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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
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Affiliations:
1 LIMSI-CNRS, Departement of Mechanics and Energetics, BP 133, 91430 Orsay Cedex, France
a) Electronic mail: li.vodinh@limsi.fr.
b) Electronic mail: berengere.podvin@limsi.fr.
c) Electronic mail: plq@limsi.fr.
Phys. Fluids 20, 045104 (2008)
/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

FIG. 1.

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

FIG. 2.

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

FIG. 3.

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

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.

FIG. 5.

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

FIG. 6.

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

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.

FIG. 8.

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

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.

FIG. 10.

Normalized drag histories for different grid spacings.

FIG. 11.

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

## Tables

Table I.

Domain parameters.

Table II.

The different control strategies.

Table III.

Drag reduction and actuation intensity associated with different control strategies.

Table IV.

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

/content/aip/journal/pof2/20/4/10.1063/1.2904993
2008-04-18
2014-04-23

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