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Background
Money vsTime
CPI
COMPARING DRAG REDUCTION TECHNIQUES
IN THE "MONEY-VS-TIME" FRAMEWORK
M. Quadrio1, Bettina Frohnapfel2, Yosuke Hasegawa3
1 Politecnico di Milano (I), Dept. of Aerospace Sciences and Technologies2 Karlsruhe Institute of Technology (D), Institute of Fluid Mechanics
3 University of Tokyo (J), Institute of Industrial Science
Background
Money vsTime
CPI
OUTLINE
1 BACKGROUND
2 MONEY VS TIME
3 CPI
Background
Money vsTime
CPI
BACKGROUND
Turbulent skin-friction drag reductionOpen-loop spanwise forcing (oscillating wall, travellingwaves)
Background
Money vsTime
CPI
MOTIVATIONBETTER UNDERSTANDING OF THE PHYSICS
SOW: "Turbulence intensity is destroyed"
Background
Money vsTime
CPI
MOTIVATIONBETTER UNDERSTANDING OF THE PHYSICS
SOW: "Turbulence intensity is destroyed"
Background
Money vsTime
CPI
MOTIVATIONBETTER UNDERSTANDING OF THE PHYSICS
SOW: "Turbulence intensity is destroyed"
Background
Money vsTime
CPI
MOTIVATIONBETTER UNDERSTANDING OF THE PHYSICS
SOW: "Turbulence intensity is destroyed"
Background
Money vsTime
CPI
MOTIVATIONOTHER COMPONENTS AND/OR DIFFERENT SCALING
Background
Money vsTime
CPI
MOTIVATIONOTHER COMPONENTS AND/OR DIFFERENT SCALING
Background
Money vsTime
CPI
MOTIVATIONOTHER COMPONENTS AND/OR DIFFERENT SCALING
Background
Money vsTime
CPI
CONSTANT FLOW RATE OR
CONSTANT PRESSURE GRADIENT?
One potential source of confusionConcerns both DNS and experimentsCFR: pumping power is reducedCPG: pumping power is increased
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Money vsTime
CPI
OUTLINE
1 BACKGROUND
2 MONEY VS TIME
3 CPI
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Money vsTime
CPI
RE-STATE THE PROBLEM
Problem setup (dimensional) for duct flows
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Money vsTime
CPI
ENERGY VS CONVENIENCE
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Money vsTime
CPI
EMPHASIS ON TOTAL ENERGY BUDGETADDING CONTROL ENERGY Ec TO THE PICTURE
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Money vsTime
CPI
COST FUNCTION
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Money vsTime
CPI
THE CONVENTIONAL C f −Re MAP
The value of C f
does not representenergyconsumptionComparison of C f
at different Re isnot meaningful
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Money vsTime
CPI
THE "MONEY-VS-TIME" DIMENSIONLESS MAP
Background
Money vsTime
CPI
OUTLINE
1 BACKGROUND
2 MONEY VS TIME
3 CPI
Background
Money vsTime
CPI
CPI: A USEFUL ALTERNATIVE?A NATURAL STRATEGY IN THE MONEY-VS-TIME PLANE
Total power input is kept constantEnergy (money) is reduced while flow rate (time) isincreased at the same timeNot "better" (it’s application-dependent!)May help understanding how turbulence is affected
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Money vsTime
CPI
WHAT DOES FLOW CONTROL DO IN CPI?
Pt = total powerγPt = control power(1− γ)Pt =pumping power
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Money vsTime
CPI
EXAMPLE RESULTSSOW
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Money vsTime
CPI
FURTHER RESULTSSOW + STTW
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Money vsTime
CPI
FURTHER RESULTSSOW + STTW
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Money vsTime
CPI
CONCLUSIONS
Need to compromise between Money and TimeCost function is application-dependentCPI might be a useful alternative to CFR and CPGOur "application" is understanding physics
Reference: Frohnapfel, Hasegawa & Quadrio, "Money versusTime", JFM 700, pp.406–418, 2012