Research progress on soot measurement by laser induced incandescence
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摘要: 激光诱导炽光法(Laser Induced Incandesence,LⅡ)是一种非接触式的光学诊断方法,可获得激光片光照射薄层内瞬时碳烟的二维分布,具有较高的时间与空间分辨率,已经成为一种重要的碳烟测量技术。本文首先介绍了LⅡ技术的发展历程和基本原理,然后从数值模拟、定性和定量测量3个方面详细综述了LⅡ用于碳烟测量的技术方法以及国内外的研究进展,并对今后的发展提出了建议。实现定量测量的标定方法主要有采样法、LⅡ结合消光法(Light Extinction Method,LEM)和双色法LⅡ(2-Color Laser Induced Incandesence,2C-LⅡ),其中2C-LⅡ因实现相对简单,可以在线实时标定,因此在国内外获得了较大的发展。本文通过总结国内外LⅡ技术在测量碳烟方面的研究成果,希望让国内同行了解该方法的研究现状以及该方法在揭示碳烟生成氧化机理方面的重要作用,为其今后的发展提供一些参考。
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关键词:
- 激光诱导炽光法 (LII) /
- 碳烟 /
- 定量测量 /
- 光学诊断 /
- 研究进展
Abstract: Laser induced incandescence is a non-contact optical diagnosis method. With this method, we can obtain the two-dimensional spatial distribution of instantaneous soot within the thin layer of incoming sheet laser. This method has become an important measurement technology of soot due to its high spatial and temporal resolution. This paper first introduces the development of LⅡ technology and basic theory. Then the technical methods of LⅡ and research progress at home and abroad are summarized detailedly from three aspects, that numerical simulation, qualitative and quantitative measurement. The LⅡ mathematical model mainly includes Melton model, Liu model and Michelsen model. These models can be used to predict the change rule of LⅡ signal and also lay a foundation for the test of soot particle size. To realize quantitative measurement, the calibration of LⅡ signal is necessary. This is also one of the difficulties in LⅡ measurement. There are mainly three methods for calibration, that are sampling technique, light extinction method (LEM) and 2-color laser induced incandescence (2C-LⅡ). The sampling technique is less used because it will disturb the combustion process and mix impurities. The LⅡ-LEM needs two laser systems and uses the measuring result of LEM to calibrate the LⅡ signal, so its operation is complicated. Nevertheless, 2C-LⅡ does not need other measurement technology and can realize online real-time calibration. Since this method is relatively simple, it develops rapidly and has achieved many significant results. Naturally, LⅡ technology still needs improvement, such as optimizing the incident laser wavelength and energy, controlling the uniformity of laser