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

4D analysis of flow around a Tumbling Ring-Type Particle using
Scanning PIV and 3D Least Squares Matching
1

1

2

Hess D. , Sastuba M. , Kitzhofer J. and Brücker Ch.

1

1

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

Dantec Dynamics, Skovlunde, Denmark, jens.kitzhofer@dantecdynamics.com

Abstract: This work describes the flow around a sphere with a longitudinal hole inside. Such ring-type particles areuseful in many applications like chemical reactors as catalysts (seed particles) to increase the reacting surface in themulti-phase flow. Both heat transfer and the flow structure in and around those catalysts are of interest for fixed bed
reactors as well as floating bed systems with solid particles. The focus of this work is the analysis of the 3D flow
structure in the borehole and the outer flow around the particle and its influence on particle motion and rotation as wellas the change of heat transfer involved herein. Since internal and external flow may induce Lift- and Magnus-forces we
expect a complex interaction of particle motion and flow field which is tested in a special flow tank. Refractive index
matching is used in combination with Light-Sheet Scanning and 3D Least Squares Matching to obtain the flow fieldaround a silicone sphere with a longitudinal hole. The results show that the flow through the hole imposes pressure
forces that lead to particle rotation and drift in a non-trivial way. Thereby, drag and lift-forces as well as torque arechanged by an order of magnitude and cannot be represented by semi-empirical equations of the global body shape
anymore.
Introduction
Particle laden flows occur in many technological processes such as, e.g., in fixed bed or fluidized bed reactors (for a
recent published review the reader is referred to van der Hoef et al. 2008). In reformers, catalysts (seed particles) areoften used to increase the reacting surface in the multi-phase flow. From numerous studies by reforming catalyst
producers it has been shown that catalyst particle can largely influence the heat transfer into the reformer-tube (Yin etal. 2007). Typical shapes of the particles are spheres or cylinders with a certain number and size of longitudinalboreholes and additional external features on the surface. Certain aspects of the catalyst particle design may positively
influence the heat transfer from the shell side to the tube side in fixed bed. On the other hand, in fluidized bed reactors
catalyst particles form individual clusters that may rise in the middle of the reactor and settle down again near the lateralwalls (Noymer & Glicksman 1998). Therefore, both heat transfer and the flow structure in and around single catalysts
and clusters are of interest. The design of the catalyst particles has been - up to now - established by trial and error inpilot plant scale setups. The only currently available data in this area has been empirically collected and correlated.
However, commercially available catalyst designs may not represent an optimum and performance must always be
tested for any change of species or plant scale. Because of their huge influence on the reactor’s performance, any
physically based knowledge of the details about the flow through such catalysts is of strong interest for future energy
savings. Spherical particles with longitudinal holes are of importance because of their good mechanical stability similar
to solid spheres and because they do not change the packing density much. In addition, manufacturing of such ring-typeparticles is possible for various outer and inner diameters of the ring. It opens the chance for future applications todesign the catalysts according the specific conditions in the reactors to obtain a more controlled heat transfer.
As much as such particles may have potential as catalysts in the applied process technology as little is known about theflow around and inside the ring as well as the heat transfer depending on the ring diameter and orientation. Features tobe investigated in fluidized beds are the orientations of the rings in the flow, the forces acting on the ring and theresulting motion behavior. In addition, as the formation of clusters is a typical feature in fluidized beds (see Noymer &Glicksman 1998), flow paths through the cluster of such catalysts needs to be studied, too. For simulations of suchcomplex flows and total heat transfer it is not yet clear to what extend the internal flows structures change the heattransfer in comparison to the often applied approximation of porous flows. However, it was concluded from detailed
simulations that heat transfer effectiveness can be improved with few large holes rather than with porosity(Nijemeisland 2004). This hints on the relevance of channeling and preferential flow path formation within such

