Online monitoring of thermal stress and heat transfer coefficient in thick-walled cylindrical elements
DOI:
https://doi.org/10.24425/ather.2025.156589Abstract
The article presents a method for online monitoring of thermal stress and heat transfer coefficient on the inner surface of a thick-walled cylindrical element using two separate applications. Both applications are based on the inverse heat conduction problem and use the control volume method. The first one allows the determination of thermal stresses based on measuring the wall temperature at a single point near the inner surface. This software is suitable for one-dimensional heat transfer, i.e. in a radial direction. The second application allows the heat transfer coefficient on the inner surface to be determined based on temperature measurements at six spatially distributed points. Knowledge of the heat transfer coefficient on the inner surface allows the stress concentration factor to be determined for elements weakened by an opening. This can be used to determine the optimum heating or cooling rates for pressure elements or to determine the thermal stresses in elements weakened by an opening. This method is suitable for heat transfer cases in the radial, longitudinal and circumferential directions. The correct operation of both original applications has been tested on a laboratory stand, where there was a sudden change in the working fluid temperature in a steam header from 16.8°C to 142.5°C. At the beginning of the temperature change, the thermal stresses on the header inner surface reached a maximum value of -195.8 MPa, and the heat transfer coefficient was approximately 5000 W/(m²K). Then, the thermal stresses began to decrease, and the heat transfer coefficient began to increase.References
[1] Chen, M., Qiu, H., & Li, F. (2023). Monitoring of thermal stress in metal plates by using bonded shear horizontal wave piezoelectric transducers. Ultrasonics, 129, 106905. doi: 10.1016/j.ultras.2022.106905
[2] Taler, D., Dzierwa, P., Kaczmarski, K., & Taler, J. (2022). Increase the flexibility of steam boilers by optimisation of critical pressure component heating. Energy, 250, 123855. doi: 10.1016/j.energy.2022.123855
[3] Taler, D., Kaczmarski, K., Dzierwa, P., Taler, J., & Trojan, M. (2024). Optimisation of the cooling of pressurised thick-walled components operating with fluid at saturation temperature. Energy, 290, 129975. doi: 10.1016/j.energy.2023.129975
[4] TRD 301 (2001). Zylinderschalen unter innerem Überdruck. Technische Regeln für Dampfkessel (TRD), Heymanns Beuth, Köln–Berlin.
[5] European Standard EN 12952-3 (2001). Water-tube boilers and auxiliary installations. Part 3: Design and calculation for pressure parts. European Committee for Standardization.
[6] Banaszkiewicz, M. (2021). Concept of advanced lifetime monitoring system for steam turbines. Diagnostyka, 22(1), 23–29. doi: 10.29354/diag/132548
[7] Rusin, A., Tomala, M., Łukowicz, H., Nowak, G., & Kosman, W. (2021). On-line control of stresses in the power unit pressure elements taking account of variable heat transfer conditions. Energies, 14(15), 4708. doi: 10.3390/en14154708
[8] Radin, Y.A., Kontorovich, T.S., & Golov, P.V. (2020). Monitoring the thermal stress state in steam turbines. Power Technology and Engineering, 53(6), 719–723. doi: 10.1007/s10749-020-01146-6
[9] Radin, Y.A., & Kontorovich, T.S. (2021). Influence of the arrangement of the high- and intermediate-pressure cylinders of steam turbines with different bypass circuits on their thermal stress state during start-ups and shutdowns. Power Technology and Engineering, 54(5), 720–725. doi: 10.1007/s10749-020-01276-x
[10] Radin, Y.A., & Kontorovich, T.S. (2024). Influence of parameter deviations vis-à-vis assignment schedule on thermally stressed state of main thermal power plant equipment. Power Technology and Engineering, 57(6), 918–921. doi: 10.1007/s10749-024-01758-2
[11] Oliver, S., Simpson, C., Collins, D.M., Reinhard, C., Pavier, M., & Mostafavi, M. (2021). In-situ measurements of stress during thermal shock in clad pressure vessel steel using synchrotron X-ray diffraction. International Journal of Mechanical Sciences, 192, 106136. doi: 10.1016/j.ijmecsci.2020.106136
