用质量、动量和能量守恒方程来表示。湍流作为气体燃烧爆炸的重要因素,采用k-ε模型。燃烧反应过程简化成基元反应,即甲烷与氧气直接生成二氧化碳和水。燃烧速率Rc表示为[25]:

    式中:Ct为量纲一因数,ρ为可燃混合气体的密度,kg/m3Γ是湍流扩散系数,Rmin可燃物、氧气和燃烧产物各自所占的质量分数中的最小值。

    湍流燃烧速度St表示为[26]:

    式中:ut为湍流强度,Lt为湍流的特征长度,m;Sl为层流火焰燃烧速度,m/s;ν是运动黏度,N·s/m2。数值模拟中的其余设置参数参考A.C.Van den Berg等[27]的研究。

    初始阶段的层流燃烧速率按照准层流模型处理。Fs是另外一个重要的修正系数,主要是为了修正压力、温度和火焰前沿褶皱对层流燃烧速度的影响。St是湍流火焰速度,其和Fs、火焰半径r和理论层流火焰速度Sl的关系表示为[28]:

    数值计算相关的初始参数可详见文献[29]。

  • 1.2.   实验验证

  • 有学者曾利用实验矿井进行了大量实验,以提高数值模拟的可靠程度,研究中发现只要数值模拟结果与实际实验误差值在±47%以内时,数值模拟的结果就能够满足工程现场的需要[30-31]。C.J.Lea等[32]也通过实验证实了AutoReaGas软件的模拟可靠性。因此,为了保证数值计算结果的准确性,通过相关实验进行验证,利用实验数据与数值计算结果的对比来验证网格划分的合理性以及模型的选取合理性。模型验证实验选取的实验管道长为5 m,横截面为8 cm×8 cm。在对比参数的选取上,采用实验方法易于获得的爆炸超压值[33]

  • 1.2.1.   实验设备
  • 实验管道示意图如图 1所示。管道左端为封闭端,也是点火端,管道右端开放;压力测点自管道左端0.5 m开始布置,每隔0.5 m安置1个,总共9个,火焰测点安装在管道左端0.25 m处,起触发开关用,采用电点火方式,点火能量是2 J。实验气体体积分数为9.5%,环境温度约25 ℃,管道内壁光滑,粗糙度可视为零。这些参数在数值模拟当中也以相同数值设定,包括点火方式的选择。

    Figure 1.  Schematic of the experimental pipe

  • 1.2.2.   实验结果和数值模拟的结果的对比
  • 数值模拟中选取2种网格进行对比。一种是每个网格尺寸为2 cm×2 cm×2 cm,另一种每个网格的尺寸为4 cm×4 cm×4 cm,2种不同网格所得的模拟结果与实验结果对比如表 1所示。从表 1中可以清晰地发现,尺寸为2 cm×2 cm×2 cm的网格划分所得的数值模拟结果与实际吻合更好。进而,利用2 cm×2 cm×2 cm的网格划分法进行了更深入的研究。图 2所示的是爆炸超压的数值模拟结果与实验数据的对比,从中可以看出数值模拟结果能与实验数据吻合较好,数值模拟与实验数据之间的最大偏差绝对值是8.35%,明显小于47%。因此,认为数值模型和网格划分具有较大的可靠性。

    测点 p/kPa ε/% p/kPa ε/%
    数值模拟(4 cm×4 cm×4 cm) 实验 数值模拟(2 cm×2 cm×2 cm) 实验
    2 213.2 196.5 8.05 202.8 196.5 -3.23
    6 199.4 179.2 11.31 186.4 179.2 -3.99
    10 141.5 120.6 17.36 110.5 120.6 8.35

    Table 1.  Comparison between experimental data and simulation results by different methods of grid partitioning

    Figure 2.  Comparison of explosion overpressure between simulation and experiment

