Prediction of Dynamic Characteristics of Thermocouples with Thin-Wire Sensing Elements

Thermocouples dynamic characteristicsʼ prediction is one of the relevant directions in the field of dynamic measurements of non-stationary temperatures of liquid and gaseous media. Thermocouples dynamic characteristicsʼ prediction makes it possible to provide effective continuous correction in automatic control systems for non-stationary temperatures. The purpose of this paper was to develop a theoretically justified relation linking the current or expected time constant of fine-wire thermocouples with the known time constant established at known parameters of liquid and gaseous media.

A formula linking the time constant of fine-wire thermocouples with the conditions of heat exchange with the measured medium and the thermophysical characteristics of the thermocouple sensing elements has been deducted. An approximate formula is also given for calculating the internal resistance of wire sensing elements of thermocouples, which must be considered when calculating the time constant of a thermocouple. In consideration of the obtained formulas, a multi-parameter relation linking the current or expected time constant of fine-wire thermocouples with the known time constant set at the known parameters of the measured media has been formed.

It is suggested to simplify the formed multi-parameter relation and make it dependent, for example, on the “expected velocity of the measured medium × expected density of the measured medium” complex (V_m2 ρ_m2 ). Simplified relations in the form of hyperbolic functions with constant parameters and argument in the form of Vm2 ρm2 complex were obtained for airflowat different temperatures, pressures, and velocities.

On the example of airflow, it is shown that the complex multi-parametric relation linking the expected

and known time constants of thermocouples can be simplified to a hyperbolic dependence, where the argument can be the V_m2 ρ_m2 complex. Moreover, the degree of approximation of hyperbolic dependencies to the exact values of the multi-parametric relation can reach the R-square = 0.9592 criterion.

A multi-parametric relation has been proposed. That relates the known time constant of a thermocouple to the expected or current time constant of the same thermocouple at other parameters of the measured medium from the point of view of the heat exchange and thermal conduction theory. The proposed relation can be used in automatic control systems of non-stationary temperature of various liquid or gaseous media to provide continuous correction of thermocouples dynamic characteristics. Depending on the number of measured medium parameters, the suggested multi-parameter relation can be replaced by simplified relations with other complexes containing, for example, density, velocity, flow rate and pressure of the measured medium.

1. Wittenmark B., Middleton R.H., Goodwin G.C. Adaptive Decoupling of Multivariable Systems. International Journal of Control, 1987, vol. 46, no. 6, pp. 1992– 2009. DOI: 10.1080/00207178708934029

2. Lutz W.J., Hakimi S.L. Design of Multi-Input Multi-Output Systems with Minimum Sensitivity. IEEE Transaction on circuits and systems, 1988, vol. 35, no. 9, pp. 1114–1122. DOI: 10.1109/31.7571

3. Kaizuka H. Multivariable servo system design method using structural features of controlled systems. International Journal of Control, 1989, vol. 49, no. 4, pp. 1409–1419. DOI: 10.1080/00207178908559712

4. Petunin V.I. [GTE gas temperature determination with the use of indirect measurements]. Izvestiya vuzov. Aviacionnaya tekhnika [News of universities. Aviation equipment], 2008, no. 1, pp. 51–55 (in Russian).

5. Zimmerschied R., Isermann R. Nonlinear time constant estimation and dynamic compensation of temperature sensors. Contr. Eng. Pract., 2010, vol. 18, no. 3, pp. 300–310. DOI: 10.1016/j.conengrac.2009.11.008

6. Petunin V.I., Sibagatullin R.R., Frid A.I. [Development of requirements for the accuracy of compensation of the inertia of the thermocouple in the gas temperature control loop]. Izvestiya vuzov. Aviacionnaya tekhnika [News of universities. Aviation equipment], 2015, no. 1, pp. 56–60 (in Russian).

7. Petunin V.I., Sibagatullin R.R., Frid A.I. [Robust self-adjusting temperature of the gas meter GTD]. Vestnik UGATU [Bulletin of the Ufa State Aviation Technical University], 2015, vol. 19, no. 1(67), pp. 147–155 (in Russian).

8. Petunin V.I., Sibagatullin R.R., Frid A.I. Development of requirements for accuracy of inertia compensation in gas turbine engine control systems with a channel selector. Russian Aeronautics, New York, 2015, no. 1(58), pp. 71–77. DOI: 10.3103/S1068799815010110

9. Petunin V.I., Sibagatullin R.R., Frid A.I. [Adaptive gas turbine engine temperature measuring instrument with model error correction]. Vestnik UGATU [Bulletin of the Ufa State Aviation Technical University], 2017, vol. 21, no. 4(75), pp. 1–8 (in Russian).

