T HE DRAG - REDUCTION OSCILLATING - WALL PROBLEM : NEW INSIGHT AFTER - - PowerPoint PPT Presentation

SLIDE 1

THE DRAG-REDUCTION OSCILLATING-WALL PROBLEM:

NEW INSIGHT AFTER 20 YEARS

Pierre Ricco†, Claudio Ottonelli⋆, Yosuke Hasegawa‡, Maurizio Quadrio•

† The University of Sheffield

⋆ ONERA, Paris ‡ The University of Tokyo

• Politecnico di Milano

9th European Fluid Mechanics Conference Universitá di Roma, “Tor Vergata”, 10 September 2012

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

1-26

SLIDE 2

TURBULENT DRAG REDUCTION

ACTIVE OPEN-LOOP TECHNIQUE Energy input into system Pre-determined forcing Channel flow DNS (Reτ = uτh/ν = 200) SPANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution CONSTANT DP/DX τw is fixed in fully-developed conditions GAIN: Ub increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

2-26

SLIDE 3

TURBULENT DRAG REDUCTION

ACTIVE OPEN-LOOP TECHNIQUE Energy input into system Pre-determined forcing Channel flow DNS (Reτ = uτh/ν = 200) SPANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution CONSTANT DP/DX τw is fixed in fully-developed conditions GAIN: Ub increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

2-26

SLIDE 4

TURBULENT DRAG REDUCTION

ACTIVE OPEN-LOOP TECHNIQUE Energy input into system Pre-determined forcing Channel flow DNS (Reτ = uτh/ν = 200) SPANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution CONSTANT DP/DX τw is fixed in fully-developed conditions GAIN: Ub increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

2-26

SLIDE 5

TURBULENT DRAG REDUCTION

ACTIVE OPEN-LOOP TECHNIQUE Energy input into system Pre-determined forcing Channel flow DNS (Reτ = uτh/ν = 200) SPANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution CONSTANT DP/DX τw is fixed in fully-developed conditions GAIN: Ub increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

2-26

SLIDE 6

SPANWISE WALL OSCILLATIONS

GEOMETRY

Mean flow x y z Lx Ly Lz Ww = A sin 2π T t

R =

Cf,r −Cf,o Cf,r

=

U2

b,o−U2 b,r

U2

b,o

Why does the skin-friction coefficent decrease? Cf = τw/(1/2ρU2

b) decreases → study why Ub increases 10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

3-26

SLIDE 7

SPANWISE WALL OSCILLATIONS

GEOMETRY

Mean flow x y z Lx Ly Lz Ww = A sin 2π T t

R =

Cf,r −Cf,o Cf,r

=

U2

b,o−U2 b,r

U2

b,o

Why does the skin-friction coefficent decrease? Cf = τw/(1/2ρU2

b) decreases → study why Ub increases 10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

3-26

SLIDE 8

SPANWISE WALL OSCILLATIONS

GEOMETRY

Mean flow x y z Lx Ly Lz Ww = A sin 2π T t

R =

Cf,r −Cf,o Cf,r

=

U2

b,o−U2 b,r

U2

b,o

Why does the skin-friction coefficent decrease? Cf = τw/(1/2ρU2

b) decreases → study why Ub increases 10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

3-26

SLIDE 9

SPANWISE WALL OSCILLATIONS

GEOMETRY

Mean flow x y z Lx Ly Lz Ww = A sin 2π T t

R =

Cf,r −Cf,o Cf,r

=

U2

b,o−U2 b,r

U2

b,o

Why does the skin-friction coefficent decrease? Cf = τw/(1/2ρU2

b) decreases → study why Ub increases 10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

3-26

SLIDE 10

ENERGY BALANCE: A SCHEMATIC

DU DW DT Puv Pvw Ubτw Ew MKE-x MKE-z TKE

+3.5

15.9

+13.2 +12.9 +2.7

9.4

+0.8

6.5

+0.3 +1.1 6.5

Energy is fed through Px (→ Ubτw) and wall motion (→ Ew) Energy is dissipated through:

