Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T20:19:43.209Z Has data issue: false hasContentIssue false

Direct numerical simulation of convective heat transfer of supercritical pressure $\textrm {CO}_2$ in a vertical tube with buoyancy and thermal acceleration effects

Published online by Cambridge University Press:  29 September 2021

Y.L. Cao
Affiliation:
Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
R.N. Xu
Affiliation:
Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
J.J. Yan
Affiliation:
Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
S. He
Affiliation:
Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD, UK
P.X. Jiang*
Affiliation:
Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
*
Email address for correspondence: [email protected]

Abstract

Supercritical pressure fluids are widely used in heat transfer and energy systems. The benefit of high heat transfer performance and the successful avoidance of phase change from the use of supercritical pressure fluids are well-known, but the complex behaviours of such fluids owing to dramatic thermal property variations pose strong challenges to the design of heat transfer applications. In this paper, the turbulent flow and heat transfer of supercritical pressure $\textrm {CO}_2$ in a small vertical tube influenced by coupled effects of buoyancy and thermal acceleration are numerically investigated using direct numerical simulation. Both upward and downward flows with an inlet Reynolds number of 3540 and pressure of 7.75 MPa have been simulated and the results are compared with corresponding experimental data. The flow and heat transfer results reveal that under buoyancy and thermal acceleration, the turbulent flow and heat transfer exhibit four developing periods in which buoyancy and thermal acceleration alternately dominate. The results suggest a way to distinguish the dominant factor of heat transfer in different periods and a criterion for heat transfer degradation under the complex coupling of buoyancy and thermal acceleration. An analysis of the orthogonal decomposition and the generative mechanism of turbulent structures indicates that the flow acceleration induces a stretch-to-disrupt mechanism of coherent turbulent structures. The significant flow acceleration can destroy the three-dimensional flow structure and stretch the vortices resulting in dissipation.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ackerman, J.W. 1970 Pseudoboiling heat transfer to supercritical pressure water in smooth and ribbed tubes. Trans. ASME J. Heat Transfer 92, 490497.CrossRefGoogle Scholar
Bae, J.H., Yoo, J.Y. & Choi, H. 2005 Direct numerical simulation of turbulent supercritical flows with heat transfer. Phys. Fluids 17, 105104.CrossRefGoogle Scholar
Bourke, P.J., Pulling, D.J., Gill, L.E. & Denton, W.H. 1970 Forced convective heat transfer to turbulent $\textrm {CO}_2$ in the supercritical region. Intl J. Heat Mass Transfer 13, 13391348.CrossRefGoogle Scholar
Cengel, Y.A. & Boles, M.A. 2014 Thermodynamics-An Engineering Approach. MacGraw-Hill.Google Scholar
Chu, X. & Laurien, E. 2016 Direct numerical simulation of heated turbulent pipe flow at supercritical pressure. J. Nucl. Engng Radiat. Sci. 2, 031019.CrossRefGoogle Scholar
Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. & Nieuwstadt, F.T.M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175210.CrossRefGoogle Scholar
Fu, S., Li, Q.B. & Wang, M.H. 2003 Depicting vortex stretching and vortex relaxing mechanisms. Chin. Phys. Lett. 20, 21952198.Google Scholar
Gnielinski, V. 1976 New equations for heat and mass transfer in turbulent pipe and channel flow. Intl Chem. Engng 75, 816.Google Scholar
Grigoriev, V.S., Polyakov, A.F. & Rosnovsky, S.V. 1977 Heat transfer of fluids at super-critical pressures with variable heat flux along length in tubes. Teplofiz. Vysok. Temp. 15, 12411247.Google Scholar
