Turbulent Drag Reduction at Moderate Reynolds Numbers via Spanwise - - PowerPoint PPT Presentation

SLIDE 1

Introduction Flow Unit for Drag Reduction Results Conclusions

Davide Gatti1,2, Maurizio Quadrio1

Turbulent Drag Reduction at Moderate Reynolds Numbers via Spanwise Velocity Waves

1POLITECNICO DI MILANO 2CENTER OF SMART INTERFACES

Technische Universit¨ at Darmstadt

SLIDE 2

Introduction Flow Unit for Drag Reduction Results Conclusions

Turbulent skin-friction Drag Reduction

Motivation

• Economical benefits
• Environmental benefits
• Better understanding of turbulence

Our focus

• The effects of Re on a particular control strategy

1/17

SLIDE 3

Introduction Flow Unit for Drag Reduction Results Conclusions

A promising strategy

Streamwise-traveling waves of spanwise wall velocity (Quadrio et al., JFM 2009)

z y x 2h Flow δ λ

ww(x, t) = A sin(κx x − ω t) c = ω κx

2/17

SLIDE 4

Introduction Flow Unit for Drag Reduction Results Conclusions

High performances

Drag reduction rate: R = P0 − P P0 Input power: Pin = 1 Lx Lz T Lx Lz T ww ∂w ∂y dtdxdz Power saving rate: S = R − Pin P0

3/17

SLIDE 5

Introduction Flow Unit for Drag Reduction Results Conclusions

High drag reduction achievable

(Quadrio et al., JFM 2009)

• 20
• 10
• 1

10 10 1 10 2 20 20 20 2 3 3 30 3 4 40 40

ω k

• 3
• 2
• 1

1 2 3 1 2 3 4 5

33 45 24 33 42 29 38 13 47 3 32 31

• 3
• 9

41 37 34 19 6

• 18

7

• 9

10 47 8 35 24 1 1

• 8
• 10
• 7

2 24 16 38

• 7
• 18
• 15

46 47 45 8 16 40 33 30 31 29 24 20 13 23 16 21 44 43 5

• 17

21

• 14

48

• 1

41 45 38 26

• 16
• 17

36 18 15 15 31 34 33 19 4

• 2

45 16

• 16

46 44

• 20
• 23
• 22
• 10
• 2
• 23
• 20
• 14

45 39 18 3

• 6
• 1

14 26 36 14 1

• 21

31 34 27 18

• 3 5

21 32 36 37 36 1 24 48 44 32 34 29

• 8

28 20 36 40 42 17 42 45 47 15 37 46 40 46 45 46 45 47 46 41 45 46 46 21 40 42 45 43 36

• 15

41

• 8

8 36 33 22 5

• 9

4 35 34 27 32

• 6
• 7

3

• 9
• 7

33 16 31 34 27 18

• 3

5 21 32 34 0 -6

• 7

3

• 9
• 7

22 32 33 33 27 5 22 32 33 33 27 5 0

! " # $% &'() δ λ ww(x, t) = A sin(κx x − ω t) c = ω κx

ω κ

4/17

SLIDE 6

Introduction Flow Unit for Drag Reduction Results Conclusions

What happens at high Re?

Two possible scenarios

Reτ 100 R

• Numerical
• Experimental

Unknown Zone ”Well-known” Zone 500 1000 1500 2000 2500 3000 10 20 30 40 50

5/17

SLIDE 7

Introduction Flow Unit for Drag Reduction Results Conclusions

What happens at high Re?

Two possible scenarios

Reτ 100 R

• Numerical
• Experimental

Unknown Zone ”Well-known” Zone 1 2 500 1000 1500 2000 2500 3000 10 20 30 40 50

5/17

SLIDE 8

Introduction Flow Unit for Drag Reduction Results Conclusions

Several means of investigation

✻

Modeling error

none high

RANS exceeds present modeling skills LES

• ur attempt: Smagorinsky model fails

Touber and Leschziner, JFM 2012 : high computational costs and low reliability DNS prohibitive computational costs for a parametric study Experiments difficult drag measurements and more

6/17

SLIDE 9

Introduction Flow Unit for Drag Reduction Results Conclusions

Our approach

Up to Reτ = 2000 with DNS of channels of reduced size

Pros

• No modeling errors
• No resolution errors

Cons

• Discretization errors

at the large scales

7/17

SLIDE 10

Introduction Flow Unit for Drag Reduction Results Conclusions

Neither minimal nor full

L+

z = 1000

L

+ x

= 2

8/17

SLIDE 11

Introduction Flow Unit for Drag Reduction Results Conclusions

Neither minimal nor full

L+

z = 1884

L

+ x

= 3 7 6 8

8/17

SLIDE 12

Introduction Flow Unit for Drag Reduction Results Conclusions

Neither minimal nor full

L+

z = 100

L

+ x

= 2 5

8/17

SLIDE 13

Introduction Flow Unit for Drag Reduction Results Conclusions

Simulation time

Larger fluctuations of the space-averaged wall shear (Ω) Ω treated as a measure: σΩ = C σΩ √Tsim

• ptimal compromise between space and time average

tUp/h MFU Full 200 400 600 800 1000 5 6 7

Jim´ enez & Moin, JFM 1991 9/17

SLIDE 14

Introduction Flow Unit for Drag Reduction Results Conclusions

Effects on drag reduction

κx = 0 (oscillating wall)

• urs

full L+

x × L+ z

100 R 105 106 107 20 25 30 35 40 45

• Reduced

DNS

10/17

SLIDE 15

Introduction Flow Unit for Drag Reduction Results Conclusions

Effects on drag reduction

κx = 0 (oscillating wall)