2.   结果与分析

    2.1.   动压随时间的演化规律

  • 动压作为气体流动的直观体现,其产生和变化被气体运动情况所控制。由于动压随时间的演化规律在不同管道中具有一致的变化特征,此处只选取横截面为8 cm×8 cm、管长为20 m内的部分测点情况进行比较,如图 3所示。由图 3可以看出,动压随时间的变化规律与流速的变化规律在不同测点都基本一致。应该说明的是,本文中所指的流速是冲击波速度,不是火焰传播速度。以10.5 m处的情况为例,前驱冲击波的到来使得流速出现首个正向峰值,与此同时,动压也对应出现首个正向峰值。而后,前驱冲击波过后,流速出现回落,动压也相应回落。接着,火焰锋面的到来使得流速再次出现正向峰值,而动压也同时出现第2个正向峰值。火焰锋面过后,测点附近的气流呈现反向流动,因而流速出现反向峰值,而动压也相应地出现反向峰值,但是其值较小。最后,波阵面以对外做功和热传递的方式不断损耗能量,最终气体不再运动,动压和流速也趋于零。

    Figure 3a.  Relationship between dynamic pressure and gas velocity at the point of 0.5 m

    Figure 3b.  Relationship between dynamic pressure and gas velocity at the point of 2.5 m

    Figure 3c.  Relationship between dynamic pressure and gas velocity at the point of 4.5 m

    Figure 3d.  Relationship between dynamic pressure and gas velocity at the point of 6.5 m

    Figure 3e.  Relationship between dynamic pressure and gas velocity at the point of 8.5 m

    Figure 3f.  Relationship between dynamic pressure and gas velocity at the point of 10.5 m

    Figure 3g.  Relationship between dynamic pressure and gas velocity at the point of 12.5 m

    Figure 3h.  Relationship between dynamic pressure and gas velocity at the point of 14.5 m

    Figure 3i.  Relationship between dynamic pressure and gas velocity at the point of 16.5 m

    Figure 3j.  Relationship between dynamic pressure and gas velocity at the point of 18.5 m

    图 3中也可看出,动压的首个正向峰值总是比第2个正向峰值大。0.5 m处,首个正向峰值是4.00 kPa,第2个正向峰值是0.16 kPa;2.5 m处,首个正向峰值是25.28 kPa,第2个正向峰值是5.68 kPa;4.5 m处,首个正向峰值是55.67 kPa,第2个正向峰值是15.72 kPa;6.5m处,首个正向峰值是90.10 kPa,第2个正向峰值是26.90 kPa;8.5 m处,首个正向峰值是122.77 kPa,第2个正向峰值是37.67 kPa;10.5 m处,首个正向峰值是158.34 kPa,第2个正向峰值是47.67 kPa;12.5 m处,首个正向峰值是197.25 kPa,第2个正向峰值是56.56 kPa;14.5 m处,首个正向峰值是239.46 kPa,第2个正向峰值是64.24 kPa;16.5 m处,首个正向峰值是286.69 kPa,第2个正向峰值是70.46 kPa;18.5 m处,首个正向峰值是343.04 kPa,第2个正向峰值是74.9 kPa。除了0.5 m处,动压的首个峰值是第2个峰值的25倍,其余测点位置的动压的首个正向峰值基本上是第2个正向峰值的3~4倍。这或许可说明前驱冲击波对动压的影响要大于火焰锋面对动压的影响。而且首个正向峰值和第2个正向峰值伴随传播距离的增大而不断增大,原因在于动压与流速的二次方呈正比关系,而流速伴随传播距离的增大不断增大的,如图 4所示。通过拟合得到动压首个正向峰值和第2个正向峰值与传播距离x的关系方程:

    Figure 4.  Relationship between dynamic pressure peak and propagation distance

    式中:pd(1)为首个正向动压峰值,kPa;pd(2)为第2个正向动压峰值,kPa;R2为相关性系数。

  • 2.2.   动压在的3个方向的演化规律

  • 动压是爆炸波压力的重要组成部分,但是在不改变爆炸流场的前提条件下,目前尚无法用实验的方法直接获取动压值。因此,可以用压力传感器在实验室内测得静压(即冲击波超压),然后借助公式$p_{\mathrm{d}}=2.5\left(\frac{p_{\mathrm{s}}^{2}}{7 p_{0}+p_{\mathrm{s}}}\right)$(ps是静压,p0是初始压力)[25]而间接得到动压。

