Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T03:47:29.389Z Has data issue: false hasContentIssue false
  • English
  • Français

A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer

Published online by Cambridge University Press:  03 February 2016

Nicolas Renard  and
Sébastien Deck
Nicolas Renard
Affiliation:
ONERA, The French Aerospace Lab, F-92190 Meudon, France
Sébastien Deck*
Affiliation:
ONERA, The French Aerospace Lab, F-92190 Meudon, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical decomposition of mean skin friction generation into physical phenomena across the whole profile of the incompressible zero-pressure-gradient smooth-flat-plate boundary layer is derived from a mean streamwise kinetic-energy budget in an absolute reference frame (in which the undisturbed fluid is not moving). The Reynolds-number dependences in the laminar and turbulent cases are investigated from direct numerical simulation datasets and Reynolds-averaged Navier–Stokes simulations, and the asymptotic trends are consistently predicted by theory. The generation of the difference between the mean friction in the turbulent and laminar cases is identified with the total production of turbulent kinetic energy (TKE) in the boundary layer, represented by the second term of the proposed decomposition of the mean skin friction coefficient. In contrast, the analysis introduced by Fukagata et al. (Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), based on a streamwise momentum budget in the wall reference frame, relates the turbulence-induced excess friction to the Reynolds shear stress weighted by a linear function of the wall distance. The wall-normal distribution of the linearly-weighted Reynolds shear stress differs from the distribution of TKE production involved in the present discussion, which consequently draws different conclusions on the contribution of each layer to the mean skin friction coefficient. At low Reynolds numbers, the importance of the buffer-layer dynamics is confirmed. At high Reynolds numbers, the present decomposition quantitatively shows for the first time that the generation of the turbulence-induced excess friction is dominated by the logarithmic layer. This is caused by the well-known decay of the relative contributions of the buffer layer and wake region to TKE production with increasing Reynolds numbers. This result on mean skin friction, with a physical interpretation relying on an energy budget, is consistent with the well-established general importance of the logarithmic layer at high Reynolds numbers, contrary to the friction breakdown obtained from the approach of Fukagata et al. (Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), essentially based on a momentum budget. The new decomposition suggests that it may be worth investigating new drag reduction strategies focusing on TKE production and on the nature of the logarithmic layer dynamics. The decomposition is finally extended to the pressure-gradient case and to channel and pipe flows.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 339 - 367
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

