Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-11T11:52:38.122Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of thermal boundary conditions on forced convection heat transfer to fluids at supercritical pressure

Published online by Cambridge University Press:  12 July 2016

Hassan Nemati ,
Ashish Patel ,
Bendiks J. Boersma  and
Rene Pecnik
Hassan Nemati
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
Ashish Patel
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
Bendiks J. Boersma
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
Rene Pecnik*
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We use direct numerical simulations to study the effect of thermal boundary conditions on developing turbulent pipe flows with fluids at supercritical pressure. The Reynolds number based on pipe diameter and friction velocity at the inlet is $Re_{{\it\tau}0}=360$ and Prandtl number at the inlet is $Pr_{0}=3.19$. The thermodynamic conditions are chosen such that the temperature range within the flow domain incorporates the pseudo-critical point where large variations in thermophysical properties occur. Two different thermal wall boundary conditions are studied: one that permits temperature fluctuations and one that does not allow temperature fluctuations at the wall (equivalent to cases where the thermal effusivity ratio approaches infinity and zero, respectively). Unlike for turbulent flows with constant thermophysical properties and Prandtl numbers above unity – where the effusivity ratio has a negligible influence on heat transfer – supercritical fluids shows a strong dependency on the effusivity ratio. We observe a reduction of 7 % in Nusselt number when the temperature fluctuations at the wall are suppressed. On the other hand, if temperature fluctuations are permitted, large property variations are induced that consequently cause an increase of wall-normal velocity fluctuations very close to the wall and thus an increased overall heat flux and skin friction.

JFM classification

Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 800 , 10 August 2016 , pp. 531 - 556
Check for updates
Copyright
© 2016 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