Mean-flow viscous effects (→ DU, DW ) Turbulent viscous effects (→ DT )

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

4-26

SLIDE 11

ENERGY BALANCE: A SCHEMATIC

DU DW DT Puv Pvw Ubτw Ew MKE-x MKE-z TKE

+3.5

15.9

+13.2 +12.9 +2.7

9.4

+0.8

6.5

+0.3 +1.1 6.5

Energy is fed through Px (→ Ubτw) and wall motion (→ Ew) Energy is dissipated through:

Mean-flow viscous effects (→ DU, DW ) Turbulent viscous effects (→ DT )

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

4-26

SLIDE 12

ENERGY BALANCE: A SCHEMATIC

DU DW DT Puv Pvw Ubτw Ew MKE-x MKE-z TKE

+3.5

15.9

+13.2 +12.9 +2.7

9.4

+0.8

6.5

+0.3 +1.1 6.5

Energy is fed through Px (→ Ubτw) and wall motion (→ Ew) Energy is dissipated through:

Mean-flow viscous effects (→ DU, DW ) Turbulent viscous effects (→ DT )

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

4-26

SLIDE 13

ENERGY BALANCE: A SCHEMATIC

DU DW DT Puv Pvw Ubτw Ew MKE-x MKE-z TKE

+3.5

15.9

+13.2 +12.9 +2.7

9.4

+0.8

6.5

+0.3 +1.1 6.5

Energy is fed through Px (→ Ubτw) and wall motion (→ Ew) Energy is dissipated through:

Mean-flow viscous effects (→ DU, DW ) Turbulent viscous effects (→ DT )

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

4-26

SLIDE 14

KEY QUESTIONS

STILL TO BE ANSWERED

Why does TKE decrease? Why does Ub increase?

DOES W ACT ON TURBULENT DISSIPATION?

Stokes-layer-type flow is generated by the wall oscillation Stokes layer’s direct action on DT =

V

ωiωidV Study the transport of turbulent enstrophy ωiωi The term enstrophy was coined by G. Nickel and is from Greek στρoφ´ η → turn

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

5-26

SLIDE 15

KEY QUESTIONS

STILL TO BE ANSWERED

Why does TKE decrease? Why does Ub increase?

DOES W ACT ON TURBULENT DISSIPATION?

Stokes-layer-type flow is generated by the wall oscillation Stokes layer’s direct action on DT =

V

ωiωidV Study the transport of turbulent enstrophy ωiωi The term enstrophy was coined by G. Nickel and is from Greek στρoφ´ η → turn

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

5-26

SLIDE 16

KEY QUESTIONS

STILL TO BE ANSWERED

Why does TKE decrease? Why does Ub increase?

DOES W ACT ON TURBULENT DISSIPATION?

Stokes-layer-type flow is generated by the wall oscillation Stokes layer’s direct action on DT =

V

ωiωidV Study the transport of turbulent enstrophy ωiωi The term enstrophy was coined by G. Nickel and is from Greek στρoφ´ η → turn

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

5-26

SLIDE 17

KEY QUESTIONS

STILL TO BE ANSWERED

Why does TKE decrease? Why does Ub increase?

DOES W ACT ON TURBULENT DISSIPATION?

Stokes-layer-type flow is generated by the wall oscillation Stokes layer’s direct action on DT =

V

ωiωidV Study the transport of turbulent enstrophy ωiωi The term enstrophy was coined by G. Nickel and is from Greek στρoφ´ η → turn

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

5-26

SLIDE 18

TURBULENT ENSTROPHY EQUATION

1 2 ∂ ωiωi ∂τ

1

= ωxωy ∂ U ∂y

2

+ ωzωy ∂ W ∂y

• 3

+

• ωj

∂u ∂xj ∂ W ∂y

• 4

−

• ωj

∂w ∂xj ∂ U ∂y

• 5

− vωx ∂2 W ∂y2

• 6

+ vωz ∂2 U ∂y2

7

+

• ωiωj

∂ui ∂xj

8

− 1 2 ∂ ∂y

• vωiωi
• 9

+ 1 2 ∂2 ωiωi ∂y2

10

−

• ∂ωi

∂xj ∂ωi ∂xj

11

.