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013clusters which cannot be treated as isotropic porosity. In addition, because the typical size of such catalysts is in therange of 1-10mm , inertia effects of internal flow cannot be neglected.
There are very few detailed simulations which provide information on the heat transfer and flow around such catalyst
particles. Moran & Glicksman (2004) investigated numerically the flow around a porous sphere but they ignored theinternal flow in the cluster. Maheshwari et al. (2006) determined the drag and heat transfer for three spherical particles
which were arranged inline in a homogeneous flow. While this work shows the interactions of the wakes, it does notallow any conclusions on the dynamic behavior of such a cluster. Richter et al. (2011) examined the flow around asphere with a longitudinal hole. It could be shown that heat transfer can be increased up to 40% when compared to asphere with the same outer diameter. Again, the sphere was fixed and no fluid-structure interaction was taken into
account. Nicolle & Eams (2011) studied the flow through a cluster of cylinders on the basis of a two-dimensional CFDsimulation. The influence of the specific form of the cluster on the internal flow decreased with increased volume
fraction of the solids. However, the results for this two-dimensional problem do not apply for three-dimensional,
spherical particles. As for all previous cited studies, the solids were held fix in the simulation domain.
Parallel to the increased computational power for 3D CFD simulations of flow in clusters (Beetstra et al. 2006),
experimental methods have been developed which allow the investigations of 3D flow processes in transparent clusters,
too. Such measurements are typically carried out in a system with transparent glass particles using the method ofrefractive index-matching. Earlier examples of two-dimensional flow studies have been published by Zachos et al.
(1995) and Tschikango et al. (2006). The 3D flow around individual non-spherical particles or bubbles was first
documented in 2000 in detail experimentally (Brücker 2000). The mechanisms of path instabilities have been broughtfor the first time in greater detail in connection with the wake dynamics of this body (Brücker 1999). Recently, 3D
Tracking PTV was used for investigation of Lagrangian turbulence in a fixed bed system (Klein et al. 2013). The
particles were made from hydrogels to achieve a good match between refractive index of the ambient water with thespherical particles. However, such particles are not stable when a hole is cut out to obtain the shape of more complex
catalysts such as the ring-type particle. Instead, the method of index matching using silicone as the material for thesolids and a water-glycerine mixture as the carrier fluid is more appropriate for such studies. There are a few studies
which have shown the potential of this method for flow studies in complex geometries such as in silicone models of thelung bifurcation or the nasal cavity (Adler & Brücker 2007). For volumetric PIV measurements of the flow in the ringtype particles, 3D Scanning PIV can provide this information easily without any problems of multi-camera calibrationin such flows. Using this method we can identify flow patterns inside the particles, look at the effects of catalyst
degradation and at the effects of particle stacking and orientation. This method is based on the experiences we havebeen developed over the last 10 years and the application of such measurements in multiphase flows (Brücker 2000,
Kitzhofer et al. 2010, Hess et al. 2011, Brücker et al. 2013). A further extension would be the analysis of the influenceof the particle geometry on the near-wall heat transfer. In addition, we are interested in the influence of orientation of
the catalysts in a cluster and what consequences they have on the global behavior of the cluster. A first step towards a
detailed understanding of the time-dependent fluid-structure interaction of a single freely mowing catalyst particle inflow is presented herein.

Experimental set-up
The experiments were carried out in a flow tank using the method of refractive index matching between the transparent
catalyst particle made from silicone (Elastosil RT 601™, measured refractive index after curing n ≈ 1,4137) and theambient liquid which was a water-glycerin mixture (refractive index n ≈ 1,4135). The liquid was at rest and relative
motion between particle and liquid was induced by a downwards-directed impact imposed onto the particle, which was
initially held below the liquid surface. The particle was casted in a split mold with a rod in the middle, acting as a
casting core. Both, the mold and the rod were made of plastics. To prevent any reflections from inside of the silicone
body, care was taken to ensure cleanness of the silicone. The mixed liquid silicon was evacuated at an absolute pressureof 20 mbar before casting to remove any air bubbles. After the casting process, the silicone particle was cured in anoven at 65 °C for 5 hours. Afterwards the molds were removed with the use of glycerin as a lubricant. The final ringtype particle had an outer diameter of about 3.5 cm and an inner bore of 1.7 cm. Pictures of several casted particles areshown in Figure 1. In the experiments, the particle is pushed down into the basin where the liquid is seeded with small
traces particles and illuminated with a light-sheet. A typical particle image taken for the flow measurements around theparticle is shown in Figure 2. It shows that the hole inside the particle is well seen as a region where tracer particles arepresent and the contour of the silicone body is visible due to a lack of particles inside of the silicon.

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

Figure 1: Image of different silicone particles

Figure 2: Inverted single light-sheet image of the catalyst
particle

The catalyst particle was pushed by a magnetic actuator from a position below the liquid surface down into the basin(Figure 3,4). The 3D flow around the sphere was measured with 3D Scanning PIV using a polygon scanner and highspeed imaging (see Hess et al. 2011). Figure 3 shows a sketch of the experimental setup from the top view with theillumination path. A high-speed Nd:Ylf-LASER in combination with a rotating polygon mirror generated 50 paralleland partially overlapping light sheets per volume scan at 132 Hz. Each light-sheet in the scan had a thickness of about
3.1 mm and an overlap of 75 % with the previous and the successive one. The light sheet images were recorded with ahigh-speed camera (Phantom 12.1, Vision Research, resolution at 1024×752 px) synchronized with the pulse-laser
running at 8200 fps. This leads to an illuminated volume of about 86×63×42 mm.

