Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-02-06T08:01:16.884Z Has data issue: false hasContentIssue false
  • English
  • Français

Dissimilarity between turbulent heat and momentum transfer induced by a streamwise travelling wave of wall blowing and suction

Published online by Cambridge University Press:  16 January 2020

Arjun J. Kaithakkal ,
Yukinori Kametani  and
Yosuke Hasegawa Open the ORCID record for Yosuke Hasegawa [Opens in a new window]
Arjun J. Kaithakkal
Affiliation:
Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo153-8505, Japan
Yukinori Kametani
Affiliation:
Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo153-8505, Japan
Yosuke Hasegawa*
Affiliation:
Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo153-8505, Japan Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: ysk@iis.u-tokyo.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

A series of direct numerical simulations of a fully developed turbulent channel flow is conducted in order to clarify the effects of travelling wave-like wall blowing and suction on dissimilar heat transfer enhancement. While the wave form is kept sinusoidal and its amplitude is set to be 5 % of the bulk mean velocity, the wavelength and phase speed of the travelling wave are systematically changed in a wide parameter space. As a result, the global optimum of the parameter set for maximizing the analogy factor, which is defined as the ratio between the Stanton number and the skin-friction coefficient, is identified. Interestingly, the obtained globally optimal mode agrees well with that predicted from the optimal control theory taking into account the future dynamics within a limited time horizon by Yamamoto et al. (J. Fluid Mech., vol. 733, 2013, pp. 189–220). The instantaneous velocity and thermal fields are decomposed into coherent and random components in order to evaluate the contribution from each component to dissimilar heat transfer enhancement. The detailed mechanisms of dissimilarity are explained by the budget analyses of the coherent and random contributions. Also, their relationships with the near-wall turbulent structures modified by the applied control are discussed through flow visualization. It is found that the random component makes a dominant contribution to dissimilarity, and this can be explained by an indirect effect through the modification of the coherent field by the applied control. Based on the above mechanisms, we propose a simple unsteady Reynolds-averaged Navier–Stokes (URANS) approach, where the phase-averaged velocity and thermal fields are solved directly whereas the effects of the random component are modelled by the Boussinesq eddy viscosity and diffusivity hypothesis. It is shown that the present URANS can capture the overall trend of dissimilar heat transfer enhancement in a wide parameter range. The present results also explain why the optimal control theory with a limited time horizon succeeds in predicting the globally optimal control mode.

JFM classification

Flow Control: Control theory Flow Control: Drag reduction Flow Control: Mixing enhancement
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A29
Copyright
© The Author(s), 2020. 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