[12] Oh, C., Lee, S., Jhung, M.J., & Huh, N.-S. (2022). Analytical approach to estimate the thermal stress distribution of reactor pressure vessel nozzle corners with a constant cooldown rate. International Journal of Pressure Vessels and Piping, 197, 104608. doi: 10.1016/j.ijpvp.2022.104608
[13] Jeong, S.-H., Chung, K.-S., Ma, W.-J., Yang, J.-S., Choi, J.-B., & Kim, M.K. (2022). Thermal stress intensity factor solutions for reactor pressure vessel nozzles. Nuclear Engineering and Technology, 54, 2188–2197. doi: 10.1016/j.net.2022.01.006
[14] Pernica, M., Létal, T., Lošák, P., Naď, M., Reppich, M., & Jegla, Z. (2021). Transient thermal stress calculation of a shell and tube condenser with fixed tubesheet. Chemie Ingenieur Technik, 93(10), 1590–1597. doi: 10.1002/cite.202100036
[15] Okrajni, J., Twardawa, M., & Wacławiak, K. (2021). Impact of heat transfer on transient stress fields in power plant boiler components. Energies, 14(4), 862. doi: 10.3390/en14040862
[16] Teixeira Júnior, M., Zilio, G., Mortean, M.V.V., de Paiva, K.V., & Oliveira, J.L.G. (2023). Experimental and numerical analysis of transient thermal stresses on thick-walled cylinder. International Journal of Pressure Vessels and Piping, 202, 104884. doi: 10.1016/j.ijpvp.2023.104884
[17] Jaremkiewicz, M., Dzierwa, P., Taler, D., & Taler, J. (2019). Monitoring of transient thermal stresses in pressure components of steam boilers using an innovative technique for measuring the fluid temperature. Energy, 175, 139–150. doi: 10.1016/j.energy.2019.03.049
[18] Taler, J., & Duda, P. (2000). Experimental verification of space marching methods for solving inverse heat conduction problems. Heat and Mass Transfer, 36, 325–331. doi: 10.1007/s002310000082
[19] Taler, J., Zima, W., & Jaremkiewicz, M. (2016). Simple method for monitoring transient thermal stresses in pipelines. Journal of Thermal Stresses, 39, 386–397. doi: 10.1080/01495739.2016.1152109
[20] Jaremkiewicz, M., & Taler, J. (2017). Measurement of transient fluid temperature in a pipeline. Heat Transfer Engineering, 39(13–14), 1227–1234. doi: 10.1080/01457632.2017.1363631
[21] Taler, D., Taler, J., Kaczmarski, K., Jaremkiewicz, M., Dzierwa, P., & Trojan, M. (2024). Monitoring of thick-walled pressure elements to determine transient temperature and stress distributions using the measured fluid's pressure and wall's temperature. Energy, 309, 133121. doi: 10.1016/j.energy.2024.133121
[22] Taler, J., Kaczmarski, K., Taler, D., Dzierwa, P., Trojan, M., & Sobota, T. (2025). Online determination of the heat transfer coefficient at the inner surface of a cylindrical component in a thermal stress monitoring system for critical boiler pressure components. Energy, 328, 136637. doi: 10.1016/j.energy.2025.136637
[23] Kushnir, R.M., Yasinskyy, A.V., & Tokovyy, Y.V. (2022). Effect of material properties in direct and inverse thermomechanical analyses of multilayer functionally graded solids. Advanced Engineering Materials, 24, 2100875. doi: 10.1002/adem.202100875
[24] Ciałkowski, M., Joachimiak, M., Mierzwiczak, M., Frąckowiak, A., Olejnik, A., & Kozakiewicz, A. (2023). The analysis of the stability of the Cauchy problem in the cylindrical double-layer area. Archives of Thermodynamics, 44(4), 563–579. doi: 10.24425/ather.2023.149735
[25] Joachimiak, M., & Joachimiak, D. (2024). Stabilization of boundary conditions obtained from the solution of the inverse problem during the cooling process in a furnace for thermo-chemical treatment. International Journal of Heat and Mass Transfer, 224, 125274. doi: 10.1016/j.ijheatmasstransfer.2024.125274
[26] Joachimiak, M., Joachimiak, D., & Ciałkowski, M. (2022). Investigation on thermal loads in steady-state conditions with the use of the solution to the inverse problem. Heat Transfer Engineering, 44(11–12), 963–969. doi: 10.1080/01457632.2022.2113451
[27] Taler, J. (1999). A new space marching method for solving inverse heat conduction problems. Forschung im Ingenieurwesen, 64, 296–306. doi: 10.1007/PL00010844
[28] Taler, J., & Duda, P. (2006). Solving direct and inverse heat conduction problems. Springer.
[29] Taler, J. (1995). Theory and practice of identifying heat transfer processes. Zakład Narodowy im. Ossolińskich (in Polish).
