10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

Combined 3D Scanning PIV and Scanning LIF for flow and phasetransfer measurements around a melting particle
1

1

2

Hess D. , Brücker Ch. and Nonn Th.
1

Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Germany
david.hess@tu-freiberg.de, bruecker@imfd.tu-freiberg.de
2

Dantec Dynamics, Skovlunde, Denmark thomas.nonn@dantecdynamics.com

Abstract Interfacial flow and phase transfer around a melting solid particle were investigated with combined 3D
Scanning PIV and Scanning LIF technique. Experiments were carried out with a spherical ice-particle, which was
initially shock-frozen from water saturated with fluorescent dye. Flow in a water tank seeded with small tracer particles
was investigated, when the ice-particle was released at the water surface in the center of the tank and the melting
process began. A scanning light-sheet was generated with a polygonal mirror and flow was recorded with two highspeed cameras with a beam splitter plate. The cameras were equipped with different color filter such that cam#1
recorded only the clean water while cam#2 recorded the molten fluid generated by the heat transfer of the frozen
fluorescent ice-particle. This allowed us to record the 3D flow and 3D concentration field simultaneous. The results
showed the complexity of induced flow process by the heat/phase transfer and buoyancy interacting with the base flowin the water tank. A small swirl in the tank was enforced by buoyancy-induced vortex stretching and resulted inincreasing particle rotation. This self-enforcing process generated a columnar vortex in the wake below the particle
which underwent vortex breakdown. Fluid originating from the phase transfer process was accumulated in the vortex.

Introduction
The physics of solid-liquid two-phase flows including physical and chemical transformations is the subject of intense
research in many engineering sciences, e.g. in chemistry, metallurgy and geophysics. The basic applications, where
solid-liquid flows play the most important role are fluidized beds, sedimentation columns, slurries and mining. Despiteof relative good practical experiences, casting technology still remains in an experimental stage due to a lack offundamental understanding of transport phenomena occurring inside the mushy zone including the transport of fluid,heat and solute in the mixture of molten metal and solid particles. These applications have motivated an increasing
number of theoretical and experimental studies of solid-liquid two-phase flows. Due to the micro-scale character of thephase-change process occurring at the interface between the solid and fluid phases, our understanding is mainly basedon detailed experiments at the interface and direct numerical simulations (DNS model) for fixed particles in a fluid, theinterested reader is referred to the review given by Hoef et al. (2008). However, motion of the particles in the ambient
fluid is another aspect which is of importance and requires not only resolving the interfacial flow but the dynamics ofthe particles and the ambient flow, too.
Hao and Tao (2001) performed an experimental investigation on flow around a non-movable melting ice sphere inhorizontally flowing water. The flow field was measured quantitatively using particle image velocimetry (PIV).
Additionally for the visualization of convective melting the dyed ice was utilized to study the motion of molten ice andits mixing patterns with the mainstream. Dietrich et al. (2011) made an approach by simulating the melting particles andtheir interaction. Parallel, the authors performed the comparisons of results with the flow around a non-melting solid
sphere in order to study the effect of melting on the boundary layer flow. In particular, it was shown that the ratio
between initial Grashof number and Reynolds number Gr/Re is responsible for the shape variation of the ice sphere in
the melting process. When Gr/Re is small (less than unity) the shape over the rear ice sphere becomes flat and theoverall shape of the ice particle transforms into a scallop. With a high Gr/Re > 6 the shape of the sphere changes into an
ellipse.
Later, the same authors investigated the influence of convection on the melting of ice particles moving in a lid driven
cavity, see Hao & Tao (2003). Using flow visualization and measurements, the authors determined experimentally thevolumes and packing patterns of the melting granular packed beds and the time variation of average melting rate perunit bed volume. In particular, video recordings and digital image processing were used to record the shapedeformations. Authors identified two basic types of packing pattern: floating and non-floating packing in dependence
on flow conditions. Using the definition of a terminal velocity, a Reynolds number ratio was developed as the criterion
that distinguishes the floating, non-floating or transitional packing pattern. In addition, the authors analzed the influenceof packing patterns on Nusselt number correlations.

