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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
Background
Money vsTime
CPI
OUTLINE
1 BACKGROUND
2 MONEY VS TIME
3 CPI
Background
Money vsTime
CPI
RE-STATE THE PROBLEM
Problem setup (dimensional) for duct flows
Background
Money vsTime
CPI
ENERGY VS CONVENIENCE
Background
Money vsTime
CPI
EMPHASIS ON TOTAL ENERGY BUDGETADDING CONTROL ENERGY Ec TO THE PICTURE
Background
Money vsTime
CPI
COST FUNCTION
Background
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
Background
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
Background
Money vsTime
CPI
WHAT DOES FLOW CONTROL DO IN CPI?
Pt = total powerγPt = control power(1− γ)Pt =pumping power
Background
Money vsTime
CPI
EXAMPLE RESULTSSOW
Background
Money vsTime
CPI
FURTHER RESULTSSOW + STTW
Background
Money vsTime
CPI
FURTHER RESULTSSOW + STTW
Background
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
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