Hall, W.B. 1971 Heat transfer near the critical point. Adv. Heat Transfer 7, 186.CrossRefGoogle Scholar
Hall, W.B. & Jackson, J.D. 1969 Laminarization of a turbulent pipe flow by buoyancy forces. In 11th ASME-AIChE National Heat Transfer Conference, Minneapolis, MN, Paper 69-HT-55. ASME.Google Scholar
He, S., He, K. & Seddighi, M. 2016 Laminarisation of flow at low Reynolds number due to streamwise body force. J. Fluid Mech. 809, 3171.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, 46594675.CrossRefGoogle Scholar
He, S. & Seddighi, M. 2013 Turbulence in transient channel flow. J. Fluid Mech. 715, 60102.CrossRefGoogle Scholar
Hiroaki, T., Ayao, T., Masaru, H. & Nuchi, N. 1973 Effects of buoyancy and of acceleration owing to thermal expansion on forced turbulent convection in vertical circular tubes–criteria of the effects, velocity and temperature profiles, and reverse transition from turbulent to laminar flow. Intl J. Heat Mass Transfer 16, 12671288.CrossRefGoogle Scholar
Huang, D., Wu, Z., Sunden, B. & Li, W. 2016 A brief review on convection heat transfer of fluids at supercritical pressures in tubes and the recent progress. Appl. Energy 162, 494505.CrossRefGoogle Scholar
Jackson, J.D. 2002 Consideration of the heat transfer properties of supercritical pressure water in connection with the cooling of advanced nuclear reactors. In The 13th Pacific Basin Nuclear Conference, Shenzhen City, China.Google Scholar
Jackson, J.D. 2009 Validation of an extended heat transfer equation for fluids at supercritical pressure. In Fourth International Symposium Supercritical Water-Cooled Reactors (ISSCWR-4), pp. 8–11.Google Scholar
Jackson, J.D. 2013 Fluid flow and convective heat transfer to fluids at supercritical pressure. Nucl. Engng Des. 264, 2440.CrossRefGoogle Scholar
Jackson, J.D., Evans Lutterodt, K.O.J. & Weinberg, R. 2003 Experimental studies of buoyancy-influenced convective heat transfer in heated vertical tubes at pressures just above and just below the thermodynamic critical value. In Proceedings of the International Conference on Global Environment and Advanced Nuclear Power Plants (GENES4/ANP2003), Paper No. 1177. AESJ.Google Scholar
Jackson, J.D. & Hall, W.B. 1979 a Forced convection heat transfer to fluids at supercritical pressure. Turbul. Forced Convect. Channels Bundles 2, 613.Google Scholar
Jackson, J.D. & Hall, W.B. 1979 b Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions. Turbul. Forced Convect. Channels Bundles 2, 613640.Google Scholar
Jiang, P.X., Li, Z.H. & Zhao, C.R. 2009 a Convection heat transfer of $\textrm {CO}_2$ at supercritical pressures in a vertical mini tube. In Proceedings of MNHMT2009 ASME 2009 2nd Micro/Nanoscale Heat & Mass Transfer International Conference, Shanghai, China, Paper No. 18343.Google Scholar
Jiang, P.X., Liu, B., Zhao, C.R. & Luo, F. 2013 Convection heat transfer of supercritical pressure carbon dioxide in a vertical micro tube from transition to turbulent flow regime. Intl J. Heat Mass Transfer 56, 741749.CrossRefGoogle Scholar
Jiang, P.X., Wang, Z.C. & Xu, R.N. 2018 A modified buoyancy effect correction method on turbulent convection heat transfer of supercritical pressure fluid based on RANS model. Intl J. Heat Mass Transfer 127, 257267.CrossRefGoogle Scholar
Jiang, P.X., Xu, R.N., Li, Z.H. & Zhao, C.R. 2010 Influence of flow acceleration on convection heat transfer of $\textrm {CO}_2$ at supercritical pressures and air in a vertical micro tube. In 2010 14th International Heat Transfer Conference, pp. 1–13.Google Scholar
Jiang, P.X., Zhang, Y., Xu, Y.J. & Shi, R.F. 2008 a Experimental and numerical investigation of convection heat transfer of $\textrm {CO}_2$ at supercritical pressures in a vertical tube at low Reynolds numbers. Intl J. Therm. Sci. 47, 9981011.CrossRefGoogle Scholar
