Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-30T23:57:24.346Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence suppression by streamwise-varying wall rotation in pipe flow

Published online by Cambridge University Press:  08 November 2022

Xu Liu Open the ORCID record for Xu Liu [Opens in a new window] ,
Hongbo Zhu Open the ORCID record for Hongbo Zhu [Opens in a new window] ,
Yan Bao Open the ORCID record for Yan Bao [Opens in a new window] ,
Dai Zhou  and
Zhaolong Han
Xu Liu
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Hongbo Zhu
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Yan Bao*
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Key Laboratory of Hydrodynamics of Ministry of Education, Shanghai 200240, PR China
Dai Zhou
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Key Laboratory of Hydrodynamics of Ministry of Education, Shanghai 200240, PR China
Zhaolong Han
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China Key Laboratory of Hydrodynamics of Ministry of Education, Shanghai 200240, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is able to achieve drag reduction and even relaminarize the flow under certain control parameters at friction Reynolds number $Re_\tau =180$. Two control parameters, which are velocity amplitude and wavelength, are considered. It is found that increasing the wavelength rather than increasing the amplitude seems to be a better choice to improve the control efficiency. An annular boundary layer, called the spatial Stokes layer (SSL), is formed by the wall rotation. Based on the thickness of the SSL, two types of drag-reduction scenarios can be identified roughly. When the thickness is low, the SSL acts as a spacer layer, inhibiting the formation of streamwise vortices and thereby reducing the shear stress. The flow structures outside the SSL are stretched in the streamwise direction due to the increased velocity gradient. Within the SSL, the turbulence intensity diminishes dramatically. When the thickness is large, a streamwise wavy pattern of near-wall streaks is formed. The streak orientation is dominated by the mean shear-strain vector outside the viscous sublayer, and there is a phase difference between the streak orientation and local mean velocity vector. The streamwise scales of near-wall flow structures are reduced significantly, resulting in the disruption of downstream development of flow structures and hence leading to the drag reduction. Furthermore, it is found that it requires both large enough thickness of the SSL and velocity amplitude to relaminarize the turbulence. The relaminarization mechanism is that the annular SSL can absorb energy continuously from wall-normal stress due to the rotational effect, thereby the turbulence self-sustaining process cannot be maintained. For the relaminarization cases, the laminar state is stable to even extremely large perturbations, which possibly makes the laminar state the only fixed point for the whole system.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Pipe flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 951 , 25 November 2022 , A35
Check for updates
Copyright
© The Author(s), 2022. Published by 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.)

References

REFERENCES

Agostini, L., Touber, E. & Leschziner, M.A. 2014 Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at ${R}e_\tau = 1000$. J. Fluid Mech. 743, 606–635.CrossRefGoogle Scholar
Agostini, L., Touber, E. & Leschziner, M.A. 2015 The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion. Intl J. Heat Fluid Flow 51, 3–15.CrossRefGoogle Scholar
