A new adaptive controller based on a neural network was constructed and applied to turbulent channel flow for drag reduction. A simple control network, which employs blowing and suction at the wall based only on the wall-shear stresses in the spanwise direction, was shown to reduce the skin friction by as much as 20% in direct numerical simulations of a low-Reynolds number turbulent channel flow. Also, a stable pattern was observed in the distribution of weights associated with the neural network. This allowed us to derive a simple control scheme that produced the same amount of drag reduction. This simple control scheme generates optimum wall blowing and suction proportional to a local sum of the wall-shear stress in the spanwise direction. The distribution of corresponding weights is simple and localized, thus making real implementation relatively easy. Turbulence characteristics and relevant practical issues are also discussed.

1.
J. Kim, “Study of turbulence structure through numerical simulations: The perspective of drag reduction,” AGARD Report No. R-786, AGARD FDP/VKI Special Course on “Skin Friction Drag Reduction,” 2–6 March 1992, VKI, Brussels (1992).
2.
H.
Choi
,
P.
Moin
, and
J.
Kim
, “
Active turbulence control for drag reduction in wall-bounded flows
,”
J. Fluid Mech.
262
,
75
(
1994
).
3.
R.
Akhavan
,
W. J.
Jung
, and
N.
Mangiavacchi
, “
Turbulence control in wall-bounded flows by spanwise oscillations
,”
Appl. Sci. Res.
51
,
299
(
1993
).
4.
J.
Kim
,
C.
Lee
,
T.
Berger
,
J.
Lim
, and
H.
Choi
, “
Effects of electromagnetic force on near-wall turbulence
,”
Bull. Am. Phys. Soc.
40
,
1989
(
1995
).
5.
H.
Choi
,
R.
Temam
,
P.
Moin
, and
J.
Kim
, “
Feedback control for unsteady flow and its application to the stochastic Burgers equation
,”
J. Fluid Mech.
253
,
509
(
1993
).
6.
P. Moin and T. Bewley, “Application of control theory to turbulence,” in the 12th Australasian Fluid Mechanics Conference, Sydney 10–15 December 1995 (unpublished), p. 109.
7.
S. L. Jacobson and W. C. Reynolds, “Active control of boundary layer wall shear stress using self-learning neural networks,” AIAA Shear Flow Conference, Orlando, 1993 (unpublished), p. 1.
8.
M. Moller, “Efficient training of feed-forward neural networks,” Ph.D. thesis, Aarhus University, Denmark, 1993.
9.
J.
Kim
,
P.
Moin
, and
R.
Moser
, “
Turbulence statistics in fully-developed channel flow at low Reynolds number
,”
J. Fluid Mech.
177
,
133
(
1987
).
10.
B. Widrow, “Adaptive inverse control,” In the Second IFAC Workshop on Adaptive Systems in Control and Signal Processing, Lund, Sweden, 1987 (unpublished), pp. 1–5.
11.
C. R.
Smith
,
J. D. A.
Walker
,
A. H.
Haidari
, and
U.
Sobrun
, “
On the dynamics of near-wall turbulence
,”
Philos. Trans. R. Soc. London Ser. A
336
,
131
(
1991
).
12.
This staggered distribution of sensors and actuators would result in actuators at only half the grid points and this might reduce the effectiveness of the control. This problem can be solved simply by increasing resolution twice so that actuators locate at every grid point of the old grid system (these correspond to half the grid points in the new grid system) still with sensors located in staggered positions. This is possible since the weight distribution does not depend on the grid distance, but depends on the grid index as shown in Figs. 5 and 7.
13.
C. Liu, Y. C. Tai, J. B. Huang, and C. M. Ho, “Surface micromachined thermal shear stress sensor,” in ASME Application of Microfabrication to Fluid Mechanics, Chicago, 1994 (unpublished), pp. 9–15.
This content is only available via PDF.
You do not currently have access to this content.