**University of Mining and Metallurgy, AGH CracowUniversity 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 SciencesIPPT PAN, Polish Academy of SciencesCenter of Mechanics and Information TechnologyCenter 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 geometryConvective flow in an axisymmetric geometry

Formulation of the problem

Convective flow in an axisymmetric geometryConvective flow in an axisymmetric geometry

Natural convection in a vertical cylindrical Natural convection in a vertical cylindrical

Isothermal cold lid

Heat flux throughbottom and side walls

Investigated GeometryInvestigated Geometry

External hot bath

Cavity diameter 37mm; side walls: 2 mm glass or Plexiglas

Numerical Modelling

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 Particle Image Velocimetry and Thermometry Using Thermochromic Liquid CrystalsUsing Thermochromic Liquid Crystals

EXPERIMENTALEXPERIMENTAL

Transient measurements of

• Temperature field • Velocity field• Particle tracking

PIV +PIT measurement processPIV +PIT measurement processLIQUID CRYSTAL TRACERSLIQUID CRYSTAL TRACERS

Flow FieldFlow Field• The flow field is The flow field is seeded with seeded with suspension of TLC suspension of TLC tracerstracers

Limitations: Limitations: • Transparent mediaTransparent media• Optical penetration Optical penetration

Multiexposed colour photograph of the convective flow in glycerolMultiexposed colour photograph of the convective flow in glycerolin a differentially heated cavity.in a differentially heated cavity.

The clock-wise flow circulation from the hot wall to the cold wall;The clock-wise flow circulation from the hot wall to the cold wall;temperature difference temperature difference T=4T=4ooC.C.

Natural Convection in a cubeNatural Convection in a cube

Hot Cold

PIV + PIT

TLC seed Light sheet RGB image Process vectors and

colour

3 CCD COLOUR

CAMERA PC + RGBFRAMEGRABBER

Liquid crystals as tracersLiquid crystals as tracers

Freezing of water in the lid cooled cavityFreezing of water in the lid cooled cavity

Lid Cooled CavityLid Cooled Cavity

Particle Image Velocimetry and ThermometryParticle Image Velocimetry and Thermometry

0.1mm/s

I C E

ICE

Hue-Temperature calibration curve

Cross-correlation of two images

Lid Cooled CavityLid Cooled Cavity

Transient flow - initial instabilitiesTransient flow - initial instabilities

Centre cross sectionCentre cross section

Lid Cooled CavityLid Cooled Cavity

Transient flow - initial instabilitiesTransient flow - initial instabilities

Freezing of water - conical phase front stabilises flow structure Freezing of water - conical phase front stabilises flow structure

Lid Cooled CavityLid Cooled Cavity

Transient flow - initial instabilitiesTransient flow - initial instabilities

Numerical - onset of convectionNumerical - onset of convection

200s200s

33s33s 100s100s

1000s1000s

Temperature distribution under the lidTemperature distribution under the lid

Transient flow - initial instabilitiesTransient flow - initial instabilities

Temperature distribution under the lidTemperature distribution under the lid

Lid Cooled Cylindrical CavityLid Cooled Cylindrical Cavity

Freezing of waterFreezing of water

Symmetry breaking for axial- symmetric flowSymmetry breaking for axial- symmetric flow

Experiment Numerical (Gelfgat et al. 1998.1999)axisymmetric Galerkin spectral model

Symmetry breaking for axial- symmetric flowSymmetry breaking for axial- symmetric flow

Temperature distribution under the lidTemperature distribution under the lidtransient full 3 D solutiontransient full 3 D solution

Symmetry breaking for axial- symmetric flowSymmetry breaking for axial- symmetric flow

Temperature distribution - transient full 3 D solutionTemperature distribution - transient full 3 D solution

Vertical & horizontal cross-section

Symmetry breaking for axial- symmetric flowSymmetry 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 flowSymmetry breaking for axial- symmetric flow

particle tracks along the lid

Numerical solution

Rayleigh - Benard InstabilityRayleigh - Benard Instability

z 3mm

T 3K

3

RazTg

2000 > Rac

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”

ConclusionsConclusions

AcknowledgementsAcknowledgements

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

http://www.ippt.gov.pl/~tkowalehttp://www.ippt.gov.pl/~tkowale

Buoyancy Driven Instability in a Vertical Cylinder

Tomasz A. Kowalewski