Akhavan, R., Jung, W. & Mangiavacchi, N. 1993 Control of wall turbulence by high frequency spanwise oscillations. In 3rd Shear Flow Conference, AIAA Paper 1993-3282.Google Scholar
Auteri, F., Baron, A., Belan, M., Campanardi, G. & Quadrio, M. 2010 Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow. Phys. Fluids 22 (11), 115103.CrossRefGoogle Scholar
Baron, A. & Quadrio, M. 1995 Turbulent drag reduction by spanwise wall oscillations. Appl. Sci. Res. 55 (4), 311–326.CrossRefGoogle Scholar
Biggi, M. 2012 Riduzione di resistenza in flussi turbolenti di parete: confronto tra esperimenti e simulazione numerica diretta. Tech. Rep. Politecnico di Milano.Google Scholar
Bird, J., Santer, M. & Morrison, J.F. 2018 Experimental control of turbulent boundary layers with in-plane travelling waves. Flow Turbul. Combust. 100 (4), 1015–1035.CrossRefGoogle ScholarPubMed
Blackburn, H.M., Lee, D., Albrecht, T. & Singh, J. 2019 Semtex: a spectral element–Fourier solver for the incompressible Navier–Stokes equations in cylindrical or Cartesian coordinates. Comput. Phys. Commun. 245, 106804.CrossRefGoogle Scholar
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), 759–778.CrossRefGoogle Scholar
Blesbois, O., Chernyshenko, S.I., Touber, E. & Leschziner, M.A. 2013 Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation. J. Fluid Mech. 724, 607–641.CrossRefGoogle Scholar
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. Phys. Fluids 22 (11), 115107.Google Scholar
Choi, K.-S. 2002 Near-wall structure of turbulent boundary layer with spanwise-wall oscillation. Phys. Fluids 14 (7), 2530–2542.CrossRefGoogle Scholar
Choi, K.-S. & Clayton, B.R. 2001 The mechanism of turbulent drag reduction with wall oscillation. Intl J. Heat Fluid Flow 22 (1), 1–9.CrossRefGoogle Scholar
Choi, J.-I., Xu, C.-X. & Sung, H.J. 2002 Drag reduction by spanwise wall oscillation in wall-bounded turbulent flows. AIAA J. 40 (5), 842–850.CrossRefGoogle Scholar
Coxe, D.J., Peet, Y.T. & Adrian, R.J. 2019 Vorticity statistics and distributions in drag reduced turbulent pipe flow with transverse wall oscillations. In 11th Int. Symp. Turbul. Shear Flow Phenomena (TSFP11), pp. 1–6.Google Scholar
Dennis, D.J.C. & Nickels, T.B. 2011 Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures. J. Fluid Mech. 673, 218–244.CrossRefGoogle Scholar
Di Cicca, G.M., Iuso, G., Spazzini, P.G. & Onorato, M. 2002 Particle image velocimetry investigation of a turbulent boundary layer manipulated by spanwise wall oscillations. J. Fluid Mech. 467, 41–56.Google Scholar
Duggleby, A., Ball, K.S. & Paul, M.R. 2007 The effect of spanwise wall oscillation on turbulent pipe flow structures resulting in drag reduction. Phys. Fluids 19 (12), 125107.CrossRefGoogle Scholar
Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. & Nieuwstadt, F.T.M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–210.CrossRefGoogle Scholar
Gatti, D. & Quadrio, M. 2013 Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number. Phys. Fluids 25 (12), 125109.Google Scholar
Gatti, D. & Quadrio, M. 2016 Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. J. Fluid Mech. 802, 553–582.CrossRefGoogle Scholar
Ge, M. & Jin, G. 2017 Response of turbulent enstrophy to sudden implementation of spanwise wall oscillation in channel flow. Appl. Maths Mech. 38 (8), 1159–1170.CrossRefGoogle Scholar
Gómez, F., Blackburn, H.M., Rudman, M., Sharma, A.S. & McKeon, B.J. 2016 Streamwise-varying steady transpiration control in turbulent pipe flow. J. Fluid Mech. 796, 588–616.CrossRefGoogle Scholar
Guala, M., Hommema, S.E. & Adrian, R.J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Hurst, E., Yang, Q. & Chung, Y.M. 2014 The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves. J. Fluid Mech. 759, 28–55.CrossRefGoogle Scholar