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
Bae, J. H., Yoo, J. Y. & McEligot, D. M. 2008 Direct numerical simulation of heated CO2 flows at supercritical pressure in a vertical annulus at Re = 8900. Phys. Fluids 20, 055108.CrossRefGoogle Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Clarendon Press.Google Scholar
Chen, H., Goswami, D. Y. & Stefanakos, E. K. 2010 A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renew. Sustainable Energy Reviews 14 (9), 3059–3067.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.CrossRefGoogle Scholar
Debenedetti, P. G., Tom, J. W., Sang-Do, Y. & Gio-Bin, L. 1993 Application of supercritical fluids for the production of sustained delivery devices. J. Control. Release 24 (1), 27–44.CrossRefGoogle Scholar
Dostal, V., Hejzlar, P. & Driscoll, M. J. 2006 The supercritical carbon dioxide power cycle: comparison to other advanced power cycles. Nucl. Technol. 154 (3), 283–301.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.CrossRefGoogle Scholar
Fages, J., Lochard, H., Letourneau, J.-J., Sauceau, M. & Rodier, E. 2004 Particle generation for pharmaceutical applications using supercritical fluid technology. Powder Technol. 141 (3), 219–226.CrossRefGoogle Scholar
Fenghour, A., Wakeham, W. A. & Vesovic, V. 1998 The viscosity of carbon dioxide. J. Phys. Chem. Ref. Data 27 (1), 31–44.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73–L76.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2005 Novel turbulence control strategy for simultaneously achieving friction drag reduction and heat transfer augmentation. In Proceedings of the 4th International Symposium Turbulence and Shear Flow Phenomena, Williamsburg, VA, June, pp. 27–29. Begell House Digital Library.Google Scholar
Fukagata, K. & Kasagi, N. 2003 Drag reduction in turbulent pipe flow with feedback control applied partially to wall. Intl J. Heat Fluid Flow 24 (4), 480–490.CrossRefGoogle Scholar
Gomez, T., Flutet, V. & Sagaut, P. 2009 Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Phys. Rev. E 79 (3), 035301.Google Scholar
Govindarajan, R. & Sahu, K. C. 2014 Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech. 46, 331–353.CrossRefGoogle Scholar
Hetsroni, G. & Rozenblit, R. 1994 Heat transfer to a liquid–solid mixture in a flume. Intl J. Multiphase Flow 20 (4), 671–689.CrossRefGoogle Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Iritani, Y., Kasagi, N. & Hirata, M. 1985 Heat transfer mechanism and associated turbulence structure in the near-wall region of a turbulent boundary layer. In Turbulent Shear Flows, vol. 4, pp. 223–234. Springer.CrossRefGoogle Scholar
Kametani, Y. & Fukagata, K. 2011 Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction. J. Fluid Mech. 681, 154–172.CrossRefGoogle Scholar
Kasagi, N., Kuroda, A. & Hirata, M. 1989 Numerical investigation of near-wall turbulent heat transfer taking into account the unsteady heat conduction in the solid wall. Trans. ASME J. Heat Transfer 111 (2), 385–392.CrossRefGoogle Scholar
Kays, W. M. & Crawford, M. E. 1993 Convective Heat and Mass Transfer. McGraw-Hill.Google 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 (5), 1293–1312.CrossRefGoogle Scholar
Kong, H., Choi, H. & Lee, J. S. 2000 Direct numerical simulation of turbulent thermal boundary layers. Phys. Fluids 12 (10), 2555–2568.CrossRefGoogle Scholar
Koren, B. 1993 A Robust Upwind Discretization Method for Advection, Diffusion and Source Terms. Centrum voor Wiskunde en Informatica Amsterdam.Google Scholar
Kunz, O. & Wagner, W. 2012 The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG-2004. J. Chem. Engng Data 57 (11), 3032–3091.CrossRefGoogle Scholar
Lee, J., Yoon Jung, S., Jin Sung, H. & Zaki, T. A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196–225.CrossRefGoogle Scholar
Lele, S. K. 1994 Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26 (1), 211–254.CrossRefGoogle Scholar
Lemmon, E. W., Huber, M. L. & McLinden, M. O.2013 NIST Standard ReferenceDatabase 23: Reference Fluid Thermodynamic and Transport Properties – REFPROP. Version 9.1. Standard Reference Data Program. National Institute of Standards and Technology.Google Scholar
Li, N. & Laizet, S. 2010 2decomp&fft – a highly scalable 2d decomposition library and fft interface. In Cray User Group Conference, pp. 1–13. CUG Conference Proceedings.Google Scholar
Li, Q., Schlatter, P., Brandt, L. & Henningson, D. S. 2009 DNS of a spatially developing turbulent boundary layer with passive scalar transport. Intl J. Heat Fluid Flow 30 (5), 916–929.CrossRefGoogle Scholar
Ma, Y., Liu, Z. & Tian, H. 2013 A review of transcritical carbon dioxide heat pump and refrigeration cycles. Energy 55, 156–172.CrossRefGoogle Scholar
Matson, D. W., Fulton, J. L., Petersen, R. C. & Smith, R. D. 1987a Rapid expansion of supercritical fluid solutions: solute formation of powders, thin films, and fibers. Ind. Engng Chem. Res. 26 (11), 2298–2306.CrossRefGoogle Scholar
Matson, D. W., Petersen, R. C. & Smith, R. D. 1987b Production of powders and films by the rapid expansion of supercritical solutions. J. Mater. Sci. 22 (6), 1919–1928.CrossRefGoogle Scholar
Mosyak, A., Pogrebnyak, E. & Hetsroni, G. 2001 Effect of constant heat flux boundary condition on wall temperature fluctuations. Trans. ASME J. Heat Transfer 123 (2), 213–218.CrossRefGoogle Scholar
Najm, H. N., Wyckoff, P. S. & Knio, O. M. 1998 A semi-implicit numerical scheme for reacting flow. I: stiff chemistry. J. Comput. Phys. 143 (2), 381–402.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
Saka, S. & Kusdiana, D. 2001 Biodiesel fuel from rapeseed oil as prepared in supercritical methanol. Fuel 80 (2), 225–231.CrossRefGoogle Scholar
Span, R. & Wagner, W. 2003 Equations of state for technical applications. I: simultaneously optimized functional forms for nonpolar and polar fluids. Intl J. Thermophys. 24, 1–39.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Tiselj, I., Bergant, R., Mavko, B., Bajsic, I. & Hetsroni, G. 2001a DNS of turbulent heat transfer in channel flow with heat conduction in the solid wall. Trans. ASME J. Heat Transfer 123 (5), 849–857.CrossRefGoogle Scholar
Tiselj, I. & Cizelj, L. 2012 DNS of turbulent channel flow with conjugate heat transfer at Prandtl number 0.01. Nucl. Engng Des. 253, 153–160.CrossRefGoogle Scholar
Tiselj, I., Pogrebnyak, E., Li, C., Mosyak, A. & Hetsroni, G. 2001b Effect of wall boundary condition on scalar transfer in a fully developed turbulent flume. Phys. Fluids 13 (4), 1028–1039.CrossRefGoogle Scholar
Verzicco, R. & Sreenivasan, K. 2008 A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux. J. Fluid Mech. 595, 203–219.CrossRefGoogle Scholar
Vesovic, V., Wakeham, W., Olchowy, G., Sengers, J., Watson, J. & Millat, J. 1990 The transport properties of carbon dioxide. J. Phys. Chem. Ref. Data 19 (3), 763–808.CrossRefGoogle Scholar
Yoo, J. Y. 2013 The turbulent flows of supercritical fluids with heat transfer. Annu. Rev. Fluid Mech. 45, 495–525.CrossRefGoogle Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2012 Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150–174.CrossRefGoogle Scholar

Nemati et al.supplemenatry movie

Velocity and enthalpy contour plots at a radial plane close to the wall and several cross sectional planes of the pipe.

Download Nemati et al.supplemenatry movie(Video)
Video 7.1 MB