Skip to main content Accessibility help
×
×
Home

Streamwise-varying steady transpiration control in turbulent pipe flow

  • F. Gómez (a1), H. M. Blackburn (a1), M. Rudman (a1), A. S. Sharma (a2) and B. J. McKeon (a3)...
Abstract

The effect of streamwise-varying steady transpiration on turbulent pipe flow is examined using direct numerical simulation at fixed friction Reynolds number $\mathit{Re}_{{\it\tau}}=314$ . The streamwise momentum equation reveals three physical mechanisms caused by transpiration acting in the flow: modification of Reynolds shear stress, steady streaming and generation of non-zero mean streamwise gradients. The influence of these mechanisms has been examined by means of a parameter sweep involving transpiration amplitude and wavelength. The observed trends have permitted identification of wall transpiration configurations able to reduce or increase the overall flow rate $-36.1\,\%$ and $19.3\,\%$ , respectively. Energetics associated with these modifications are presented. A novel resolvent formulation has been developed to investigate the dynamics of pipe flows with a constant cross-section but with time-mean spatial periodicity induced by changes in boundary conditions. This formulation, based on a triple decomposition, paves the way for understanding turbulence in such flows using only the mean velocity profile. Resolvent analysis based on the time-mean flow and dynamic mode decomposition based on simulation data snapshots have both been used to obtain a description of the reorganization of the flow structures caused by the transpiration. We show that the pipe flows dynamics are dominated by a critical-layer mechanism and the waviness induced in the flow structures plays a role on the streamwise momentum balance by generating additional terms.