• urs

full L+

x × L+ z

100 R 105 106 107 20 25 30 35 40 45

• Reduced

DNS

10/17

SLIDE 16

Introduction Flow Unit for Drag Reduction Results Conclusions

Wave parameters

λ+

x = 1256

• 20
• 1
• 1

1 1 10 10 2 20 20 20 2 30 30 30 30 40 40 4

ω k

• 3
• 2
• 1

1 2 3 1 2 3 4 5

33 45 24 33 42 29 38 13 47 3 32 31

• 3
• 9

41 37 34 19 6

• 18

7

• 9

10 47 8 35 24 1 1

• 8
• 10
• 7

2 24 16 38

• 7
• 18
• 15

46 47 45 8 16 40 33 30 31 29 24 20 13 23 16 21 44 43 5

• 17

21

• 14

48

• 1

41 45 38 26

• 16
• 17

36 18 15 15 31 34 33 19 4

• 2

45 16

• 16

46 44

• 20
• 23
• 22
• 10
• 2
• 23
• 20
• 14

45 39 18 3

• 6
• 1

14 26 36 14 1

• 21

31 34 27 18

• 3 5

21 32 36 37 36 1 24 48 44 32 34 29

• 8

28 20 36 40 42 17 42 45 47 15 37 46 40 46 45 46 45 47 46 41 45 46 46 21 40 42 45 43 36

• 15

41

• 8

8 36 33 22 5

• 9

4 35 34 27 32

• 6
• 7

3

• 9
• 7

33 16 31 34 27 18

• 3

5 21 32 34 0 -6

• 7

3

• 9
• 7

22 32 33 33 27 5 22 32 33 33 27 5 0

ω κ

11/17

SLIDE 17

Introduction Flow Unit for Drag Reduction Results Conclusions

Drag reduction

λ+

x = 1256

ω+ 100 R Reτ

• 200

1000

• △ 2000
• 0.2
• 0.1

0.1 0.2 0.3

• 10

10 20 30 40 50

12/17

SLIDE 18

Introduction Flow Unit for Drag Reduction Results Conclusions

Input power

λ+

x = 1256

ω+ 100 Pin/P0 Reτ 200 •

• 1000

2000

△

• 0.2
• 0.1

0.1 0.2 0.3

• 200
• 150
• 100
• 50

13/17

SLIDE 19

Introduction Flow Unit for Drag Reduction Results Conclusions

Reynolds effect

100 200 400 1000 2000 10000 15 20 25 30 35 40 45 50 55

49 36.5 29.2

Reτ 100 R

−0.2 −0.1 0.1 0.2 0.3 20 40

ω+

100 R

Rmax ∼ Re−0.22

Reduced

14/17

SLIDE 20

Introduction Flow Unit for Drag Reduction Results Conclusions

Reynolds effect

100 200 400 1000 2000 10000 15 20 25 30 35 40 45 50 55

22.4 19.7

Reτ 100 R

−0.2 −0.1 0.1 0.2 0.3 20 40

ω+

100 R

R ∼ Re−0.08

Reduced

15/17

SLIDE 21

Introduction Flow Unit for Drag Reduction Results Conclusions

Reynolds effect

100 200 400 1000 2000 10000 15 20 25 30 35 40 45 50 55

21.7 20.5

Reτ 100 R

−0.2 −0.1 0.1 0.2 0.3 20 40

ω+

100 R

R ∼ Re−0.08

DNS

15/17

SLIDE 22

Introduction Flow Unit for Drag Reduction Results Conclusions

“Conclusions”

R ∼ Re−0.22

τ

16/17

SLIDE 23

Introduction Flow Unit for Drag Reduction Results Conclusions

“Conclusions”

...or even better!

R ∼ Re−0.08

τ

S increases with Re

16/17

SLIDE 24

Introduction Flow Unit for Drag Reduction Results Conclusions

A broader result Need for extensive parametric studies

focusing on optimal parameters gives a limited view!

17/17

SLIDE 25

Davide Gatti1,2, Maurizio Quadrio1

Turbulent Drag Reduction at Moderate Reynolds Numbers via Spanwise Velocity Waves

1POLITECNICO DI MILANO 2CENTER OF SMART INTERFACES

Technische Universit¨ at Darmstadt 17/17

SLIDE 26

Box size

L+

x = 1000 ÷ 2000

L+

z = L+ x /2

Criteria:

• “Healthy” turbulence up to yd apart from wall

if L+

z = 3y + d

and L+

x ≈ h+

(Florez and Jim´ enez, PoF 2010)

• At least one wavelength long Lx = 2π/κx

17/17

SLIDE 27

Simulation data

Simulation time: T +

sim = 12000 ÷ 24000

Resolution: ∆x+ = ∆z+ = 10 ∆y + < 4 Grid points: 128 × Reτ/2 × 64 192 × Reτ/2 × 96

17/17

SLIDE 28

Effects on wall skin friction

Fixed wall

L+

x × L+ z

Cf × 103 Dean

• Reτ = 200
• Reτ = 1000
• △

Reτ = 2000 2 4 6 8 10 12 ×106 3 4 5 6 7 8 9

17/17

SLIDE 29

Effects on input power

κx = 0

T + 100 Pin/P0 L+

x

3746

• 666
• 1000
• 1326
• 2000

85 90 95 100 105 110 115 120

• 90
• 85
• 80
• 75
• 70

17/17