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Effect of streamwise-periodic wall transpiration on turbulent friction drag

Published online by Cambridge University Press:  28 March 2007

M. QUADRIO ,
J. M. FLORYAN  and
P. LUCHINI
M. QUADRIO
Affiliation:
Department of Aerospace Engineering, Politecnico di Milano, Italy
J. M. FLORYAN
Affiliation:
Department of Mechanical and Materials Engineering, University of Western Ontario, Ontario, Canada
P. LUCHINI
Affiliation:
Department of Mechanical Engineering, Università di Salerno, Italy
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Abstract

In this paper a turbulent plane channel flow modified by a distributed transpiration at the wall, with zero net mass flux, is studied through direct numerical simulation (DNS) using the incompressible Navier–Stokes equations. The transpiration is steady, uniform in the spanwise direction, and varies sinusoidally along the streamwise coordinate. The transpiration wavelength is found to dramatically affect the turbulent flow, and in particular the frictional drag. Long wavelengths produce large drag increases even with relatively small transpiration intensities, thus providing an efficient means for improved turbulent mixing. Shorter wavelengths, on the other hand, yield an unexpected decrease of turbulent friction. These opposite effects are separated by a threshold of transpiration wavelength, shown to scale in viscous units, related to a longitudinal length scale typical of the near-wall turbulence cycle. Transpiration is shown to affect the flow via two distinct mechanisms: steady streaming and direct interaction with turbulence. They modify the turbulent friction in two opposite ways, with streaming being equivalent to an additional pressure gradient needed to drive the same flow rate (drag increase) and direct interaction causing reduced turbulent activity owing to the injection of fluctuationless fluid. The latter effect overwhelms the former at small wavelengths, and results in a (small) net drag reduction. The possibility of observing large-scale streamwise-oriented vortical structures as a consequence of a centrifugal instability mechanism is also discussed. Our results do not demonstrate the presence of such vortices, and the same conclusion can be arrived at through a stability analysis of the mean velocity profile, even though it is possible that a higher value of the Reynolds number is needed to observe the vortices.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 425 - 444
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Ahn, J., Sung Jung, I. & Lee, J. 2003 Film cooling from two rows of holes with opposite orientation angles: injectant behavior and adiabatic film cooling effectiveness. Intl J. Heat Fluid Flow 24 1, 91–99.CrossRefGoogle Scholar
Antonia, R., Zhu, Y. & Sokolov, M. 1995 Effect of concentrated wall suction on a turbulent boundary layer. Phys. Fuids 7, 2465–2474.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
Chung, Y., Sung, H. & Krogstad, P.-A. 2002 Modulation of near-wall turbulence structure with wall blowing and suction. AIAA J. 40 8, 1529–1535.CrossRefGoogle Scholar
Crighton, D. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413.CrossRefGoogle Scholar
Floryan, J. 1997 Stability of wall-bounded shear layers in the presence of simulated distributed roughness. J. Fluid Mech. 335, 29–55.CrossRefGoogle Scholar
Floryan, J. 2003 Wall-transpiration-induced instabilities in plane Couette flow. J. Fluid Mech. 488, 151–188.CrossRefGoogle Scholar
Gad-el Hak, M. & Bushnell, D. 1991 Separation control: review. Trans. ASME: J. Fluids Engng 113 3, 5–29.Google Scholar
Gong, W., Taylor, P. & Dörnbrack, A. 1996 Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J. Fluid Mech. 312, 1–37.CrossRefGoogle Scholar
Gschwind, P., Regele, P. & Kottke, V. 1995 Sinusoidal wavy channel with Taylor–Göortler vortices. Expl Therm. Fluid Sci. 11, 270–275.CrossRefGoogle Scholar
Günther, A. & Rudolphvon Rohr, P. von Rohr, P. 2003 Large-scale structures in a developed flow over a wavy wall. J. Fluid Mech. 478, 257–285.CrossRefGoogle Scholar
Iwamoto, K., Fukagata, K., Kasagi, N. & Suzuki, Y. 2005 Friction drag reduction achievable with near-wall manipulation at high Reynolds numbers. Phys. Fluids 17, 011702.CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.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.CrossRefGoogle Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulation. Annu. Rev. Fluid Mech. 15, 391–427.CrossRefGoogle Scholar
Luchini, P. & Quadrio, M. 2006 A low-cost parallel implementation of direct numerical simulation of wall turbulence. J. Comput. Phys. 211 2, 551–571.CrossRefGoogle Scholar
Park, J. & Choi, H. 1999 Effects of uniform blowing or suction from a spanwise slot on a turbulent boundary layer flow. Phys. Fluids 11 10, 3095–3105.CrossRefGoogle Scholar
Park, S.-H., Lee,, I. & Sung, H. 2001 Effect of local forcing on a turbulent boundary layer. Exps. Fluids 31, 384–393.CrossRefGoogle Scholar
Quadrio, M., Floryan, J. & Luchini, P. 2005 Modification of Turbulent Flow using Distributed Transpiration. Can. Aeron. Space J. 51 2, 61–69.CrossRefGoogle Scholar
Quadrio, M. & Luchini, P. 2003 Integral time-space scales in turbulent wall flows. Phys. Fluids 15 8, 2219–2227.CrossRefGoogle Scholar
Rayleigh, Lord 1883 On the circulation of air observed in {K}undt's tubes and some allied acoustical problems. Phil. Trans. R. Soc. Lond. A 175, 1–21.Google Scholar
Reau, N. & Tumin, A. 2002 On harmonic perturbations in a turbulent mixing layer. Eur. J. Mech. B Fluids 21, 143–155.CrossRefGoogle Scholar
Reynolds, W. & Tiedermann, W. 1967 Stability of turbulent channel flow, with application to Malkus' theory. J. Fluid Mech. 27, 253–272.CrossRefGoogle Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 1998 A large-scale control strategy for drag reduction in turbulent boundary layers. Phys. Fluids 10 5, 1049–1051.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Sumitani, Y. & Kasagi, N. 1995 Direct numerical simulation of turbulent transport with uniform wall injection and suction. AIAA J. 33 7, 1220–1228.CrossRefGoogle Scholar
Tardu, S. 2001 Active control of near-wall turbulence by local oscillating blowing. J. Fluid Mech. 439, 217–253.CrossRefGoogle Scholar