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Study of Variable Turbulent Prandtl Number Model for Heat Transfer to Supercritical Fluids in Vertical Tubes

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Abstract

In order to improve the prediction performance of the numerical simulations for heat transfer of supercritical pressure fluids, a variable turbulent Prandtl number (Prt) model for vertical upward flow at supercritical pressures was developed in this study. The effects of Prt on the numerical simulation were analyzed, especially for the heat transfer deterioration conditions. Based on the analyses, the turbulent Prandtl number was modeled as a function of the turbulent viscosity ratio and molecular Prandtl number. The model was evaluated using experimental heat transfer data of CO2, water and Freon. The wall temperatures, including the heat transfer deterioration cases, were more accurately predicted by this model than by traditional numerical calculations with a constant Prt. By analyzing the predicted results with and without the variable Prt model, it was found that the predicted velocity distribution and turbulent mixing characteristics with the variable Prt model are quite different from that predicted by a constant Prt. When heat transfer deterioration occurs, the radial velocity profile deviates from the log-law profile and the restrained turbulent mixing then leads to the deteriorated heat transfer.

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References

  1. Pioro I., Mokry S., Draper S., Specifics of thermophysical properties and forced-convective heat transfer at critical and supercritical pressures. Reviews in Chemical Engineering, 2011, 27: 191–214.

    Article  Google Scholar 

  2. Shin B., Kim D., Son M., Koo J., Effects of supercritical environment on hydrocarbon-fuel injection. Journal of Thermal Science, 2017, 26(2): 183–191.

    Article  ADS  Google Scholar 

  3. Tian R., An Q., Zhai H., Shi L., Performance analyses of transcritical organic Rankine cycles with large variations of the thermophysical properties in the pseudocritical region. Applied Thermal Engineering, 2016, 101: 183–190.

    Article  Google Scholar 

  4. Wang X., Shuai D., Lyu Q., Experimental study on structural optimization of a supercritical circulating fluidized bed boiler with an annular furnace and six cyclones. Journal of Thermal Science, 2017, 26(5): 472–482.

    Article  ADS  Google Scholar 

  5. Jackson J., Fluid flow and convective heat transfer to fluids at supercritical pressure. Nuclear Engineering and Design, 2013, 264: 24–40.

    Article  Google Scholar 

  6. Pioro I., Duffey R., Heat transfer and hydraulic resistance at supercritical pressures in power engineering applications, ASME Press, New York, NY, USA, 2007.

    Book  Google Scholar 

  7. Lei X., Li H., Zhang Y., Zhang W., Effect of buoyancy on themechanism of heat transfer deterioration of supercritical water in horizontal tubes. ASME Journal of Heat Transfer, 2013, 135(7): 071703.

    Article  Google Scholar 

  8. Pioro I., Duffey R., Experimental heat transfer in supercritical water flowing inside channels (survey). Nuclear Engineering and Design, 2005, 235(22): 2407–2430.

    Article  Google Scholar 

  9. Pioro I., Khartabil H., Duffey R., Heat transfer to supercritical fluids flowing in channels-empirical correlations (survey). Nuclear Engineering and Design, 2004, 230(1): 69–91.

    Article  Google Scholar 

  10. Jiang P., Zhao C., Liu B., Flow and heat transfer characteristics of r22 and ethanol at supercritical pressures. Journal of Supercritical Fluids, 2012, 70: 75–89.

    Article  Google Scholar 

  11. Jackson J., A Semi-Empirical Model of Turbulent Convective Heat Transfer to Fluids at Supercritical Pressure, in: 16th International Conference on Nuclear Engineering, American Society of Mechanical Engineers, Orlando, Florida, USA, May 11–15, 2008.

    Google Scholar 

  12. He S., Kim W., Jiang P., Jackson J., Simulation of mixed convection heat transfer to carbon dioxide at supercritical pressure. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2004, 218(11): 1281–1296.

    Google Scholar 

  13. Licht J., Anderson M., Corradini M., Heat Transfer and Fluid Flow Characteristics in Supercritical Pressure Water. ASME Journal of Heat Transfer, 2009, 131(7): 072502.

    Article  Google Scholar 

  14. Chu X., Laurien E., Flow stratification of supercritical CO2 in a heated horizontal pipe. Journal of Supercritical Fluids, 2016, 116: 172–189.

    Article  Google Scholar 

  15. Bae J., Yoo J., Choi H, Direct numerical simulation of turbulent supercritical flows with heat transfer. Physics of Fluids, 2005, 17: 105104.

    Article  ADS  MATH  Google Scholar 

  16. Zhao C., Zhang Z., Jiang P., Bo H., Influence of various aspects of low Reynolds number k-ε turbulence models on predicting in-tube buoyancy affected heat transfer to supercritical pressure fluids. Nuclear Engineering and Design, 2017, 313: 401–413.

    Article  Google Scholar 

  17. Cheng X., Kuang B., Yang Y., Numerical analysis of heat transfer in supercritical water cooled flow channels. Nuclear Engineering and Design, 2007, 237(3): 240–252.

    Article  Google Scholar 

  18. He S., Kim W., Bae J., Assessment of performance of turbulence models inpredicting supercritical pressure heat transfer in a vertical tube. International Journal Heat and Mass Transfer, 2008, 51(19): 4659–4675.

