One-dimensional analysis of unsteady temperature measurement error characteristics of thermocouple
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摘要:
为揭示热电偶非稳态测温误差的影响机制，建立了热电偶测温一维非稳态计算模型，综合评估了不同安装结构、黏合材料和表面传热系数工况对热电偶非稳态测温误差的影响，深入探究了毕渥数对非稳态测温的影响规律。研究结果表明：考虑环境辐射是必要的，与不考虑辐射传热相比测温时间300 s时的温度相差1.48 K。不同的安装方式对测温误差的影响较大，最大测量温差1.85 K。黏合材料的导热系数越大，正规状况阶段非稳态测温误差越小，测温时间150 s后绝对误差小于0.5 K。表面传热系数对非稳态测温误差起着重要的影响，表面传热系数越大，受初始温度场影响的测温误差越大。黏合材料导热系数为2.4 W/（m·K）时，表面传热系数为50～250 W/（m2·K）的范围内测温误差的变化范围为0.2～1.5 K。研究结果为发动机传热实验中壁温非稳态测量提供了参考。
Abstract:To reveal the influence mechanism of temperature measurement error of thermocouple under unsteady operating conditions, one-dimensional unsteady calculation model of temperature measurement of thermocouple was established. A comprehensive evaluation was conducted to reveal the influence of different installation structures, bonding materials and surface heat transfer coefficient conditions on the unsteady temperature measurement error for the thermocouple. The influence of Biot number on unsteady temperature measurement was further explored. Results showed that it is necessary to consider environmental radiation effect. Temperature error was 1.48 K at 300 s temperature measurement time compared with that without consideration of environmental radiation effect. Different installation structures of thermocouple had a greater impact on the temperature measurement error, with a maximum measurement temperature difference of 1.85 K. Moreover, the greater thermal conductivity of the bonding material indicated, the smaller temperature measurement error in the stage of unsteady regular status, and the absolute error was less than 0.5 K after 150 s temperature measurement time. Especially, the surface heat transfer coefficient played an important role in the unsteady temperature measurement error. The larger surface heat transfer coefficient indicated the greater temperature measurement error due to initial temperature field. When the thermal conductivity of bonding material was 2.4 W/(m·K), the variation range of temperature measurement error within the surface heat transfer coefficient range of 50−250 W/(m2·K) was 0.2−0.5 K. Therefore, the research results can provide a reference for the unsteady measurement of wall temperature in the heat transfer experiments of aero-engine.
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图 1 无限大平板一维非稳态导热模型
Figure 1. One-dimensional unsteady thermal conduction model for infinite plate
图 2 实验中测温对象的热电偶安装示意图
Figure 2. Schematic diagram of thermocouple installation locations of temperature measurement object in the experiment
图 4 空间离散的热电偶测温一维计算模型
Figure 4. One-dimensional calculation model of thermocouple temperature measurement with spatial discrete
图 5 热电偶测温一维计算模型求解步骤流程图
Figure 5. Flow chart of the steps for solving the one-dimensional calculation model of thermocouple temperature measurement
图 6 未安装热电偶模型计算方法对比
Figure 6. Comparison of calculation methods for calculation model without thermocouples installation
图 7 安装热电偶模型计算方法对比
Figure 7. Comparison of calculation methods for the calculation model with thermocouples installation
图 8 一维传热计算模型考虑辐射的温度随测温时间变化对比图
Figure 8. Comparison of temperature changes with the temperature measurement time considering the radiation effect in the one-dimensional heat transfer calculation model
图 9 不同安装方式的表面温度随时间变化
Figure 9. Surface temperature variation with time under different thermocouple installation structures
图 10 不同的热电偶安装方式的测温误差
Figure 10. Temperature measurement error of different thermocouple installation structures
图 11 黏结材料包裹热电偶模型不同第1层厚度的测温误差
Figure 11. Temperature measurement error of different thickness of first layer in thermocouple model wrapped with the bonding material
图 12 不同黏结材料导热系数对热电偶测温误差的影响
Figure 12. Effect of temperature measurement error of thermocouples with thermal conductivity of different bonding material
图 13 不同表面传热系数工况对热电偶测温误差的影响
Figure 13. Effect of temperature measurement error of thermocouples with different surface heat transfer coefficient
图 14 Fo=0.2时测温模型Bi对测温误差的影响规律
Figure 14. Influence of Bi on temperature measurement error when Fo=0.2
图 15 Fo=0.55时测温模型Bi对测温误差的影响规律
Figure 15. Influence of Bi on temperature measurement error when Fo=0.55
表 1 热电偶测温一维计算模型的初边值条件
Table 1. Initial and boundary conditions of one-dimensional calculation model for thermocouple temperature measurement
参数 数值 热流体温度/K 330 平板初始温度/K 300 表面传热系数/（W/（m2·K）） 50～250 黏合材料的导热系数/（W/（m·K）） 0.05～3.2 总传热时间/s 300 
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