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利用激光吸收光谱技术对气体参数进行测量时,当激光频率与被测气体分子的共振频率相同时,激光能量被吸收。激光的衰减程度可以表示为:
$$\frac{{{I_t}}}{{{I_0}}} = \exp ( - {\alpha _v}) = \exp \left[ { - PS(T)\phi (v)\chi L} \right]$$ (1) 式中:I0为入射激光强度;It为穿过被测流场后激光强度;α为光谱吸收吸收率信号;P为气体总压;χ为待测气体组分浓度;S(T)为所用谱线ν在温度T时的谱线强度;L为激光束穿过被测流场的长度;ϕ(ν)为线型函数,在整个频域上的积分值为1,公式(1)可以改写为:
$$A = \int_{ - \infty }^\infty {{\alpha _v}{\rm d}v = } P\chi S(T)L$$ (2) 式中:A表示积分吸收面积。
将吸收光谱技术与CT技术相结合,成为激光吸收光谱层析技术(LAT),其基本原理是通过在被测流场截面内布置多条光线,利用每条光线穿过流场不同位置实现携带流场的分布信息,获得的数据为光线沿着光路径的积分结果,再利用重建算法,实现对流场的二维分布测量。其中光线分布设计和光学系统搭建是实验数据获取的关键步骤。
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在光路设计中,需要考虑发射和接收单元最小尺寸、光线穿过流场最短长度、发射光线最大偏转角度等因素,以最小间隔为5 mm,根据实际被测发动机尺寸,被测区域尺寸为7 cm×5 cm,在矩形区域的四条边上等间隔设计发射端或接收端位置,同时设扇形光转换系统可以将线光转换为扇形光的最大张角为90°,研究发射端位置对测量结果的影响。
设原始模型温度为双高斯分布,范围为500~1300 K,组分浓度为单高斯分布,范围为0.02~0.1,原始模型分布如图1所示。
采用代数迭代算法对原始温度和组分浓度分布进行二维重建,不同光线分布下重建结果如图2所示。其中前4种扇形光线布局的投影光线数目为96条,发射端数目为4个,第5种为平行光投影,光线数目为24条,第6种为仅有1层光线投影时的重建结果。
图 2 不同光线分布下的温度和组分浓度重建结果
Figure 2. Temperature and concentration reconstructed results for different line distribution
计算重建结果的归一化平均绝对误差:
$$Er = \frac{{\displaystyle\sum\limits_{m = 1}^M {\displaystyle\sum\limits_{n = 1}^N {\left| {f_{m,n}^{{\rm{rec}}} - f_{m,n}^{{\rm{orig}}}} \right|} } }}{{\displaystyle\sum\limits_{m = 1}^M {\displaystyle\sum\limits_{n = 1}^N {\left| {f_{m,n}^{{\rm{orig}}}} \right|} } }}$$ (3) 式中:fm, n表示被测区域被离散为m × n个网格;f表示网格的温度或者组分浓度。图3为图2对应光线分布的温度和组分浓度的重建误差。从图中可知,发射端的位置越靠近边角区域,重建效果越好,在第4种情况时,发射端位于矩形截面的顶点位置,温度和浓度的重建误差为0.028和0.046,平行光线温度重建误差为0.17。
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2.1节数值模拟发现端位置的实验中得出发射端位于边角时重建精度最高,然而在实际测量中,由于扇形光束发散角和能量限制无法实现。将一个发射端一分为二,分别放在边角的两边,这样可以使光线最接近于发射端在边角的情况。图4 (a)为发射端位于边角的理想情况,图4 (b)为改进后发射端示意图,近似为发射端在边角的情况。
扇形光的投影需要完备的投影角度,此时需要解决的问题是一个发射端接收两个光线信号的问题。扇形光需要通过偏转镜准直再由聚焦透镜聚焦至光纤端面,而不同的光线的偏转角不同,因此,无法用一个偏转镜实现两个光线的准直。为了解决这一问题,将探头设计为双层结构,层析过程忽略两层间隔,假设两层流场分布相同,一个发射端对应一层的接收探头,这样每个接收端只需接收一条光线,避免了上述问题。图5为双层探头结构示意图。
以7 cm×5 cm的流道截面为对象,用上述光学系统设计测量环。采用4个发射端,光线接收端的间隔为5 mm。双层结构的光线布局如图6所示,一层与二层的光线布局呈镜像关系,每层接收端的高度为5 mm,两层之间间隔为4 mm。根据最小光线间隔,长边有14个探头器位置,短边有10个探测器位置,两者都需要匀出一个用于发射端,故面向长边的发射端有13条光线,面向短边的发射端有9条光线,测量环总体可布设88条光线。
发射端采用面-点的结构形式,利用自由曲面准直设计方法,获得高均匀性矩形线光源。激光从入射光纤(NA=0.14)输出经准直透镜(Thorlabs, 354350-C)准直,由自由曲面透镜转换为扇形光,穿过入第一个窗口玻璃进入流场,穿过第二个窗口玻璃离开流场,由楔形棱镜偏转和聚焦透镜聚焦,进入接收光纤后传送至探测器。收发端结构设计如图7所示。
自由曲面特指面型没有具体表达式,由离散点拟合而成的面型。根据扇形光的投射需要设计面型,具体步骤如下:
(1)确定扇形光发射位置与接收位置,设计入射光面与投射像面。入射光的高斯光束强度分布为:
$$A(x) = \int_0^x {P \cdot {{\rm e}^{ - \frac{{2{R^2}}}{{{\omega ^2}}}}} \cdot 2\pi R \cdot {\rm{d}}R} $$ (4) 式中:R为沿着束腰方向往外方向的坐标;ω为高斯光束的束腰;A(x)表示高斯光束在半径为x的圆形以内包含的能量。
投射像面强度分布为:
$$B(t) = EtK$$ (5) 式中:B为高斯光束强度;E为投射像面的光强分布;K为投射目标面的宽度;t为线光源上某一处的位置坐标。
