Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-31T06:10:22.187Z Has data issue: false hasContentIssue false
  • English
  • Français

Assessment of suboptimal control for turbulent skin friction reduction via resolvent analysis

Published online by Cambridge University Press:  04 September 2017

Satoshi Nakashima ,
Koji Fukagata Open the ORCID record for Koji Fukagata [Opens in a new window]  and
Mitul Luhar Open the ORCID record for Mitul Luhar [Opens in a new window]
Satoshi Nakashima
Affiliation:
Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
Koji Fukagata*
Affiliation:
Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
Mitul Luhar
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles,  CA 90089, USA
*
†Email address for correspondence: fukagata@mech.keio.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to elucidate the drag reduction mechanisms for the suboptimal control laws proposed by Lee, Kim & Choi (J. Fluid Mech., vol. 358, 1998, pp. 245–258). Under the resolvent formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes identified via a gain-based decomposition of the Navier–Stokes equations. This decomposition enables targeted analyses of the effects of suboptimal control on high-gain modes that serve as useful low-order models for dynamically important coherent structures such as the near-wall (NW) cycle or very-large-scale motions. The control laws generate blowing and suction at the wall that is proportional to the fluctuating streamwise (Case ST) or spanwise (Case SP) wall shear stress, with the magnitude of blowing and suction being a design parameter. It is shown that both Case ST and SP can suppress resolvent modes resembling the NW cycle. However, for Case ST, the analysis reveals that control leads to substantial amplification of flow structures that are long in the spanwise direction. Quantitative comparisons show that these predictions are broadly consistent with results obtained in previous direct numerical simulations. Further, the predicted changes in mode structure suggest that suboptimal control can be considered a modified version of opposition control. In addition to the study of modes resembling the NW cycle, this paper also considers modes of varying speed and wavelength to provide insight into the effects of suboptimal control across spectral space.

JFM classification

Flow Control: Drag reduction Flow Control: Flow Control Turbulent Flows: Turbulent Flows

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 496 - 526
Check for updates
Copyright
© 2017 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.)