    通过数值模拟可以直接获得动压的变化规律。在管道横截面为8 cm×8 cm,管长为20 m的情况下模拟得到的3个方向(xyz)的爆炸动压如图 5所示。应该说明的是,x方向指的是管道的纵向方向,即爆燃波的传播方向;而yz方向是管道的径向上的2个方向。由于我们关心压力大小,因而在研究动压在3个向的变化时并不考虑正负。从图中可清晰看出,动压的变化规律分为前后2个部分,结合图 3可知,后一部分的动压产生源于火焰锋面的影响。相较而言,前一部分的动压值要大得多,因而只关注前一部分的动压在3个方向演化规律。由图 5可知,动压的最大值在3个方向上都随爆炸传播距离的增大而逐渐变大。此外,动压最大值也是伴随传播时间的增大而不断增大。换而言之,前一部分动压直观体现了前驱冲击波在管道内传播过程中伴随时间的变化规律。在通过拟合最大动压值和传播时间关系中可清晰看出两者呈明显的正相关,各个方向上的最大动压值随时间的拟合方程:

    Figure 5a.  Dynamic pressure in x direction varying with time

    Figure 5b.  Dynamic pressure in y direction varying with time

    Figure 5c.  Dynamic pressure in z direction varying with time

    式中:pd, x(kPa)、pd, y(Pa)和pd, z(Pa)为xyz方向上的最大动压值。

    在爆炸传播方向(x方向)上的最大动压值要远大于其他方向(yz)上的最大动压值,以19.5 m处测点为例,x方向上为381.13 kPa,y方向上为190.29 Pa,z方向上为190.19 Pa,这说明x方向上的最大动压值是其他2个方向上的最大动压值的数千倍。与爆炸超压(静压)相较而言,yz方向上的动压显然小几个数量级。因此,在探究开口型系统内的爆炸破坏效应时,yz方向的动压影响基本可以不考虑。但是x方向上的动压则较大,所以探究爆炸破坏效应时需将它的影响考虑在内。

  • 2.3.   动压和流速的定量关系

  • 动压与流速的关系可用公式$p_{\mathrm{d}}=\frac{1}{2} \rho v^{2}$来进行计算。但是相对于冲击波超压而言,爆炸冲击波波阵面的气体密度、流速以及动压在实验当中都较难测量。此前的研究中已经研究了流速和冲击波超压的关系[34-35]。因此,倘若能够建立动压和流速的关系,将有助于进一步建立动压和冲击波超压的关系。为此,本文研究了管道横截面分别为8 cm×8 cm、20 cm×20 cm和30 cm×30 cm,管长为5、10、15和20 m等12种管道情况内的动压与流速耦合关系。图 6所示为计算得到的动压和流速的关系,其中L为管长,S为管道横截面,a为管道边长。图 6(a)~(l)按照L/a由小到大进行排列。每幅图给出了3条曲线,数值模拟曲线是由计算散点拟合而得;理论曲线是按公式$p_{\mathrm{d}}=\frac{1}{2} \rho v^{2}$直接描绘而得,其中气体密度按体积分数9.5%瓦斯算得;偏差曲线是利用理论值和数值模拟值之间的相互差值描绘而得,同时也给出了偏差曲线的二次拟合方程。从图中可以清晰看出,理论曲线和数值模拟曲线的变化趋势一致,由此也可证明数值模拟结果的可靠性。此外,理论值总是稍大于数值模拟值,原因在于理论值的计算是基于常温常压下的混合气体密度,而数值模拟中密度随温度和压力变化,两者之间必然存在一定偏差。

    Figure 6a.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=16.7

    Figure 6b.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=25

    Figure 6c.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=33.3

    Figure 6d.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=50

    Figure 6e.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=50

    Figure 6f.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=62.5

    Figure 6g.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=66.7

    Figure 6h.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=75

    Figure 6i.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=100

    Figure 6j.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=125

    Figure 6k.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=187.5

    Figure 6l.  Relationship between dynamic pressure and gas velocity behind the shock wave in the pipe with a geometrical size L/a=250

