Skip to main content Accessibility help
×
Home

The linear response of turbulent flow to a volume force: comparison between eddy-viscosity model and DNS

  • S. Russo (a1) and P. Luchini (a2)

Abstract

We identify a benchmark problem simple enough that it can be solved both by an eddy-viscosity model and by direct numerical simulation: this is the linear response of a turbulent flow’s mean-velocity profile to an external volume force. An example of such a force was found in a study of the perturbation induced by bottom topography by Luchini & Charru (J. Fluid Mech., vol. 656, 2010, pp. 337–341). On the other hand, a modification of the method by Quadrio & Luchini (Proceedings of the IX European Turbulence Conference, Southampton, UK, 2002, pp. 715–718) and Luchini et al. (Phys. Fluids, vol. 18, 2006, 121702) to compute the linear impulse response of a wall-bounded turbulent flow allows the response to a volume force to be computed directly. The comparison exhibits significant differences and suggests that there might be fundamental obstacles to designing an eddy-viscosity model that provides the correct result.

Copyright

Corresponding author

Email address for correspondence: aneres85@gmail.com

References

Hide All
Abrams, J. 1979 A nonlinear boundary layers analysis for turbulent flow over a solid wavy surface. University of Illinois, Department of Chemical Engineering, Urbana/IL, USA.
del Alamo, J. C. & Jimenez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.
Cess, R. D.1958 A survey of the literature on heat transfer in turbulent tube flow. Rep. 8-0529-R24, Westinghouse Research.
Frederick, K. A. & Hanratty, T. J. 1988 Velocity measurements for a turbulent non separated flow over solid waves. Exp. Fluids 6, 477486.
Frohnapfel, B., Hasegawa, Y. & Quadrio, M. 2012 Money versus time: evaluation of flow control in terms of energy consumption and convenience. J. Fluid Mech. 700, 406418.
Hamilton, J. 1994 Time Series Analysis, 1st edn. Princeton University Press.
Hasegawa, Y., Quadrio, M. & Frohnapfel, B. 2014 Numerical simulation of turbulent duct flows with constant power input. J. Fluid Mech. 750, 191209.
Henn, D. S. & Sykes, R. I. 1999 Large-eddy simulation of flow over wavy surfaces. J. Fluid Mech. 383, 75112.
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hœpffner, J. & Fukagata, K. 2009 Pumping or drag reduction. J. Fluid Mech. 635, 171187.
Hoyas, S. & Jimenez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_{{\it\tau}}=2003$ . Phys. Fluids 18, 011702.
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41 (2), 241258.
Jackson, P. S. & Hunt, J. C. R. 1975 Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929955.
Jimenez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89117.
Luchini, P. 2008 Acoustic streaming and lower-than-laminar drag in controlled channel flow. In Progress in Industrial Mathematics at ECMI 2006, vol. 12, pp. 169177. Springer.
Luchini, P. & Charru, F. 2010a Consistent section-averaged equations of quasi-one-dimensional laminar flow. J. Fluid Mech. 656, 337341.
Luchini, P. & Charru, F. 2010b The phase lead of shear stress in shallow-water flow over a perturbed bottom. J. Fluid Mech. 665, 516539.
Luchini, P., Quadrio, M. & Zuccher, S. 2006 The phase-locked mean impulse response of a turbulent channel flow. Phys. Fluids 18, 121702.
McLean, J. W. 1983 Computation of turbulent flow over a moving wavy boundary. Phys. Fluids 26, 20652073.
Meketon, M. S. & Schmeiser, B. 1984 Overlapping batch means: something for nothing? In Winter Simulation Conference, pp. 227230. IEEE Press.
Myong, H. K. & Kasagi, N. 1990 New approach to the improvement of – turbulence model for wall-bounded shear flows. JSME Intl J. 33 (1), 6372.
Kasagi, N., Hasegawa, Y. & Fukagata, K. 2009 Towards cost-effective control of wall turbulence for skin-friction drag reduction. In Advances in Turbulence XII, vol. 132, pp. 189200. Springer.
Nezu, I. & Rodi, W. 1986 Open-channel flow measurements with a laser Doppler anemometer. J. Hydraul. Engng 112, 335355.
Patel, V. C., Rodi, W. & Scheuerer, G. 1985 Turbulence models for near-wall and low Reynolds number flows – A review. AIAA J. 23 (9), 13081319.
Pope, S. B. 2011 Turbulence Modeling for CFD, 11th edn. Cambridge University Press.
Quadrio, M. & Luchini, P. 2002 The linear response of turbulent channel flow. In Proceedings of the IX European Turbulence Conference, Southampton, UK, pp. 715718.
Quadrio, M. & Luchini, P. 2006 A low-cost parallel implementation of direct numerical simulation of wall turbulence. J. Comput. Phys. 211 (2), 551571.
Quadrio, M. & Ricco, P. 2011 The laminar generalized Stokes layer and turbulent drag reduction. J. Fluid Mech. 667, 135157.
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263288.
Sarkar, A. & So, R. M. C. 1997 A critical evaluation of near-wall two-equation models against direct numerical simulation data. Intl J. Heat Fluid Flow 18 (2), 197208.
Wilcox, D. C. 1993 Turbulence Modeling for CFD, 1st edn. DCW Industries, Inc.
Zilker, D. P., Cook, G. W. & Hanratty, T. J. 1977 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J. Fluid Mech. 82, 2951.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

The linear response of turbulent flow to a volume force: comparison between eddy-viscosity model and DNS

  • S. Russo (a1) and P. Luchini (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed