An experimental study of

bypass transition

in plane Couette flow

S. AMALFI, F. LAADHARI & J. F. SCOTTS. AMALFI, F. LAADHARI & J. F. SCOTT

Laboratoire de Mécanique des Fluides et Laboratoire de Mécanique des Fluides et d’Acoustiqued’Acoustique

Unité Mixte de Recherche 5509Unité Mixte de Recherche 550969 134 ECULLY, France69 134 ECULLY, France

Euromech 10 th European Turbulence Conference

29 June – 2 July 2004, Trondheim, Norway

22

Introduction

• Plane Couette flow (PCF) is of particular interest :

simplicity of the basic flow and the absence of linear instability.

• Recent scenario* :

streamwise vortices streaks secondary instabilities turbulence

• The aim of the present study : investigate such a scenario in PCF introducing Counter rotating pairs of streamwise vortices based on optimal criteria.

TransitioTransitionn

Perturbation ratePerturbation rate knowledgeknowledgeOccurrenceOccurrence

in naturein nature

Classicalinfinitesimal

perturbations(≤ 0.1%)

Wellknown

seldomseldom

Bypassfinite perturbations

(≥ 1%)poorly

understood most casesmost cases

• 2 different kinds of transition to turbulence in 2D bounded flows:

*Reddy et al. (1998), J. Fluid Mech., 365, 269-299

33

Outline

• Experimental setup and perturbation generating

system

• Tomography animation and flow characteristics

based on LDA measurements

• Visualization of vortical structures and statistical

analysis based on PIV measurements

• Conclusion and perspectives

44

Experimental setup

Experimental facilities

Tomography and LDA results PIV analysis

• PCF : flow between one or two moving belts

• Very few experimental PCF studies, considering several setup difficulties (moving belts stability, free stream perturbations, etc.)

• Reynolds number of interest is 470 with .walle

U hR

Water

Lx=200 cm Ly=2h=2.6 cm Lz=30 cm

ZOOM

Laminar

Re ≤ 470

Turbulent

Re ≥ 500

Top viewMotor Encoder

55

Experimental facilities

Tomography and LDA results PIV analysis

66

50 mm

5 mm30°

40 mm

Perturbation system based on optimal perturbations*

Experimental facilities

Tomography and LDA results PIV analysis

* Butler & Farrell (1992), Phys. Fluids, 4, 1637-1650

77

Experimental facilities

Tomography and LDA results PIV analysis

plexiglasswall

moving belt

88

Experimental facilities

Tomography and LDA results PIV analysis

99

-4 -3 -2 -1 0 1 2 3 4

-1

-0.5

0

0.5

1

Before injection

Averaged streamwise velocity (cm/s)

Y(cm)

After injection

Experimental facilities

Tomography and LDA results PIV analysis

Time (s)

Y(mm)

cm/sInstantaneous streamwise velocity

1010

• PIV measurements (2 000 snapshots) performed in the transverse

plane. Snapshot size : 26 mm (y) x 96 mm (z) giving two velocity

components : v and w (along y et z).

• Dynamical analysis of structures possible, considering very low

velocities of moving walls (3.6 cm/s) with a 4 Hz frequency

acquisition

• Normalized Angular Momentum* is a good tool to visualize

vortical structures

Visualization of vortical structures

Experimental facilities

Tomography and LDA results PIV analysis

* Michard et al. (1997), 11th Int. Symp. Turbulent Shear Flows, F. Durst, Springer, 278-290

1111

Time

Time (s)

Z

001 ≤ Time (s) ≤ 050

Z(mm

)Y

(mm)

Time (s)

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Time (s)

Z

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Z(mm

)Y

(mm)

Time (s)

050 ≤ Time (s) ≤ 100

Time (s)

Z

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Z(mm

)Y

(mm)

Time (s)

100 ≤ Time (s) ≤ 150

Time (s)

Z

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Z(mm

)Y

(mm)

Time (s)

150 ≤ Time (s) ≤ 200

Time (s)

Z

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Z(mm

)Y

(mm)

Time (s)

200 ≤ Time (s) ≤ 250

Time (s)

Z

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Z(mm

)Y

(mm)

Time (s)

250 ≤ Time (s) ≤ 300

Time (s)

Z

Z(mm

)Y

(mm)

Time (s)

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

300 ≤ Time (s) ≤ 350

Time (s)

Z

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

Z(mm

)Y

(mm)

Time (s)

350 ≤ Time (s) ≤ 400

Times (s)

Z

Z(mm

)Y

(mm)

Time (s)

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

400 ≤ Time (s) ≤ 450

Time (s)

Z

Z(mm

)Y

(mm)

Time (s)

0 100 200 300 400 5000

0.5

1

1.5

2

2.5x 10

-5

Time (s)

Energy(m²/s²)

450 ≤ Time (s) ≤ 500

Experimental facilities

Tomography and LDA results PIV analysis

1212

50 100 150 200 250 300 350 400 450 5000

5

10

15

Time (s)

vR

Experimental facilities

Tomography and LDA results PIV analysis

50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 10-5

Energy(m²/s²)

Time (s)

2

x

v

dA

R

50 100 150 200 250 300 350 400 450 5000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

d/h

Time (s)

1313

Conclusion and Perspectives

• First PIV database concerning PCF

• Transient growth of secondary instabilities has been observed

using visualizations and PIV measurements

• Mean size of structures doesn’t play a key role in the transition

process

but vortex intensity does !

• LDA measurements confirming PIV study

• Comparison with other complex cases : Boundary Layer over a

flat plate