(2)建立入射光面到投射像面的映射关系。令A(x)=B(t),设边界条件为:x趋于无穷大时,t趋近于目标投射面宽度H,可得:
$$t = H\left( {1 - {{\rm e}^{ - \frac{{2{x^2}}}{{{\omega ^2}}}}}} \right)$$ (6) (3)建立自由曲面与入射光面积投射光面之间的映射关系。设入射光矢量为
$\overrightarrow {In} = (0,0,1)$ ,出射光矢量为$\overrightarrow {Out} = (x/h,y/h,{\textit{z}}/h)$ ,其中$h = 1/\sqrt {{x^2} + {y^2} + {{\textit{z}}^2}} $ ,自由曲面的法线矢量为:$$\overrightarrow N = \left(\frac{{\partial f}}{{\partial x}},\frac{{\partial f}}{{\partial y}},\frac{{\partial f}}{{\partial z}}\right)$$ (7) 式中:f为自由曲面方程f (x,y,z),根据折射定律
$\overrightarrow N {\rm{ = }}\overrightarrow {out} - \overrightarrow {in} $ ,建立了自由曲面f与投射像面的映射关系。(4)通过数值方法解算步骤(3)建立的偏微分方程,得出自由曲面f的面型分布。
产生折射的扇形光经偏转镜准直,然后通过聚焦透镜将光束聚焦于接收光纤的端面中心,实现耦合输出。不同位置的光束其角度不同,因此偏转镜的斜面角度也不相同,需要分别计算优化不同位置的偏折镜的斜面角,从而实现最佳的准直效果。聚焦透镜的最小间隔为5 mm,接收端最小间隔为5 mm。测量区域为50 mm×70 mm,其中短边的接收端为9个,长边的接收端为13个,两层结构中共有接收光线88路。线光源实际光斑测量结果照片如图8所示。
实验中采用功率计对整个光学系统进行传输效率测试,测试结果如表1所示。实验首先对每路接收端光纤入射光强进行测试,当入射光强为12 mW时,分别记录8个发射端对应的接收端的光强,然后将激光接入到发射端,记录同一发射端对应不同接收端的光强,根据测量结果计算整个光学系统的能量利用效率和光强均匀性。表中发射端编号1~4为下层光线测试结果,发射端编号5~8为上层发射端光线测试结果。能量利用效率η计算公式为:
表 1 光学系统功率测试结果
Table 1. Power measurement results of optical system
(a) Long edge test results/mW Transmitter number 1 3 5 7 Input power: P 11.7 13 13 12.8 Output power: qi 1 0.36 0.58 0.37 0.35 2 0.56 0.57 0.67 0.45 3 0.44 0.56 0.6 0.57 4 0.51 0.55 0.54 0.59 5 0.54 0.55 0.57 0.6 6 0.37 0.56 0.63 0.57 7 0.57 0.57 0.61 0.62 8 0.56 0.53 0.64 0.57 9 0.45 0.54 0.48 0.5 10 0.53 0.43 0.62 0.58 11 0.57 0.58 0.61 0.59 12 0.65 0.52 0.63 0.62 13 0.36 0.32 0.41 0.44 Total output power: Q 6.47 6.86 7.38 7.05 Energy efficiency: $\eta $ 55.30% 52.77% 56.77% 55.08% Receiver uniformity: θ 55.38% 55.17% 55.22% 56.45% $$\eta = \frac{Q}{P} = \frac{{\displaystyle\sum\nolimits_{i = 1}^n {{q_i}} }}{P}$$ (8) 式中:P为入射激光总能量,为图7中进入入射光纤前测量的激光能量值;Q为接收端能量和,为图7中在接收光纤处测量结果总和。接收端均匀性θ计算公式为:
$$\theta = \frac{{{q_{\min }}}}{{{q_{\max }}}}$$ (9) 即同一发射端发出的光线最小值与最大值的比。
由表1测量结果可知,整个光学系统的光线利用效率大于50%,光强均匀性为大于55%。由于长边接收端数目较多,所以每个接收端的功率低于短边的功率。
(b) Short edge test results/mW Transmitter number 2 4 6 8 Input power: P 11.8 12 12.9 11.68 Output power: qi 1 0.63 0.69 0.68 0.55 2 0.52 0.62 0.58 0.65 3 0.7 0.7 0.58 0.52 4 0.67 0.71 0.65 0.64 5 0.79 0.8 0.64 0.92 6 0.82 0.8 1.04 0.88 7 0.72 0.82 1.05 0.9 8 0.93 0.83 1.03 0.93 9 0.61 0.46 0.59 0.53 Total output power: Q 6.39 6.43 6.84 6.52 Energy efficiency: $\eta $ 54.15% 53.58% 53.02% 55.82% Receiver uniformity:θ 55.91% 55.42% 55.24% 55.91%
Design of a high-resolution optical measuring ring for supersonic combustion flow field