sheet, perfecting the LⅡ mathematical model, and extending the application in complex environment. Through summarizing the research achievements of LⅡ technology, this paper aims to emphasize the research status and the importance of this method in understanding the soot formation and oxidation mechanism, and providing some references for its future development. -
0 引 言
随着高超声速武器的加速发展,高超声速飞行器地面考核试验任务需求快速增加[1-3]。常规高超声速风洞是高超声速飞行器测热(力)地面试验考核的主力风洞,为满足不断增加的任务需求,亟待提升高超声速风洞的试验效率[4-5]。目前,常规高超声速风洞测热(力)地面试验主要采用模型阶梯变迎角和连续变迎角方式。连续变迎角方式可以减省迎角变送机构多次启停及等待的无效时间,大幅缩短风洞实际运行时间,获得更多不同迎角下的热(力)数据,极大地提高试验效率、降低试验成本[6-7]。
常规高超声速风洞中测试模型的表面热流很低,一般在几kW/m2至几十kW/m2范围内。因此,常规高超声速风洞连续变迎角测热试验具有低幅值、长时间、动态变化等特点。现阶段,国内常用的基于磷光热图等的大面积测热方法[8-9]和基于同轴热电偶等的点测热方法[10-11]均不满足长时间动态测试的要求。国外部分研究者尝试使用戈登计测热,但戈登计响应时间相对较慢[12-13],不能满足动态测热需求。Kidd等[14-15]研制出了能够连续测试的Schmidt–Boelter(S–B)热流传感器,并在AEDC高超声速风洞试验实际应用中得到了可用的热流数据。目前,MEDTHERM公司[16]和VATELL公司[17]生产的一部分较大尺寸(0.5~1.0 inch,约1.27~2.54 cm)的S–B热流传感器已成为标准产品。
受原理研究不够深入、工艺不够先进等限制,国内早期S–B热流传感器尺寸较大、响应较慢[18-19]。朱新新等[20]基于仿真研究从结构设计到工艺的突破,掌握了小尺寸S–B热流传感器的研制方法。针对常规高超声速风洞连续变迎角试验的动态低热流长时间测试需求,本文拟对该小尺寸S–B热流传感器进行改进,标定测试改进后的传感器性能参数,评估其在连续变迎角试验中测量热流的可行性。
1 S–B热流传感器的改进
1.1 测量原理
首先简要阐述S–B热流传感器测热原理(详见文献[14-20])。S–B热流传感器主要感应元件为热阻层(包括热阻块、热电偶和封装胶),如图1所示。
设热阻块厚度为$ d $,在该热阻块上紧密缠绕由铜和康铜构成的N对T型热电偶(正极为铜,负极为康铜)。当高温气流作用于传感器外(上)表面时,即可根据傅里叶一维传热定律计算出表面热流q:
$$ q = \frac{k}{d}\Delta T = \frac{k}{{Nd{S_T}}}E $$ (1) 式中:ΔT为外(上)表面温度TH与内(下)表面温度Tc的温度差,N为有效线圈数(热电偶结点对数),k为热阻层上下表面间的热导率,ST为seebeck系数,E为热电偶对输出的总电势差。
S–B热流传感器主要用于测量低幅值动态热流,其灵敏度系数和响应时间是最为关键的性能参数。灵敏度系数Sq定义如下:
$$ {S_q} = \frac{{Nd{S_T}}}{k} = \frac{E}{q} $$ (2) 在传感器制作过程中,很难获得seebeck系数ST和热导率k,灵敏度系数主要通过热流标定的方式获得[21-24]。另外,定义响应时间为t0.95,表示传感器实际输出电势差(对应热流水平)从加载热流信号开始直至达到稳定值95%的时间。
1.2 改进措施
为进一步增大S–B热流传感器灵敏度系数、提高连续变迎角试验低热流测试抗噪性,以0.025 mm康铜丝代替之前使用的0.05 mm康铜丝,采用精准控力的电动绕线技术,将其绕制于2 mm长的热阻块上。在热阻块长度相同的前提下,康铜丝变细,可绕制的线圈数目增加,从而增大了总的热电势输出,达到提高灵敏度系数的目的。
为缩短响应时间,提高S–B热流传感器测试动态热流的响应能力,需提高热阻层的总热导率[20]。在热电偶确定后,影响S–B热流传感器热阻层热导率的因素包括2部分:一是热阻块热导率较高,约为230 W/(m·K);二是表面封装胶热导率相对很低,仅约1 W/(m·K)。提高热导率的措施包括提高热阻块和封装胶热导率、减小热阻块和封装胶厚度。材料一旦选定,热阻块和封装胶热导率就不能改变,且为了保证一定灵敏度,热阻块厚度也不能太小。因此,在本次改进中采用了新的喷胶工艺,可将热导率较低的封装胶厚度控制在0.01 mm以内,与之前涂抹封装胶的方式(涂抹厚度约0.05 mm)相比,封装胶厚度显著减小,有助于提高热阻层的热导率。灵敏度系数和响应时间的改进效果详见第2节。
另外,为满足更薄模型和更小间隙的测试需求,将S–B热流传感器封装长度由10 mm降低至7 mm。图2为改进后的S–B热流传感器实物照片,直径为3 mm,长为7 mm。图2左下角为放大镜下涂胶前的热电偶结点对照片(左半灰色金属丝为康铜,右半橙色金属丝为镀铜)。每支S–B热流传感器均有2对热电偶输出线:一对为热电偶结点对引出线,可根据其热电势输出值计算热流;另一对为T型热电偶引出线,用于测量热阻层背面温度(可用于计算传感器外表面温度)。
