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如图 1所示,光纤F-P温度、压力复合传感器有两个F-P干涉腔[15],一般由两种不同折射率材料的3个光滑平行端面构成,如两块不同材质光学玻璃相对平行不接触放置,分别用于测量温度和和压力,称为温度腔和压力腔,通常温度腔为光学玻璃,压力腔为压力敏感膜片与温度腔之间的空气腔。压力腔直接与外界环境接触,用于测量外界压力;温度腔用于测量温度,与压力腔为串联关系。这种传感器的基本原理是外界压力和温度的变化会引起压力腔和温度腔的腔长或折射率改变,从而引起输出干涉光谱的漂移。当一束光I0从左侧射入,通过算法解调反射光Ir就可以计算出外界物理量的变化。
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当入射光从左侧入射时会在折射率变化的界面发生反射,如图 1所示,反射光在交汇时就会发生F-P干涉,形成有明显特征的双F-P腔干涉光谱[16]。假设3个端面的反射系数分别为r1, r2和r3,透射系数分别为t1, t2和t3,形成两个F-P腔的腔长分别为d1和d2,两个腔的折射率分别为n1和n2。在垂直入射的情况下,两个腔产生的相位差分别为φ1和φ2,3个端面的反射率分别为R1, R2和R3,透射率分别为T1, T2和T3,它们之间满足以下关系[17]:
$ \left\{\begin{array}{l} t_i^2=T_i \\ r_i^2=R_i \\ T_i+R_i=1 \end{array}\right. $
(1) 温度腔和压力腔的相位差φ1, φ2与F-P腔的折射率和腔长之间满足:
$ \left\{\begin{array}{l} \varphi_1=\frac{4 \pi}{\lambda} n_1 d_1 \\ \varphi_2=\frac{4 \pi}{\lambda} n_2 d_2 \end{array}\right. $
(2) 在不考虑光传输损耗时,复合腔的整体反射率为:
$ R_{\mathrm{t}}=1-\frac{\left(t_1 t_2 t_3\right)^2}{D} $
(3) $ \begin{gathered} D=1+\left(r_1 r_2\right)^2+\left(r_2 r_3\right)^2+\left(r_1 r_3\right)^2+2 r_1 r_2(1+ \\ \left.r_3^2\right) \cos \varphi_1+2 r_2 r_3\left(1+r_1^2\right) \cos \varphi_2+ \\ 2 r_1 r_3 \cos \left(\varphi_1+\varphi_2\right)+2 r_1 r_2^2 r_3 \cos \left(\varphi_1-\varphi_2\right) \end{gathered} $
(4) 假设压力腔和温度腔的腔长分别为100μm和300μm。一般光学玻璃的端面反射率约为4%,即反射系数为r1=r2=0.2。将压力敏感膜片的反射系数r3分别设置为0.3,0.6,0.9,利用(3)式可以得到r3在不同反射系数下复合腔的归一化输出光谱, 如图 2所示。
由图 2可以看出,复合式F-P腔在r1=r2的情况下,随着r3的增大,其光谱特性由差到好再到差,在r3=0.6时, 其光谱特性相对较好。因此,由(1)式可知,压力敏感膜片的反射率设置约为0.36时,可以得到相对较好的干涉光谱。
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由复合型F-P腔的结构可知,需要分别对压力腔和温度腔进行设计,以获得特性最好的传感器。
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对于压力腔的设计,采用结构稳定、高敏感性的膜片式结构[18]。典型的膜片式F-P腔结构如图 3所示。当弹性膜片受到外部压力的作用时,会产生弯曲形变,从而引起压力敏感腔长度的变化,压力敏感膜片的尺寸直接决定传感器测量压力的量程范围和灵敏度。图 3中,h为膜片的厚度,a为圆形膜片的有效半径或方形膜片有效边长的一半,Y为膜片发生形变时的挠度,p为外界施加应力。膜片的应力特性与其材料的杨氏模量E和泊松比μ有关。
压力敏感膜片的结构通常有圆形和方形两种。在相同的横向尺寸下,方形膜片比圆形膜片具有更好的压力灵敏度,而圆形膜片则比方形膜片具有更好的耐压性能。由于石化反应器内部为高压环境,因此选用圆形膜片结构形式进行压力敏感腔的设计。对于圆形压力膜片,其最大扰度位于膜片中心位置,最大应力为径向应力F,可表示为:
$ F=\frac{3 a^2}{4 h^2} p $
(5) 对应的圆形压力膜片的灵敏度S为[19]:
$ S=\frac{Y}{p}=\frac{3\left(1-\mu^2\right)}{16 E} \cdot \frac{a^4}{h^3} $
(6) 假设采用石英作为压力膜片,在外界5MPa的均匀压力下,利用(5)式和(6)式得到膜片所受最大应力及压力灵敏度与膜片有效半径、厚度之间的关系,如图 4a和图 4b所示。可以看出, 压力膜片所受最大应力及灵敏度都随着厚度的增大而减小,随有效半径的增大而增大。在进行膜片结构的设计时应当综合考虑膜片的压力灵敏度和所受最大应力,希望提高灵敏度的同时减小膜片所承受的最大应力。
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当外界环境温度发生变化时,F-P腔结构会因材料热光效应使得折射率n改变,从而会引腔长的变化。设温度敏感材料的热膨胀系数为σ,热光系数为ξ,初始折射率为n0,初始腔长为d0,则光程差与温度变化量之间的关系可表示为[20]:
$ \Delta D_{\mathrm{OPD}}=2(\sigma+\xi) n_0 d_0 \Delta T $
(7) 由(7)式可知,光程差随温度变化量呈二次曲线变化。在选择制作温度腔的敏感材料时,应选择热膨胀系数和热光系数大的材料;对于特定的材料,适当增大初始腔长可以提高温度灵敏度。
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从表 1可以看出, 3种玻璃中蓝宝石玻璃的热膨胀系数与热光系数最好,且杨氏模量最大,受温度影响效果最明显,同时对压力又最不敏感;石英玻璃和Pyrex7740玻璃的杨氏模量比较接近,且比蓝宝石小得多,但石英玻璃的热膨胀系数更小,用作压力敏感膜片时受温度的影响更小。因此,选择石英玻璃制作压力敏感膜片,蓝宝石玻璃则用作温度腔。
Table 1. Comparison of common glass parameters
