Simulating Error Due to Acquired Thermoelectric Inhomogeneity
Abstract
:1. Introduction
2. State of the Art
- Error due to drift of the CF of a TC. It is a gradual change in the developed thermal electromotive force (thermo-emf) in time in a constant temperature field along the TC legs. This error appears because of the degradation of TC legs under the influence of temperature and time of their operation.
- Error due to acquired thermoelectric inhomogeneity. It is a change in the developed thermo-emf when the temperature distribution along TC legs changes (i.e., the temperature field along the TC changes), even for constant temperatures of the measuring and reference junctions. This error appears because of the degradation of the TC legs and changes in the temperature field along them.
3. The Technique of Modelling Error Due to Inhomogeneity
- The temperature of the reference junctions of the TC is 0 °C. At this temperature, the TC sections from 1 to 8 are operated.
- The temperature of the measuring junction of the TC is 800 °C. At this operating temperature, the TC sections from 17 to 24 are operated.
- The sections of TC from 9 to 16 are operated in the zone of the temperature gradient.
- The temperatures of sections can change within the range from 0 °C to 800 °C. The temperature drop across the i-th section is as follows: .
- The sections of the TC are homogeneous along their length (i.e., there is no error due to acquired heterogeneity within each section).
- The operating temperature of each TC section is considered the average temperature of temperatures of its ends before the change in temperature field.
- The instantaneous temperature of the TC section is considered the average temperature of the ends of each section after the change in temperature field.
4. The Results of the Modelling of Error Due to Inhomogeneity
5. Conclusions
- The maximum deviation of the CF from the nominal for the whole type K TC is 430 μV. The initial sensitivity of the type K TC is 40 μV/°C; thus, maximum temperature measurement error due to thermoelectric inhomogeneity of the conventional TC acquired during long-term operation can exceed 10 °C, which cannot be neglected.
- The maximum sensitivity of both the conventional TC and the TCTF to changes in the temperature field of the measurement object is for small changes in the temperature field, which makes this error even more dangerous.
- The efficiency of the TCTF is quite high—the maximum value of error due to acquired thermoelectric inhomogeneity of the legs of the MTC is reduced by several tens of times to 0.2. The high efficiency of error compensation allows using all drift correction methods considered in [15] with high reliability.
- The high efficiency of the TCTF was confirmed in the studies above. The bigger the changes in the temperature field of the measurement object, the higher the efficiency of the use of the TCTF. However, it is achieved due to the relatively large structural complexity of the proposed sensor [15,25,26].
- The limit of effective use of the TCTF is determined by the changes in temperature along the TC legs. In this particular case, when the temperature changes exceed 7 °C, it is reasonable to use the TCTF, because its error due to inhomogeneity is less than that of the conventional type K TC.
- On the other hand, in a stable temperature field of the measurement object, the TCTF has a greater error due to acquired inhomogeneity than the conventional TC. This is because of the influence of the error in the temperature-control system. The reduction in this error will expand the limits of the effective application of the TCTF.
- The dependence of residual error due to acquired thermoelectric inhomogeneity of the MTC of the TCTF on its structural complexity for given changes in the temperature field of the object remains unexplored. It is necessary to create a theoretical basis for designing the TCTF to ensure the necessary accuracy of temperature measurement results under the given conditions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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The Direction of Change in the Temperature Field | |
---|---|
Towards the Reference Junctions | Towards the Measuring Junction |
7 °C | 6.5 °C |
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Li, Z.; Chen, J. Simulating Error Due to Acquired Thermoelectric Inhomogeneity. Sensors 2024, 24, 5256. https://doi.org/10.3390/s24165256
Li Z, Chen J. Simulating Error Due to Acquired Thermoelectric Inhomogeneity. Sensors. 2024; 24(16):5256. https://doi.org/10.3390/s24165256
Chicago/Turabian StyleLi, Zida, and Jingliang Chen. 2024. "Simulating Error Due to Acquired Thermoelectric Inhomogeneity" Sensors 24, no. 16: 5256. https://doi.org/10.3390/s24165256
APA StyleLi, Z., & Chen, J. (2024). Simulating Error Due to Acquired Thermoelectric Inhomogeneity. Sensors, 24(16), 5256. https://doi.org/10.3390/s24165256