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Experimental and numerical verification of transient spatial temperature distribution in thick-walled pressure components

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Abstract

The aim of this work is to present a method to determine the transient-state spatial temperature distribution in a cylindrical component. The presented method involves solving the inverse heat conduction problem based on the Finite volume method (FVM). This approach enables determination of transient-state temperature fields with boundary conditions known on one surface of the component only. The proposed method is verified using the laboratory installation located at the Cracow University of Technology. The main components of the laboratory stand are, among others, a steam outlet header and a steam boiler. During the experiment, the steam header is heated up abruptly from the inside by contact with dry saturated steam. The spatial transient-state temperature distribution within the steam outlet header is determined using the proposed method, which is based on temperature measurements made by 19 thermocouples located on the outer surface of the component. The temperature histories in three selected nodes are compared with the measurement results obtained from thermocouples located inside the component wall. The exact location of the thermocouples corresponds to the nodal position at selected control volumes. Moreover, the Ansys Mechanical APDL software is used to verify calculations and experimental data. A transient- state simulation is performed. The temperature histories at the inner and outer surfaces are set as the model boundary conditions. In order to enable verification of the temperature measurements, the component discrete model includes nodes at appropriate locations. An error analysis is performed between calculated and measured temperature values. The results obtained from the numerical and experimental validation demonstrate fully satisfactory agreement. Additionally, a stress analysis of the outlet header is performed in the Ansys software based on the transient-state temperature distribution within the steam outlet header. The method proposed in this paper is a convenient and accurate tool for monitoring working conditions of the power boiler thick-walled components.

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References

  1. J. Taler et al., Analysis to speed up the start-up of steam boiler OP-380, J. of Power Techn., 94 (2014) 1–8.

    Google Scholar 

  2. J. Taler et al., Determination of start-up curves for a boiler with natural circulation based on the analysis of stress distribution in critical pressure components, Energy, 92 (2015) 153–159.

    Article  Google Scholar 

  3. D. Taler and K. Kaczmarski, Mathematical modelling of the transient response of pipeline, J. of Thermal Science, 25 (2016) 1–9.

    Article  Google Scholar 

  4. F.-B. Liu, Particle swarm optimization-based algorithms for solving inverse heat conduction problems of estimating surface heat flux, International J. of Heat and Mass Transfer, 55 (2012) 2062–2068.

    Article  Google Scholar 

  5. L. Ran et al., A modified space marching method using future temperature measurements for transient nonlinear inverse heat conduction problem, International J. of Heat and Mass Transfer, 106 (2017) 1157–1163.

    Article  Google Scholar 

  6. C.-H. Huang et al., A nonlinear inverse problem in simultaneously estimating the heat and mass production rates for a chemically reacting fluid, Chem. Eng. Sci., 58 (16) (2003) 3741–3752.

    Article  Google Scholar 

  7. J. Beck et al., Inverse heat conduction: Ill-posed problems, Wiley-Interscience, New York (1982).

    Google Scholar 

  8. Z. Jianhua et al., Inverse heat conduction in a composite slab with pyrolysis effect and temperature-dependent thermophysical properties, J. Heat Transf., 132 (3) (2010) 3.

    Google Scholar 

  9. G. Wang et al., An inverse method to reconstruct the heat flux produced by bone grinding tools, Int. J. Therm. Sc., 101 (2016) 85–92.

    Article  Google Scholar 

  10. J. Taler, W. Zima and M. Jaremkiewicz, Simple method for monitoring transient thermal stresses in pipelines, J. of Thermal Stresses, 39 (4) (2016) 386–397.

    Article  Google Scholar 

  11. M. Prud’homme and T. H. Nguyen, Solution of inverse free convection problems by conjugate gradient method: Effects of Rayleigh number, Int. J. Heat Mass Transf., 44 (11) (2001) 2011–2027.

    Article  MATH  Google Scholar 

  12. S. Farahani et al., Direct estimation of local convective boiling heat transfer coefcient in mini-channel by using conjugated gradient method with adjoint equation, Int. J. Heat Mass Transf., 55 (2014) 1–7.

    Article  Google Scholar 

  13. J. Taler and W. Zima, Solution of inverse heat conduction problems using control volume approach, Int. J. Heat Mass Transf., 42 (1999) 1123–1140.

