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A framework for studying the effect of compliant surfaces on wall turbulence

Published online by Cambridge University Press:  10 March 2015

M. Luhar ,
A. S. Sharma  and
B. J. McKeon
M. Luhar
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA
A. S. Sharma
Affiliation:
Engineering and the Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
B. J. McKeon
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA
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Abstract

This paper extends the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider turbulence–compliant wall interactions. Under this 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. Compliant surfaces, modelled as a complex wall admittance linking pressure and velocity, affect the gain and structure of these modes. With minimal computation, this framework accurately predicts the emergence of the quasi-two-dimensional propagating waves observed in recent direct numerical simulations. Further, the analysis also enables the rational design of compliant surfaces, with properties optimized to suppress flow structures energetic in wall turbulence. It is shown that walls with unphysical negative damping are required to interact favourably with modes resembling the energetic near-wall cycle, which could explain why previous studies have met with limited success. Positive-damping walls are effective for modes resembling the so-called very-large-scale motions, indicating that compliant surfaces may be better suited for application at higher Reynolds number. Unfortunately, walls that suppress structures energetic in natural turbulence are also predicted to have detrimental effects elsewhere in spectral space. Consistent with previous experiments and simulations, slow-moving spanwise-constant structures are particularly susceptible to further amplification. Mitigating these adverse effects will be central to the development of compliant coatings that have a net positive influence on the flow.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Drag reduction Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 415 - 441
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Copyright
© 2015 Cambridge University Press 

