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Drag-reducing characteristics Travelling waves of the generalized - - PowerPoint PPT Presentation

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Travelling waves (DNS) Drag-reducing characteristics Travelling waves of the generalized spanwise Stokes layer: (experiment) experiments and numerical simulations The GSL How do the waves work? Conclusions M.Quadrio Politecnico di

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Drag-reducing characteristics

  • f the generalized spanwise Stokes layer:

experiments and numerical simulations

M.Quadrio

Politecnico di Milano

Tokyo, March 18th, 2010

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outline

1

Travelling waves (DNS)

2

Travelling waves (experiment)

3

The GSL

4

How do the waves work?

5

Conclusions

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outline

1

Travelling waves (DNS)

2

Travelling waves (experiment)

3

The GSL

4

How do the waves work?

5

Conclusions

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The travelling waves

y x z Flow δ 2h λ c

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The original idea: spanwise wall oscillation

Quadrio & Ricco, JFM ’04

w(x,y = 0,z,t) = Asin(ωt) Large reductions of turbulent friction Unpractical

T

+

100 * R

200 400 600 800 10 20 30 40 A

+=18

A

+=12

A

+=4.5

T

+

  • pt
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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The oscillating wall made stationary

Viotti, Quadrio & Luchini, ETC 2007

w(x,y = 0,z,t) = Asin(κx) Existence of an

  • ptimal wavelength

λopt = UcTopt Can be implemented as a passive device (sinusoidal riblets)

λ

+

100 * R

2000 4000 6000 8000 10 20 30 40 A

+=12

A

+=6

A

+=12, temporal

λ

+

  • pt
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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The sinusoidal riblets

A new concept under experimental testing

Promising roughness distribution Better than straight riblets?

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The traveling waves: a natural extension

Purely temporal forcing The oscillating wall: w = Asin(ωt) Infinite phase speed Purely spatial forcing The steady waves: w = Asin(κx) Zero phase speed Combined space-time forcing The traveling waves: w = Asin(κx −ωt) Finite phase speed c = ω/κ

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Results from DNS (plane channel)

Quadrio et al., JFM 2009

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

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

How much power to generate the waves?

Map of Pin is similar to map of R! S and G may get very high

ω k

  • 3
  • 2
  • 1

1 2 3 1 2 3 4 5

72 40 89 96 51 81 62 103 30 116 39 29 54 78 61 78 93 96 105 148 87 69 39 29 48 84 133 70 58 75 87 51 141 120 173 65 88 124 114 34 36 40 177 172 64 95 107 106 109 134 153 179 136 175 149 42 44 116 162 147 91 33 52 49 43 67 31 108 116 67 164 186 188 95 35 43 67 157 121 46 177 125 55 67 129 150 156 167 172 146 142 97 34 24 34 46 62 82 92 113 27 31 37 132 61 88 125 166 3539 49 97 80 54 42 31 135 31 48 65 78 110 36 108 155 82 59 43 152 49 38 39 171 68 37 29 40 42 31 42 33 40 50 53 42 37 143 60 35 44 51 71 129 41 102 137 72 51 38 31 28 47 62 87 68 85 36 32 31 38 30 10 72 177 61 88 125 166 35 39 49 65 78 36 32 31 38 30 10 148 93 80 71 56 39 36 148 93 80 71 56 39 36
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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Power efficiency

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Power efficiency

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Power efficiency

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SLIDE 14

Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Power efficiency

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outline

1

Travelling waves (DNS)

2

Travelling waves (experiment)

3

The GSL

4

How do the waves work?

5

Conclusions

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Why?

A proof-of-principle experiment to: confirm drag reduction improve understanding of the travelling waves

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Main design choices

Cylindrical pipe Friction is measured through pressure drop Spanwise wall velocity: wall movement Temporal variation: unsteady wall movement Spatial variation: the pipe is sliced into thin, independently-movable axial segments

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The concept

Flow

traveling wave wall velocity

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

A global view

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Closeup of the rotating segments

60 slabs with 6 independent motors

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The transmission system

Shafts, belts and rotating segments

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The control system

Slab motion is feedback-controlled Tachimetric sensors Vertically-moving reservoir

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Flow parameters

Water, Re = 4900 or Reτ = 175 Reference pressure drop ≈ 10 Pa! Anticorrosion device Pressure sensors flooded in water Friction factor verifies Prantl’s empirical correlation

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Experimental conditions

ω

+

k

+

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.005 0.01 0.015 0.02

s=6 s=3

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Drag variation (1)

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Drag variation (2)

ω

+

100 * R

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 10 20 30 40 s=3 s=6

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Comments

Quantitative agreement between DNS and experiment is not expected: Spatial transient Cylindrical vs planar geometry Difference (small) in Re and A Waveform effects