10. Pao G.P., Sivakumar L. [Order and Parameter Identification in Continuous Linear Systems via Walsh Functions]. Trudy institute inzhenerov po elektrotekhnike i radioelektronike (TIIJeR) [Proceedings of the Institute of Electrical and Electronics Engineers], 1982, vol. 70, no. 7, pp. 89–91 (in Russian).

11. Sherbakov M.A., Iosifov V.P. [Restoration of the input signal based on the results of identification of dynamic characteristics of measuring instruments]. Izvestija vysshih uchebnyh zavedenij. Povolzhskij region. Tehnicheskie nauki [Proceedings of the higher educational institutions. Volga region. Technical science], 2007, no. 3, pp. 3–8 (in Russian).

12. Jamroz P. Relationship between dynamic coefficients of two temperature sensors under non stationary flow conditions. IEEE Sens. J., 2011, vol. 11, no. 1–2, pp. 335–340. DOI: 10.1109/JSEN.2010.2073463

13. Dubovitskii V.F., Sebina L.P, Godunov M.V., Maksimova E.M. Use of a data measurement system for studying the characteristics of temperature sensors. Fibre Chemistry, 2011, vol. 42, no. 6, pp. 399–403. DOI: 10.1007/s10692-011-9297-0

14. Iosifov V.P. [Determination of the full dynamic characteristics of measuring instruments with the use of recurrent procedures]. Izvestiya vysshikh uchebnykh zavdenij. Povolzhskij region. Tekhnicheskije nauki [Proceedings of the higher educational institutions. Volga region. Technical science], 2011, no. 1(17), pp. 126–131 (in Russian).

15. Bekenova Y.A., Komshilova V.A., Komshilova K.O. [Dynamic characteristics of measurements systems based on industrial automation systems]. Izvestiya Sankt-Peterburgskogo gosudarstvennogo elektrotekhnicheskogo universiteta “LETI”, 2013, no. 1. pp. 81–86 (in Russian).

16. Froehlich T., Augustin S., Ament C. Temperature-Dependent Dynamic Behavior of Process Temperature Sensors. International Journal of Thermophysics, 2015, vol. 36, no. 8, pp. 2115–2123. DOI: 10.1007/s10765-015-1869-4

17. Marshalov E.D., Nikonorov A.N., Murav'ev I.K. [Determination of thermal reaction time of thermal resistance converters]. Vestnik Ivanovskogo gosudarstvennogo energeticheskogo universiteta, 2017, no. 3, pp. 54–59 (in Russian).

18. Vavirovskaja S.L., Zaharov D.L., Korneev M.V. [Automation determination of dynamic and high-speed characteristics of temperature sensors in the installation of air УВ-010 CIAM]. Avtomatizacia v promyshlennosti [Automation industry], 2016, vol. 4, pp. 28–29 (in Russian).

19. Sabitov A.F., Safina I.A. [Identification of nominal dynamic characteristics aircraft gas temperature sensors]. Pribory i metody izmerenii [Devices and Methods of Measurements], 2017, vol. 8, no. 1, pp. 7–14 (in Russian). DOI: 10.21122/2220-9506-2017-8-1-7-14

20. Sabitov A.F., Safina I.A. [Method for determination of the characteristic curve of the thermal inertia of aircrcraft gas temperature sensors]. Pribory i metody izmerenii [Devices and Methods of Measurements], 2017, vol. 8, no. 4, pp. 357–364 (in Russian). DOI: 10.21122/2220-9506-2017-8-4-357-364

21. Tyurina M., Sabitov A., Safina I. Identification of Dynamic Characteristics of Temperature Sensors. Journal of Engineering Thermophysics, 2020, vol. 29, no. 4, pp. 618–631. DOI: 10.1134/S1810232820040104

22. Sabitov A.F., Safina I.A. [Implementation of the Spectral Method for Determining of Measuring Instrumentsʼ Dynamic Characteristics]. Pribory i metody izmerenii [Devices and Methods of Measurements], 2020, vol. 11, no. 2, pp. 155–162 (in Russian). DOI: 10.21122/2220-9506-2020-11-2-155-162

23. Sabitov A., Safina I. Determining Dynamic Characteristics of Measuring Instruments with a Spectral Method Insensitive to Harmonic Interference. Journal of Engineering Thermophysics, 2021, vol. 30, no. 3, pp. 508–514. DOI: 10.1134/S1810232821030139