TY - JOUR

T1 - On the lower bound of net driving power in controlled duct flows

AU - Fukagata, Koji

AU - Sugiyama, Kazuyasu

AU - Kasagi, Nobuhide

N1 - Funding Information:
The authors are grateful to Dr. Thomas R. Bewley (UCSD), Dr. Yuji Suzuki (The University of Tokyo), Dr. Kaoru Iwamoto (Tokyo University of Agriculture and Technology), and Dr. Jérôme Hœpffner (Keio University) for helpful comments and fruitful discussions. This work was supported through the Project for Organized Research Combination System “Smart Control of Turbulence” and the Grant-in-Aid for Scientific Research (A) (No. 20246036) by the Ministry of Education, Culture, Sports and Technology of Japan (MEXT).

PY - 2009/6/15

Y1 - 2009/6/15

N2 - We examine mathematically the lower bound of the net driving power (i.e., the summation of pumping and actuation powers) of a controlled duct flow under a constant flow rate. The net power in a duct with arbitrary cross-section in the presence of the inertial term, blowing/suction from the wall, and arbitrary body forces can be decomposed into four terms: (1) dissipation due to the velocity profile of the Stokes flow (in other words, pumping power for the Stokes flow); (2) dissipation due to deviation of the mean velocity from the Stokes flow profile; (3) dissipation due to velocity fluctuations; and (4) correlation between the wall-pressure of the Stokes flow and the time-averaged blowing/suction velocity. Of these, the first three terms are shown to be non-negative, while the sign of the fourth term is indefinite. The fourth term vanishes in cases where the duct has a constant-shape cross-section, such as cylindrical pipes and plane channels. Namely, in such cases, the lower bound of net power is exactly given by the dissipation rate (pumping power) of the Stokes flow at the same flow rate.

AB - We examine mathematically the lower bound of the net driving power (i.e., the summation of pumping and actuation powers) of a controlled duct flow under a constant flow rate. The net power in a duct with arbitrary cross-section in the presence of the inertial term, blowing/suction from the wall, and arbitrary body forces can be decomposed into four terms: (1) dissipation due to the velocity profile of the Stokes flow (in other words, pumping power for the Stokes flow); (2) dissipation due to deviation of the mean velocity from the Stokes flow profile; (3) dissipation due to velocity fluctuations; and (4) correlation between the wall-pressure of the Stokes flow and the time-averaged blowing/suction velocity. Of these, the first three terms are shown to be non-negative, while the sign of the fourth term is indefinite. The fourth term vanishes in cases where the duct has a constant-shape cross-section, such as cylindrical pipes and plane channels. Namely, in such cases, the lower bound of net power is exactly given by the dissipation rate (pumping power) of the Stokes flow at the same flow rate.

KW - Dissipation

KW - Drag reduction

KW - Flow control

KW - Incompressible flow

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U2 - 10.1016/j.physd.2009.03.008

DO - 10.1016/j.physd.2009.03.008

M3 - Article

AN - SCOPUS:67349201456

VL - 238

SP - 1082

EP - 1086

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 13

ER -