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References

Benjamin, T. B. 1960 Effects of a flexible boundary on hydrodynamic stability. J. Fluid Mech. 9, 513–532.CrossRefGoogle Scholar
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450.Google Scholar
Bourguignon, J.-L., Tropp, J. A., Sharma, A. S. & McKeon, B. J. 2014 Compact representation of wall-bounded turbulence using compressive sampling. Phys. Fluids 26, 015109.Google Scholar
Bushnell, D. M., Hefner, J. N. & Ash, R. L. 1977 Effect of compliant wall motion on turbulent boundary layers. Phys. Fluids 20, S31–S48.Google Scholar
Carpenter, P. W. 1990 Status of transition delay using compliant walls. In Viscous Drag Reduction in Boundary Layers (ed. Bushnell, D. M. & Hefner, J. N.), Progress in Aeronautics and Astronautics, vol. 123, pp. 79–113. AIAA.Google Scholar
Carpenter, P. W., Davies, C. & Lucey, A. D. 2000 Hydrodynamics and compliant walls: does the dolphin have a secret? Curr. Sci. 79, 758–765.Google Scholar
Carpenter, P. W. & Garrad, A. D. 1985 The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien–Schlichting instabilities. J. Fluid Mech. 155, 465–510.Google Scholar
Carpenter, P. W. & Garrad, A. D. 1986 The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech. 170, 199–232.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.CrossRefGoogle Scholar
Choi, K. S., Yang, X., Clayton, B. R., Glover, E. J., Atlar, M., Semenov, B. N. & Kulik, V. M. 1997 Turbulent drag reduction using compliant surfaces. Proc. R. Soc. Lond. A 453 (1965), 2229–2240.Google Scholar
Davies, C. & Carpenter, P. W. 1997 Instabilities in a plane channel flow between compliant walls. J. Fluid Mech. 352, 205–243.Google Scholar
Dixon, A. E., Lucey, A. D. & Carpenter, P. W. 1994 Optimization of viscoelastic compliant walls for transition delay. AIAA J. 32 (2), 256–267.Google Scholar
Duncan, J. H. 1986 The response of an incompressible viscoelastic coating to pressure fluctuations in a turbulent boundary layer. J. Fluid Mech. 171, 339–363.CrossRefGoogle Scholar
Endo, T. & Himeno, R. 2002 Direct numerical simulation of turbulent flow over a compliant surface. J. Turbul. 3, 1–10.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 (11), 73–76.Google Scholar
Fukagata, K., Kern, S., Chatelain, P., Koumoutsakos, P. & Kasagi, N. 2008 Evolutionary optimization of an anisotropic compliant surface for turbulent friction drag reduction. J. Turbul. 9 (35), 1–17.Google Scholar
Gad-el-Hak, M. 1986 The response of elastic and viscoelastic surfaces to a turbulent boundary layer. Trans. ASME: J. Appl. Mech. 53 (1), 206–212.Google Scholar
Gad-el-Hak, M. 2000 Flow Control: Passive, Active, and Reactive Flow Management. Cambridge University Press.CrossRefGoogle Scholar
Gad-el-Hak, M., Blackwelder, R. F. & Riley, J. J. 1984 On the interaction of compliant coatings with boundary-layer flows. J. Fluid Mech. 140, 257–280.CrossRefGoogle Scholar
Hooke, R. & Jeeves, T. A. 1961 Direct search solution of numerical and statistical problems. J. ACM 8 (2), 212–229.Google Scholar
Hoyas, S. & Jimenez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $\mathit{Re}_{{\it\tau}}=2003$ . Phys. Fluids 18, 011702.Google Scholar
Kim, E. & Choi, H. 2014 Space–time characteristics of a compliant wall in a turbulent channel flow. J. Fluid Mech. 756, 30–53.CrossRefGoogle Scholar
Kireiko, G. V. 1990 Interaction of wall turbulence with a compliant surface. Fluid Dyn. 25 (4), 550–554.CrossRefGoogle Scholar
Koumoutsakos, P. 1999 Vorticity flux control for a turbulent channel flow. Phys. Fluids 11, 248–250.Google Scholar
Kramer, M. O. 1961 The dolphin’s secret. J. Am. Soc. Nav. Engrs 73, 103–108.Google Scholar
Landahl, M. T. 1962 On the stability of laminar incompressible boundary layer flow over a flexible surface. J. Fluid Mech. 13, 609–632.Google Scholar
Lee, T., Fisher, M. & Schwarz, W. H. 1993 Investigation of the stable interaction of a passive compliant surface with a turbulent boundary layer. J. Fluid Mech. 257, 373–401.Google Scholar
Lucey, A. D. & Carpenter, P. W. 1995 Boundary layer instability over compliant walls: comparison between theory and experiment. Phys. Fluids 7, 2355–2363.Google Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2014a On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis. J. Fluid Mech. 751, 38–70.CrossRefGoogle Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2014b Opposition control within the resolvent analysis framework. J. Fluid Mech. 749, 597–626.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.CrossRefGoogle ScholarPubMed
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.Google Scholar
Moarref, R. & Jovanovic, M. 2012 Model-based design of transverse wall oscillations for turbulent drag reduction. J. Fluid Mech. 707, 205–240.CrossRefGoogle 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. & Chong, M. S. 2009 Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation. J. Fluid Mech. 633, 461–474.CrossRefGoogle 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
Rempfer, D., Blossey, P., Parsons, L. & Lumley, J. 2001 Low-dimensional dynamical model of a turbulent boundary layer over a compliant surface: preliminary results. In Fluid Mechanics and the Environment: Dynamical Approaches, pp. 267–283. Springer.CrossRefGoogle 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.Google Scholar
Riley, J. J., Gad-el-Hak, M. & Metcalfe, R. W. 1988 Compliant coatings. Annu. Rev. Fluid Mech. 20, 393–420.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary-layer. Annu. Rev. Fluid Mech. 23, 601–639.Google Scholar
Sen, P. K. & Arora, D. S. 1988 On the stability of laminar boundary-layer flow over a flat plate with a compliant surface. J. Fluid Mech. 197, 201–240.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., Monty, J., Hultmark, M., Bailey, S. C. C., Hutchins, N. & Marusic, I. 2011 Spatial resolution correction for wall-bounded turbulence measurements. J. Fluid Mech. 676, 41–53.Google Scholar
Trefethen, L. N. 2000 Spectral Methods in MATLAB. SIAM.Google Scholar
Weideman, J. A. C. & Reddy, S. C. 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 26, 465–519.Google Scholar
Xu, S., Rempfer, D. & Lumley, J. 2003 Turbulence over a compliant surface: numerical simulation and analysis. J. Fluid Mech. 478, 11–34.Google Scholar