classification E/GPa μ σ/℃-1 n0 ξ/℃-1 quartz 73.5 0.17 0.55×10-6 1.46 1.25×10-5 sapphire 380 0.28 5.8×10-6 1.76 1.3×10-5 Pyrex7740 62.76 0.20 3.25×10-6 1.47 — -
基于对复合型F-P腔结构压力腔和温度腔的理论分析,拟定压力腔和温度腔的结构参数如下:(1)压力敏感膜片为石英玻璃,有效半径设为4mm,厚度1mm,其中反射端面的反射率设置为36%;由(6)式可以得到压力膜片的理论灵敏度约为0.634nm/kPa;(2)温度敏感腔采用蓝宝石玻璃,初始腔长/厚度拟设为300μm。
根据压力膜片参数建立3维模型并进行有限元仿真分析,设置边界条件为:周围固定,施加压力5MPa,得到如图 5所示的分析结果。
Figure 5. a—total deformation diagram b—equivalent elastic strain diagram and c—equivalent stress diagram of pressure sensitive diaphragm
从图 5a中可以看出,该模型的最大形变位于波片中心,最大形变量为3.916×10-6m,假设膜片产生线性均匀的形变,则膜片的灵敏度为0.783nm/kPa;由图 5b可以看出, 膜片中心位置的等效弹性应变仅约为0.0003565m/m,说明石英作为压力膜片复合设计要求;图 5c为压力膜片所受应力情况,最大应力位于膜片边缘处,所受最大应力为7.4465×107Pa。
用于石化反应器的光纤F-P温/压复合传感器
Optical fiber F-P temperature and pressure composite sensor for petrochemical reactor
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摘要: 为了实时监测石化反应器内部高温、高压环境下压力和温度变化, 严格控制原料的反应过程, 采用法布里-珀罗(F-P)多腔干涉理论, 设计并制备了一种光纤F-P温度、压力复合传感器。该传感器由石英玻璃和蓝宝石玻璃构成, 石英与蓝宝石之间的空气腔为压力腔, 温度腔则为蓝宝石本身。通过理论计算和仿真验证, 分析了压力腔和温度腔不同参数对传感器性能的影响, 从而取得了最佳的传感器结构参数数据。结果表明, 该传感器制作工艺简单且性能可靠, 能够实现0MPa~5MPa和-20℃~300℃范围内压力和温度的同时测量; 该传感器在压力0.1MPa~5MPa和温度20℃~180℃环境下有良好压力温度线性响应关系, 压力灵敏度为796nm/MPa, 温度灵敏度为3.864nm/℃。该传感器适用于石化反应器内部高温高压环境下压力和温度的同时监测。
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关键词:
- 传感器技术 /
- 光纤F-P复合传感器 /
- 高温高压 /
- 温度腔 /
- 压力腔
Abstract: In order to monitor the pressure and temperature changes in petrochemical reactor under high temperature and high pressure in real time and strictly control the reaction process of raw materials, an optical fiber Fabry-Perot (F-P) temperature and pressure composite sensor was designed and fabricated by using F-P multi cavity interference theory. The sensor was composed of quartz glass and sapphire glass. The air chamber between quartz and sapphire was pressure chamber, and the temperature chamber was sapphire itself. Through theoretical calculation and simulation verification, the effects of different parameters of pressure chamber and temperature chamber on the performance of the sensor were analyzed, and the best structural parameter data of the sensor were obtained. The results show that the sensor has simple fabrication process and reliable performance, and can realize the simultaneous measurement of pressure and temperature in the range of 0MPa~5MPa and -20℃~300℃. The experimental results show that the sensor has a good linear response relationship between pressure and temperature under the environment of pressure 0.1MPa~5MPa and temperature 20℃~180℃. The pressure sensitivity is 796nm/MPa and the temperature sensitivity is 3.864nm/℃. The sensor is suitable for simultaneous monitoring of pressure and temperature in high temperature and high pressure environment in petrochemical reactor. -
Table 1. Comparison of common glass parameters
classification E/GPa μ σ/℃-1 n0 ξ/℃-1 quartz 73.5 0.17 0.55×10-6 1.46 1.25×10-5 sapphire 380 0.28 5.8×10-6 1.76 1.3×10-5 Pyrex7740 62.76 0.20 3.25×10-6 1.47 — -
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