* University of Mining and Metallurgy, AGH Cracow Experimental and Numerical Investigations of Buoyancy Driven Instability in a Vertical Cylinder Tomasz A. Kowalewski & ** A. Cybulski, J. Szmyd *, M.. Jaszczur * IPPT PAN, Polish Academy of Sciences Center of Mechanics and Information Technology

Common configuration for many technological processes Usually assumed flow axisymmetry is not necessarily present Why we are interested? The flow structure has direct effect on a quality of materials in: Metallurgy: casting, melting, alloys structure  morphology of crystalline-like structure, mushy regions, components segregation, anisotropy Electronics: crystal growth for semiconductors, superconductors  imperfections of the crystal structure Convective flow in an axisymmetric geometry

Formulation of the problem Convective flow in an axisymmetric geometry Natural convection in a vertical cylindrical Isothermal cold lid Heat flux through bottom and side walls

Investigated Geometry External hot bath Cavity diameter 37mm; side walls: 2 mm glass or Plexiglas

Numerical Modelling F Navier-Stokes and energy equations in cylindrical coordinates, 3D representation incompressible, viscous fluid finite volume method with staggered mesh SIMPLER algorithm to solve the pressure QUICK scheme for convection terms fully implicit method for unsteady terms

Numerical Modelling Numerical mesh 50 x 72 x 50 for r, , z

Particle Image Velocimetry and Thermometry Using Thermochromic Liquid Crystals EXPERIMENTAL Transient measurements of Temperature field Velocity field Particle tracking

PIV +PIT measurement process LIQUID CRYSTAL TRACERS Flow Field The flow field is seeded with suspension of TLC tracers The flow field is seeded with suspension of TLC tracers Limitations: Transparent media Transparent media Optical penetration Optical penetration

Multiexposed colour photograph of the convective flow in glycerol in a differentially heated cavity. The clock-wise flow circulation from the hot wall to the cold wall; temperature difference  T=4 o C. Natural Convection in a cube Hot Cold

PIV + PIT F TLC seed F Light sheet F RGB image F Process vectors and colour 3 CCD COLOUR CAMERA PC + RGB FRAME GRABBER

Liquid crystals as tracers Freezing of water in the lid cooled cavity

Lid Cooled Cavity Particle Image Velocimetry and Thermometry ICE Hue-Temperature calibration curve Cross-correlation of two images

Lid Cooled Cavity Transient flow - initial instabilities Centre cross section

Lid Cooled Cavity Transient flow - initial instabilities Freezing of water - conical phase front stabilises flow structure

Lid Cooled Cavity Transient flow - initial instabilities

Numerical - onset of convection 200s 33s100s 1000s

Temperature distribution under the lid Transient flow - initial instabilities

Temperature distribution under the lid

Lid Cooled Cylindrical Cavity Freezing of water

Symmetry breaking for axial- symmetric flow Experiment Numerical (Gelfgat et al ) axisymmetric Galerkin spectral model

Symmetry breaking for axial- symmetric flow Temperature distribution under the lid transient full 3 D solution

Symmetry breaking for axial- symmetric flow Temperature distribution - transient full 3 D solution Vertical & horizontal cross-section

Symmetry breaking for axial- symmetric flow Particle Tracks Observed at Edge of the Lid Why quasi-periodic structure with constant number of spikes ? => Rayleigh - Benard type instability ?

Symmetry breaking for axial- symmetric flow particle tracks along the lid Numerical solution

Rayleigh - Benard Instability  z  3mm  T  3K  2000 > Ra c 2  R/  r  18  r  6mm

New experimental technique - true-colour image processing of liquid crystal patterns allowed for identification and quantitative evaluation of the flow details Full 3D numerical simulations confirmed presence of the initial instabilities of the flow and final development of periodic structure Experimental observations and numerical simulations indicate on development of spiral structures under the lid The Rayleigh-Benard like instability may decide on creation of the structures and resulting number of “spikes” Conclusions

Acknowledgements I would like to acknowledge the contribution of W. Hiller and C. Söller from Max-Planck Institute in Goettingen with whom the experimental study was initiated

Buoyancy Driven Instability in a Vertical Cylinder Tomasz A. Kowalewski