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摘要: 超燃冲压发动机激光吸收光谱测量系统目前主要采用分立式光学探头形式与发动机机体固定,但是受到探头尺寸的限制,无法获得高分辨率的流场信息。文中设计了一种基于自由曲面透镜和透镜阵列相结合的燃烧场高密度光学测量环。该测量环采用两层结构,发射端分别位于每条边最边缘位置,激光准直透镜和自由曲面透镜形成扇形光束,扇形光束穿过被测流场后,经过楔形镜偏转和聚焦透镜聚焦,进入接收光纤后传送至探测器。测量环接收单元最小间隔为5 mm,实现了在5 cm×7 cm空间内88条光线的密集排列。重点讨论光学系统光线分布设计方案,并给出收发端结构设计方案,实验结果表明,光线利用效率大于50%,光线总传输效率大于55%。设计的高密度光学测量环可以直接与发动机机体相衔接,避免环境因素干扰,可以实现对超燃冲压发动机隔离段、燃烧室出口等处温度、组分浓度的二维分布测量。Abstract: The separate optical probes have been widely used in scramjet laser absorption spectroscopy measured system. High resolution flow field cannot be obtained because of the limitation of the probe size. A high-resolution optical measuring ring based on free-curved lens and cylindrical lens was designed for combustion flow field. The beam distribution was determined by numerical simulation. The measuring ring adopted double-layer structure, the transmitters were located at the most edge of each edge. The fan-beam was formed by collimating lens and free-form lens. And then after passing the measuring flow field, the laser beam was defected by the wedge lens and focused by the focusing lens. The measuring ring receiving unit minimum interval was 5 mm, achieved dense array of 88 beams in 5 cm×7 cm space. The beam distribution of the optical system was discussed. The structural design scheme suitable for engine measurement was given. The measurement result shows that the light efficiency is greater than 50%, the total transmission efficiency is greater than 55%. The high-resolution optical measuring ring can be directly connected with the engine body to avoid the interference of environmental factors. The two-dimensional distribution of temperature and concentration in the isolation and outlet of the combustion can be measured.
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表 1 光学系统功率测试结果
Table 1. Power measurement results of optical system
(a) Long edge test results/mW Transmitter number 1 3 5 7 Input power: P 11.7 13 13 12.8 Output power: qi 1 0.36 0.58 0.37 0.35 2 0.56 0.57 0.67 0.45 3 0.44 0.56 0.6 0.57 4 0.51 0.55 0.54 0.59 5 0.54 0.55 0.57 0.6 6 0.37 0.56 0.63 0.57 7 0.57 0.57 0.61 0.62 8 0.56 0.53 0.64 0.57 9 0.45 0.54 0.48 0.5 10 0.53 0.43 0.62 0.58 11 0.57 0.58 0.61 0.59 12 0.65 0.52 0.63 0.62 13 0.36 0.32 0.41 0.44 Total output power: Q 6.47 6.86 7.38 7.05 Energy efficiency: $\eta $ 55.30% 52.77% 56.77% 55.08% Receiver uniformity: θ 55.38% 55.17% 55.22% 56.45% (b) Short edge test results/mW Transmitter number 2 4 6 8 Input power: P 11.8 12 12.9 11.68 Output power: qi 1 0.63 0.69 0.68 0.55 2 0.52 0.62 0.58 0.65 3 0.7 0.7 0.58 0.52 4 0.67 0.71 0.65 0.64 5 0.79 0.8 0.64 0.92 6 0.82 0.8 1.04 0.88 7 0.72 0.82 1.05 0.9 8 0.93 0.83 1.03 0.93 9 0.61 0.46 0.59 0.53 Total output power: Q 6.39 6.43 6.84 6.52 Energy efficiency: $\eta $ 54.15% 53.58% 53.02% 55.82% Receiver uniformity:θ 55.91% 55.42% 55.24% 55.91% -
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