    Article  MATH  Google Scholar 

  14. C. Weber et al., Analysis and solution of the ill-posed inverse heat conduction problem, Int. J. Heat Mass Transf., 24 (11) (1981) 1783–1792.

    Article  MATH  Google Scholar 

  15. J. V. Beck, B. Blackwell, C. R. St. Clair, Inverse heat conduction, Ill-posed problems, Wiley (1985).

    Google Scholar 

  16. A. Tikhonov and V. Arsenin, Solutions of Ill-posed problems, Winston & Sons (1977).

    MATH  Google Scholar 

  17. L. Dantas et al., An inverse problem of parameter estimation for heat and mass transfer in capillary porous media, Int. J. Heat Mass Transf., 46 (2003) 1587–1598.

    Article  MATH  Google Scholar 

  18. W. Brasil et al., An inverse problem for the estimation of upstream velocity probles in an incompressible turbulent boundary layer, Int. J. Heat Mass Transf., 47 (2014) 1267–1274.

    Article  MATH  Google Scholar 

  19. J. Frankel, Residual-minimization least-squares method for inverse heat conduction, Computers and Mathematics with Applications, 32 (1996) 117–130.

    Article  MathSciNet  MATH  Google Scholar 

  20. C.-H. Huang and Y.-L. Tsai, A transient 3-D inverse problem in imaging the time-dependent local heat transfer coefficients for plate fin, Applied Thermal Engineering, 25 (2005) 2478–2495.

    Article  Google Scholar 

  21. C.-H. Huang and C.-A. Chen, A three-dimensional inverse geometry problem in estimating the space and timedependent shape of an irregular internal cavity, Int. J. Heat Mass Transf., 52 (2009) 2079–2091.

    Article  MATH  Google Scholar 

  22. C.-H. Huang et al., A three-dimensional inverse problem in estimating the applied heat flux of a titanium drilling - Theoretical and experimental studies, Int. J. Heat Mass Transf., 50 (2007) 3265–3277.

    Article  MATH  Google Scholar 

  23. S. Kim and W. Lee, Solution of inverse heat conduction problems using maximum entropy method, Int. J. Heat Mass Transf., 45 (2002) 381–391.

    Article  MATH  Google Scholar 

  24. J. Zueco et al., Inverse determination of temperaturedependent thermal conductivity using network simulation method, Journal of Materials Processing Technology, 174 (2006) 137–144.

    Article  Google Scholar 

  25. W.-L. Chen et al., Inverse problem in determining convection heat transfer coefficient of an annular fin, Energy Conversion and Management, 48 (2007) 1081–1088.

    Article  Google Scholar 

  26. D. Lin et al., Inverse problem of unsteady conjugated forced convection in parallel plate channels, Int. J. Heat Mass Transf., 51 (2008) 993–1002.

    Article  MATH  Google Scholar 

  27. T. Lu et al., A two-dimensional inverse heat conduction problem in estimating the fluid temperature in a pipeline, Applied Thermal Engineering, 30 (2010) 1574–1579.

    Article  Google Scholar 

  28. T. Lu et al., A two-dimensional inverse heat conduction problem for simultaneous estimation of heat conduction coefficient, fluid temperature and wall temperature on the inner wall of a pipeline, Progress in Nuclear Energy, 81 (2015) 161–168.

    Google Scholar 

  29. M. Cui et al., A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems, International J. of Heat and Mass Transfer, 90 (2015) 491–498.

    Article  Google Scholar 

  30. R. Pourgholi, H. Dana and S. H. Tabasi, Solving an inverse heat conduction problem using genetic algorithm: Sequential and multi-core parallelization approach, Appl. Math. Model., 38 (2014) 1948–1958.

    Article  MathSciNet  Google Scholar 

  31. H. Y. Li and C. Y. Yang, A genetic algorithm for inverse radiation problems, International J. of Heat and Mass Transfer, 40 (1997) 1545–1549.

    Article  MATH  Google Scholar 

  32. X. Wang et al., Real-time temperature field reconstruction of boiler drum based on fuzzy adaptive Kalman filter and order reduction, International J. of Thermal Sciences, 113 (2017) 145–153.

    Article  Google Scholar 

  33. J. Taler and W. Zima, Solution of inverse heat conduction problems using control volume approach, International Journal of Heat and Mass Transfer, 42 (1999) 1123–1140.

