Background Money vs C OMPARING DRAG REDUCTION TECHNIQUES Time IN THE "M ONEY - VS -T IME " FRAMEWORK CPI M. Quadrio 1 , Bettina Frohnapfel 2 , Yosuke Hasegawa 3 1 Politecnico di Milano (I), Dept. of Aerospace Sciences and Technologies 2 Karlsruhe Institute of Technology (D), Institute of Fluid Mechanics 3 University of Tokyo (J), Institute of Industrial Science
O UTLINE Background Money vs Time B ACKGROUND 1 CPI M ONEY VS T IME 2 CPI 3
B ACKGROUND Background Money vs Time CPI Turbulent skin-friction drag reduction Open-loop spanwise forcing (oscillating wall, travelling waves)
M OTIVATION B ETTER UNDERSTANDING OF THE PHYSICS SOW: "Turbulence intensity is destroyed" Background Money vs Time CPI
M OTIVATION B ETTER UNDERSTANDING OF THE PHYSICS SOW: "Turbulence intensity is destroyed" Background Money vs Time CPI
M OTIVATION B ETTER UNDERSTANDING OF THE PHYSICS SOW: "Turbulence intensity is destroyed" Background Money vs Time CPI
M OTIVATION B ETTER UNDERSTANDING OF THE PHYSICS SOW: "Turbulence intensity is destroyed" Background Money vs Time CPI
M OTIVATION O THER COMPONENTS AND / OR DIFFERENT SCALING Background Money vs Time CPI
M OTIVATION O THER COMPONENTS AND / OR DIFFERENT SCALING Background Money vs Time CPI
M OTIVATION O THER COMPONENTS AND / OR DIFFERENT SCALING Background Money vs Time CPI
C ONSTANT F LOW R ATE OR C ONSTANT P RESSURE G RADIENT ? Background Money vs Time CPI One potential source of confusion Concerns both DNS and experiments CFR: pumping power is reduced CPG: pumping power is increased
O UTLINE Background Money vs Time B ACKGROUND 1 CPI M ONEY VS T IME 2 CPI 3
R E - STATE THE PROBLEM Problem setup (dimensional) for duct flows Background Money vs Time CPI
E NERGY VS C ONVENIENCE Background Money vs Time CPI
E MPHASIS ON TOTAL ENERGY BUDGET A DDING CONTROL ENERGY E c TO THE PICTURE Background Money vs Time CPI
C OST FUNCTION Background Money vs Time CPI
T HE CONVENTIONAL C f − Re MAP Background Money vs Time CPI The value of C f does not represent energy consumption Comparison of C f at different Re is not meaningful
T HE "M ONEY - VS -T IME " DIMENSIONLESS MAP Background Money vs Time CPI
O UTLINE Background Money vs Time B ACKGROUND 1 CPI M ONEY VS T IME 2 CPI 3
CPI: A USEFUL ALTERNATIVE ? A NATURAL STRATEGY IN THE M ONEY - VS -T IME PLANE Background Money vs Time Total power input is kept constant CPI Energy (money) is reduced while flow rate (time) is increased at the same time Not "better" (it’s application-dependent!) May help understanding how turbulence is affected
W HAT DOES FLOW CONTROL DO IN CPI? Background Money vs Time CPI t = total power P t = control power γ P ( 1 − γ ) P t = pumping power
E XAMPLE RESULTS SOW Background Money vs Time CPI
F URTHER RESULTS SOW + S T TW Background Money vs Time CPI
F URTHER RESULTS SOW + S T TW Background Money vs Time CPI
C ONCLUSIONS Background Money vs Time Need to compromise between Money and Time CPI Cost function is application-dependent CPI might be a useful alternative to CFR and CPG Our "application" is understanding physics Reference: Frohnapfel, Hasegawa & Quadrio, "Money versus Time", JFM 700 , pp.406–418, 2012
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