2 S–B热流传感器性能测试
在中国空气动力研究与发展中心超高速空气动力研究所的高频响热流传感器标定装置[25]中完成了S–B热流传感器的性能测试。该装置能够提供稳定可靠、波形可变、不同幅值大小的均匀热流,并配有高采样率的数据采集设备和光电探测器监测装置。
2.1 静态校准
开展了静态校准试验,以获得S–B热流传感器的灵敏度系数,具体方式为热流比对标定[21-24]。向经过校准的戈登计和待测S–B热流传感器加载相同的热流,改变激光器驱动电压,获得18个不同驱动电压下戈登计测得的热流值与S–B热流传感器电压值的对应关系(图3,横轴为戈登计测得的热流,最小0.72 kW/m2,最大132.60 kW/m2,纵轴为S–B热流传感器输出电压)。以最小二乘法进行线性拟合,得到灵敏度系数(即斜率)为57.67 μV·m2/kW,拟合最大非线性度为0.85%,相关系数R2 =
0.9999 ,表明热流传感器灵敏度系数线性度和拟合相关性较好。另外,针对连续变迎角试验的长时间测试需求,考察了S–B热流传感器的长时间稳定性。选取图3中的低、中、高热流状态(热流分别为3.34、70.13和132.60 kW/m2),分别连续加热100 s,得到图4所示的温度和热流曲线。如图4所示,传感器被持续加热,温度不断升高,但热流输出相当稳定。
进一步地,定义S–B热流传感器的不稳定度为:
$$ \varepsilon = \frac{{{q_{\max }} - {q_{\min }}}}{{{q_{\max }} + {q_{\min }}}} \cdot 100\% $$ (3) 式中,qmax、qmin分别为近100 s稳定区间内输出热流的最大值和最小值。根据式(3)可得到低、中、高热流状态100 s内的不稳定度分别为1.39%、0.94%和1.00%,表明该传感器在一定温度区间内几乎不受温度变化影响,具有较好的长时间稳定性。
2.2 动态测试
为获得较准确的响应时间,对S–B热流传感器输出电压归一化,仍选取低、中、高热流状态(3.34、70.13和132.60 kW/m2)分析响应时间。如图5所示,以光电探测器的归一化输出电压作为激光出光到达传感器外表面的参照,得到3个热流状态的响应时间t0.95分别为23、26和23 ms,说明该传感器的响应时间处于约26 ms的水平。
为考察该传感器的频响特性,以不同频率的正弦波激光作为输入信号,考察传感器输出波形。激光输入波形如下式所示:
$$ {x}_{{\rm{laser}}}(t)=A\mathrm{sin}(2\pi \omega t + \theta ) + D $$ (4) 式中,A为振幅,ω为频率,θ为初相角,D为直流偏移量。将激光器正弦波形驱动低电压设为1.5 V(对应图3的稳态热流6.19 kW/m2)、高电压设为1.9 V(对应图3中的稳态热流10.07 kW/m2),数据采集设备的采样频率为10 kHz。图6给出了ω分别为1和10 Hz的S–B热流传感器输出电压波形(S–B)和光电探测器(light detector)的输出电压波形。如图6(a)所示,当ω = 1 Hz时,在5 s加热时间内,光电探测器和S–B热流传感器都呈现了5个完整的正弦波形,除幅值存在差异外,两者在时间上几乎同步。光电探测器为纳秒级响应,基本可以忽略其延迟效应,其输出波形可作为激光源波形参考,因此可以认为S–B热流传感器能够很好地反映1 Hz动态正弦波形输入热流的变化。图6(b)为ω = 10 Hz时的波形比对(其他试验条件与ω = 1 Hz时相同)。图6(a)和(b)中的光电探测器输出波形几乎完全相同;在0.5 s加热时间内,光电探测器呈现了5个完整的正弦波形,而S–B热流传感器第5个波形未完全输出,且5个波形整体时间响应上稍许滞后,输出幅值(正弦波波峰与波谷的差值)也有所下降,即开始出现信号失真和功率衰减现象。
为进一步定量评估该传感器的频响特性,令S–B热流传感器正弦输出波形和光电探测器正弦输出波形的表达式分别为式(5)和(6):
$$ {x}_{{\rm{SB}}}(t)={A}_{{\rm{SB}}}\mathrm{sin}(2\pi {\omega }_{{\rm{SB}}}t + {\theta }_{{\rm{SB}}}) + {D}_{{\rm{SB}}} $$ (5) $$ {x}_{{\rm{LD}}}(t)={A}_{{\rm{LD}}}\mathrm{sin}(2\pi {\omega }_{{\rm{LD}}}t + {\theta }_{{\rm{LD}}}) + {D}_{{\rm{LD}}} $$ (6) 根据类似图6中的实际输出波形,可得到激光光源频率ω对应的ASB、ALD、ωSB和ωLD。
在ωSB = ωLD = ω前提下,20 lg[2ASB/(USB1.9 −USB1.5)]和20 lg[2ALD/(ULD1.9 − ULD1.5)]分别为频率ω下S–B热流传感器和光电探测器的频带宽度。其中,USB1.9为1.9 V驱动电压对应的S–B热流传感器稳态电压输出,其值为0.566 mV;ULD1.9为1.9 V驱动电压对应的光电探测器稳态电压输出,其值为0.675 mV。同理有USB1.5 = 0.349 mV,ULD1.5 = 0.406 mV。改变频率,得到一系列对应的频带宽度,然后作出S–B热流传感器和光电探测器的频响特性曲线,如图7所示。
