Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T13:30:40.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence attenuation in simultaneously heated and cooled annular flows at supercritical pressure

Published online by Cambridge University Press:  28 June 2016

Jurriaan W. R. Peeters Open the ORCID record for Jurriaan W. R. Peeters [Opens in a new window] ,
R. Pecnik ,
M. Rohde ,
T. H. J. J. van der Hagen  and
B. J. Boersma
Jurriaan W. R. Peeters*
Affiliation:
Energy Technology, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands Nuclear Energy and Radiation Applications, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
R. Pecnik
Affiliation:
Energy Technology, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
M. Rohde
Affiliation:
Nuclear Energy and Radiation Applications, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
T. H. J. J. van der Hagen
Affiliation:
Nuclear Energy and Radiation Applications, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
B. J. Boersma
Affiliation:
Energy Technology, 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

Heated or cooled fluids at supercritical pressure show large variations in thermophysical properties, such as the density, dynamic viscosity and molecular Prandtl number, which strongly influence turbulence characteristics. To investigate this, direct numerical simulations were performed of a turbulent flow at supercritical pressure (CO$_{2}$ at 8 MPa) in an annulus with a hot inner wall and a cold outer wall. The pseudo-critical temperature lies close to the inner wall, which results in strong thermophysical property variations in that region. The turbulent shear stress and the turbulent intensities significantly decrease near the hot inner wall, but increase near the cold outer wall, which can be partially attributed to the mean dynamic viscosity and density stratification. This leads to decreased production of turbulent kinetic energy near the inner wall and vice versa near the outer wall. However, by analysing a transport equation for the coherent streak flank strength, it was found that thermophysical property fluctuations significantly affect streak evolution. Near the hot wall, thermal expansion and buoyancy tend to decrease streak coherence, while the viscosity gradient that exists across the streaks interacts with mean shear to act as either a source or a sink in the evolution equation for the coherent streak flank strength. The formation of streamwise vortices on the other hand is hindered by the torque that is the result of the kinetic energy and density gradients. Near the cold wall, the results are reversed, i.e. the coherent streak flank strength and the streamwise vortices are enhanced due to the variable density and dynamic viscosity. The results show that not only the mean stratification but also the large instantaneous thermophysical property variations that occur in heated or cooled fluids at supercritical pressure have a significant effect on turbulent structures that are responsible for the self-regeneration process in near-wall turbulence. Thus, instantaneous density and dynamic viscosity fluctuations are responsible for decreased (or increased) turbulent motions in heated (or cooled) fluids at supercritical pressure.

JFM classification

Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , pp. 505 - 540
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.Google 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
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.Google Scholar
Bladel, J. 2007 Electromagnetic Fields. Wiley, IEEE Press.Google Scholar
Boersma, B. J. 2011a A 6th order staggered compact finite difference method for the incompressible Navier–Stokes and scalar transport equations. J. Comput. Phys. 230 (12), 4940–4954.CrossRefGoogle Scholar
Boersma, B. J. 2011b Direct numerical simulation of turbulent pipe flow up to a Reynolds number of 61 000. J. Phys.: Conf. Ser. 318.Google Scholar
Boersma, B. J. & Breugem, W.-P. 2011 Numerical simulation of turbulent flow in concentric annuli. Flow Turbul. Combust. 86 (1), 113–127.CrossRefGoogle Scholar
Carr, A. D., Connor, M. A. & Buhr, H. O. 1973 Velocity, temperature, and turbulence measurements in air for pipe flow with combined free and forced convection. Trans. ASME C: J. Heat Transfer 95 (4), 445–452.Google Scholar
Cheng, R. K. & Ng, T. T. 1982 Some aspects of strongly heated turbulent boundary layer flow. Phys. Fluids 25 (8), 1333–1341.Google Scholar
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1–30.Google Scholar
Duan, L., Beekman, I. & Martin, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.Google Scholar
Fenghour, A., Wakeham, W. A. & Vesovic, V. 1998 The viscosity of carbon dioxide. J. Phys. Chem. Ref. Data 27, 31–44.Google Scholar
Gurtin, M. E., Fried, E. & Anand, L. 2010 The Mechanics and Thermodynamics of Continua. Cambridge University Press.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
Jackson, J. D. 2013 Fluid flow and convective heat transfer to fluids at supercritical pressure. Nucl. Engng Des. 264, 24–40.Google Scholar
Jimenez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Kawamura, H., Ohsaka, K., Abe, H. & Yamamoto, K. 1998 DNS of turbulent heat transfer in channel flow with low to medium-high Prandtl number fluid. Intl J. Heat Fluid Flow 19, 482–491.Google Scholar
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. Lond. A 369, 1396–1411.Google Scholar
Kunz, O., Klimeck, R, Wagner, W. & Jaeschke, M.2007 The GERG-2004 wide-range equation of state for natural gases and other mixtures. Tech. Rep., GERG Technical Monograph 15, Fortschritt-Berichte VDI. VDI-Verlag.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 (4), 465–478.Google Scholar
Lee, J., Jung, A. Y., Sung, J. J. & Zaki, T. A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196–225.CrossRefGoogle Scholar
Lemmon, E. W., Huber, M. L. & McLinden, M. O.2013 NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties – REFPROP Version 9.1. Standard Reference Data Program. National Institute of Standards and Technology.Google Scholar
McMurtry, P. D., Jou, W.-H., Riley, J. & Metcalfe, R. W. 1986 Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24 (6), 962–970.Google 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.Google 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.Google Scholar
Nishikawa, K. & Tanaka, I. 1995 Correlation lengths and density fluctuations in supercritical states of carbon dioxide. Chem. Phys. Lett. 244, 149–152.Google 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, 095101.Google Scholar
Petukhov, B. S. & Polyakov, A. F. 1988 Heat Transfer in Turbulent Mixed Convection. Hemisphere.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Shiralkar, B. B. & Griffith, P. 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 (3), 465–471.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google 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, 763–808.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.Google Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. T. & Chen, S. 2012 Effect of compressibility on the small-scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631.Google Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65–92.Google Scholar
Yoo, J. Y. 2013 The turbulent flows of supercritical fluids with heat transfer. Annu. Rev. Fluid Mech. 45 (1), 495–525.Google Scholar
Zappoli, B., Beysens, D. & Garrabos, Y. 2015 Heat Transfers and Related Effects in Supercritical Fluids. Springer.Google Scholar
Zonta, F. 2013 Nusselt number and friction factor in thermally stratified turbulent channel flow under non-Oberbeck–Boussinesq conditions. Intl J. Heat Fluid Flow 44, 489–494.Google Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2012 Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150–174.Google Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2012 Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties. J. Fluid Mech. 697, 175–203.Google Scholar
Zonta, F. & Soldati, A. 2014 Effect of temperature dependent fluid properties on heat transfer in turbulent mixed convection. Trans. ASME: J. Heat Transfer 136, 022501.Google Scholar