Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-17T16:16:07.122Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity

Published online by Cambridge University Press:  31 May 2013

Jin Lee ,
Seo Yoon Jung ,
Hyung Jin Sung  and
Tamer A. Zaki
Jin Lee
Affiliation:
Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Korea
Seo Yoon Jung
Affiliation:
Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Hyung Jin Sung
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Korea
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) of turbulent boundary layers over isothermally heated walls were performed, and the effect of viscosity stratification on the turbulence statistics and skin friction were investigated. An empirical relation for temperature-dependent viscosity for water was adopted. Based on the free-stream temperature (30°C), two wall temperatures (70°C and 99°C) were selected. In the heated flows, the turbulence energy diminishes in the buffer layer, but increases near the wall. The reduction in turbulence kinetic energy in the buffer layer is accompanied by smaller levels of Reynolds shear stresses and, hence, weaker turbulence production. The enhanced turbulence energy near the wall is attributed to enhanced transfer of energy via additional diffusion-like terms due to the viscosity stratification. Despite the lower fluid viscosity near the wall, dissipation is also increased owing to the augmented near-wall fine-scale motion. Wall heating results in reduction in the skin-friction coefficient by up to 26 %. An evaluation of the different contributions to the skin friction demonstrates that drag reduction is primarily due to the changes in the Reynolds shear stresses across the boundary layer. Quadrant and octant analyses showed that ejections (Q2) and sweeps (Q4) are significantly reduced, a result further supported by an examination of outer vortical structures from linear stochastic estimation of the ejection events and spanwise vortices.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 196 - 225
Copyright
©2013 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

Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.Google Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292.CrossRefGoogle Scholar
Brodkey, R. S., Wallace, J. M. & Eckelmann, H 1974 Some properties of truncated turbulence signals in bounded shear flows. J. Fluid Mech. 63, 209–224.CrossRefGoogle Scholar
Bushnell, D. M. & Moore, K. J. 1991 Drag reduction in nature. Annu. Rev. Fluid Mech. 23, 65–79.Google Scholar
Ceccio, S. L. 2010 Friction drag reduction of external flows with bubble and gas injection. Annu. Rev. Fluid Mech. 42, 183–203.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.Google Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.Google Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.Google Scholar
Dixit, S. A. & Ramesh, O. N. 2010 Large-scale structures in turbulent and reverse-transitional sink flow boundary layers. J. Fluid Mech. 649, 233–273.Google Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73–L76.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.Google Scholar
Incropera, F. P. & Dewitt, D. P. 1985 Fundamentals of Heat and Mass Transfer. John Wiley and Sons.Google Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kader, B. A. 1981 Temperature and concentration profiles in fully-turbulent boundary layers. Intl J. Heat Mass Transfer 24, 1541–1544.Google 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, K., Li, C.-F., Sureshkumar, R., Balachandar, S. & Adrian, R. J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281–299.Google Scholar
Kong, H., Choi, H. & Lee, J. S. 2000 Direct numerical simulation of turbulent thermal boundary layers. Phys. Fluids 12, 2555–2568.CrossRefGoogle Scholar
Kral, L. D. & Fasel, H. F. 1994 Direct numerical simulation of passive control of three-dimensional phenomena in boundary-layer transition using wall heating. J. Fluid Mech. 264, 213–254.Google Scholar
Kravchenko, A. G., Choi, H. & Moin, P. 1993 On the relation of nearwall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5, 3307–3309.CrossRefGoogle Scholar
Lauchle, G. C. & Gurney, G. B. 1984 Laminar boundary-layer transition on a heated underwater body. J. Fluid Mech. 144, 79–101.Google Scholar
Lee, J.-H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101–131.CrossRefGoogle Scholar
Li, Q. 2011 Direct and large-eddy simulations of turbulent boundary layers with heat transfer. PhD thesis, Royal Institute of Technology (KTH), Stockholm, Sweden.Google Scholar
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M. & Smits, A. J. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16, L55–L58.CrossRefGoogle Scholar
Min, T., Yoo, J. Y., Choi, H. & Joseph, D. D. 2003 Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213–238.Google Scholar
Moin, P., Adrian, R. J. & Kim, J. 1987 Stochastic estimation of organized structures in turbulent channel flow. In Proceedings of 6th Symposium on Turbulent Shear Flows, Toulouse, France, pp. 16.9.1–16.9.8.Google Scholar
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.CrossRefGoogle Scholar
Nourgaliev, R. R. & Theofanous, T. G. 2007 High-fidelity interface tracking in compressible flows: unlimited anchored adaptive level set. J. Comput. Phys. 224, 836–866.CrossRefGoogle Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802–811.CrossRefGoogle Scholar
Ricco, P., Ottonelli, C., Hasegawa, Y. & Quadrio, M. 2012 Changes in turbulent dissipation in a channel flow with oscillating walls. J. Fluid Mech. 700, 77–104.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.Google Scholar
Rosenfeld, M., Kwak, D. & Vinokur, M. 1991 A fractional step solution method for the unsteady incompressible Navier–Stokes equations in generalized coordinate systems. J. Comput. Phys. 94, 102–137.Google Scholar
Sameen, A. & Govindarajan, R. 2007 The effect of wall heating on instability of channel flow. J. Fluid Mech. 577, 417–442.Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
Smits, A. J., Matheson, N. & Joubert, P. N. 1983 Low-Reynolds-number turbulent boundary layers in zero and favourable pressure gradients. J. Ship Res. 27, 147–157.Google Scholar
Soria, J., Sondergaard, R., Cantwell, B. J., Chong, M. S. & Perry, A. E. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6, 871–884.Google Scholar
Tiselj, I., Pogrebnyak, E., Li, C., Mosyak, A. & Hetsroni, G. 2001 Effect of wall boundary condition on scalar transfer in a fully developed turbulent flume. Phys. Fluids 13, 1028–1039.CrossRefGoogle Scholar
Wall, D. P. & Wilson, S. K. 1996 The linear stability of channel flow of fluid with temperature-dependent viscosity. J. Fluid Mech. 323, 107–132.Google Scholar
Wall, D. P. & Wilson, S. K. 1997 The linear stability of flat-plate boundary-layer flow of fluid with temperature-dependent viscosity. Phys. Fluids 9, 2885–2898.Google Scholar
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.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
Wu, X. & Moin, P. 2010 Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22, 085105.CrossRefGoogle Scholar
Zaki, T. A., Wissink, J. G., Rodi, W. & Durbin, P. A. 2010 Direct numerical simulations of transition in a compressor cascade: the influence of free stream turbulence. J. Fluid Mech. 665, 57–98.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