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

Comprehensive 2D DNS modeling of single cylindrical particles settling and melting in a hot fluid with Prandtl numberof Pr = 0.7 has been carried out by Gan et al (2003). It was shown that the melting rate of each particle has a local
character and strongly depends on the sedimentation velocity of the particle. However, the influence of particle-particle
and particle-wall collisions as well as the hydrodynamic influence of the wall on the particle dynamics was notinvestigated. Recently Feng et al. (2008) reported about direct numerical simulations of non-isothermal particulate
flows for different Grashof numbers. The Prandtl number of the fluid was set to unity. Simulation of two particles
demonstrated that heat convection around the particles modifies the drafting-kissing-tumbling (DKT) scenario of theirmotion. In particular, it was observed that the buoyancy currents induced by the hotter particles reverse the DTK motionof the particles or suppress it altogether. A number of 500 particles rising in an enclosure were recently simulated by
Dan & Wachs (2010) including the effect of thermal buoyancy on the fluidization of particles. The computational meshcomprised 107 tetrahedral elements, where each particle was resolved using approximately 10-20 nodes on the particle
diameter. However, resolution was not sufficient to determine the thermal boundary layer in detail.
To sum up, our understanding of the complex interaction between melting particles and the surrounding fluid and walls
is far from being complete. Motivated by this fact, this work presents detailed investigations of the interfacial heat andmass transfer between solid and liquid phase in a reference system of a melting ice-particle in container flow at welldefined boundary conditions. In this work we consider the case of a single melting ice particle placed at the free surface
of a water column. Local convection flow is induced due to the temperature gradients caused by the melting of the ice
particle and the resulting density difference in the three-dimensional container. The method of combined 3D Scanning
PIV and Scanning LIF was used to investigate the flow and phase transfer measurements around the particle.

Experimental Methods
The experiments were carried out in an octagonal water basin with an ice-particle floating on top of the water surface.
In order to distinguish the melt flow due to phase-transfer of the ice particle from the flow of the surrounding liquid wemarked the particle with fluorescent dye and seeded the water basin with small tracer particles (VESTOSINT®,
Hoechst). To generate the ice particle, distilled water used which was mixed homogeneous with rhodamine dye before it
was shock-frozen in a spherical mold (diameter 3.5cm). The ice-particle was then carefully launched on the surface of
the water column to avoid any flow disturbances. Initially, the water in the basin was at rest. Flow was then generated
by the convection in the tank induced by the heat transfer across the particle. It was observed that the particle set into
rotational motion after a while which continued until the size of the particle was below a critical value.

Figure 1: Left: sketch of experimental set-up for combined 3D Scanning PIV and Scanning LIV. Right: picture of thescene with a standard camera from the side during the melting process
In order to capture the 3D fluid motion and the 3D concentration field separately, we used a 2-camera high-speedrecording system with different optical filters and the method of light-sheet scanning (figure 1). The illumination was
generated by a high speed laser (Litron Nd:YLF laser, 30 mJ at 1 kHz repetition rate, wavelength 527 nm) combinedwith a polygonal scanner, which rapidly shifted a single light sheet through the volume of interest (Hess et al. 2011).
Each light sheet image was captured by the two high speed camera systems simultaneous and along the same opticalpath, which was realized with a beam splitter plate. The lens systems were equipped with different color filters. One
camera obtained images from the tracer particles in the ambient fluid (filter 527 nm ± 10 nm) without any cross-talk

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

from molten fluid. The other filter blanked out the particles and took only pictures of the concentration of Rhodaminedye (filter 576 nm ± 27 nm) released into the water by the melting process. Note that the diffusion coefficient of themarker is low (D=3.6 × 10-9 m²/s see Rani et al. 2005) such that the diffusive transport is much weaker than convection
and phase transfer. An overview of the experimental set-up is shown in figure 1 on the left side. The volume of interest
had a size of 102×64×48 mm³ and was scanned by 200 light sheets at frame rate of 6 kHz between each sheet andrespectively a volume scan rate of about 25 Hz. The two image sets were stacked together to span a voxel space, seealso Hess et al. (2011). The particle volumes were then restructured to obtain isotropic particle representations inside
the voxel volumes (Brücker et al. 2013). Two successive particle volumes were then analyzed by using 3D LeastSquares Matching (LSM) to gather information about the 3D flow velocities. A combination of the reconstructed 3D
particle field and the 3D rhodamine concentration is given in figure 2. The pictures demonstrate the good quality ofparticle reconstruction and the structure of the molten fluid in the wake of the ice-particle as visualized with therhodamine dye.

Figure 2: Overlaid image of the reconstructed 3D particle volume and the 3D rhodamine concentration in different
levels below the ice-particle. Left: upper edge of volume is below the water surface; right: upper level of the volume is
10cm below the water surface.

Results
A complex interaction of the melting flow with the surrounding liquid is observed. Due to heat transfer and phasechange, convection flow is induced downwards along the axis into the wake of the sphere. As a consequence, massbalance requires a radial inflow induced at the upper fluid levels and a circulation flow is induced. Because of small
disturbances in the ambient liquid, a small swirl was induced similar to the process generated in a bathtub vortex. The
convection flow induces vortex stretching and due to conservation of angular momentum, auto-rotation of the iceparticle is induced and increases over time. This is documented in figure 3. On the other hand, the melting reduces theparticle size which finally reduces the induced convection flow. Downstream of the vortex core, one can recognize theso-called phenomenon of vortex breakdown, which is induced by the opposed pressure gradient.

