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单色激光与待测气体的相互作用过程可以用受激吸收模型来表示,量子级联激光器发出的单色激光光强为I0, 经待测气体传输后的光强衰减至It,二者满足Beer-Lambert定律, 可表述为:
$ I_{\mathrm{t}}=I_{0} \exp \left(-\sigma x_{\mathrm{CO}} L\right) $
(1) 式中,I0, It分别为量子级联激光器的激光光束入射光强和出射光强,σ为吸收截面,L为待测气体沿激光水平方向上的平均吸收路径, xCO为CO气体的体积分数。
待测体积分数xCO通过(1)式可以进一步表示为:
$ x_{\mathrm{CO}}=-\frac{1}{\sigma(\lambda) L} \ln \frac{I_{\mathrm{t}}(\lambda)}{I_{0}(\lambda)} $
(2) 式中,λ为激光器的中心波长。
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最优谱线的选取是量子级联激光吸收光谱浓度测量传感器模型设计尤为关键的一步,直接决定着传感器性能的优良,因此合适的目标工作波段选择会为传感器的设计建立较好的基础。发动机碳氢燃料不完全燃烧产生的CO气体在近红外第一泛频带2.3μm(分子谱带跃迁能级Δν=2)、第二泛频带1.55μm(Δν=3)以及中红外基频带4.6μm(Δν=0)处均有吸收,其中4.6μm处的CO分子属于基频跃迁,谱线强度最强。如图 1所示,根据HITRAN 2016数据库[21]计算了中红外波段2000cm-1~2250cm-1范围内,发动机常见的燃烧产物H2O, CO2, CO等标准大气压下吸收谱线强度分布,可以明显看出,在此波段内CO谱线吸收较强,并且周围H2O与CO2的干扰较小,有利于提高传感器的信噪比,增加测量结果的精度。
分子谱线强度S(T)是温度T的函数,可以表示为:
$ \begin{array}{c}{S(T)=S\left(T_{0}\right) \frac{Q\left(T_{0}\right)}{Q(T)} \times} \\ {\exp \left[-\frac{h c E^{\prime \prime}}{k_{\mathrm{B}}}\left(\frac{1}{T}-\frac{1}{T_{0}}\right) \frac{1-\exp \left(\frac{-h c \nu}{k_{\mathrm{B}} T}\right)}{1-\exp \left(\frac{-h c \nu}{k_{\mathrm{B}} T_{0}}\right)}\right]}\end{array} $
(3) 式中, S(T0)是温度296K的谱线强度,S(T)为温度T的谱线强度,Q(T0)为296K的配分函数,Q(T)为温度T的配分函数, ν为分子跃迁中心频率, E″为低能级能量。由(3)式可知,谱线强度S(T)受温度T变化而变化,其谱线温度敏感性可表示为:
$ \left|\frac{\partial R / R}{\partial T / T}\right|=\frac{h c}{k_{\mathrm{B}}} \frac{\Delta E^{\prime \prime}}{T} $
(4) 式中,ΔE″为低能级能量的差值,h, c, kB分别为普朗克常数、光速、玻尔兹曼常数, R为谱线强度的比值。
如图 2所示,根据机动车尾气中CO气体逸散过程中温度变化范围大致为300K~400K的实际情况,计算了CO在300K, 350K, 400K下的谱线强度,可以看出各支谱线强度对温度敏感程度也大不相同。其中,R支中R(12)与P支中P(10)谱线温度敏感性较低,由于本工作所使用的量子级联激光器工作波段为2010.00cm-1~2200.00cm-1,因此初步选择P支中温度敏感性较低的P(9), P(10), P(11), P(12)谱线作为候选谱线,可以最大程度上降低CO气体体积分数反演结果受温度变化的影响。
根据图 2中的计算结果,对低温度敏感性谱线P(12), P(11), P(10), P(9)谱线做进一步温度敏感性计算,候选谱线详细参量在表 1中已经列出。计算结果如图 3所示,并在表 2中列出其差值数值结果,其中,4条谱线温度敏感性改变量最低的为P(10)谱线。
Figure 3. Temperature sensitivity of candidate lines for P(12), P(11), P(10), P(9) at temperature range of 300K~400K
Table 1. Parameters of candidate lines
line center frequency/ cm-1 absorption line-strength/ (cm·mol-1) energy of low state/ cm-1 P(9) 2107.42 3.607×10-19 172.98 P(10) 2103.26 3.319×10-19 211.40 P(11) 2099.08 2.967×10-19 253.67 P(12) 2094.86 2.581×10-19 299.77 Table 2. Temperature sensitivity difference of candidate spectra in the range of 300K~400K
line P(9) P(10) P(11) P(12) the decrease of temperature sensitivity 0.466 0.29182 0.34267 0.39802 针对实际应用环境,对候选谱线P(10)及其邻近谱线吸光度以及归一化谱线强度做了进一步计算,模拟结果如图 4、图 5所示。结果表明,在300K和400K温度下,中心波数为2103.26cm-1的低温度敏感性候选谱线P(10)谱线强度相差为9.2%,受温度波动影响较小,可以作为发动机CO排放监测实际应用候选谱线。
QCLAS在JLMPGF6.5发动机CO体积分数测量中的应用
Application of QCLAS in measurement of CO volume fraction from JLMPGF6.5 engine
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摘要: 为了精确测量吸收光谱,并尽量减小温度与湍流波动对光谱测量结果的影响,采用谱线模拟仿真模拟和20kHz高频扫描的方法,选取中红外基频跃迁带内低温度敏感性谱线P(10),进行了理论分析和实验验证,取得了发动机CO吸收光谱及其体积分数随时间变化的数据,变化范围为(153±123)×10-6。结果表明,P支谱线扫描范围内可降低48.28%目标气体温度变化对体积分数反演的影响。该方案能够为发动机尾气CO激光遥感测量提供一个高速、精准、实时的监测方案。Abstract: In order to measure the absorption spectrum accurately and reduce the influence of temperature and turbulence fluctuation on spectral measurement, the method of spectrum simulation and 20kHz high frequency scanning was adopted. The low temperature sensitivity line P(10) in mid-infrared fundamental frequency transition band was selected. The data of absorption spectra and volume fraction of engine CO with the change of time were obtained. The theoretical analysis and experimental verification were carried out. The results show that, the influence of target gas temperature change on volume fraction can be reduced by 48.28% within the scanning range of P branch line. The range of variation is (153±123)×10-6. The scheme can provide a high-speed, accurate and real-time monitoring scheme for CO laser remote sensing measurement of engine exhaust.
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Key words:
- spectroscopy /
- remote sensing /
- pollution monitoring /
- hyperspectral resolution
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Table 1. Parameters of candidate lines
line center frequency/ cm-1 absorption line-strength/ (cm·mol-1) energy of low state/ cm-1 P(9) 2107.42 3.607×10-19 172.98 P(10) 2103.26 3.319×10-19 211.40 P(11) 2099.08 2.967×10-19 253.67 P(12) 2094.86 2.581×10-19 299.77 Table 2. Temperature sensitivity difference of candidate spectra in the range of 300K~400K
line P(9) P(10) P(11) P(12) the decrease of temperature sensitivity 0.466 0.29182 0.34267 0.39802 -
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