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
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. 189–200. Springer.CrossRefGoogle Scholar
Kim, K.C. & Adrian, R.J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.Google Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids A 5 (3), 695–706.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
Laadhari, F., Skandaji, L. & Morel, R. 1994 Turbulence reduction in a boundary layer by a local spanwise oscillating surface. Phys. Fluids 6 (10), 3218–3220.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.CrossRefGoogle Scholar
Mansour, N.N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.CrossRefGoogle Scholar
Marusic, I., Chandran, D., Rouhi, A., Fu, M.K., Wine, D., Holloway, B., Chung, D. & Smits, A.J. 2021 An energy-efficient pathway to turbulent drag reduction. Nat. Commun. 12 (1), 5808.Google ScholarPubMed
Marusic, I., Joseph, D.D. & Mahesh, K. 2007 Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570, 467–477.Google Scholar
Mishra, M. & Skote, M. 2015 Drag reduction in turbulent boundary layers with half wave wall oscillations. Math. Prob. Engng 2015, 253249.Google Scholar
Miyake, Y., Tsujimoto, K. & Takahashi, M. 1997 On the mechanism of drag reduction of near-wall turbulence by wall oscillation. JSME Intl J. B 40 (4), 558–566.CrossRefGoogle Scholar
Morrison, J.F., McKeon, B.J., Jiang, W. & Smits, A.J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.CrossRefGoogle Scholar
Murakami, M. & Kikuyama, K. 1980 Turbulent flow in axially rotating pipes. ASME. J. Fluids Eng. March 102 (1), 97–103.CrossRefGoogle Scholar
Negi, P.S., Mishra, M. & Skote, M. 2015 DNS of a single low-speed streak subject to spanwise wall oscillations. Flow Turbul. Combust. 94 (4), 795–816.CrossRefGoogle Scholar
Nikitin, N.V. 2000 On the mechanism of turbulence suppression by spanwise surface oscillations. Fluid Dyn. 35 (2), 185–190.CrossRefGoogle Scholar
Orlandi, P. & Fatica, M. 1997 Direct simulations of turbulent flow in a pipe rotating about its axis. J. Fluid Mech. 343, 43–72.Google Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Quadrio, M. & Ricco, P. 2003 Initial response of a turbulent channel flow to spanwise oscillation of the walls. J. Turbul. 4 (1), 007.CrossRefGoogle Scholar
Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251–271.Google Scholar
Quadrio, M. & Ricco, P. 2011 The laminar generalized Stokes layer and turbulent drag reduction. J. Fluid Mech. 667, 135–157.CrossRefGoogle Scholar
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
Quadrio, M. & Sibilla, S. 2000 Numerical simulation of turbulent flow in a pipe oscillating around its axis. J. Fluid Mech. 424, 217–241.CrossRefGoogle Scholar
Ricco, P. 2004 Modification of near-wall turbulence due to spanwise wall oscillations. J. Turbul. 5, 024.CrossRefGoogle Scholar
Ricco, P., Ottonelli, C., Hasegawa, Y. & Quadrio, M. 2012 Changes in turbulent dissipation in a channel flow with oscillating walls. J. Fluid Mech. 700, 77–104.CrossRefGoogle Scholar
Ricco, P. & Quadrio, M. 2008 Wall-oscillation conditions for drag reduction in turbulent channel flow. Intl J. Heat Fluid Flow 29 (4), 891–902.CrossRefGoogle Scholar
Ricco, P., Skote, M. & Leschziner, M.A. 2021 A review of turbulent skin-friction drag reduction by near-wall transverse forcing. Prog. Aerosp. Sci. 123, 100713.CrossRefGoogle Scholar
Ricco, P. & Wu, S. 2004 On the effects of lateral wall oscillations on a turbulent boundary layer. Expl Therm. Fluid Sci. 29 (1), 41–52.CrossRefGoogle Scholar
Skandaji Rezg, L. 1997 Etude de la structure d'une couche limite turbulente soumise à des oscillations transversales de la paroi. PhD thesis, Ecully, Ecole centrale de Lyon.Google Scholar