Figure 3: Oblique view on the water surface showing therotation of the ambient fluid (4 min after release of theice-particle on the surface). The period of one revolutionof the ice-particle is T = 3s.

Figure 4: Light-sheet picture of the rhodamine
concentration in the center plane of the sphere. A red
circle indicates the contour of the sphere and next to it theboundary layer (thickness is about δ/ D = 0.023).

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

Figure 5: 3D LIF reconstruction of the concentration of molten liquid around the melting ice particle 1 min after
release of the particle on the surface of the water column. Left: 3D view, note the ribbon-like areas of rhodaminewith high concentrations around the circumference of the sphere. In the top-view (top image on the upper righthand side) one can clearly see an approx. constant angular spacing of those ribbons. The regular behavior is shownin lower image on the right hand side. Between each red line there is an angular displacement of ∆θ ≈ 27.7°.
Major interest was the development of flow instabilities
around the particle and the structure of the resulting
convection flow. Figures 5 and 6 show the 3D LIF and 3D PIV
results approx. 1 min after the particle was put in the basin and
Figs. 7,8 show the results about 3 minutes later. Around thesphere, fluid cools down and moves deeper into the basin
together with the molten ice in a vertical column. The typicalconvection velocity is in the order of 1 cm/s and the resulting
Biot number is about 13 (estimated from alpha conditions in a
simple convection flow in water). The results in fig. 6 showsuch a vertical transport below the sphere down into the deeper
levels of the basin. Only regions of high velocities in verticaldirection (larger than 0.007m/s) are shown and the resulting
flow region clearly shows the columnar structure.
Interestingly, the 3D LIF reconstruction shows a regularpattern of regions of high concentrations of molten fluid
Figure 6: Reconstructed 3D velocity field in the around the sphere along the circumference. These regions lookwake of the sphere (only velocity vectors larger than like ribbons arranged along the longitudinal lines of the0.007 m/s are plotted). Left: velocity vector fields, sphere. A rough estimation of the wavelength of the structures
right: surface of constant vertical velocity. Note the gives a value of λ/πD = 1/13. Note that most of the ribbons
double-helical structure of the surface.
seem to originate from the upper part near the contact line of
the sphere with the water surface. However, there are also other ribbons which originate in deeper layers of the sphere10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

below the water surface. Molten fluid is transported along these ribbons down into the wake of the sphere where theribbons intertwine and form a pigtail-like columnar wake.
This type of sink flow leads to the generation of swirl similar to a bathtub vortex. As a result, the ice-particle starts torotate around its axis while melting. The rotation is still weak after 1 minute but it increases to about 20 rpm after 4
minutes. Results for the later state are given in Fig. 7 and 8. Herein one can recognize in the vertical cross-section thecirculatory flow induced around the sphere with inwards motion in the upper layers and downwards directed motion
below the sphere. On the other hand, the flow in the horizontal cross-section clearly reveals are swirling flow. The 3D
LIV reconstructions indicated the swirl by means of the strong intertwining of the ribbons. In the vertical cross-section,
the structures show the pattern of Christmas tree. The flow field along the axis of the tree let recognize a spiral-type
pattern which is wound around the tree. This hints on the presence of spiral type instabilities that deform the axis of thebathtub vortex similar as in spiral-type vortex breakdown. This phenomenon needs further investigation of the flow
details which is beyond the paper.

Figure 7: 3D LIF reconstruction of Rhodamine concentration and 3D PIV velocity field in the wake of the ice-particle
at 4min after release of the particle on the water surface. Left: 3D view, note the intertwining and folding of the ribbons
in the wake. The rotation of the flow leads to separation of the ribbons from the surface of the sphere where they windaround the center part of the sink flow. In the topview (top image on the right hand side) one can see the circulararrangements of different ribbons around the circumference. The flow in the horizontal cross-section below the sphereshows the swirl motion induced by the sink flow.
A closer look into the structure of the wake is given Figure 8. It is seen that sheets of concentrated molten fluid separate
from the sphere surface near to the equator and are transported down into the wake. The induced convection flow brings

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

those sheets closer to the axis and vortex stretching finally concentrates the fluid along the axis. Therefore the LIF
structures show a pattern typical for the cut through an earpiece. On the other hand, the flow fields show that theconvection flow in the wake is not axisymmetric but reveals a spiral-type patternFigure 8: 3D Flow structure in the wake of the ice-particle. Left: cut through the center of the wake out of the 3D
LIF reconstruction; right: structure of the sink flow shown by 3D streamlines, vector fields and regions of low andhigh vertical velocity (blue: downwards flow, red: weak upwards flow in vertical direction).