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The discrete waveform

  • 1
  • 0.5

0.5 1 1 2 x/L Reference Approximation

i=0 i=1 i=2 i=3 i=4 i=5

  • 1
  • 0.5

0.5 1 1 2 x/L

i=0 i=1 i=2 i=3 i=4 i=5

uθ uθ

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Fourier expansion of the discrete wave

s=3 ˜ w = 3 √ 3 2π A

  • sin
  • ωt −κx
  • + 1

2 sin

  • ωt +2κx
  • +...
  • s=6

˜ w = 3 π A

  • sin
  • ωt −κx
  • + 1

5 sin

  • ωt +5κx
  • +...
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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Integral representation of the R map

R(ω,κ) = K(τ,ξ)fω,κ(τ,ξ)dτdξ fω,κ(τ,ξ) is the sinusoidal wave (monocromatic) Kernel K empirically determined by fitting DNS results

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The monocromatic R map

ω

+

100 * R

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

  • 20

20 40

s=3

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The non-monocromatic wave

The generating wave does not need be monocromatic Suppose linear superposition: ˜ R(ω,κ) = K(τ,ξ)

  • fω,κ + 1

2fω,−2κ

  • dτdξ
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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The non-monocromatic ˜ R map

ω

+

k

+

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.005 0.01 0.015 0.02

s=3

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Wiggles are predicted!

ω

+

100 * R

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

  • 20

20 40

s=3

Wiggles in the experimental data are discretization effects

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outline

1

Travelling waves (DNS)

2

Travelling waves (experiment)

3

The GSL

4

How do the waves work?

5

Conclusions

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The spanwise laminar flow

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

w(y,t) w(y,x) w(y,x −ct)

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Laminar: the GSL equation

∂w ∂t +u ∂w ∂x = ν ∂ 2w ∂x2 + ∂ 2w ∂y2

  • TSL (Stokes)

SSL (Viotti et al, PoF 2009)

  • ne-way coupling with streamwise flow
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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The analytical solution

1 δ ≪ h (translates into λ/h ≪ Reb) 2 Linear u profile

w(x,y,t) = Aℜ

  • Ce2πi(x−ct)/λAi
  • eπi/6

2πuy,w λν 1/3 y − c uy,w

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SLIDE 39

Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Spanwise turbulent flow agrees with the GSL

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Using the GSL solution (1)

Turbulent (DNS) vs laminar (analytical) δGSL

Black points are “good” waves

δlam δturb

2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Using the GSL solution (2)

Map of analytical δGSL

3.5 3.5 3.5 1 . 5 1 7 . 5

ω

+

k

+

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.005 0.01 0.015 0.02 0.025

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Using the GSL solution (3)

R vs analytical δGSL

Black points are “good” waves

δlam

+

100 * R

2 4 6 8 10 12 14 16 18 20

  • 30
  • 20
  • 10

10 20 30 40 50

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outline

1

Travelling waves (DNS)

2

Travelling waves (experiment)

3

The GSL

4

How do the waves work?

5

Conclusions

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The near-wall convection velocity Uc

Quadrio & Luchini, PoF 2003

y

+

Uc

+

10 10

1

10

2

5 10 15 20 mean vel. convection vel.

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Near-wall physics 2: the turbulence lifetime Tℓ

Quadrio & Luchini, PoF 2003

Space-time autocorrelation of wall friction τ

+

ξ

+

  • 50

50 100 150 200

  • 2253

2253 4506

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

How the waves increase drag

Waves lock with the convecting structures ’Steady’ forcing: c+ ≈ U+

c

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

How the waves decrease drag

Drag reduction is proportional to δGSL (WHY?) Large δGSL ⇒ large T Too large a T implies quasi-steady forcing

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Limit to drag reduction

Forcing must be unsteady

Oscillating wall Forcing on a timescale ≫ Tℓ does not yield DR Forcing timescale: oscillation period T

T

+

100 * R

200 400 600 800 10 20 30 40 A

+=18

A

+=12

A

+=4.5

T

+

  • pt
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SLIDE 49

Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Limit to drag reduction

Forcing must be ’unsteady’

Travelling waves Forcing on a timescale ≫ Tℓ does not yield DR Timescale: oscillation period T as seen by the convecting structures T = λ Uc −c

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Waves and turbulent friction

Four regions in each half-plane:

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outline

1

Travelling waves (DNS)

2

Travelling waves (experiment)

3

The GSL

4

How do the waves work?

5

Conclusions

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Conclusions

Streamwise-travelling waves: Useful for understanding drag-reduction mechanism (Flatland) Extremely energy-efficient Still incomplete understanding

Example

Issue of spatial discretization

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Outlook

Further understanding (why is δGSL ∼ R?) Further increase in efficiency Further development of actuators Explore Re effects

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

Credits

Pierre Ricco Fulvio Martinelli Claudio Viotti Franco Auteri Arturo Baron Marco Belan Paolo Luchini

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The scaling issue (1)

Drag reduction

ω

+

k

+

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.005 0.01 0.015 0.02 0.025

+12

  • 8
  • 7.5

+5

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Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions

The scaling issue (2)

Do streamwise vorticity fluctuations decrease?

“The streamwise vorticity fluctuation near the wall is reduced by the spanwise wall

  • scillation.”

y

+

ω

+

10 10

1

10

2

0.1 0.2 0.3 0.4 Ref Waves Waves, no GSL

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