    图 6中管道尺寸相关参量L/a下各条偏差曲线均为二次函数,设二次函数为:y=Ax2+Bx+C,则当L/a=16.7时,偏差曲线方程为y=1 143.33-25.3x+0.408x2;当L/a=25时,偏差曲线方程为y=2 177.87-46.58x+0.433x2;当L/a=33.3时,偏差曲线方程为y=2 694.04-50.63x+0.36x2;当L=10 m、a=20 cm,L/a=50时,偏差曲线方程为y=2 890.10-22.49x+0.2x2,改变La的值,当L=15 m、a=30 cm时,L/a仍为50,偏差曲线方程为y=5 822.06-65.5x+0.31x2;当L/a=62.5时,偏差曲线方程为y=-18 075.87-207.66x-0.083x2;当L/a=66.7时,偏差曲线方程为y=229.22-58.11x-0.037x2;当L/a=75时,偏差曲线方程为y=-3 853.72+113.67x-0.133x2;当L/a=100时,偏差曲线方程为y=-16 261.77+251.21x-0.322x2;当L/a=125时,偏差曲线方程为y=-13 434.32+57.42x+0.23x2;当L/a=187.5时,偏差曲线方程为y=-3 959.33-38.65x+0.287x2;当L/a=250时,偏差曲线方程为y=-12 902.61+25.43x+0.106x2

    将所有偏差曲线的二次项系数A提取出来,与相对应的L/a值结合,分别得到12个离散点:(16.7, 0.408)、(25, 0.433)、(33.3, 0.360)、(50, 0.200)、(50, 0.310)、(62.5, -0.083)、(66.7, -0.037)、(75, -0.133)、(100, -0.322)、(125, 0.230)、(187, 0.287)、(250, 0.106);将一次项系数B提取出来,与相对应的L/a值结合,分别得到12个离散点:(16.7, -25.30)、(25, -46.58)、(33.3, -50.63)、(50, -22.49)、(50, -65.50)、(62.5, 207.66)、(66.7, 58.11)、(75, 113.67)、(100, 251.21)、(125, 57.42)、(187.5, -38.65)、(250, 25.43);最后再将常数项C提取出来,又得到12个离散点:(16.7, 1143.33)、(25, 2 177.87)、(33.3, 2 694.04)、(50, 2 890.10)、(50, 5 822.06)、(62.5, -18 075.87)、(66.7, 229.22)、(75, -3 853.72)、(100, -16 261.77)、(125, -13 434.32)、(187, -3 959.33)、(250, -12 902.61)。

    将这些点拟合可以得到3条曲线,如图 7所示,得到关于二次项系数A的方程为:

    Figure 7a.  Relationship between quadratic coefficient and pipe size

    Figure 7b.  Relationship between monomial coefficient and pipe size

    Figure 7c.  Relationship between constant and pipe size

    关于一次项系数B的方程为:

    关于常数项C的方程为:

    结合理论方程$p_{\mathrm{d}}=\frac{1}{2} \rho v^{2}$和式(9)~(11),可得到适合本条件下的动压经验公式:

3.   结论
  • (1) 动压与流速在时间上存在较好的对应关系,基本同时出现正向和反向的峰值。而且动压的首个正向峰值总是比第2个正向峰值大数倍,这说明前驱冲击波对动压的影响要大于火焰锋面对动压的影响。此外,还给出了动压的首个正向峰值和第2个正向峰值基于传播距离的预测方程。

    (2) 动压在管道的纵向和管道径向上的变化规律较为简单,都伴随这传播距离的增大而不断增大,同时也伴随传播时间的增大而增大。火焰传播方向(管道纵向)上的最大动压值要比其他2个方向上的最大动压值大数千倍。相较爆炸超压而言,管道径向上动压对爆炸破坏效应的影响极其有限,但是火焰传播方向上的动压对爆炸破坏效应的影响不可忽略。此外,还给出了各个方向上最大动压值基于传播时间的预测方程。

    (3) 在对动压与流速的关系的研究中,验证了动压与流速的平方呈正比关系。此外,由于实际密度小于理论密度,是故所得实验曲线会低于理论曲线。同时通过分析给出了动压基于长径比和流速的经验公式,可为下一步管道实验内的动压研究提供参考。

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