    Article  MATH  Google Scholar 

  34. J. Taler, B. Węglowski and M. Pilarczyk, Monitoring of thermal stresses in pressure components using inverse heat conduction methods, International J. of Numerical Methods for Heat & Fluid Flow, 27 (2017) 740–756.

    Article  Google Scholar 

  35. F. Mohebbi and M. Sellier, Estimation of thermal conductivity, heat transfer coefficient, and heat flux using a three dimensional inverse analysis, International Journal of Thermal Sciences, 99 (2016) 258–270.

    Google Scholar 

  36. F. Mohebbi et al., Estimation of linearly temperaturedependent thermal conductivity using an inverse analysis, International Journal of Thermal Sciences, 117 (2017) 68–76.

    Article  Google Scholar 

  37. B. Węglowski, The computer system for on-line thermal monitoring of power boilers, Zeszyty naukowe Politechniki Krakowskiej, series: Mechanika, Kraków (2001) (in Polish).

    Google Scholar 

  38. J. Taler, Theory and practice of identification of heat flux processes, Ossolineum, Wrocław (1995) (in Polish).

    Google Scholar 

  39. F. Richter, The physical properties of steels “The 100 steels programme” Part I: Tables and figures.

  40. M. Jaremkiewicz and J. Taler, Measurement technique of transient fluid temperature in a pipeline, Procedia Engineering, 157 (2016) 58–65.

    Article  Google Scholar 

  41. J. Taler, B. Węglowski, S. Sobota, M. Jaremkiewicz and D. Taler, Inverse space marching method for determining temperature and stress distributions in pressure components, Marco Aurélio dos Santos Bernardes (Ed.), Developments in Heat Transfer, InTech. (2011) 273–292.

    Google Scholar 

  42. Thermocouples catalog, Alf-Sensor Company, Cracow, Poland (2017).

  43. ANSYS® academic research, release 17.0.

  44. J. Taler and P. Ocłoń, Finite element method in steady-state and transient heat conduction, Encyclopedia of thermal stresses, R. Hetnarski (Ed.), Springer, Dordrecht Heidelberg New York London, 4 (2014) 1604–1633.

    Google Scholar 

  45. B. Węglowski, P. Ocłoń and A. Majcher, Monitoring of the stress state in the boiler drum using finite element method, Advanced Materials Research, 875 (2014) 1176–1182.

    Article  Google Scholar 

  46. B. Węglowski and P. Ocłoń, Analysis of operating conditions for pressure components of steam boilers, Rynek Energii, 6 (2012) 99–106.

    Google Scholar 

  47. P. Cisek and D. Taler, Numerical and experimental study of a solid matrix electric thermal storage unit dedicated to environmentally friendly residential heating system, Energy and Buildings, 130 (2016) 747–760.

    Article  Google Scholar 

  48. D. Taler, Experimental investigations of heat exchangers, D. Taler (Ed.), Calculations and experimental studies of heat exchangers, Cracow University of Technology Press (2016).

  49. K. Wanjae et al., Welding residual stress analysis of 347H austenitic stainless steel boiler tubes using experimental and numerical approaches, J. of Mechanical Science and Techn., 30 (2016) 1773–1779.

    Article  Google Scholar 

Download references

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Correspondence to Marcin Pilarczyk.

Additional information

This paper was presented at the ICCHM2T2017, Sejong Hotel, Seoul, Korea, May 28–June 1, 2017. Recommended by Guest Editor Heuy Dong Kim.

Bohdan Węglowski is a Professor of Faculty of Mechanical Engineering at Cracow University of Technology, Poland. His current research interests include the exploitation of steam boilers, monitoring of thick-walled pressure components and fatigue analysis.

Marcin Pilarczyk received his B.Eng. and M.S. in Faculty of Mechanical Engineering from Cracow University of Technology, Poland, in 2012 and 2013. His research interests are a thermal and structural analysis of pressure vessels, steam boiler exploitation and energy systems.

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Węglowski, B., Pilarczyk, M. Experimental and numerical verification of transient spatial temperature distribution in thick-walled pressure components. J Mech Sci Technol 32, 1087–1098 (2018). https://doi.org/10.1007/s12206-018-0211-z

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  • DOI: https://doi.org/10.1007/s12206-018-0211-z

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