Lorentz Center - Leiden, August 23 rd 2006 DISPERSION IN ROTATING TURBULENCE the development of a 3D-PTV system, Herman Clercx, Ruben Trieling
MOTIVATIONS AND GOALS Two main goals give reasons for this project: The fundamental investigation of the influence of background rotation on the properties of turbulence and of turbulent dispersion: 2-dimensionalisation effect of the Coriolis force; Reduced direct energy cascade and energy dissipation; Effects of Ekman layer; Study of the production terms in the evolution equations for vorticity, strain rate and enstrophy. The validation of KS, DNS and LES models, especially with regards to the description of dispersion processes.
MEASUREMENTS AND POST-PROCESSING Through the access to Lagrangian Trajectories, Velocities and the complete tensor of Velocity Derivatives along particle tracks Study of Vorticity, Strain Rate, mean Energy, Enstrophy Analysis of the weight of self-amplification and forcing terms in the evolution equations for Vorticity, Strain Rate, Enstrophy II order Lagrangian Structure Functions and comparison with K41b derived models Evolution of passive and active objects and their alignment in respect to the Strain Rate eigenframe One and two-particles Dispersion and the influence of: Particle density [0.8~2.0] Turbulence intensity [Reλ=0~150] Particle size [20~300 µm]
EXPERIMENTAL PARAMETERS Effect of background rotation on turbulence, to simulate geophysical flows at large scales (tens of km) Ro = nonlinear acceleration Coriolis force = U 2 L 2U Ωsin θ Rotation speed Ω = 0~2.5π rad/s Ro = ~0.08 Continuously forced flow Central and bottom measuring volumes
MET HODS: THE EXPERIMENTAL SET-UP Required accessibility to Lagrangian 3D trajectories and the complete tensor of velocity derivatives cu i /cx j accuracy: measuring volume: x = η 10 3 V L t = τ η 10 Lagrangian tracks (Voth, 2000) Turbulence will be generated via ELECTROMAGNETICAL FORCING bottom 1T-magnets array Na-Cl aqueous solution two electrodes connected to a PC-controlled power supply (up to 8.4A)
MET HODS: THE EXPERIMENTAL SET-UP 3D Particle Tracking Velocimetry system, four points of view CAMERAS SEEDED SALT SOLUTION LED ARRAY ELECTRODE MAGNETS ROTATI NG TABLE ACQUISITION HARDWARE front view side view
MET HODS: THE EXPERIMENTAL SET-UP Perspex container with inner dimensions 500x500x275 mm Rotating table diameter 1500 mm max rotation speed 10 rad/s
MET HODS: PRELIMINARY EST IMATES PIV and STEREO-PIV measurements on horizontal plane 5mm above the bottom at maximum driven current (8.4A) Energy dissipation Kolmogorov length scale Kolmogorov time scale Integral length scale Taylor based Reynolds number ε = 8.3 10-4 m 2 s -3 η = 187 µm τ η = 0.022 s L y magnet spacing = 7 cm Reλ = 150 fast cameras: 1000 2 px 500 fps
MET HODS: DIGITAL CAMERAS Two options: single camera and image-splitter four independent cameras Photron FASTCAM-X 1024 PCI cmos sensor with 17 µm pixels 1024 2 pixels 1000 fps frame rate 10 bit depht 12 Gb internal memory (8 s recording)
MET HODS: CAMERA ARRANGEMENT Axial-symmetric optical setup with 30 o angle in water between the cameras OPTICAL PATH MEASURING VOLUME
MET HODS: LIGHT SYSTEM Requirements: 150W of light in a volume of 10 cm side not monochromatic light not collimated light Luxeon K2 LED 3.85V, 1.5A, 11% efficiency dominant WL 455nm LED array, 238 units, 1370W dissipation
MET HODS: LIGHT SYSTEM 238-leds array front view ALLUMINIUM WATER-COOLED PLATE 6 o LEDCOLLIMATOR 7-CELL CLUSTER OPTIC top view COOLING PIPE
METHODS: FROM PICTURES TO TRACKS, THE CODE Thanks to a starting collaboration with ETH (CH) and Risoe (DK).. 3D-PTV code ETH Zurich A spatio-temporal matching algorithm: 3D positions, from image to object space time tracking (4x2 image coord) - (3 object coord) = = 5 redundant observations (Willneff, 2004) These are used, together with predictions over successive time steps, to establish spatio-temporal connections even in case of high seeding density and high particle accelerations.
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