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Turbulence in a heated pipe at supercritical pressure

Published online by Cambridge University Press:  15 June 2021

J. He ,
R. Tian ,
P.X. Jiang  and
S. He Open the ORCID record for S. He [Opens in a new window]
J. He
Affiliation:
Department of Mechanical Engineering, University of Sheffield, SheffieldS1 3JD, UK
R. Tian
Affiliation:
Department of Mechanical Engineering, University of Sheffield, SheffieldS1 3JD, UK School of Mechanical Engineering, Beijing Institute of Technology, Beijing100084, PR China
P.X. Jiang
Affiliation:
Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
S. He*
Affiliation:
Department of Mechanical Engineering, University of Sheffield, SheffieldS1 3JD, UK
*
†Email address for correspondence: s.he@sheffield.ac.uk
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Abstract

The purpose of this research is to provide a new understanding of the turbulence dynamics in a heated flow of fluid at supercritical pressure. A unified explanation has been established for the laminarisation mechanisms due to the variations of thermophysical properties, buoyancy and inertia, the last of which plays a significant role in a developing flow. In the new understanding, the various factors can all be treated similarly as (pseudo-)body forces, the effect of which is to cause a reduction in the so-called apparent Reynolds number. The partially laminarising flow is represented by an equivalent-pressure-gradient reference flow plus a perturbation flow. Full laminarisation is used in the paper referring to a region where no new vortical structures are generated. This region is akin to the pre-transition region of a boundary layer bypass transition, and in both cases, the free-stream or pipe-core turbulence decays exponentially, but elongated streaks are formed in the boundary layer. Turbulence kinetic energy in this region may still be significant due to the decaying turbulence as well as newly generated streaks. The latter lead to an increase in streamwise velocity fluctuations near the wall. Later, re-transition occurs when the streaks break down and multi-scale vortices are generated, leading to an increase in the radial and circumferential velocity fluctuations. The structural effect of buoyancy on turbulence is weak and negative in the partially laminarising flow, but is dominant in the full laminarisation and re-transition regions.

