Spanwise generalized Stokes layer and turbulent drag reduction - - PowerPoint PPT Presentation

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Spanwise generalized Stokes layer and turbulent drag reduction - - PowerPoint PPT Presentation

Nov 16, 2022 27 likes •233 views

Turbulent drag reduction Laminar GSL Putting things together Spanwise generalized Stokes layer and turbulent drag reduction M.Quadrio 1 & P. Ricco 2 1 Politecnico di Milano 2 Kings College, London VIII Euromech Fluid Mechanics Conference

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Turbulent drag reduction Laminar GSL Putting things together

Spanwise generalized Stokes layer and turbulent drag reduction

M.Quadrio1 & P. Ricco2

1 Politecnico di Milano 2 King’s College, London

VIII Euromech Fluid Mechanics Conference Bad Reichenhall, September 14th, 2010

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Turbulent drag reduction Laminar GSL Putting things together

Outline

Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

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Turbulent drag reduction Laminar GSL Putting things together

Outline

Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

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Turbulent drag reduction Laminar GSL Putting things together

The travelling waves

y x z Flow δ 2h λ c

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Turbulent drag reduction Laminar GSL Putting things together

Results from DNS (plane channel)

Quadrio et al., JFM 2009

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

ω kx

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

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41 37 34 19 6

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7

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10 47 8 35 24 1 1

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2 24 16 38

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

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48

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41 45 38 26

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36 18 15 15 31 34 33 19 4

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46 44

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45 39 18 3

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14 26 36 14 1

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31 34 27 18

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

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41

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8 36 33 22 5

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4 35 34 27 32

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3

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33 16 31 34 27 18

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5 21 32 34 0 -6

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3

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

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Turbulent drag reduction Laminar GSL Putting things together

Laboratory experiment (cylindrical pipe)

Auteri et al, Phys. Fluids (2010), in press

Flow

traveling wave wall velocity

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Turbulent drag reduction Laminar GSL Putting things together

Drag variation

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Turbulent drag reduction Laminar GSL Putting things together

Outline

Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

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Turbulent drag reduction Laminar GSL Putting things together

Laminar flow: the GSL equation

Quadrio & Ricco JFM 2010, in press

∂w ∂t + u ∂w ∂x = ν ∂2w ∂x2 + ∂2w ∂y2

  • TSL (Stokes)
  • SSL
  • All together: GSL
  • one-way coupling with streamwise flow
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Turbulent drag reduction Laminar GSL Putting things together

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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Turbulent drag reduction Laminar GSL Putting things together

Outline

Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

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Turbulent drag reduction Laminar GSL Putting things together

Turbulent spanwise flow agrees with laminar GSL!

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Turbulent drag reduction Laminar GSL Putting things together

Using the GSL solution

R vs analytical δGSL

Black points are “good” waves

δlam

+

100 * R

2 4 6 8 10 12 14 16 18 20

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10 20 30 40 50

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Turbulent drag reduction Laminar GSL Putting things together

How the waves increase drag

Key parameter: phase speed

  • Waves lock with the convecting structures
  • Steady forcing in the convective reference frame: c+ ≈ U+

c

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Turbulent drag reduction Laminar GSL Putting things together

How the waves decrease drag

Key parameter: unsteadiness

  • Drag reduction is proportional to δGSL (WHY?)
  • Large δGSL ⇒ large T
  • Quasi-steady forcing when T ≫ Tℓ
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Turbulent drag reduction Laminar GSL Putting things together

Limit to drag reduction

Forcing must be ’unsteady’

Forcing on a timescale ≫ Tℓ does not yield DR

Oscillating wall

  • Forcing timescale: oscillation period T

Travelling waves

  • Forcing timescale: oscillation period T as seen by the

convecting structures T = λ Uc − c

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Turbulent drag reduction Laminar GSL Putting things together

Waves and turbulent friction

Waves in (1) and (2) are ”good” waves

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Turbulent drag reduction Laminar GSL Putting things together

Conclusions

  • Waves reduce drag and are energy-efficient
  • Waves useful for understanding drag-reduction mechanism
  • Still incomplete understanding of the physics
  • Analytical solution for the GSL
  • Relation between laminar GSL and turbulent drag reduction
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Turbulent drag reduction Laminar GSL Putting things together

Issues

  • Further understanding (why is δGSL ∼ R?)
  • Actuators
  • Higher efficiency?
  • Re effects
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Turbulent drag reduction Laminar GSL Putting things together

THANK YOU