アクティブ制御下の任意断面ダクト内流れにおける散逸の下限(解析・予測・制御流れの制御(2),一般講演)

概要

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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 the presence of control input is shown to be decomposed into four terms: (1) pumping power for the Stokes flow; (2) dissipation due to mean deviation from the Stokes flow; (3) dissipation due to velocity fluctuations; and (4) correlation between the wall-pressure of Stokes flow and the time-averaged blowing/suction velocity. The first three terms are shown to be non-negative, while the sign of the fourth term is indefinite. The fourth term vanishes in the cases where the duct has a constant-shape cross-section, such as cylindrical pipes and plane chan the lower bound of net power is exactly given by the dissipation rate (pumping power) of the Stokes flow at the same flow rate.
日本流体力学会の論文
2009-09-02