Antonia, R. A., Krishnamoorthy, L. V. & Fulachier, L. 1988 Correlation between the longitudinal velocity fluctuation and temperature fluctuation in the near-wall region of a turbulent boundary layer. Intl J. Heat Mass Transfer 31, 723–730.CrossRefGoogle Scholar
Araya, G., Leonardi, S. & Castillo, L. 2008 Numerical assessment of local forcing on the heat transfer in a turbulent channel flow. Phys. Fluids 20, 085105.CrossRefGoogle Scholar
Audier, P., Fénot, M., Bénard, N. & Moreau, E. 2016 Film cooling effectiveness enhancement using surface dielectric barrier discharge plasma actuator. Intl J. Heat Fluid Flow 62, 247–257.CrossRefGoogle Scholar
Bejan, A. 2013 Convection Heat Transfer. Wiley.CrossRefGoogle Scholar
Bewley, T. R., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179–225.CrossRefGoogle Scholar
Fiedler, H. E. 1975 Transport of heat across a plane turbulent mixing layer. Adv. Geophys. 18, 93–109.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flow. Phys. Fluids 14, L73–L76.CrossRefGoogle Scholar
Fulachier, L. & Dumas, R. 1976 Spectral analogy between temperature and velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 77, 257–277.CrossRefGoogle Scholar
Gad-el-Hak, M. 2006 Flow Control: Passive, Active, and Reactive Flow Management. Cambridge University Press.Google Scholar
Hasegawa, Y. & Kasagi, N. 2011 Dissimilar control of momentum and heat transfer in a fully developed turbulent channel flow. J. Fluid Mech. 683, 57–93.CrossRefGoogle Scholar
Higashi, K., Mamori, H. & Fukagata, K. 2011 Simultaneous control of friction drag reduction and heat transfer augmentation by traveling wave-like blowing/suction. Comput. Thermal Sci. 3, 521–530.CrossRefGoogle Scholar
Hoepffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171–187.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. In Center for Turbulence Research, Proceedings of the Summer Program, pp. 193–208. Stanford University.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241–258.CrossRefGoogle Scholar
Inaoka, K., Yamamoto, J. & Suzuki, K. 1999 Dissimilarity between heat transfer and momentum transfer in a disturbed turbulent boundary layer with insertion of a rod – modeling and numerical simulation. Intl J. Heat Fluid Flow 20, 290–301.CrossRefGoogle Scholar
Kametani, Y. & Fukagata, K. 2011 Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction. J. Fluid Mech. 681, 154–172.CrossRefGoogle Scholar
Kasagi, N., Hasegawa, Y., Fukagata, K. & Iwamoto, K. 2012 Control of turbulent transport: less friction and more heat transfer. Trans. ASME: J. Heat Transfer 134, 031009.CrossRefGoogle Scholar
Katul, G., Hsieh, C., Kuhn, G., Ellsworth, D. & Nie, D. 1997 Turbulent eddy motion at the forest-atmosphere interface. J. Geophys. Res. 102, 13409–13421.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Kong, H., Choi, H. & Lee, J. S. 2001 Dissimilarity between the velocity and temperature fields in a perturbed turbulent thermal boundary layer. Phys. Fluids 13, 1466–1479.CrossRefGoogle Scholar
Kühnen, J., Song, B., Scarselli, D., Budanur, N. B., Riedl, M., Willis, A. P., Avila, M. & Hof, B. 2018 Destabilizing turbulence in pipe flow. Nat. Phys. 14, 386–390.CrossRefGoogle Scholar
Lee, C., Min, T. & Kim, J. 2008 Stability of a channel flow subject to wall blowing and suction in the form of a traveling wave. Phys. Fluids 20, 101513.CrossRefGoogle Scholar
Li, D. & Bou-Zeid, E. 2011 Coherent structures and the dissimilarity of turbulent transport of momentum and scalars in the unstable atmospheric surface layer. Boundary-Layer Meteorol. 140, 243–262.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
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, 015101.Google ScholarPubMed
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
Maslowe, S. A. 1986 Critical layers in shear flows. Annu. Rev. Fluid Mech. 18, 405–432.CrossRefGoogle Scholar
Matsubara, K., Miura, T. & Ohta, H. 2015 Transport dissimilarity in turbulent channel flow disturbed by rib protrusion with aspect ratio up to 64. Intl J. Heat Mass Transfer 86, 113–123.CrossRefGoogle Scholar
Min, T., Kang, S. M., Speyer, J. L. & Kim, J. 2006 Sustained sub-laminar drag in a fully developed turbulent channel flow. J. Fluid Mech. 558, 309–318.CrossRefGoogle 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.CrossRefGoogle Scholar
Pasinato, H. D. 2011 Velocity and temperature dissimilarity in fully developed turbulent channel and plane Couette flows. Intl J. Heat Fluid Flow 32, 11–25.CrossRefGoogle Scholar
Quadrio, M., Floryan, J. M. & Luchini, P. 2007 Effect of streamwise-periodic wall transpiration on turbulent friction drag. J. Fluid Mech. 576, 425–444.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
Roy, S. & Wang, C. C. 2008 Plasma actuated heat transfer. Appl. Phys. Lett. 92, 231501.CrossRefGoogle Scholar
Suzuki, H., Suzuki, K. & Sato, T. 1988 Dissimilarity between heat and momentum transfer in a turbulent boundary layer disturbed by a cylinder. Intl J. Heat Mass Transfer 31, 259–265.CrossRefGoogle Scholar
Suzuki, T. & Hasegawa, Y. 2017 Estimation of turbulent channel flow at Re 𝜏 = 100 based on the wall measurement using a simple sequential approach. J. Fluid Mech. 830, 760–796.CrossRefGoogle Scholar
Woodcock, J. D., Sader, J. E. & Marusic, I. 2009 Induced flow due to blowing and suction flow control: an analysis of transpiration. J. Fluid Mech. 690, 366–398.CrossRefGoogle Scholar
Yamamoto, A., Hasegawa, Y. & Kasagi, N. 2013 Optimal control of dissimilar heat and momentum transfer in a fully developed turbulent channel flow. J. Fluid Mech. 733, 189–220.CrossRefGoogle Scholar
Zhao, M. X., Huang, W. X. & Xu, C. X. 2019 Drag reduction in turbulent flows along a cylinder by streamwise-travelling waves of circumferential wall velocity. J. Fluid Mech. 862, 75–98.CrossRefGoogle Scholar
Zhou, A., Klewicki, J. & Pirozzoli, S. 2019 Properties of the scalar variance transport equation in turbulent channel flow. Phys. Rev. Fluids 4, 024606.CrossRefGoogle Scholar