Terms scaled in viscous units Stokes layer influences dynamics of turbulent enstrophy Three terms: which is the dominating one?

→ Let’s look at the terms of the equation

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

6-26

SLIDE 19

TURBULENT ENSTROPHY EQUATION

1 2 ∂ ωiωi ∂τ

1

= ωxωy ∂ U ∂y

2

+ ωzωy ∂ W ∂y

• 3

+

• ωj

∂u ∂xj ∂ W ∂y

• 4

−

• ωj

∂w ∂xj ∂ U ∂y

• 5

− vωx ∂2 W ∂y2

• 6

+ vωz ∂2 U ∂y2

7

+

• ωiωj

∂ui ∂xj

8

− 1 2 ∂ ∂y

• vωiωi
• 9

+ 1 2 ∂2 ωiωi ∂y2

10

−

• ∂ωi

∂xj ∂ωi ∂xj

11

.

Terms scaled in viscous units Stokes layer influences dynamics of turbulent enstrophy Three terms: which is the dominating one?

→ Let’s look at the terms of the equation

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

6-26

SLIDE 20

TURBULENT ENSTROPHY EQUATION

1 2 ∂ ωiωi ∂τ

1

= ωxωy ∂ U ∂y

2

+ ωzωy ∂ W ∂y

• 3

+

• ωj

∂u ∂xj ∂ W ∂y

• 4

−

• ωj

∂w ∂xj ∂ U ∂y

• 5

− vωx ∂2 W ∂y2

• 6

+ vωz ∂2 U ∂y2

7

+

• ωiωj

∂ui ∂xj

8

− 1 2 ∂ ∂y

• vωiωi
• 9

+ 1 2 ∂2 ωiωi ∂y2

10

−

• ∂ωi

∂xj ∂ωi ∂xj

11

.

Terms scaled in viscous units Stokes layer influences dynamics of turbulent enstrophy Three terms: which is the dominating one?

→ Let’s look at the terms of the equation

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

6-26

SLIDE 21

TURBULENT ENSTROPHY EQUATION

1 2 ∂ ωiωi ∂τ

1

= ωxωy ∂ U ∂y

2

+ ωzωy ∂ W ∂y

• 3

+

• ωj

∂u ∂xj ∂ W ∂y

• 4

−

• ωj

∂w ∂xj ∂ U ∂y

• 5

− vωx ∂2 W ∂y2

• 6

+ vωz ∂2 U ∂y2

7

+

• ωiωj

∂ui ∂xj

8

− 1 2 ∂ ∂y

• vωiωi
• 9

+ 1 2 ∂2 ωiωi ∂y2

10

−

• ∂ωi

∂xj ∂ωi ∂xj

11

.

Terms scaled in viscous units Stokes layer influences dynamics of turbulent enstrophy Three terms: which is the dominating one?

→ Let’s look at the terms of the equation

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

6-26

SLIDE 22

TURBULENT ENSTROPHY PROFILES

FIXED WALL

10 10

1

10

2

• 0.025
• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015

y+ 2 5 7 8 9 10 11

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

7-26

SLIDE 23

TURBULENT ENSTROPHY PROFILES

OSCILLATING-WALL PROFILES

10 10

1

10

2

• 0.025
• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015

y+ 2 3 4 5 6 7 8 9 10 11

Term 3, ωzωy∂ W/∂y → turbulent enstrophy production is dominant Turbulent dissipation of turbulent enstrophy increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

8-26

SLIDE 24

TURBULENT ENSTROPHY PROFILES

OSCILLATING-WALL PROFILES

10 10

1

10

2

• 0.025
• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015

y+ 2 3 4 5 6 7 8 9 10 11

Term 3, ωzωy∂ W/∂y → turbulent enstrophy production is dominant Turbulent dissipation of turbulent enstrophy increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

