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由于碰撞影响主导电离机制,气体击穿阈值Eth受激光作用区域粒子密度ρ的影响很大,粒子密度越小越难击穿,击穿阈值越大。在气体温度T恒定的情况下,击穿阈值会受气体压力p的影响。DAVIS等人[25]的研究表明,对于相同气体成分,在相同入射激光条件下,击穿阈值与气体压力的关系可以表示为:
$ {E_{{\rm{th}}}} \propto {p^\beta },{\rm{ }}(\beta < 0) $
(1) 式中,β是一个小于0的常数。值得提及的是,真正影响击穿阈值的是击穿区域粒子密度,而非压力。根据ZCLDOVICI等人的火焰传播热力理论, 在恒定大气压条件下,理想气体状态方程p=ρRT是近似成立的[26](R为理想气体常数)。因而在理想状态下气体的击穿阈值就可以转换为以下简单方程:
$ {E_{{\rm{th}}}} = \alpha {T^\delta },{\rm{ }}(\alpha ,{\rm{ }}\delta > 0) $
(2) 式中, α是正比例常数,δ是与实验台架相关参量,α和δ的值可以通过标定得到。根据(2)式可以看出, 击穿阈值与温度成正相关。KIEFER和TRÖGER[27]就以此提出了一种利用击穿阈值来定量测量火焰温度的方法,他们的实验结果表明,火焰中击穿阈值受气体化学组成成分的影响相对于粒子密度(或者说火焰温度)来说可以忽略。但是,击穿阈值的测量方法(见下文)很复杂且测量精确度有限,而且击穿阈值只能单独测量无法同步采集光谱数据,因为入射能量仅够用来击穿,等离子体发射的光谱信号极弱。
等离子体能量表征激光作用区域粒子所吸收溅射的激光能量,也与作用区域的粒子密度相关[28], 即作用区域粒子密度越大,在相同入射激光能量条件下粒子所能吸收的能量就越高,所测等离子体能量就越高。根据之前的讨论,可以推断出在恒定大气压条件下等离子体能量与火焰温度成负相关。为了探究验证等离子能量Ep与火焰温度之间的变化关系,作者同步测量了甲烷流量为0.120L/min的扩散火焰不同高度上(h=9mm, 11mm)的击穿阈值和等离子体能量水平分布情况。由于火焰是轴对称的,实验只需研究半边火焰。实验中,击穿阈值测量采用半击穿法,即调整入射激光能量使得该点处火焰被击穿的概率约为50%。每个测量点观测50个激光脉冲,若有25次左右击穿成功,则此时的入射激光能量为火焰该测量点处的击穿阈值。在完成一个高度上的击穿阈值测量后,将入射激光能量调高并固定为90.07mJ(测量50次取平均),测量残余脉冲能量(测量点与击穿阈值的相同),通过入射激光能量与残余能量之差得到等离子体能量。
实验结果如图 3所示,竖虚线标示出曲线顶点。两图中击穿阈值变化规律类似,表征火焰温度由中心到外围先升高后降低。而且由两图中可以清晰地看出击穿阈值和等离子体能量变化规律正好相反,且步调一致。因此可以证明等离子体能量与火焰温度成负相关,即可以用等离子体能量来定性描述甲烷扩散火焰温度分布情况。而且等离子体能量测量简单,只需在采集光谱数据的同时测量尾部残余激光能量即可,因而有利于将其与光谱数据同步分析,结合起来探究火焰结构及反应机理。
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为了研究甲烷扩散火焰空间分布特性,分别在流量为q=0.100L/min, q=0.120L/min的火焰中心剖面上3个高度(h=7mm, 9mm, 11mm)水平线(从火焰中心到外界)以及轴线上进行实验。由于轴向真正h=0mm位置点(本生灯口)无法进行实验而且较难确定,因此实验中选取的轴向h=0mm位置略高1mm。实验每个位置点测量50次。入射激光能量固定在90.07mJ,采集光谱的同时对末端的激光残余能量进行测量,取50次测量平均值。考虑到火焰内外反应剧烈程度差异,所取的测量位置点疏密不同。图 4为甲烷流量为0.100L/min的火焰中心轴线9mm高度上单次测量光谱图。可以看到几条清晰高信噪比的谱线:656.35nm Hα, 777.34nm O(Ⅰ), 746.89nm N(Ⅰ), 247.87nm C(Ⅰ)以及分子光谱388.20nm CN。
图 5为流量q=0.100L/min扩散火焰的不同高度上的等离子能量水平分布情况。根据之前得出的等离子体能量分布可以表征火焰温度分布情况的结论可看出,各高度上温度水平变化规律基本相同:从火焰中心到外,先缓慢升高达到最高温度后又逐渐降低直到接近外界空气击穿水平。在火焰内部,随着高度的升高,温度也变高,当然这是在有限高度内。由图 6中不同甲烷流量的火焰轴线等离子体能量分布曲线可以看出, 温度沿轴向先升高,达到一定高度后燃料被大部分消耗,温度开始降低。参照图 5中3条曲线变化趋势,大致选择等离子能量低于37mJ(横向虚线表示)的区域为高温区,由图 5中可以看出, 随着高度的升高,高温区的宽度在增加,h在7mm, 9mm, 11mm高度上,高温区宽度约为1.0mm, 1.2mm, 1.5mm。另外由图 6可以看出, 火焰轴向高温区宽度远比径向的宽,约为10mm。这是因为一方面火焰下部反应产生的热量被带到火焰上部,另一方面受浮力作用燃料空气向上流动,火焰上部混合更加充分、反应更为剧烈。
Figure 5. Horizontal distribution of plasma energy at different heights with methane flow rate of 0.100L/min
Figure 6. Axial distributions of plasma energy in the central line of flames with different flow rates
根据相关理论分析及实验结果表明[18-23],气体火焰中特定谱线强度之比(例如甲烷空气燃烧火焰中的H/O, C/O等)与火焰局部当量比呈线性关系。图 7为流量q=0.100L/min的甲烷火焰中心剖面不同高度上656.35nm Hα与777.34nm O(Ⅰ)谱线强度比水平分布图。由图中可以看出, 由于外界空气不断地掺混扩散,H/O谱线强度比(也可以说当量比)从火焰中心到外部不断下降,到径向半径r=11mm时基本达到空气击穿水平。而且可以清晰地看出3条曲线中途出现一个拐点,且3个拐点对应的H/O强度比大致相同(由横虚线标出)。参照图 5也可以看出,这3个拐点的径向位置对应着所在高度上高温区开始的点。之前介绍过,扩散火焰前沿位于当量比Φ=1的表面,而此表面内可燃物和氧化剂刚好可以完全反应,所以能够放出大量的热向外扩散形成扩散火焰高温区。因此可以确定此拐点对应着火焰该高度上火焰前沿的位置。而火焰前沿到外部空气击穿水平位置的距离即为扩散火焰第二燃烧区域,如图 7中双向箭头所示,h在7mm, 9mm, 11mm高度上,第二燃烧区域的宽度约为6.5mm, 7.0mm, 8.0mm。