Adeyinka, O. B. & Naterer, G. F. 2004 Modeling of entropy production in turbulent flows. Trans. ASME J. Fluids Engng 126, 893–899.Google Scholar
Arntz, A. & Atinault, O. 2015 Exergy-based performance assessment of a blended wing-body with boundary-layer ingestion. AIAA J 53 (12), 3766–3776.Google Scholar
Arntz, A., Atinault, O. & Merlen, A. 2015 Exergy-based formulation for aircraft aeropropulsive performance assessment: theoretical development. AIAA J. 53 (6), 1627–1639.Google Scholar
Aupoix, B.2010 Couches Limites Bidimensionnelles Compressibles. Descriptif et Mode demploi du Code CLICET – Version 2010. Tech Rep. RT 1/117015 DMAE. Onera.Google Scholar
Aupoix, B., Pailhas, G. & Houdeville, R. 2012 Towards a general strategy to model riblet effects. AIAA J. 50 (3), 708–716.Google Scholar
Aupoix, B. & Spalart, P. R. 2003 Extensions of the Spalart–Allmaras turbulence model to account for wall roughness. Intl J. Heat Fluid Flow 24, 454–462.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665–681.Google Scholar
Bannier, A., Garnier, E. & Sagaut, P. 2015 Riblet flow model based on an extended FIK identity. Flow Turbul. Combust. 95 (2), 351–367.Google Scholar
Cousteix, J. 1989 Aérodynamique. Turbulence et couche limite, Cepadues Editions.Google Scholar
Deck, S., Renard, N., Laraufie, R. & Weiss, P.-E. 2014 Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to $Re_{{\it\theta}}=13\hspace{2.22198pt}650$ . J. Fluid Mech. 743, 202–248.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.Google Scholar
Destarac, D. 2003 Far-field/near-field drag balance and applications of drag extraction in CFD. In CFD-Based Aircraft Drag Prediction and Reduction, VKI Lecture Series, pp. 1–65. Von Karman Inst. for Fluid Dynamics.Google Scholar
Drela, M. 2009 Power balance in aerodynamic flows. AIAA J. 47 (7), 1761–1771.Google Scholar
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to $Re_{{\it\theta}}=8300$ . Intl J. Heat Fluid Flow 47, 57–69.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), 73–76.CrossRefGoogle Scholar
García-Mayoral, R. & Jiménez, J. 2011 Drag reduction by riblets. Phil. Trans. R. Soc. Lond. A 369, 1412–1427.Google Scholar
George, W. K. 2006 Recent advancements toward the understanding of turbulent boundary layers. AIAA J. 44 (11), 2435–2449.Google Scholar
Hinze, J. O. 1959 Turbulence: An Introduction to its Mechanism and Theory. McGraw-Hill.Google Scholar
Iwamoto, K., Fukagata, K., Kasagi, N. & Suzuki, Y. 2005 Friction drag reduction achievable by near-wall turbulence manipulation at high Reynolds numbers. Phys. Fluids 17, 011702.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25, 101302.Google Scholar
Jones, W. P. & Launder, B. E. 1972 The prediction of laminarization with a two-equation model of turbulence. Intl J. Heat Mass Transfer 15 (2), 301–314.Google 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.Google Scholar
Kametani, Y., Fukagata, K., Örlü, R. & Schlatter, P. 2015 Effect of uniform blowing/suction in a turbulent boundary layer at moderate Reynolds number. Intl J. Heat Fluid Flow 55, 132–142.Google Scholar
Laadhari, F. 2007 Reynolds number effect on the dissipation function in wall-bounded flows. Phys. Fluids 19, 038101,1–4.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418–428.Google Scholar
Mehdi, F., Johansson, T. G., White, C. M. & Naughton, J. W. 2014 On determining wall shear stress in spatially developing two-dimensional wall-bounded flows. Exp. Fluids 55, 1656,1–9.Google Scholar
Michel, R., Quémard, C. & Durant, R.1969 Application d’un schéma de longueur de mélange à l’étude des couches limites turbulentes d’équilibre. Note Technique 154. ONERA.Google Scholar
Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101,1–12.Google Scholar
Nagib, H. M., Chauhan, K. A & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755–770.Google Scholar
Orlandi, P. & Jiménez, J. 1994 On the generation of turbulent wall friction. Phys. Fluids 6, 634–641.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.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
Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill.Google Scholar
Sillero, J. A., Jimenez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to ${\it\delta}^{+}\approx 2000$ . Phys. Fluids 25, 105102.Google Scholar
Sillero, J. A., Jimenez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to ${\it\delta}^{+}\approx 2000$ . Phys. Fluids 26, 105109.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.Google Scholar
Spalart, P. R. & McLean, J. D. 2011 Drag reduction: enticing turbulence, and then an industry. Phil. Trans. R. Soc. Lond. A 369, 1556–1569.Google ScholarPubMed
Sreenivasan, K. R. 1995 The energy dissipation in turbulent shear flows. In Symposium on Developments in Fluid Dynamics and Aerospace Engineering (ed. Deshpande, S. M., Prabhu, A., Sreenivasan, K. R. & Viswanath, P. R.), pp. 159–190. Interline Publishers.Google Scholar
Stroh, A., Frohnapfel, B., Schlatter, P. & Hasegawa, Y. 2015 A comparison of opposition control in turbulent boundary layer and turbulent channel flow. Phys. Fluids 27, 075101.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Toubin, H. & Bailly, D. 2015 Development and application of a new unsteady far-field drag decomposition method. AIAA J. 53 (11), 3414–3429.CrossRefGoogle Scholar
van der Vooren, J. & Destarac, D. 2004 Drag/thrust analysis of jet-propelled transonic transport aircraft; Definition of physical drag components. Aerosp. Sci. Technol. 8, 545–556.Google Scholar