8-26

SLIDE 25

TURBULENT ENSTROPHY PROFILES

OSCILLATING-WALL PROFILES

10 10

1

10

2

• 0.025
• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015

y+ 2 3 4 5 6 7 8 9 10 11

Term 3, ωzωy∂ W/∂y → turbulent enstrophy production is dominant Turbulent dissipation of turbulent enstrophy increases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

8-26

SLIDE 26

INTERESTING, BUT...

We have not answered questions on TKE and Ub, yet Key: transient from start-up of wall motion

100 200 300 400 500 2.5 5 7.5 10 12.5 15

t+

USEFUL INFORMATION

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

9-26

SLIDE 27

INTERESTING, BUT...

We have not answered questions on TKE and Ub, yet Key: transient from start-up of wall motion

100 200 300 400 500 2.5 5 7.5 10 12.5 15

t+ Term 3

USEFUL INFORMATION

RED: term 3 increases abruptly, then decreases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

10-26

SLIDE 28

INTERESTING, BUT...

We have not answered questions on TKE and Ub, yet Key: transient from start-up of wall motion

100 200 300 400 500 2.5 5 7.5 10 12.5 15

t+ Term 3 Enstrophy

USEFUL INFORMATION

RED: term 3 increases abruptly, then decreases BLACK: turbulent enstrophy increases, then decreases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

11-26

SLIDE 29

INTERESTING, BUT...

We have not answered questions on TKE and Ub, yet Key: transient from start-up of wall motion

100 200 300 400 500 2.5 5 7.5 10 12.5 15

t+ Term 3 Enstrophy

USEFUL INFORMATION

RED: term 3 increases abruptly, then decreases BLACK: turbulent enstrophy increases, then decreases

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

12-26

SLIDE 30

INTERESTING, BUT...

We have not answered questions on TKE and Ub, yet Key: transient from start-up of wall motion

100 200 300 400 500 2.5 5 7.5 10 12.5 15

t+ Term 3 Enstrophy TKE

USEFUL INFORMATION

RED: term 3 increases abruptly, then decreases BLACK: turbulent enstrophy increases, then decreases BLUE: TKE decreases monotonically

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

13-26

SLIDE 31

DRAG REDUCTION MECHANISM

Initial state

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

14-26

SLIDE 32

DRAG REDUCTION MECHANISM

Short t+ < 50 Initial state ωzωy

+ ∂W+ ∂y+ ↑ ωiωi + ↑ 10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

15-26

SLIDE 33

DRAG REDUCTION MECHANISM

Short t+ < 50 Initial state ωzωy

+ ∂W+ ∂y+ ↑ ωiωi + ↑

D+

T ↑ 10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

16-26

SLIDE 34

DRAG REDUCTION MECHANISM

Short t+ < 50 Intermediate 50 < t+ < 400 Initial state

∂uv+ ∂y+ ↓

ωzωy

+ ∂W+ ∂y+ ↑ ωiωi + ↑

D+

T ↑

TKE ↓

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

17-26

SLIDE 35

DRAG REDUCTION MECHANISM

Short t+ < 50 Intermediate 50 < t+ < 400 Initial state ∂U

+

∂t+ > 0

∂uv+ ∂y+ ↓

ωzωy

+ ∂W+ ∂y+ ↑ ωiωi + ↑

D+

T ↑

TKE ↓

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

18-26

SLIDE 36

DRAG REDUCTION MECHANISM

Short t+ < 50 Intermediate 50 < t+ < 400 Long t+ > 400 Initial state ‘Drag reduction’

h+

U

+dy+ ↑

∂U

+

∂t+ > 0

∂uv+ ∂y+ ↓

ωzωy

+ ∂W+ ∂y+ ↑ ωiωi + ↑

D+

T ↑

TKE ↓

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

19-26

SLIDE 37

OSCILLATION PERIOD VS. TERM 3

0.02 0.04 0.06 0.08 0.1 0.05 0.1 0.15 0.2 0.25 0.3 0.35

• ωzωy∂

W/∂y+

g

R T +=8 T +=21 T +=42 T +=100

Drag reduction grows monotonically with global production term This happens up to optimum period

