What happens to turbulent drag reduction at higher Re ? Davide Gatti - - PowerPoint PPT Presentation

SLIDE 1

What happens to turbulent drag reduction at higher Re ?

Davide Gatti1,2, Maurizio Quadrio1

1 Dept. for Aeronautical Sciences and Technologies, Politecnico di Milano 2 Center for Smart Interfaces, TU-Darmstadt

EFMC IX, Rome, September 2012

SLIDE 2

Skin-friction drag reduction and high Re

• Several techniques are under development
• DNS and experiments at low Re, applications at high Re
• Focus on active techniques, spanwise forcing
• Drop of max. drag reduction Rm as Re grows (data for

200 < Reτ < 1000)

• Literature (Choi AIAA J. 02, Touber JFM12) suggests

Rm ∼ Re−0.20

τ

SLIDE 3

What happens at high Re?

Numerical / experimental information for spanwise forcing Reτ 100 Rm

1000 2000 3000 10 20 30 40 50

SLIDE 4

What happens at high Re?

Numerical / experimental information for spanwise forcing Reτ 100 Rm

1000 2000 3000 10 20 30 40 50 2 1

SLIDE 5

Several attack strategies

✻

Modeling error

none high

RANS exceeds present modeling skills LES we did non succeed with standard models Touber JFM 2012 : high computational cost DNS prohibitive computational costs for a parametric study Experiments difficulties measuring drag, spatial transient

SLIDE 6

Our workaround

DNS of turbulence in channels of reduced size

• No modeling errors (like in full DNS)
• Discretization errors like in full DNS, but...
• ...truncation of large scales is potentially larger!

SLIDE 7

Neither minimal nor full

L+

z = 1884

L

+ x

= 3 7 6 8

SLIDE 8

Neither minimal nor full

L+

z = 100

L

+ x

= 2 5

SLIDE 9

Neither minimal nor full

L+

z = 1000

L

+ x

= 2

SLIDE 10

Choosing the simulation time

Larger fluctuations of the space-averaged wall shear (Ω) tUp/h MFU Full 200 400 600 800 1000 5 6 7

Jim´ enez & Moin, JFM 1991

Need to compromise between space and time average σΩ = C σΩ √Tsim

SLIDE 11

Drag reduction with error bars

(oscillating wall, A+ = 12, T + = 125) Box size (length*width)

+

100 R

10

5

10

6

10

7

20 25 30 35 40 45

Standard "large" box Our "small" box DNS asymptote

SLIDE 12

The oscillating wall, up to Reτ = 1000

A+ = 12 T

+

100 R

50 100 150 200 250 300 10 20 30 40

200 DNS 200 1000

SLIDE 13

The travelling wave

A+ = 12, λ+

x = 1256

• 20
• 10
• 1

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

ω κ

SLIDE 14

The travelling wave, up to Reτ = 2000

A+ = 12, λ+

x = 1256

ω

+

100 R

• 0.2
• 0.1

0.1 0.2 0.3 20 40

200 DNS 200 1000 2000

SLIDE 15

Effect of Re: maximum R

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

SLIDE 16

Effect of Re: region at high-ω

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

SLIDE 17

Conclusions

... of suggestive nature!

• Doable strategy for higher-Re parametric studies
• Decreasing trend of max R confirmed: R ∼ Re−0.22

τ

• Low-Re effects identified
• More optimistic view: R ∼ Re−0.08

τ

SLIDE 18

Effect of Re: region at high-ω

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

SLIDE 19

Full DNS confirms the slow decrease!

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

Full DNS

SLIDE 20

Open questions

• Generality?
• What happens at even higher Re?
• How to achieve real (non-suggestive) results?

SLIDE 21

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

SLIDE 22

Simulation data

Simulation time: T +

sim = 12000 ÷ 24000

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

SLIDE 23

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

SLIDE 24

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