JFM classification

Convection: Buoyant boundary layers Boundary Layers: Pipe flow boundary layer
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A45
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Ackerman, J.W. 1970 Pseudoboiling heat transfer to supercritical pressure water in smooth and ribbed tubes. Trans. ASME J. Heat Transfer 92 (3), 490–497.CrossRefGoogle Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D.S 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Azih, C. & Yaras, M.I 2018 Effects of spatial gradients in thermophysical properties on the topology of turbulence in heated channel flow of supercritical fluids. Phys. Fluids 30 (1), 015108.CrossRefGoogle Scholar
Bae, J.H., Yoo, J.Y. & Choi, H. 2005 Direct numerical simulation of turbulent supercritical flows with heat transfer. Phys. Fluids 17 (10), 105104.CrossRefGoogle Scholar
Bruch, A., Bontemps, A.é & Colasson, S.éphane 2009 Experimental investigation of heat transfer of supercritical carbon dioxide flowing in a cooled vertical tube. Intl J. Heat Mass Transfer 52 (11-12), 2589–2598.CrossRefGoogle Scholar
Cheng, X, Kuang, B & Yang, Y.H. 2007 Numerical analysis of heat transfer in supercritical water cooled flow channels. Nucl. Engng Des. 237 (3), 240–252.CrossRefGoogle Scholar
Coleman, G.N, Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–184.CrossRefGoogle Scholar
Duan, L, Beekman, I & Martin, M.P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers: part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.CrossRefGoogle Scholar
Fransson, J.H.M., Matsubara, M. & Alfredsson, P.H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.CrossRefGoogle Scholar
He, J, Yan, J, Wang, W, Jiang, P & He, S 2020 Effects of buoyancy and thermophysical property variations on the flow of supercritical carbon dioxide. Intl J. Heat Fluid Flow 86, 108697.CrossRefGoogle Scholar
He, S, He, K & Seddighi, M 2016 Laminarisation of flow at low Reynolds number due to streamwise body force. J. Fluid Mech. 809, 31–71.CrossRefGoogle Scholar
He, S, Kim, W.S. & Bae, J.H. 2008 Assessment of performance of turbulence models in predicting supercritical pressure heat transfer in a vertical tube. Intl J. Heat Mass Transfer 51 (19-20), 4659–4675.CrossRefGoogle Scholar
He, S & Seddighi, M 2013 Turbulence in transient channel flow. J. Fluid Mech. 715, 60–102.CrossRefGoogle Scholar
He, S & Seddighi, M 2015 Transition of transient channel flow after a change in Reynolds number. J. Fluid Mech. 764, 395–427.CrossRefGoogle Scholar
Huang, P.C., Coleman, G.N. & Bradshaw, P 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Jackson, J.D. 2013 Fluid flow and convective heat transfer to fluids at supercritical pressure. Nucl. Engng Des. 264, 24–40.CrossRefGoogle Scholar
Jackson, J.D. & Hall, W.B. 1979 Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions. Turbul. Forced Convection Channels Bundles 2, 613–640.Google Scholar
Jacobs, R.G. & Durbin, P.A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiang, P.-X., Zhang, Y., Zhao, C.-R. & Shi, R.-F. 2008 Convection heat transfer of CO$_2$ at supercritical pressures in a vertical mini tube at relatively low Reynolds numbers. Exp. Therm. Fluid Sci. 32 (8), 1628–1637.CrossRefGoogle Scholar
Koshizuka, S, Takano, N. & Oka, Y 1995 Numerical analysis of deterioration phenomena in heat transfer to supercritical water. Intl J. Heat Mass Transfer 38 (16), 3077–3084.CrossRefGoogle Scholar
Kurganov, V.A. & Kaptil'Ny, A.G. 1992 Velocity and enthalpy fields and eddy diffusivities in a heated supercritical fluid flow. Exp. Therm. Fluid Sci. 5 (4), 465–478.CrossRefGoogle Scholar
Lagha, M., Kim, J., Eldredge, J.D. & Zhong, X. 2011 A numerical study of compressible turbulent boundary layers. Phys. Fluids 23 (1), 015106.CrossRefGoogle Scholar
Lemmon, E.W., Huber, M.L. & McLinden, M.O. 2010 NIST standard reference database 23, reference fluid thermodynamic and transport properties (REFPROP), version 9.0, National Institute of Standards and Technology. R1234yf. fld file dated December 22, 2010.Google Scholar
Licht, J., Anderson, M. & Corradini, M. 2009 Heat transfer and fluid flow characteristics in supercritical pressure water. Trans. ASME J. Heat Transfer 131 (7), 072502.CrossRefGoogle Scholar
Liu, B., Zhu, Y., Yan, J.-J., Lei, Y., Zhang, B. & Jiang, P.-X. 2015 Experimental investigation of convection heat transfer of n-decane at supercritical pressures in small vertical tubes. Intl J. Heat Mass Transfer 91, 734–746.CrossRefGoogle Scholar