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

20-26

SLIDE 38

THANK YOU! REFERENCE

Ricco, P . Ottonelli, C. Hasegawa, Y. Quadrio, M. Changes in turbulent dissipation in a channel flow with oscillating walls

• J. Fluid Mech., 700, 77-104, 2012.

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

21-26

SLIDE 39

MEAN FLOW

25 50 75 100 125 150 175 0.05 0.1 0.15 0.2 0.25 0.3 0.35 10 10

1

10

2

5 10 15 20 25

y+

• U+

R T +

Mean velocity increases in the bulk of the channel Mean wall-shear stress is unchanged Optimum period of oscillation T + ≈ 75

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

22-26

SLIDE 40

TURBULENCE STATISTICS

10 10

1

10

2

• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2 10 10

1

10

2

• 1

1 2 3 4 5 6 7

y+

• u2

+

,

• v2

+

,

• w2

+

, uv+ y+

• vw

+ φ = 0 φ = π 4 φ = π 2 φ = 3π 4

Turbulence kinetic energy decreases Streamwise velocity fluctuations are attenuated the most New oscillatory Reynolds stress term vw in created, vw = 0

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

23-26

SLIDE 41

ENERGY BALANCE: EQUATIONS

GLOBAL MEAN KINETIC ENERGY EQUATION

U+ b τ+ w +

• A+

∂ W+ ∂y+

• y+=0
• Ew

= −

• uv

+ ∂ U+ ∂y+

• g
• Puv

−

• vw

+ ∂ W+ ∂y+

• g
• Pvw

+

• ∂

U+ ∂y+

2

g

• DU

+

• ∂

W+ ∂y+

2

g

• DW

GLOBAL TURBULENT KINETIC ENERGY EQUATION

• uv+ ∂

U+ ∂y+

• g
• Puv

+

• vw

+ ∂

W + ∂y+

• g
• Pvw

+

• ∂u+

i

∂x+

j

∂u+

i

∂x+

j

• g

= 0

TOTAL KINETIC ENERGY BALANCE

U+

b τ + w + E+ w = D+ U + D+ W + D+ T

TURBULENT DISSIPATION

D+

T =

ωiωi

+

g

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

24-26

SLIDE 42

PHYSICAL INTERPRETATION OF ωzωy∂ W/∂y

• ωzωy∂

W/∂y is key term leading to drag reduction

• ωzωy∂

W/∂y → ∂ W/∂y acts on ωzωy

• ωzωy ≈

∂u ∂y ∂u ∂z ∂u ∂y → upward eruption of near-wall low-speed fluid ∂u ∂z → lateral flanks of the low-speed streaks 200 400 600 800 200 400

x+ z+

∂u ∂y ∂u ∂z located at the sides of high-speed streaks

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

25-26

SLIDE 43

MODELLING TURBULENT ENSTROPHY PRODUCTION

THANKS TO ANDREA FOR THE HELP! y z xn xs α ωyz

SIMPLIFIED TURBULENT ENSTROPHY EQUATION

1 2 ∂ ∂t

• ω2

y + ω2 z

• = ωzωyG −

∂ωy

∂y

2

−

∂ωz

∂y

2

Rotation of axis 1 2 ∂ω2

n

∂t = Snnω2

n −

∂ωn

∂y

2

Integration by Charpit’s method ωn = ωn,0 esin α cos αGt

• stretching

e−β2te−βy

• dissipation

, β = ∂ωn/∂t ∂ωn/∂y ∼ λy λt

10 SEPTEMBER 2012

WALL-OSCILLATION DRAG-REDUCTION PROBLEM

26-26