Article purchase

Temporarily unavailable

References

Abdulbari, H. A., Yunus, R. M., Abdurahman, N. H. & Charles, A. 2013 Going against the flow – a review of non-additive means of drag reduction. J. Ind. Engng Chem. 19, 27–36.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.Google Scholar
Chang, Y., Collis, S. S. & Ramakrishnan, S. 2002 Viscous effects in control of near-wall turbulence. Phys. Fluids 14, 4069–4080.CrossRefGoogle Scholar
Chernyshenko, S. I. & Baig, M. F. 2005 The mechanism of streak formation in near-wall turbulence. J. Fluid Mech. 544, 99–131.CrossRefGoogle Scholar
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
Choi, J.-I. & Sung, H. J. 2002 Assessment of suboptimal control for drag reduction in turbulent channel flow. J. Turbul. 3 (29), 1–17.Google Scholar
Chung, Y. M. & Talha, T. 2011 Effectiveness of active flow control for turbulent skin friction drag reduction. Phys. Fluids 23, 025102.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.Google Scholar
Fukagata, K. & Kasagi, N. 2003 Drag reduction in turbulent pipe flow with feedback control applied partially to wall. Intl J. Heat Fluid Flow 24, 480–490.CrossRefGoogle Scholar
Fukagata, K. & Kasagi, N. 2004 Suboptimal control for drag reduction via suppression of near-wall Reynolds shear stress. Intl J. Heat Fluid Flow 25, 341–350.Google Scholar
Fukagata, K., Kasagi, N. & Koumoutsakos, P. 2006 A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18, 051703.Google Scholar
Gad-el-Hak, M. 1994 Interactive control of turbulent boundary layers-a futuristic overview. AIAA J. 32, 1753–1765.CrossRefGoogle Scholar
Gad-el-Hak, M. 2000 Flow Control: Passive, Active, and Reactive Flow Management. 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
Hammond, E. P., Bewley, T. R. & Moin, P. 1998 Observed mechanisms for turbulence attenuation and enhancement in opposition controlled wall-bounded flows. Phys. Fluids 10, 2421–2423.CrossRefGoogle Scholar
Hoepffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171–187.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.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
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.Google Scholar
Karniadakis, G. E. & Choi, K.-S. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62.Google Scholar
Kasagi, N., Suzuki, Y. & Fukagata, K. 2009 Microelectromechanical systems-based feedback control of turbulence for skin friction reduction. Annu. Rev. Fluid Mech. 41, 231–251.Google Scholar
Kawahara, G. & Kida, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291–300.Google Scholar
Kim, J. 2003 Control of turbulent boundary layers. Phys. Fluids 15, 1093–1105.CrossRefGoogle Scholar
Kim, J. & Lim, J. 2000 A linear process in wall-bounded turbulent shear flows. Phys. Fluids 12, 1885–1888.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully-developed channel flow at low Reynolds-number. J. Fluid Mech. 177, 133–166.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadl, P. W. 1967 Structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.Google Scholar
Lee, C., Kim, J. & Choi, H. 1998 Suboptimal control of turbulent channel flow for drag reduction. J. Fluid Mech. 358, 245–258.CrossRefGoogle Scholar
Lieu, B. K., Moarref, R. & Jovanović, M. R. 2010 Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation. J. Fluid Mech. 663, 100–119.Google Scholar
Lim, J. & Kim, J. 2004 A singular value analysis of boundary layer control. Phys. Fluids 16, 1980–1988.CrossRefGoogle Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2014 Opposition control within the resolvent analysis framework. J. Fluid Mech. 749, 597–626.Google Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415–441.Google Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2016 On the design of optimal compliant walls for turbulence control. J. Turbul. 17, 787–806.Google Scholar
Mamori, H., Iwamoto, K. & Murata, A. 2014 Effect of the parameters of traveling waves created by blowing and suction on the relaminarization phenomena in fully developed turbulent channel flow. Phys. Fluids 26, 015101.CrossRefGoogle Scholar
Mamori, H., Fukagata, K. & Hoepffner, J. 2010 Phase relationship in laminar channel flow controlled by traveling-wave-like blowing or suction. Phys. Rev. E 81, 046304.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.Google Scholar
McKeon, B. J., Jacobi, I. & Sharma, A. S. 2013 Experimental manipulation of wall turbulence: a systems approach. Phys. Fluids 25, 031301.Google Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
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.Google Scholar
Moarref, R. & Jovanović, M. R. 2010 Controlling the onset of turbulence by streamwise travelling waves. Part 1. Receptivity analysis. J. Fluid Mech. 663, 70–99.Google Scholar
Moarref, R., Sharma, A. S., Tropp, J. A. & McKeon, B. J. 2013 Model-based scaling and prediction of the streamwise energy intensity in high-Reynolds number turbulent channels. J. Fluid Mech. 734, 275–316.Google Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.Google Scholar
Nakanishi, R., Mamori, H. & Fukagata, K. 2012 Relaminarization of turbulent channel flow using traveling wave-like wall deformation. Intl J. Heat Fluid Flow 35, 152–159.Google Scholar
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. Lond. A 369, 1428–1442.Google Scholar
Reynolds, W. C. & Tiederman, W. G. 1967 Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech. 27, 253–272.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary-layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Sharma, A. S. & McKeon, B. J. 2013 On coherent structure in wall turbulence. J. Fluid Mech. 728, 196–238.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Tomiyama, N. & Fukagata, K. 2013 Direct numerical simulation of drag reduction in a turbulent channel flow using spanwise traveling wave-like wall deformation. Phys. Fluids 25, 105115.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.Google Scholar
Walsh, M. J. & Weinstein, L. M. 1979 Drag and heat-transfer characteristics of small longitudinally ribbed surfaces. AIAA J. 17, 770–771.Google Scholar
Weideman, J. A. & Reddy, S. C. 2000 A matlab differentiation matrix suite. ACM Trans. Math. Softw. 26, 465–519.Google Scholar
Yoshino, T., Suzuki, Y. & Kasagi, N. 2008 Drag reduction of turbulence air channel flow with distributed micro sensors and actuators. J. Fluid Sci. Technol. 3, 137–148.Google Scholar