Liu, J., Zhao, P., Lei, M., Yang, S. & Nemati, H. 2020 Numerical investigation of spatial-developing turbulent heat transfer in forced convections at different supercritical pressures. Intl J. Heat Mass Transfer 159, 120128.CrossRefGoogle Scholar
Ma, P.C, Yang, X.I.A. & Ihme, M. 2018 Structure of wall-bounded flows at transcritical conditions. Phys. Rev. Fluids 3 (3), 034609.CrossRefGoogle Scholar
Marensi, E., He, S. & Willis, A.P. 2021 Suppression of turbulence and travelling waves in a vertical heated pipe. J. Fluid Mech. 919, A17.CrossRefGoogle Scholar
McEligot, D.M, Chu, X., Bae, J.H., Laurien, E. & Yoo, J.Y. 2020 Some observations concerning ‘laminarization’ in heated vertical tubes. Intl J. Heat Mass Transfer 163, 120101.CrossRefGoogle Scholar
Morinishi, Y., Tamano, S. & Nakabayashi, K. 2004 Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273–308.CrossRefGoogle Scholar
Nemati, H., Patel, A., Boersma, B.J. & Pecnik, R. 2015 Mean statistics of a heated turbulent pipe flow at supercritical pressure. Intl J. Heat Mass Transfer 83, 741–752.CrossRefGoogle Scholar
Nemati, H., Patel, A., Boersma, B.J & Pecnik, R. 2016 The effect of thermal boundary conditions on forced convection heat transfer to fluids at supercritical pressure. J. Fluid Mech. 800, 531–556.CrossRefGoogle Scholar
Orlandi, P. 2012 Fluid Flow Phenomena: A Numerical Toolkit. Springer Science & Business Media.Google Scholar
Patel, A., Boersma, B.J & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793–820.CrossRefGoogle Scholar
Patel, A., Boersma, B.J & Pecnik, R. 2017 Scalar statistics in variable property turbulent channel flows. Phys. Rev. Fluids 2 (8), 084604.CrossRefGoogle Scholar
Patel, A., Peeters, J.W.R., Boersma, B.J & Pecnik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27 (9), 095101.CrossRefGoogle Scholar
Pecnik, R. & Patel, A. 2017 Scaling and modelling of turbulence in variable property channel flows. J. Fluid Mech. 823, R1.CrossRefGoogle Scholar
Peeters, J.W.R., Pecnik, R., Rohde, M., Van Der Hagen, T.H.J.J. & Boersma, B.J. 2016 Turbulence attenuation in simultaneously heated and cooled annular flows at supercritical pressure. J. Fluid Mech. 799, 505–540.CrossRefGoogle Scholar
Peeters, J.W.R, Pecnik, R., Rohde, M., van der Hagen, T.H.J.J. & Boersma, B.J. 2017 Characteristics of turbulent heat transfer in an annulus at supercritical pressure. Phys. Rev. Fluids 2 (2), 024602.CrossRefGoogle Scholar
Petukhov, B.S, Polyakov, A.F. & Launder, B.E. 1988 Heat Transfer in Turbulent Mixed Convection. Hemisphere.Google Scholar
Pioro, I.L & Duffey, R.B 2005 Experimental heat transfer in supercritical water flowing inside channels (survey). Nucl. Engng des. 235 (22), 2407–2430.CrossRefGoogle Scholar
Pioro, I.L, Khartabil, H.F & Duffey, R.B 2004 Heat transfer to supercritical fluids flowing in channels–empirical correlations (survey). Nucl. Engng Des. 230 (1–3), 69–91.CrossRefGoogle Scholar
Pope, S.B 2001 Turbulent Flows. Cambridge University Press.Google Scholar
Reinink, S.K & Yaras, M.I 2015 Study of coherent structures of turbulence with large wall-normal gradients in thermophysical properties using direct numerical simulation. Phys. Fluids 27 (6), 065113.CrossRefGoogle Scholar
Seddighi, M. 2011 Study of turbulence and wall shear stress in unsteady flow over smooth and rough wall surfaces. PhD thesis, University of Aberdeen.Google Scholar
Sharabi, M, Ambrosini, W., He, S & Jackson, J.D. 2008 Prediction of turbulent convective heat transfer to a fluid at supercritical pressure in square and triangular channels. Ann. Nucl. Energy 35 (6), 993–1005.CrossRefGoogle Scholar
Smits, A.J & Dussauge, J.-P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer Science & Business Media.Google Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.CrossRefGoogle Scholar
Van Driest, E.R 1951 Turbulent boundary layer in compressible fluids. J. Aeronaut. Sci. 18 (3), 145–160.CrossRefGoogle Scholar
Wan, T., Zhao, P., Liu, J., Wang, C. & Lei, M. 2020 Mean velocity and temperature scaling for near-wall turbulence with heat transfer at supercritical pressure. Phys. Fluids 32 (5), 055103.Google Scholar
Wang, W. & He, S. 2015 Mechanisms of buoyancy effect on heat transfer in a horizontal flow. In Proceedings of the 7th International Symposium on Supercritical Water-Cooled Reactors (ISSCWR-7), pp. 15–18. VTT Technical Research Centre of Finland.Google Scholar
Yamagata, K, Nishikawa, K, Hasegawa, S, Fujii, T & Yoshida, S 1972 Forced convective heat transfer to supercritical water flowing in tubes. Intl J. Heat Mass Transfer 15 (12), 2575–2593.CrossRefGoogle Scholar
Yoo, J.Y. 2013 The turbulent flows of supercritical fluids with heat transfer. Annu. Rev. Fluid Mech. 45, 495–525.CrossRefGoogle Scholar