Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-01T02:43:37.652Z Has data issue: false hasContentIssue false
  • English
  • Français

Money versus time: evaluation of flow control in terms of energy consumption and convenience

Published online by Cambridge University Press:  30 April 2012

Bettina Frohnapfel ,
Yosuke Hasegawa  and
Maurizio Quadrio
Bettina Frohnapfel
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany
Yosuke Hasegawa
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany Department of Mechanical Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan
Maurizio Quadrio*
Affiliation:
Dipartimento di Ingegneria Aerospaziale del Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Flow control with the goal of reducing the skin-friction drag on the fluid–solid interface is an active fundamental research area, motivated by its potential for significant energy savings and reduced emissions in the transport sector. Customarily, the performance of drag reduction techniques in internal flows is evaluated under two alternative flow conditions, i.e. at constant mass flow rate or constant pressure gradient. Successful control leads to reduction of drag and pumping power within the former approach, whereas the latter leads to an increase of the mass flow rate and pumping power. In practical applications, however, money and time define the flow control challenge: a compromise between the energy expenditure (money) and the corresponding convenience (flow rate) achieved with that amount of energy has to be reached so as to accomplish a goal which in general depends on the specific application. Based on this idea, we derive two dimensionless parameters which quantify the total energy consumption and the required time (convenience) for transporting a given volume of fluid through a given duct. Performances of existing drag-reduction strategies as well as the influence of wall roughness are re-evaluated within the present framework; how to achieve the (application-dependent) optimum balance between energy consumption and convenience is addressed. It is also shown that these considerations can be extended to external flows.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 406 - 418
Copyright
Copyright © Cambridge University Press 2012

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

1. Bewley, T. R. 2009 A fundamental limit on the balance of power in a transpiration-controlled channel flow. J. Fluid Mech. 632, 443–446.CrossRefGoogle Scholar
2. 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
3. Colebrook, C. F. 1939 Turbulent flows in pipes with particular reference to the transition between the smooth- and rough-pipe laws. J. Inst. Civil Engrs Lond. 11, 133–156.CrossRefGoogle Scholar
4. Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME I: J. Fluids Engng 100, 215.Google Scholar
5. Delfos, R., Hoving, J., Westerweel, J. & Boersma, B. J. 2011 Experiments on drag reduction by fibres in turbulent flows. In Euromech Meeting 513: Dynamics of Non-spherical Particles in Fluid Turbulence, April 6–8, 2011, Udine (I).Google Scholar
6. Frohnapfel, B., Jovanović, J. & Delgado, A. 2007 Experimental investigation of turbulent drag reduction by surface-embedded grooves. J. Fluid Mech. 590, 107–116.CrossRefGoogle Scholar
7. 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
8. Fukagata, K., Sugiyama, K. & Kasagi, N. 2009 On the lower bound of net driving power in controlled duct flows. Physica D 238, 1082–1086.CrossRefGoogle Scholar
9. Garcia-Mayoral, R. & Jiménez, J. 2011 Hydrodynamic stability and the breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317–347.CrossRefGoogle Scholar
10. Grüneberger, R. & Hage, W. 2011 Drag characteristics of longitudinal and transverse riblets at low dimensionless spacings. Exp. Fluids 50 (2), 363–373.CrossRefGoogle Scholar
11. Hœpffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171–187.CrossRefGoogle Scholar
12. Itoh, M., Tamano, S., Iguchi, R., Yokota, K., Akino, N., Hino, R. & Kubo, S. 2006 Turbulent drag reduction by the seal fur surface. Phys. Fluids 18, 065102.CrossRefGoogle Scholar
13. Iwamoto, K., Suzuki, Y. & Kasagi, N. 2002 Reynolds number effect on wall turbulence: toward effective feedback control. Intl J. Heat Fluid Flow 23, 678–689.CrossRefGoogle Scholar
14. Jung, W. J., Mangiavacchi, N. & Akhavan, R. 1992 Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4 (8), 1605–1607.CrossRefGoogle Scholar
15. Kasagi, N., Hasegawa, Y. & Fukagata, K. 2009 Towards Cost-effective Control of Wall Turbulence for Skin-friction Drag Reduction, Advances in Turbulence XII , vol. 132, pp. 189–200. Springer.Google Scholar
16. Lee, W. K., Vaselesky, R. C. & Metzner, A. B. 1974 Turbulent drag reduction in polymerics solutions containing suspended fibres. AIChE J. 20 (1), 128–133.CrossRefGoogle Scholar
17. Marusic, I., Joseph, D. D. & Mahesh, K. 2007 Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570, 467–477.CrossRefGoogle Scholar
18. Min, T., Kang, S. M., Speyer, J. L. & Kim, J. 2006 Sustained sub-laminar drag in a fully developed channel flow. J. Fluid Mech. 558, 309–318.CrossRefGoogle Scholar
19. Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillation. J. Fluid Mech. 521, 251–271.CrossRefGoogle Scholar
20. Quadrio, M. & Ricco, P. 2011 The laminar generalized Stokes layer and turbulent drag reduction. J. Fluid Mech. 667, 135–157.CrossRefGoogle Scholar
21. Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.CrossRefGoogle Scholar
22. Schlichting, H. 1979 Boundary-layer Theory. McGraw Hill.Google Scholar
23. Spalart, P. R. & McLean, J. D. 2011 Drag reduction: enticing turbulence, and then an industry. Phil. Trans. R. Soc. Lond. A 369 (1940), 1556–1569.Google ScholarPubMed
24. Virk, P. S., Mickley, H. S. & Smith, K. A. 1974 The ultimate asymptote and mean flow structure in Tom’s phenomenon. J. Appl. Mech. 37 (2), 488–493.CrossRefGoogle Scholar