Jiang, P.X., Zhang, Y., Zhao, C.R. & Shi, R.F. 2008 b Convection heat transfer of $\textrm {CO}_2$ at supercritical pressures in a vertical mini tube at relatively low Reynolds numbers. Exp. Therm. Fluid Sci. 32, 16281637.CrossRefGoogle Scholar
Jiang, P.X., Zhao, C.R. & Liu, B. 2012 Flow and heat transfer characteristics of R22 and ethanol at supercritical pressures. J. Supercrit. Fluids 70, 7589.CrossRefGoogle Scholar
Jiang, P.X., Zhao, C.R., Shi, R.F., Chen, Y. & Ambrosini, W. 2009 b Experimental and numerical study of convection heat transfer of $\textrm {CO}_2$ at super-critical pressures during cooling in small vertical tube. Intl J. Heat Mass Transfer 52, 47484756.CrossRefGoogle Scholar
Kim, W.S., He, S. & Jackson, J.D. 2008 Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection. Intl J. Heat Mass Transfer 51, 12931312.CrossRefGoogle Scholar
Kirillov, P.L. 2000 Heat and mass transfer at supercritical parameters. The short review of researches in Russia. Theory and experiments. In Proceedings of the First International Symposium on Supercritical Water-Cooled Reactor Design (SCR-2000), Paper No. 105. The University of Tokyo.Google Scholar
Krasnoshchekov, A.E., Protopopov, S.V., Van, F. & Kuraeva, L.V. 1964 Experimental investigation of heat transfer for carbon dioxide in the supercritical region. In Proceedings of the 2nd All-Soviet Union Conference on Heat and Mass Transfer, pp. 26–35.Google 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, 465478.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, Standard Reference Data Program.Google Scholar
Li, Z.H., Jiang, P.X., Zhao, C.R. & Zhang, Y. 2010 Experimental investigation of convection heat transfer of $\textrm {CO}_2$ at supercritical pressures in a vertical circular tube. Exp. Therm. Fluid Sci. 34, 11621171.CrossRefGoogle Scholar
Mceligot, D.M. & Jackson, J.D. 2004 “Deterioration” criteria for convective heat transfer in gas flow through non-circular ducts. Nucl. Engng Des. 232, 327333.CrossRefGoogle Scholar
Nemati, H., Patel, A., Boersma, B.J. & Pechik, R. 2015 Mean statistics of a heated turbulent pipe flow at supercritical pressure. Intl J. Heat Mass Transfer 83, 741752.CrossRefGoogle Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21 (3), 251269.CrossRefGoogle Scholar
Patel, A., Peeters, J.W.R., Boersma, B.J. & Pechik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27, 095101.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, 505540.CrossRefGoogle Scholar
Petukhov, B.S. 1970 Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv. Heat Transfer 6, 503564.CrossRefGoogle Scholar
Petukhov, B.S., Polyakov, A.F. & Launder, B.E. 1988 Heat Transfer in Turbulent Mixed Convection. Springer.Google Scholar
Polyakov, A.F. 1991 Heat transfer under supercritical pressures. Adv. Heat Transfer 21, 153.CrossRefGoogle Scholar
Protopopov, V.S. 1977 Generalized correlations for the local heat transfer coefficient in turbulent flow of water and carbon dioxide at supercritical pressures in uniformly heated tubes. Teplofiz. Vysok. Temp. 15, 815821.Google 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
Shiralkar, B. & Griffith, P. 1970 The effect of swirl, inlet conditions, flow direction, and tube diameter on the heat transfer to fluids at supercritical pressure. Trans. ASME J. Heat Transfer 92, 465471.CrossRefGoogle Scholar
Wang, Z.C., Jiang, P.X. & Xu, R.N. 2018 Turbulent convection heat transfer analysis of supercritical pressure $\textrm {CO}_2$ flow in a vertical tube based on the field synergy principle. Heat Transfer Engng 40, 476486.CrossRefGoogle Scholar
Xu, R.N., Luo, F. & Jiang, P.X. 2017 Buoyancy effects on turbulent heat transfer of supercritical $\textrm {CO}_2$ in a vertical mini-tube based on continuous wall temperature measurements. Intl J. Heat Mass Transfer 110, 576586.CrossRefGoogle Scholar
Yoo, J.Y. 2013 The turbulent flows of supercritical fluids with heat transfer. Annu. Rev. Fluid Mech. 45, 495525.CrossRefGoogle Scholar