Thermal Behavior of Laminar Flow of Supercritical CO2 in a Long Vertical Mini-Pipe under Constant and Stepped Wall Heat Flux

Document Type : Full Lenght Research Article


Department of Mechanical Engineering, Qom University of Technology, Qom, Iran


In this study, the convective heat transfer of supercritical carbon dioxide in a long vertical mini-pipe has been investigated numerically. The numerical solution has been performed with the finite volume method and by developing a CFD code. The pipe has a length of 5.5 m and a diameter of 1 mm which is exposed to a constant heat flux at the wall with values of 300, 400, 500, and 600 W/m2 or step changes. In addition to the wall heat flux, the effects of gravity and flow direction have also been examined. Furthermore, some differences between the results of laminar and turbulent flows have been addressed. The results show that in the laminar flow, unlike the turbulent flow in the improvement regime of heat transfer, the system's thermal performance increases with increasing the wall heat flux, while in the deterioration mode, the two have similar behavior. Moreover, in part of the downward flow, reverse flow occurs, and its length can be understood by using the negative amount of wall shear stress. Furthermore, the thermal efficiency of the supercritical carbon dioxide is better at the upward flow and near the critical point than the constant property flow. In addition, from the applied stepped wall heat flux, it is concluded that the deterioration can be partially controlled or reduced by correctly determining the location of the step or any wall heat flux variations.