Discussion and conclusion
The present work describes the analysis of the 3D flow and concentration field for the convection flow induced by amelting ice-sphere on the surface of a water basin. The method of combined 3D Scanning LIF and 3D Scanning PIV isapplied to determine both, the flow and concentration field of the molten part of the ice-sphere. This method allowed us
to reconstruct a final-scale instability induced near the surface of the sphere and its relation to the induced convection
flow. The Prandtl number of the flow is about 7 and the Biot number is 7. Initial temperature difference is 20°C.
A major result is the observation of induced auto-rotation of the particle as a consequence of the generation of swirling
motion similar to a bathtub-like vortex. This is driven by the sink flow below the particle where cold fluid is transported
in deeper layers of the basin and mass conservation requires that inwards directed flow is generated at the upper layer
near the surface. Small disturbances in the ambient fluid are brought to the axis where conservation of angularmomentum and vortex stretching lead to formation of a swirling motion in the tank after a certain period of time. The
resulting flow field below the sphere let recognize spiral-type motion patterns around the axis which hints on a possible
relevance of helical instabilities that are connected with the phenomenon of spiral-type vortex breakdown.
Furthermore, the results show that the molten fluid in the boundary layer of the sphere accumulates in ribbon-likestructures with a regular pattern around the circumference of the sphere. This instability is assumed to be a consequenceof the interplay of Marangoni-convection at the surface and 3D Taylor-Couette vortices generated around thecircumference of the rotating sphere. The initial location of the ribbons is dominated by the Marangoni-convection. The
weak rotation of the sphere induces a radial pressure gradient which acts on the particles around the sphere. Because of
the density differences between the liquid layers of ambient fluid and molten fluid the latter heavier fluid is forced tomove radially outwards against the radial pressure gradient. This centrifugal instability known as Taylor-Couette
instability in rotating system may generate small vortex pairs along the longitudinal line of the sphere where the molten
fluid is accumulated and transported downwards into the wake. The present results give a first impression of thecomplexity of this behavior. A detailed analysis of the process under variations of the boundary conditions is necessary
to further elucidate the physics of this process in detail which is part of ongoing work.

Acknowledgements
The authors appreciate the financial support of the Government of Saxony and the Federal Ministry of Education andScience of the Federal Republic of Germany as a part of the Centre of Innovation Competence VIRTUHCON.

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

References
Brücker Ch, Hess D, Kitzhofer J (2013) “Single-View Volumetric PIV via High-Resolution Scanning, isotropic voxel restructuring and 3D
Least-Squares Matching (3D-LSM)” , Meas Sci Technol 24 024001 (2013) doi:10.1088/0957-0233/24/2/024001
Brücker Ch (1999) “Structure and dynamics of the wake of bubbles and its relevance for bubble interaction”, Phys Fluids 11, 1781-1796.
Brücker Ch (2000) “PIV in multiphase flows”, In: Particle Image Velocimetry and Associated Techniques. VKI Lecture Series, 2000-01.
Dan C & Wachs A (2010) “Direct Numerical Simulation of particulate flow with heat transfer”, Int J Heat Fluid Flow 31, 1050–1057.
Dierich F, Nikrityuk P.A, Ananiev S(2011) “2D modeling of moving particles with phase-change effect” Chemical Engineering Science. p.
5459-5473
Feng ZG & and Michaelides EE (2009) “Heat transfer in particulate flows with direct numerical simulation”. Int. J. Heat Mass Transfer,
52:777–786, 2009.
Gan H, Feng JJ, & Hu HH (2003) “Simulation of the sedimentation of melting solid particles”. Int J Multiphase Flow 29(5), 751–769.
Hao YL & Tao YX (2001) “Melting of a solid sphere under forced and mixed convection: flow characteristics”. J. Heat Transfer 123, 930–
950.
Hao YL & Tao YX (2003) “Non-thermal equilibrium melting of granular packed bedin horizontal forced convection. Part I: experiment”
International Journal of Heat and Mass Transfer 46, 5017–5030.
Hess D, Brücker Ch, Kitzhofer J, Nonn T (2011) “Single-View Volumetric PIV using High-resolution Scanning and Least Squares
Matching”. 9th Int. Symp. Particle Image Velocimetry – PIV’11. Kobe, Japan, July 21-23, 2011
Hoef, van der MA, Annaland, van Sint M, Deen NG, & Kuipers JAM (2008) “Numerical Simulation of Dense Gas-Solid Fluidized Beds: A
Multiscale Modeling Strategy”, Ann Rev Fluid Mech 40, 47-70.
Rani SA, Pitts B, Stewart PS (2005) “ Rapid Diffusion of Fluorescent Tracers into Staphylococcus epidermidis Biofilms Visualized by Time
Lapse Microscopy”. Antimicrob Agents Chemother 49(2), 728-732.