An experimental study of bypass transition in plane Couette flow S. AMALFI, F. LAADHARI & J. F. SCOTT Laboratoire de Mécanique des Fluides et d’Acoustique Unité Mixte de Recherche ECULLY, France Euromech 10 th European Turbulence Conference 29 June – 2 July 2004, Trondheim, Norway

2 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. Transition Perturbation rate knowledgeOccurrence in nature Classical infinitesimal perturbations (≤ 0.1%) Well knownseldom Bypass finite perturbations (≥ 1%) poorly understood most cases 2 different kinds of transition to turbulence in 2D bounded flows: *Reddy et al. (1998), J. Fluid Mech., 365,

3 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

4 Experimental setup Experimental facilities Tomography and LDA resultsPIV 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. Water Lx=200 cm Ly=2h=2.6 cm Lz=30 cm ZOOM Laminar Re ≤ 470 Turbulent Re ≥ 500 Top view Motor Encoder

5 Experimental facilities Tomography and LDA resultsPIV analysis

6 50 mm 5 mm 30° 40 mm Perturbation system based on optimal perturbations* Experimental facilities Tomography and LDA resultsPIV analysis * Butler & Farrell (1992), Phys. Fluids, 4,

7 Experimental facilities Tomography and LDA resultsPIV analysis plexiglass wall moving belts

8 Experimental facilities Tomography and LDA resultsPIV analysis

Before injection Averaged streamwise velocity (cm/s) Y (cm) After injection Experimental facilities Tomography and LDA resultsPIV analysis Time (s) Y (mm) cm/s Instantaneous streamwise velocity

10 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 resultsPIV analysis * Michard et al. (1997), 11th Int. Symp. Turbulent Shear Flows, F. Durst, Springer,

11 Time Time (s) Z 001 ≤ Time (s) ≤ 050 Z (mm) Y (mm) Time (s) Energy (m²/s²) Time (s) Z Energy (m²/s²) Z (mm) Y (mm) Time (s) 050 ≤ Time (s) ≤ 100 Time (s) Z Energy (m²/s²) Z (mm) Y (mm) Time (s) 100 ≤ Time (s) ≤ 150 Time (s) Z Energy (m²/s²) Z (mm) Y (mm) Time (s) 150 ≤ Time (s) ≤ 200 Time (s) Z Energy (m²/s²) Z (mm) Y (mm) Time (s) 200 ≤ Time (s) ≤ 250 Time (s) Z Energy (m²/s²) Z (mm) Y (mm) Time (s) 250 ≤ Time (s) ≤ 300 Time (s) Z Z (mm) Y (mm) Time (s) Energy (m²/s²) 300 ≤ Time (s) ≤ 350 Time (s) Z Energy (m²/s²) Z (mm) Y (mm) Time (s) 350 ≤ Time (s) ≤ 400 Times (s) Z Z (mm) Y (mm) Time (s) Energy (m²/s²) 400 ≤ Time (s) ≤ 450 Time (s) Z Z (mm) Y (mm) Time (s) Energy (m²/s²) 450 ≤ Time (s) ≤ 500 Experimental facilities Tomography and LDA resultsPIV analysis

12 Time (s) Experimental facilities Tomography and LDA resultsPIV analysis Energy (m²/s²) Time (s) d/h Time (s)

13 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