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Application of compact neural network for drag reduction in a turbulent channel flow at low Reynolds numbers
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10.1063/1.2904993
/content/aip/journal/pof2/20/4/10.1063/1.2904993
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/4/10.1063/1.2904993

Figures

Image of FIG. 1.
FIG. 1.

The numerical configurations and subdivisions—the six-box subdomain roughly corresponds to the size of the reduced domain.

Image of FIG. 2.
FIG. 2.

Drag history for different control strategies in the reduced domain. Solid line: No control. × symbols: Fourier-truncated control . ◻ symbols: POD-truncated control .

Image of FIG. 3.
FIG. 3.

Estimation of the first POD mode (real part) for training sets of different lengths.

Image of FIG. 4.
FIG. 4.

Streamwise vortex structure in the channel. The black and light gray structures represent, respectively, two isovalues, and 0.2 in outer units, of the streamwise vorticity.

Image of FIG. 5.
FIG. 5.

Weights denoted as for (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 6.
FIG. 6.

Estimations of (a) , (b) , (c) , (d) , (e) , and (f) using the neural networks trained with 500 and 2500 samples.

Image of FIG. 7.
FIG. 7.

Drag reduction with Fourier-truncated control (see Table II for details) for different spanwise cutoffs: + symbols, ; × symbols, ; and ∗ symbols, . The control is of the form , where Ntr is the number of retained spanwise modes and is the size of the box in the spanwise direction.

Image of FIG. 8.
FIG. 8.

Weight vector component as a function of where for selected estimates: (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 9.
FIG. 9.

Drag histories for different estimation methods. Solid line: No control. ◻ symbols: Truncated Fourier control . × symbols: Truncated Fourier control with estimated from neural networks. ○ symbols: Truncated Fourier control with estimated from LSE.

Image of FIG. 10.
FIG. 10.

Normalized drag histories for different grid spacings.

Image of FIG. 11.
FIG. 11.

Estimation of the mode with shear measurements obtained for different grid spacings.

Tables

Generic image for table
Table I.

Domain parameters.

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Table II.

The different control strategies.

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Table III.

Drag reduction and actuation intensity associated with different control strategies.

Generic image for table
Table IV.

Influence of streamwise averaging length for opposition control strategy of Choi et al.

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/content/aip/journal/pof2/20/4/10.1063/1.2904993
2008-04-18
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Application of compact neural network for drag reduction in a turbulent channel flow at low Reynolds numbers
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/4/10.1063/1.2904993
10.1063/1.2904993
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