Main Subjects

  1. Yamaguchi, H. et al., 2010. Preliminary Study on a Solar Water Heater Using Supercritical Carbon Dioxide as Working Fluid. Journal of Solar Energy Engineering, 132(1), p.011010.
  2. Pecnik, R., Rinaldi, E., and Colonna, P., 2012. Computational fluid dynamics of a radial compressor operating with supercritical CO2. ASME Journal of Engineering Gas Turbines Power, 134 (12), p.122301.
  3. Serrano, I.P. et al., 2014. Modeling and sizing of the heat exchangers of a new supercritical CO2 Brayton power cycle for energy conversion for fusion reactors. Fusion Engineering and Design, 89(9), pp.1905–1908.
  4. Gkountas, A.A. et al., 2020. Heat transfer improvement by an Al2O3-water nanofluid coolant in printed-circuit heat exchangers of supercritical CO2 Brayton cycle. Thermal Science and Engineering Progress, 20, p.100694.
  5. Lee, Y., and Lee, J.I. 2014. Structural assessment of intermediate printed circuit heat exchanger for sodium-cooled fast reactor with supercritical CO2 cycle, Annual Nuclear Energy, 73, pp.84–95.
  6. Besarati, S. M., Goswami, D. Y., and Stefanakos, E. K., 2015. Development of a solar receiver based on compact heat exchanger technology for supercritical carbon dioxide power cycles. ASME Journal of Solar Energy Engineering, 137(3) p.031018.
  7. Jin, K., Krishna, A.B., Wong, Z., Ayyaswamy, P.S., Catton, I., and Fisher, T.S., 2023. Thermohydraulic experiments on a supercritical carbon dioxide–air microtube heat exchanger. International Journal of Heat and Mass Transfer, 203, p.123840.
  8. Krishna, A.B., Jin, K., Ayyaswamy, P.S., Catton, I., and Fisher, T.S., 2023. Technoeconomic optimization of superalloy supercritical CO2 microtube shell-and-tube-heat exchangers. Applied Thermal Engineering, 220, p.119578.
  9. Simoneau, R.J. and Williams, J.C., 1969. Laminar couette flow with heat transfer near the thermodynamic critical point. International Journal of Heat and Mass Transfer, 12, pp.120-124.
  10. Kim, J.K., and Aihara, T., 1992. A numerical study of heat transfer due to an axisymmetric laminar impinging jet of supercritical carbon dioxide. International Journal of Heat and Mass Transfer, 35 (10), pp.2515-2526.
  11. Lee, S.H. and Howel, J.R., 1996. Laminar forced convection at zero gravity to water near the critical region. Journal of Thermophysics and heat transfer, 10 (3), p.504.
  12. Liao, S.M. and Zhao, T.S., 2002. A numerical investigation of laminar convection of supercritical carbon dioxide in vertical mini/micro tubes. Progress in Computational Fluid Dynamics, 2 (2/3/4) pp.144–152.
  13. Khalesia, J., Sarunac, N. and Razzaghpanaha, Z., 2020. Supercritical CO2 conjugate heat transfer and flow analysis in a rectangular microchannel subject to uniformly heated substrate wall. Thermal Science and Engineering Progress, 19, p.100596.
  14. Saeed, M. Berrouk, A.S. AlShehhi, M.S. and AlWahedi, Y.F., 2021. Numerical investigation of the thermohydraulic characteristics of microchannel heat sinks using supercritical CO2 as a coolant. The Journal of Supercritical Fluids, 176, p. 105306.
  15. Rafee, R., 2014. Entropy generation calculation for laminar fully developed forced flow and heat transfer of nanofluids inside annuli, Journal of Heat and Mass Transfer Research, 1(1), pp. 25–33.
  16. Zolfaghar, M. and Mohseni, M., 2021. Numerical study of the effect of hole arrangement on thermal efficiency of a pipe containing perforated porous media. Thermal Science Engineering Progress, 25, p.100999.
  17. Dang C., and Hihara E., 2010. Numerical study on in-tube laminar heat transfer of supercritical fluids. Applied Thermal Engineering, 30, pp.1567-1573.
  18. Viswanathan, K. and Krishnamoorthy, G., 2021. The effects of wall heat fluxes and tube diameters on laminar heat transfer rates to supercritical CO2. International Communications in Heat and Mass Transfer, 123, p.105197.
  19. Zhang, X.R. and Yamaguchi, H., 2007. Forced convection heat transfer of supercritical CO2 in a horizontal circular tube. Journal of Supercritical Fluids, 41, pp.412–420.
  20. Cao, X.L., Rao, Z.H., Liao, S.M., 2011. Laminar convective heat transfer of supercritical CO2 in horizontal miniature circular and triangular tubes. Applied Thermal Engineering, 31, pp.2374-2384.
  21. Hassan Zaim, E., and Gandjalikhan Nassab, S.A., 2010. Numerical investigation of laminar forced convection of water upwards in a narrow annulus at supercritical pressure. Energy 35, pp.4172-4177.
  22. Peeters, J.W.R., T'Joen, C. and Rohde, M., 2013. Investigation of the thermal development length in annular upward heated laminar supercritical fluid flows. International Journal of Heat and Mass Transfer, 61, pp.667–674.
  23. Gao, W., Abdi-khanghah, M., Ghoroqi, M., Daryasafar, A., and Lavasani, M., 2018. Flow reversal of laminar mixed convection for supercritical CO2 flowing vertically upward in the entry region of asymmetrically heated annular channel. The Journal of Supercritical Fluids, 131, pp.87-98.
  24. Mohseni, M., and Bazargan, M., 2012. A new analysis of heat transfer deterioration on basis of turbulent viscosity variations of supercritical fluids. Journal of Heat Transfer, T-ASME, 134 (12), p.122503.
  25. Mohseni, M., and Bazargan, M., 2012. New analysis of heat transfer deterioration based on supercritical fluid property variations. Journal of Thermophysics and Heat Transfer, 26, pp.197-200.
  26. Lemmon, E., Huber, M. and McLinden, M., 2013. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, Natl Std. Ref. Data Series (NIST NSRDS), National Institute of Standards and Technology, Gaithersburg, MD, [online],
  27. Bird, R.B., Stewart, W.E., Lightfoot, E.N., Klingenberg, D.J., 2015. Introductory Transport Phenomena. John Wiley & Sons, Inc, USA.
  28. Versteeg, H.K., and Malalasekera, W., 2007. An Introduction to Computational Fluid Dynamic, The Finite Volume Method. 2nd ed., Pearson Education Limited, London, UK.
  29. Cengel, Y.A., Cimbala, J.M., Turn, R.H., 2017. Fundamentals of thermal-fluid sciences. 5th edition, McGraw Hill Education, New York, USA.
  30. Bazargan, M. and Mohseni, M., 2009. The significance of the buffer zone of boundary layer on convective heat transfer to a vertical turbulent flow of a supercritical fluid. The Journal of Supercritical Fluids, 51, pp.221-229.
  31. Mohseni, M., and Bazargan, M., 2011. The effect of the low Reynolds number k-e turbulence models on simulation of the enhanced and deteriorated convective heat transfer to the supercritical fluid flows. Heat and Mass Transfer, 47, pp.609–619.
  32. Kumar, D.S, Suresh , and Sundaravel, A., 2019. Heat Transfer Studies of Supercritical Water Flows in an Upward Vertical Tube. Journal of Heat and Mass Transfer Research, 6(2), pp.155–167.
  33. Yamagata, K., Nishikawa, K., Hasegawa, S., Fuji, T., and Yoshida, S., 1972. Forced convective heat transfer to supercritical water flowing in tubes. International Journal of Heat and Mass Transfer, 15 (12), pp.2575-2593.
  34. Shiralkar B.S., Griffith P., 1970. The effect of swirl, inlet condition, flow direction and tube diameter on heat transfer to fluids at supercritical pressure. ASME J. Heat Transfer, 92, pp.465-474.
  35. Jackson, J.D., Cotton, M.A., and Axcell, B.P., 1989. Studies of mixed convection in vertical tubes. International Journal of Heat and Fluid Flow, 10 (1), pp.2-15.