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Optimal control of dissimilar heat and momentum transfer in a fully developed turbulent channel flow

  • A. Yamamoto (a1), Y. Hasegawa (a2) and N. Kasagi (a3)

Abstract

Sustained friction drag reduction and heat transfer augmentation are simultaneously achieved in a fully developed channel flow where the averaged transport equations and wall boundary conditions for momentum and heat have identical form. Zero-net-mass-flux wall blowing and suction is assumed as a control input and its spatio-temporal distribution is determined based on optimal control theory. When the root-mean-square value of the control input is 5 % of the bulk mean velocity, the friction drag is decreased by 24 % from the uncontrolled value, whereas the heat transfer is more than doubled. Optimizations with different amplitudes of the control input and different Reynolds numbers reveal that the optimal control inputs commonly exhibit the property of a downstream travelling wave, whose wavelength is ∼250 in wall units and phase velocity is ∼30 % of the bulk mean velocity. Detailed analyses of the controlled velocity and thermal fields show that the travelling wave input contributes to dissimilar heat transfer enhancement through two distinct mechanisms, i.e. direct modification of the coherent velocity and thermal fields and an indirect effect on the random fields. The present results show that the divergence-free velocity vector and the conservative scalar are essentially different, and this is a key to achieving dissimilar heat transfer enhancement in turbulent shear flows.

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Corresponding author

Email address for correspondence: ysk@iis.u-tokyo.ac.jp

References

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Abergel, F. & Temam, R. 1990 On some control problems in fluid mechanics. Theor. Comput. Fluid Dyn. 1, 303325.
Antonia, R. A. & Krishnamoorthy, L. V. 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, 723730.
Bejan, A. E. 1978 General criterion for rating heat-exchanger performance. Intl J. Heat Mass Transfer 21, 655658.
Bewley, T., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179225.
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75110.
Eiamsa-ard, S. & Promvonge, P. 2011 Influence of double-sided delta-wing tape insert with alternate-axes on flow and heat transfer characteristics in a heat exchanger tube. Chin. J. Chem. Engng 19 (3), 410423.
Frohnapfel, B., Hasegawa, Y. & Kasagi, N. 2010 Friction drag reduction through damping of the near-wall spanwise velocity fluctuation. Intl J. Heat Fluid Flow 31, 434441.
Frohnapfel, B., Hasegawa, Y. & Quadrio, M. 2012 Money versus time: evaluation of flow control in terms of energy consumption and convenience. J. Fluid Mech. 700, 406418.
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73–L76.
Hasegawa, Y. & Kasagi, N. 2011 Dissimilar control of momentum and heat transfer in a fully developed turbulent channel flow. J. Fluid Mech. 683, 5793.
Iida, O. & Kasagi, N. 1997 Direct numerical simulation of unstably stratified turbulent channel flow. Trans. ASME: J. Heat Transfer 119, 5361.
Iida, O., Kasagi, N. & Nagano, Y. 2002 Direct numerical simulation of turbulent channel flow under stable density stratification. Intl J. Heat Mass Transfer 45, 16931703.
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.
Kasagi, N., Kuroda, A. & Tomita, Y. 1992 Direct numerical simulation of passive scalar field in a turbulent channel flow. Trans. ASME: J. Heat Transfer 114, 598606.
Keys, W., Crawford, M. E. & Weigand, B. 2005 Convective Heat and Mass Transfer, 4th edn. McGraw-Hill.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Lee, C., Kim, J. & Choi, H. 1998 Suboptimal control of turbulent channel flow for drag reduction. J. Fluid Mech. 358, 245258.
Manglik, R. M. & Bergles, A. E. 1995 Heat transfer and pressure drop correlations for the rectangular offset strip fin compact heat exchanger. Exp. Therm. Fluid Sci. 10, 171180.
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.
Morimoto, K., Suzuki, Y. & Kasagi, N. 2010 Optimal shoe design of compact heat exchangers based on adjoint analysis of momentum and heat transfer. J. Therm. Sci. Tech. 5, 2435.
Nagano, Y., Hattori, H. & Houra, T. 2004 DNS of velocity and thermal fields in turbulent channel flow with transverse-rib roughness. Intl J. Heat Fluid Flow 25, 393403.
Nakanishi, R., Mamori, H. & Fukagata, K. 2012 Relaminarization of turbulent channel flow using travelling wave-like wall deformation. Intl J. Heat Fluid Flow 35, 152159.
Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161178.
Rai, M. & Moin, K. 1991 Direct simulations of turbulent flow using finite-difference scheme. J. Comput. Phys. 96, 1553.
Reynolds, O. 1874 On the extent and action of the heating surface of steam boilers. Manchester Lit. Phil. Soc. Mem. Proc. 14, 712.
Satake, S. & Kasagi, N. 1996 Turbulence control with wall-adjacent thin layer damping spanwise velocity fluctuations. Intl J. Heat Fluid Flow 17, 343352.
Spalart, P., Moser, R. & Rogers, M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297324.
Stasiek, J., Collins, M. W., Ciofalo, M. & Chew, P. E. 1996 Investigation of flow and heat transfer in corrugated passages – l. Experimental results. Intl J. Heat Mass Transfer 39, 149164.
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Optimal control of dissimilar heat and momentum transfer in a fully developed turbulent channel flow

  • A. Yamamoto (a1), Y. Hasegawa (a2) and N. Kasagi (a3)

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