C ONSTANT P RESSURE G RADIENT ? Background Money vs Time CPI One - - PowerPoint PPT Presentation

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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

SLIDE 1

Background Money vs Time 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 Technologies 2 Karlsruhe Institute of Technology (D), Institute of Fluid Mechanics 3 University of Tokyo (J), Institute of Industrial Science

SLIDE 2

Background Money vs Time CPI

OUTLINE

1

BACKGROUND

2

MONEY VS TIME

3

CPI

SLIDE 3

Background Money vs Time CPI

BACKGROUND

Turbulent skin-friction drag reduction Open-loop spanwise forcing (oscillating wall, travelling waves)

SLIDE 4

Background Money vs Time CPI

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

SLIDE 5

Background Money vs Time CPI

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

SLIDE 6

Background Money vs Time CPI

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

SLIDE 7

Background Money vs Time CPI

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

SLIDE 8

Background Money vs Time CPI

MOTIVATION

OTHER COMPONENTS AND/OR DIFFERENT SCALING

SLIDE 9

Background Money vs Time CPI

MOTIVATION

OTHER COMPONENTS AND/OR DIFFERENT SCALING

SLIDE 10

Background Money vs Time CPI

MOTIVATION

OTHER COMPONENTS AND/OR DIFFERENT SCALING

SLIDE 11

Background Money vs Time CPI

CONSTANT FLOW RATE OR CONSTANT PRESSURE GRADIENT?

One potential source of confusion Concerns both DNS and experiments CFR: pumping power is reduced CPG: pumping power is increased

SLIDE 12

Background Money vs Time CPI

OUTLINE

1

BACKGROUND

2

MONEY VS TIME

3

CPI

SLIDE 13

Background Money vs Time CPI

RE-STATE THE PROBLEM

Problem setup (dimensional) for duct flows

SLIDE 14

Background Money vs Time CPI

ENERGY VS CONVENIENCE

SLIDE 15

Background Money vs Time CPI

EMPHASIS ON TOTAL ENERGY BUDGET

ADDING CONTROL ENERGY Ec TO THE PICTURE

SLIDE 16

Background Money vs Time CPI

COST FUNCTION

SLIDE 17

Background Money vs Time CPI

THE CONVENTIONAL Cf −Re MAP

The value of Cf does not represent energy consumption Comparison of Cf at different Re is not meaningful

SLIDE 18

Background Money vs Time CPI

THE "MONEY-VS-TIME" DIMENSIONLESS MAP

SLIDE 19

Background Money vs Time CPI

OUTLINE

1

BACKGROUND

2

MONEY VS TIME

3

CPI

SLIDE 20

Background Money vs Time CPI

CPI: A USEFUL ALTERNATIVE?

A NATURAL STRATEGY IN THE MONEY-VS-TIME PLANE

Total power input is kept constant 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

SLIDE 21

Background Money vs Time CPI

WHAT DOES FLOW CONTROL DO IN CPI?

P

t = total power

γP

t = control power

(1−γ)P

t =

pumping power

SLIDE 22

Background Money vs Time CPI

EXAMPLE RESULTS

SOW

SLIDE 23

Background Money vs Time CPI

FURTHER RESULTS

SOW + STTW

SLIDE 24

Background Money vs Time CPI

FURTHER RESULTS

SOW + STTW

SLIDE 25

Background Money vs Time CPI

CONCLUSIONS

Need to compromise between Money and Time 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

COMPARING DRAG REDUCTION TECHNIQUES

IN THE "MONEY-VS-TIME" FRAMEWORK

OUTLINE

1

BACKGROUND

2

MONEY VS TIME

3

CPI

BACKGROUND

Turbulent skin-friction drag reduction Open-loop spanwise forcing (oscillating wall, travelling waves)

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

MOTIVATION

BETTER UNDERSTANDING OF THE PHYSICS

SOW: "Turbulence intensity is destroyed"

MOTIVATION

OTHER COMPONENTS AND/OR DIFFERENT SCALING

MOTIVATION

OTHER COMPONENTS AND/OR DIFFERENT SCALING

MOTIVATION

OTHER COMPONENTS AND/OR DIFFERENT SCALING

CONSTANT FLOW RATE OR CONSTANT PRESSURE GRADIENT?

One potential source of confusion Concerns both DNS and experiments CFR: pumping power is reduced CPG: pumping power is increased

OUTLINE

1

BACKGROUND

2

MONEY VS TIME

3

CPI

RE-STATE THE PROBLEM

Problem setup (dimensional) for duct flows

ENERGY VS CONVENIENCE

EMPHASIS ON TOTAL ENERGY BUDGET

ADDING CONTROL ENERGY Ec TO THE PICTURE

COST FUNCTION

THE CONVENTIONAL Cf −Re MAP

The value of Cf does not represent energy consumption Comparison of Cf at different Re is not meaningful

THE "MONEY-VS-TIME" DIMENSIONLESS MAP

OUTLINE

1

BACKGROUND

2

MONEY VS TIME

3

CPI

CPI: A USEFUL ALTERNATIVE?

A NATURAL STRATEGY IN THE MONEY-VS-TIME PLANE

Total power input is kept constant 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

WHAT DOES FLOW CONTROL DO IN CPI?

P

t = total power

γP

t = control power

(1−γ)P

t =

pumping power

EXAMPLE RESULTS

SOW

FURTHER RESULTS

SOW + STTW

FURTHER RESULTS

SOW + STTW

CONCLUSIONS

Need to compromise between Money and Time 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