    Article  MATH  Google Scholar 

  19. De Rosa M., Guetta G., Ambrosini W., Forgione N., He S., Jackson J., Lessons learned from the application of CFD models in the prediction of heat transfer to fluids at supercritical pressure, In The 5th International Symposium on Supercritical Water-Cooled Reactors (ISSCWR-5), Vancouver, BC, Canada, Mar. 2011.

    Google Scholar 

  20. Li Z., Wu Y., Tang G., Long D., Lu J., Comparison between heat transfer to supercritical water in a smooth tube and in an internally ribbed tube. International Journal Heat and Mass Transfer, 2015, 84: 529–541.

    Article  Google Scholar 

  21. Liu X., Xu X., Liu C., Ye J., Li H. Bai W., Dang C., Numerical study of the effect of buoyancy force and centrifugal force on heat transfer characteristics of supercritical CO2 in helically coiled tube at various inclination angles. Applied Thermal Engineering, 2017, 116: 500–515.

    Article  Google Scholar 

  22. Reynolds A., The prediction of turbulent Prandtl and Schmidt numbers. International Journal Heat and MassTransfer, 1975, 18: 1055–1069.

    Article  ADS  Google Scholar 

  23. Kays W., Turbulent Prandtl number–where are we. ASME Journal of Heat Transfer, 1994, 116 (2): 284–295.

    Article  ADS  Google Scholar 

  24. Hasan B., Turbulent Prandtl number and its use in prediction of heat transfer coefficient for liquids. Nahrain University, College of Engineering Journal (NUCEJ) 2007, 10(1): 53–64.

    MathSciNet  Google Scholar 

  25. Mohseni M., Bazargan M., Effect of turbulent Prandtl number on convective heat transfer to turbulent flow of a supercritical fluid in a vertical round tube. ASME Journal of Heat Transfer, 2011, 133(7): 071701.

    Article  Google Scholar 

  26. Mohseni M., Bazargan M., A New Correlation for the Turbulent Prandtl Number in Upward Rounded Tubes in Supercritical Fluid Flows. ASME Journal of Heat Transfer, 2016, 138(8): 081701.

    Article  Google Scholar 

  27. Bae Y., A new formulation of variable turbulent Prandtl number for heat transfer to supercritical fluids. International Journal Heat and Mass Transfer, 2016, 92: 792–806.

    Article  Google Scholar 

  28. Tang G., Shi H., Wu Y., Lu J., Li Z., Liu Q., Zhang H., A variable turbulent Prandtl number model for simulating supercritical pressure CO2 heat transfer. International Journal Heat and Mass Transfer, 2016, 102: 1082–1092.

    Article  Google Scholar 

  29. Lemmon E., Huber M., MeLinden M., NIST reference fluid thermodynamicand transport properties-RFFPROP, version 9.1. National Institute of Standard Technology, 2013.

    Google Scholar 

  30. Gu H, Zhao M., Cheng X., Experimental studies on heat transfer to supercritical water in circular tubes at high heat fluxes. Experimental Thermal Fluid and Science, 2015, 65: 22–32.

    Article  Google Scholar 

  31. Jiang P., Liu B., Zhao C., Luo F., Convection heat transfer of supercritical pressure carbon dioxide in a vertical micro tube from transition to turbulent flow regime. International Journal of Heat and Mass Transfer, 2013, 56(1-2): 741–749.

    Article  Google Scholar 

  32. Li ZH, Research on convection heat transfer of CO2 at supercritical pressires in Mini/Micro scale tubes. Ph.D. thesis, Tsinghua Univerisity, Beijing, China, 2008.

    Google Scholar 

  33. Zahlan H., Groeneveld D., Tavoularis S., Measurements of convective heat transfer to vertical upward flows of CO2 in circular tubes at near-critical and supercritical pressures. Nuclear Engineering and Design, 2015, 289: 92–107.

    Article  Google Scholar 

  34. Feuerstein F., Coelho S., Klingel D., Cheng X., Largescale heat transfer experiments with supercritical R134a flowing upward in a circular tube. Atw. Internationale Zeitschriftfuer Kernenergie, 2017, 62(2): 121–125.

    Google Scholar 

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Authors and Affiliations

  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China

    Ran Tian, Dabiao Wang & Lin Shi

  2. Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China

    Xiaoye Dai

Authors
  1. Ran Tian
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  2. Xiaoye Dai
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  3. Dabiao Wang
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  4. Lin Shi
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Corresponding author

Correspondence to Lin Shi.

Additional information

This study is financially supported by the National Key Research and Development Program of China under Grant No. 2016YFB0901405, the State Key Program of the National Natural Science Foundation of China (Grant No. 51236004) and the Science Fund for Creative Research Groups (No. 51621062)

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Tian, R., Dai, X., Wang, D. et al. Study of Variable Turbulent Prandtl Number Model for Heat Transfer to Supercritical Fluids in Vertical Tubes. J. Therm. Sci. 27, 213–222 (2018). https://doi.org/10.1007/s11630-018-1002-7

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  • DOI: https://doi.org/10.1007/s11630-018-1002-7

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