Figure 7. Radial distributions of H/O intensity ratio at different heights with methane flow rate of 0.100L/min
火焰前沿对应的H/O强度比约为3.29(3点平均值),而在远离火焰处的空气击穿的H/O强度比约为0.34,而这两个位置的H/O强度比对应的火焰局部当量比约为1和0。通过取这两组特殊值,可以求出近似的H/O强度比IH/O和火焰局部当量比Φ的公式,如下:
$ {I_{{\rm{H/O}}}} = 2.95\Phi + 0.34 $
(3) 利用此关系式求出不同甲烷流量的扩散火焰中心轴向当量比分布情况, 如图 8所示。对两组数据进行了指数拟合,拟合公式如下:
$ \begin{array}{l} \mathit{\Phi} = 1.93{{\rm{e}}^{ - h/14.88}} + 9.32{{\rm{e}}^{ - h/3.04}} + 0.36,\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;(q = 0.100L/{\rm{min}}) \end{array} $
(4) $ \begin{array}{l} \mathit{\Phi} = 5.27{{\rm{e}}^{ - h/8.5}} + 18.33{{\rm{e}}^{ - h/2.29}} + 0.48,\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;(q = 0.120L/{\rm{min}}) \end{array} $
(5) Figure 8. Axial distributions of local equivalent ratio in the central line of flames with different flow rates
两组拟合相关性系数分别为0.989和0.991,具有很好的相关性。将Φ=1代带入(4)式和(5)式得出h=15mm和h=18mm,由于实验中h=0mm位置点比本生灯口略高1mm,因此可以得出的甲烷流量为0.100L/min和0.120L/min的火焰长度分别约为16mm和19mm。
LIBS应用于甲烷层流扩散火焰空间分布研究
Laser-induced breakdown spectroscopy in spatial distribution of methane laminar diffusion flame
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摘要: 为了研究扩散火焰空间分布特性,采用具有空间分辨能力的激光诱导击穿光谱技术对甲烷/空气本生灯扩散火焰进行了实验研究,得到了不同流量(0.100L/min,0.120L/min)、不同高度(7mm,9mm,11mm)的火焰以及中心轴线上的击穿阈值、等离子体能量、光谱强度比等相关参量的分布情况。结果表明,等离子体能量可以用来定性描述扩散火焰温度空间变化规律,结合分析等离子体能量和H/O谱线强度比的分布情况可确定扩散火焰不同高度上火焰前沿的位置以及第二燃烧区域的宽度;根据相关实验点近似得到H/O谱线强度比与火焰局部当量比线性关系式,可得到不同流量条件下扩散火焰轴向当量比分布情况以及火焰长度。此研究结果对于激光诱导击穿光谱技术应用于燃烧诊断方面具有重要意义。Abstract: In order to explore spatial distribution characteristics of diffusion flame, spatially-resolved laser-induced breakdown spectroscopy (LIBS) was used to study the laminar diffusion methane-air flame. The spatial distributions of the threshold energy, the plasma energy and the intensity ratio were obtained at different heights (7mm, 9mm and 11mm) with the flow rate of 0.100L/min and 0.120L/min. The results show that the spatial distribution of flame temperature can be qualitatively described by the plasma energy. Combining the analysis of the plasma energy distribution and the H/O intensity ratio distribution, the positions of the flame front and the width of secondary combustion region can be determined. In addition, according to the relevant measurement, the linear equation for H/O intensity ratio and equivalent ratio can be determined approximately. By this linear equation, the axial distribution of local equivalent ratio and the flame length is obtained. These results have important significance for LIBS application in combustion diagnosis.
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