Skote, M. 2011 Turbulent boundary layer flow subject to streamwise oscillation of spanwise wall-velocity. Phys. Fluids 23 (8), 081703.CrossRefGoogle Scholar
Skote, M. 2012 Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall. Intl J. Heat Fluid Flow 38, 1–12.CrossRefGoogle Scholar
Skote, M. 2013 Comparison between spatial and temporal wall oscillations in turbulent boundary layer flows. J. Fluid Mech. 730, 273–294.CrossRefGoogle Scholar
Skote, M. 2022 Drag reduction of turbulent boundary layers by travelling and non-travelling waves of spanwise wall oscillations. Fluids 7 (2), 65.CrossRefGoogle Scholar
Skote, M., Mishra, M. & Wu, Y. 2015 Drag reduction of a turbulent boundary layer over an oscillating wall and its variation with Reynolds number. Intl J. Aerosp. Engng 2015, 891037.Google Scholar
Skote, M., Mishra, M. & Wu, Y. 2019 Wall oscillation induced drag reduction zone in a turbulent boundary layer. Flow Turbul. Combust. 102 (3), 641–666.Google Scholar
Sreenivasan, K.R. 1982 Laminarescent, relaminarizing and retransitional flows. Acta Mech. 44 (1), 1–48.CrossRefGoogle Scholar
Straub, S., Vinuesa, R., Schlatter, P., Frohnapfel, B. & Gatti, D. 2017 Turbulent duct flow controlled with spanwise wall oscillations. Flow Turbul. Combust. 99 (3), 787–806.CrossRefGoogle Scholar
Touber, E. & Leschziner, M.A. 2012 Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200.CrossRefGoogle Scholar
Trujillo, S.M., Bogard, D.G. & Ball, K.S. 1997 Turbulent boundary layer drag reduction using an oscillating wall. AIAA Paper 1997-1870.Google Scholar
Viotti, C., Quadrio, M. & Luchini, P. 2009 Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction. Phys. Fluids 21 (11), 115109.Google Scholar
White, A. 1964 Flow of a fluid in an axially rotating pipe. J. Mech. Engng Sci. 6 (1), 47–52.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.Google Scholar
Wu, X., Moin, P., Adrian, R.J. & Baltzer, J.R. 2015 Osborne Reynolds pipe flow: direct simulation from laminar through gradual transition to fully developed turbulence. Proc. Natl Acad. Sci. 112 (26), 7920–7924.CrossRefGoogle ScholarPubMed
Xie, W. 2014 Turbulence skin-friction reduction by traveling waves: a DNS study. PhD thesis, Politecnico di Milano.Google Scholar
Xu, C.-X. & Huang, W.-X. 2005 Transient response of Reynolds stress transport to spanwise wall oscillation in a turbulent channel flow. Phys. Fluids 17 (1), 018101.CrossRefGoogle Scholar
Yakeno, A., Hasegawa, Y. & Kasagi, N. 2009 Spatio-temporally periodic control for turbulent friction drag reduction. In Sixth Int. Symp. Turbul. Shear Flow Phenomena (TSFP-6 Conf.), pp. 598–603.Google Scholar
Yakeno, A., Hasegawa, Y. & Kasagi, N. 2014 Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation. Phys. Fluids 26 (8), 085109.CrossRefGoogle Scholar
Yao, J., Chen, X. & Hussain, F. 2019 Reynolds number effect on drag control via spanwise wall oscillation in turbulent channel flows. Phys. Fluids 31 (8), 085108.Google Scholar
Yuan, W., Zhang, M., Cui, Y. & Khoo, B.C. 2019 Phase-space dynamics of near-wall streaks in wall-bounded turbulence with spanwise oscillation. Phys. Fluids 31 (12), 125113.Google Scholar
Yudhistira, I. & Skote, M. 2011 Direct numerical simulation of a turbulent boundary layer over an oscillating wall. J. Turbul. 12, N9.CrossRefGoogle Scholar
Zhao, M.-X., Huang, W.-X. & Xu, C.-X. 2019 a Drag reduction in turbulent flow along a cylinder by circumferential oscillating Lorentz force. Phys. Fluids 31 (9), 095104.Google Scholar
Zhao, M.-X., Huang, W.-X. & Xu, C.-X. 2019 b Drag reduction in turbulent flows along a cylinder by streamwise-travelling waves of circumferential wall velocity. J. Fluid Mech. 862, 75–98.Google Scholar