根据截止频率的一般定义,当某一频率下的频带宽度为−3 dB,此时对应输出幅值为最大值(或稳态值)的0.707倍、对应输出功率为最大值的0.5倍,认为此时该频率下的输出信号已明显失真,该频率即为截止频率。从图7可以看到,随着频率增大,光电探测器的频带宽度几乎不变,而S–B热流传感器的频带宽度快速减小,在约26 Hz时达到−3 dB,则该S–B热流传感器的截止频率为26 Hz。因此,为防止热流测量值明显失真,被测热流变化频率应小于26 Hz。
3 S–B热流传感器的动态适用范围
在连续变迎角试验中,迎角速度变化越快,要求S–B热流传感器响应也越快,否则就会因时间滞后而产生较大测量误差。
基于一组阶梯变迎角试验中测得的热流数据,对S–B热流传感器在一定误差范围内所允许的最大变迎角速度进行定量分析。如2.2节的图5所示,在归一化响应时间曲线中,光电探测器的输出可视为光源的输入热流qin,S–B热流传感器的输出为实际测得的热流qmea。借助文献[15]对特征时间常数的定义,可得到如下关系式:
$$ \int\limits_0^\infty {({q_{{\rm{in}}}} - {q_{{\rm{mea}}}}){\rm{d}}t} = {q_{{\rm{in}}}} \cdot {\tau ^*} $$ (7) 式中,τ*为特征时间常数。式(7)的含义为:S–B热流传感器达到稳定(t→∞)后,传感器因时间滞后而少测得的能量总和等于输入热流qin乘以特征时间常数τ*。对式(7)微分并除以输入热流后可得:
$$ \frac{{{\rm{d}}{q_{{\rm{in}}}}/{\rm{d}}t}}{{{q_{{\rm{in}}}}}} = \frac{{1 - {q_{{\rm{mea}}}}/{q_{{\rm{in}}}}}}{{{\tau ^*}}} $$ (8) 等式左边为被测热流t时刻的相对变化率;等式右边分母为特征时间常数τ*,为传感器自身属性,其值与输入热流无关。
根据式(7),采用数值积分方法可求得本文中S–B热流传感器的τ*为0.027。式(8)等式右边的分子(1 − qmea/qin)为t时刻的测量误差,其值为0~1。记测量时间内最大热流相对变化率为$ {\dot q_{\max }} $,此时对应的最大测量误差为η,则由式(8)可得:
$$ {\dot q_{\max }} = \frac{\eta }{{{\tau ^*}}} $$ (9) 图8为S–B热流传感器在某飞行器阶梯变迎角试验中测得的热流值(11个不同迎角下的稳态热流值,因风洞变送机构局部故障,未能实现连续变迎角热流测量),横轴为迎角(−10°~10°,间隔2°),纵轴为热流值。假定连续变迎角试验时,变迎角速度vω = k (°)/s,k > 0,暂不考虑变送机构起动停止时的短暂加减速过程,则迎角从−10°匀速变化至10°需时20k−1 s。设t = 0 s时刻的迎角为−10°,t = 20k−1 s时刻的迎角为10°,在0~20k−1 s时间段内对图8中的热流测点数据进行最优拟合,可得到变迎角速度vω下的时间与热流的函数q(t),进而可根据式(10)求得变迎角速度vω下的最大热流相对变化率:
$$ ({\dot{q}}_{\mathrm{max}}{)}_{v}=\mathrm{max}\left(\left|\frac{{\rm{d}}q/{\rm{d}}t}{q}\right|\right)_{v} , 0 \leqslant t \leqslant \frac{{20}}{k} $$ (10) 基于不同变迎角速度下的拟合结果,根据式(10)可得到变迎角速度为1、3、5、10和20 (°)/s时对应的热流最大相对变化率分别为0.275、0.821、1.377、2.724和5.416。可以看出,变迎角速度与热流最大相对变化率存在明显的线性关系。采用最小二乘法进行线性拟合,得到二者关系如下:
$$ {\dot q_{\max }} = 0.271{v_\omega } $$ (11) 由式(9)和(11)可求得变迎角速度和最大测量误差的关系式为:
$$ v = \frac{\eta }{{0.271 \cdot {\tau ^*}}} $$ (12) 从式(12)可知,在图8的热流状态下,采用常用的3 (°)/s变迎角速度时,以本文的S–B热流传感器开展连续变迎角试验,测量误差约2.2%。若要求测量误差小于5%,则变迎角速度不得大于6.8 (°)/s。通过上述算例可知,S–B热流传感器能够满足的最大变迎角速度与传感器特征响应时间常数τ*、允许的最大测量误差η以及具体的热流状态有关,需具体问题具体分析,如在来流状态和测量误差要求确定的前提下,选用特征响应时间常数较小的S–B热流传感器能够满足更大的变迎角速度。
4 结 论
1)改进后的S–B热流传感器的有效量程为1~130 kW/m2,灵敏度系数为57.67 μV·m2/kW,优于改进前(约30 μV·m2/kW),响应时间t0.95约26 ms,优于改进前(约100 ms),与国外公开文献[16-17]中的水平相当。
2)S–B热流传感器在连续变迎角试验中能够满足的最大变迎角速度与传感器特征响应时间常数、允许的最大测量误差以及具体热流状态有关。
下一步拟选用方便计算的校测模型,分别获取阶梯变迎角和连续变迎角试验热流数据,结合数值计算结果对连续测量的精准度开展分析评估。
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