Copyright
Corresponding author
Email address for correspondence: francisco.gomez-carrasco@monash.edu
References
Hide All
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.
Bailey, S. C. C. & Smits, A. J. 2010 Experimental investigation of the structure of large- and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 651, 339356.
Blackburn, H. M., Hall, P. & Sherwin, S. J. 2013 Lower branch equilibria in Couette flow: the emergence of canonical states for arbitrary shear flows. J. Fluid Mech. 726, 5885.
Blackburn, H. M., Ooi, A. S. H. & Chong, M. S. 2007 The effect of corrugation height on flow in a wavy-walled pipe. In 16th Australasian Fluid Mechanics Conference, pp. 559574. The University of Queensland.
Blackburn, H. M. & Sherwin, S. J. 2004 Formulation of a Galerkin spectral element – Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys. 197 (2), 759778.
Blasius, H. 1913 The Law of Similarity of Frictional Processes in Fluids (originally in German). p. 131. Forsch Arbeit Ingenieur-Wesen.
Chen, K. K., Tu, J. H. & Rowley, C. W. 2012 Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses. J. Nonlinear Sci. 22 (6), 887915.
Chin, C., Ooi, A. S. H., Marusic, I. & Blackburn, H. M. 2010 The influence of pipe length on turbulence statistics computed from direct numerical simulation data. J. Fluid Mech. 22 (11), 115107.
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75110.
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73L76.
Gómez, F., Blackburn, H. M., Rudman, M., Mckeon, B. J., Luhar, M., Moarref, R. & Sharma, A. S. 2014 On the origin of frequency sparsity in direct numerical simulations of turbulent pipe flow. Phys. Fluids 26 (10), 101703.
Gómez, F., Blackburn, H. M., Rudman, M., Mckeon, B. J. & Sharma, A. S. 2015 On the coupling of direct numerical simulation and resolvent analysis. In Progress in Turbulence VI: Proceedings of the iTi Conference in Turbulence, Springer.
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333358.
Hellström, L. H. O., Sinha, A. & Smits, A. J. 2011 Visualizing the very-large-scale motions in turbulent pipe flow. Phys. Fluids 23 (1), 011703.
Hellström, L. H. O. & Smits, A. J. 2014 The energetic motions in turbulent pipe flow. Phys. Fluids 26 (12), 125102.
Hoepffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171187.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.
Jimenez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89117.
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97 (2), 414443.
Kasagi, N., Hasegawa, Y. & Fukagata, K. 2009 Toward cost-effective control of wall turbulence for skin friction drag reduction. In Advances in Turbulence XII, pp. 189200. Springer.
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. Lond. A 369 (1940), 13961411.
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39 (1), 383417.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Luchini, P. 2008 Acoustic streaming and lower-than-laminar drag in controlled channel flow. In Progress in Industrial Mathematics at ECMI 2006, pp. 169177. Springer.
Luhar, M., Sharma, A. S. & Mckeon, B. J. 2014 Opposition control within the resolvent analysis framework. J. Fluid Mech. 749, 597626.
Mao, X., Blackburn, H. M. & Sherwin, S. J. 2015 Nonlinear optimal suppression of vortex shedding from a circular cylinder. J. Fluid Mech. 775, 241265.
Marusic, I., Joseph, D. D. & Mahesh, K. 2007 Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570, 467477.
Mckeon, B. J. & Sharma, A. S. 2010 A critical layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.
Mckeon, B. J., Sharma, A. S. & Jacobi, I. 2013 Experimental manipulation of wall turbulence: a systems approach. Phys. Fluids 25 (3), 031301.
Meseguer, A. & Trefethen, L. N. 2003 Linearized pipe flow to Reynolds number 107 . J. Comput. Phys. 186 (1), 178197.
Mezić, I. 2013 Analysis of fluid flows via spectral properties of the Koopman operator. Annu. Rev. Fluid Mech. 45, 357378.
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, 309318.
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. Lond. A 369 (1940), 14281442.
Quadrio, M., Floryan, J. M. & Luchini, P. 2007 Effect of streamwise-periodic wall transpiration on turbulent friction drag. J. Fluid Mech. 576, 425444.
Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251271.
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115127.
Saha, S., Chin, C., Blackburn, H. M. & Ooi, A. S. H. 2011 The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer. Intl J. Heat Fluid Flow 32 (6), 10831097.
Saha, S., Klewicki, J. C., Ooi, A. S. H. & Blackburn, H. M. 2015a Comparison of thermal scaling properties between turbulent pipe and channel flows via DNS. Intl J. Therm. Sci. 89, 4357.
Saha, S., Klewicki, J. C., Ooi, A. S. H. & Blackburn, H. M. 2015b Scaling properties of pipe flows with sinusoidal transversely-corrugated walls. J. Fluid Mech. 779, 245274.
Saha, S., Klewicki, J. C., Ooi, A. S. H., Blackburn, H. M. & Wei, T. 2014 Scaling properties of the equation for passive scalar transport in wall-bounded turbulent flows. Intl J. Heat Mass Transfer 70, 779792.
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39 (1), 129162.
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 528.
Sharma, A. S. & Mckeon, B. J. 2013 On coherent structure in wall turbulence. J. Fluid Mech. 728, 196238.
Sharma, A. S., Morrison, J. F., Mckeon, B. J., Limebeer, D. J. N., Koberg, W. H. & Sherwin, S. J. 2011 Relaminarisation of Re 𝜏 = 100 channel flow with globally stabilising linear feedback control. Phys. Fluids 23 (12), 125105.
Smits, A. J., Mckeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.
Spalart, P. R. & Mclean, J. D. 2011 Drag reduction: enticing turbulence, and then an industry. Phil. Trans. R. Soc. Lond. A 369 (1940), 15561569.
Sumitani, Y. & Kasagi, N. 1995 Direct numerical simulation of turbulent transport with uniform wall injection and suction. AIAA J. 33 (7), 12201228.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
den Toonder, J. M. J. & Nieuwstadt, F. T. M. 1997 Reynolds number effects in a turbulent pipe flow for low to moderate Re. Phys. Fluids 9 (11), 33983409.
Woodcock, J. D., Sader, J. E. & Marusic, I. 2012 Induced flow due to blowing and suction flow control: an analysis of transpiration. J. Fluid Mech. 690, 366398.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

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