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Research Papers

Control of Turbulent Transport: Less Friction and More Heat Transfer

[+] Author and Article Information
Nobuhide Kasagi1

Fellow ASME  The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japankasagi@thtlab.t.u-tokyo.ac.jp

Yosuke Hasegawa

 The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan;  Center of Smart Interfaces, TU Damrstadt, Petersenstr. 32, 64287 Darmstadt, Germany

Koji Fukagata

 Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan

Kaoru Iwamoto

 Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei-shi, Tokyo 184-8588, Japan

1

Corresponding author.

J. Heat Transfer 134(3), 031009 (Jan 13, 2012) (10 pages) doi:10.1115/1.4005151 History: Received August 28, 2010; Revised March 22, 2011; Published January 13, 2012; Online January 13, 2012

Because of the importance of fundamental knowledge on turbulent heat transfer for further decreasing entropy production and improving efficiency in various thermofluid systems, we revisit a classical issue whether enhancing heat transfer is possible with skin friction reduced or at least not increased as much as heat transfer. The answer that numerous previous studies suggest is quite pessimistic because the analogy concept of momentum and heat transport holds well in a wide range of flows. Nevertheless, the recent progress in analyzing turbulence mechanics and designing turbulence control offers a chance to develop a scheme for dissimilar momentum and heat transport. By reexamining the governing equations and boundary conditions for convective heat transfer, the basic strategies for achieving dissimilar control in turbulent flow are generally classified into two groups, i.e., one for the averaged quantities and the other for the fluctuating turbulent components. As a result, two different approaches are discussed presently. First, under three typical heating conditions, the contribution of turbulent transport to wall friction and heat transfer is mathematically formulated, and it is shown that the difference in how the local turbulent transport of momentum and that of heat contribute to the friction and heat transfer coefficients is a key to answer whether the dissimilar control is feasible. Such control is likely to be achieved when the weight distributions for the stress and flux in the derived relationships are different. Second, we introduce a more general methodology, i.e., the optimal control theory. The Fréchet differentials obtained clearly show that the responses of velocity and scalar fields to a given control input are quite different due to the fact that the velocity is a divergence-free vector, while the temperature is a conservative scalar. By exploiting this inherent difference, the dissimilar control can be achieved even in flows where the averaged momentum and heat transport equations have the same form.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Coordinate system and mean velocity and temperature distributions (u: streamwise velocity, and θA and θB : temperature in CTD and CHF conditions, respectively)

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Figure 2

Time traces of (a) Cf , (b) St, and (c) j/f factor in case CTD (b+  = 0.01)

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Figure 3

Turbulence statistics in case CTD (b+  = 0.01): (a) Reynolds shear stress; (b) turbulent heat flux

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Figure 4

Time traces of friction coefficient Cf and Stanton number St with different magnitudes of control input φ

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Figure 5

Time traces of j/f factor with different magnitudes of control input φ

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Figure 6

Instantaneous distributions of the control input φ (red contours: wall blowing; blue contours: wall suction): (a) bottom wall, (b) top wall

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Figure 7

Instantaneous distributions of (a) streamwise velocity and (b) temperature in the x-y plane at z = 1.5

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