Figure 3: Top view of the experimental set-up

Figure 4: Front view of the basin

Volumetric reconstruction
Due to the high spatial resolution of the scanning, voxel-based reconstruction of the particles can be achieved bystacking each light sheet to a voxel space (Hess et al. 2011, Brücker et al. 2013). This requires the following boundary
conditions: a) the light sheet intensity profile needs to be homogeneous from pulse to pulse such that the illumination
remains approximately constant over the height and width of the sheet; b) the shift of each consecutive light sheet
should be constant over the whole scanning depth; c) the spacing must be adjusted in such a way that each light sheet
overlaps the subsequent light sheet for at least 66 % in width; d) the scanning velocity needs to be much higher, than theflow velocity within the measurement volume (see Hess et al. 2011). All these conditions were fulfilled within ourscanning experiments using the polygonial mirror. To calibrate the position of each light sheet within the measurement

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

volume and to check the correct overlap, a target was inserted in the basin and illuminated by the scanning light sheets.
Figure 5 shows an arrangement of all light sheets in one image. In order to gain a better visibility, every sheet was
displayed with an additional shift in the image for half the width of the sheet in horizontal direction and every 2nd sheet
was dislocated vertically for 300 px, otherwise the overlap would not allow to recognize the spacing of successive
sheets.

Figure 5: Arrangement of the light sheets in a single
scan. The images are overlaid in a staggered arrangement to illustrate the shift of the originally overlapping
light-sheets. Jitter of the positions is less than 0.1 px inthe image plane. Note the homogeneity of the lightsheet intensity and thickness over all planes within thescanning procedure

Figure 6: Gaussian regression to replace ellipsoidal
particle reconstructions with spherical Gaussian blobs
at position of maximum of the Gaussian fit. Left row
shows the ellipsoidal particle shape over 4 light sheets
and its fitted Gaussian intensity distribution with Imax
representing the new center of the particle. Right row
shows the spherical particle with its center at Imax

Due to the overlap of the light sheets and multiple stacked images, the particle reconstructions from the plain stacking
procedure resulted in ellipsoidal shape. However, the intensity distribution of each ellipsoidal can be used to apply aGaussian regression in order to replace the ellipsoids with spherical blobs (Brücker et al. 2013). Going in scanning
direction line by line through the voxel volume, a Gaussian fit determined the center of each ellipsoidal particle
fragment with better resolution and re-ordered the voxel intensities in the line such that the particles appeared asspherical blobs, see Figure 6. Finally, a weighting function was applied to the voxel volume in the different coordinate
directions to re-locate the particle center position in the other directions and to enforce a Gaussian blob at each particle
center with the size of 3×3×3 voxel.

Figure 7: Time series of the reconstructed 3D voxel volumes of the ring-type particle from top left image to bottom
right (time step is t=0.1 s).
Figure 7 shows a time series of the reconstructed voxel volumes. The silicone catalyst particle dived in (upper left
image), reached the bottom dead center position and started is rise to the top of the reconstructed volume again. Notethe hull shape of the silicone sphere in the particle reconstruction which stems from particles sticking to the silicone

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

surface. Particles in the hole were reconstructed as well due to the applied refractive index matching method. Note thatthe particle also showed a rotational motion. The direction of the rotation was clockwise throughout the complete
measurement. To visualise the particles motion the center position and its rotation angle was evaluated, too.

Velocity field computation
The reprocessed voxel volumes of each consecutive time steps were analyzed using 3D-LSM to evaluate the flow
fields, velocities and the velocity gradient matrix. The LSM is an iterative process where the grey values of voxel
cuboids from one time step are shifted, rotated sheared and stretched until they best fit the voxel representation of time
step two (see Westfeld et al 2010). One advantage of this method is that the velocity gradient matrix is a direct solutionof the algorithms and it must not be computed with all its problems with numerical derivations. Typical cuboid sizes of
61³ voxel were applied for the LSM in our voxel fields. With a median seeding density of about
0.075 particles per pixel the overlapping percentage of the cuboid was set to 80 % resulting in about 110,000 vectors foreach time step at adequate computational costs. This corresponded to a spatial resolution of approx. 0.5 vectors / mm³
that ensured an adequate spatial resolution to investigate the flow around the particle and insight of the hole. A range
validation and an outliner interpolation were used to filter out velocities higher than 0.2 m/s and replacing theirpositions with the average value of their neighbors. Finally, a temporal low pass filter was applied to reduce velocity
fluctuations. Therefore, a local regression using weighted linear least squares and a 1st degree polynomial filter with arange of 5 time steps for each velocity component was applied on each vector position. The resulting data field showedsmooth behavior in its temporal distribution as well as its spatial formation.

Results
Major focus is laid upon the analysis on the interaction between the particle motion (translation and rotation) and thesurrounding flow. Figure 8 shows the path of the ring-type particle during its dive. One can recognize that the vertical
impact leads to a downwards diving motion with an overlaid lateral motion resulting from generated lift. Surprisingly,
the particle returns back to the top of the basin approximately along the same path that it has moved in the phase of
downwards motion. Thus, the lift force must have changed direction after the bottom dead center has reached. Angularvelocity increases from the beginning from zero to a maximum of 380°/s at a time t=0.22s after impact. Then angularvelocity drops to values of about 220°/s until the particle leaves the measurement volume again. Mean angular velocityof the catalyst particle is 275 °/s.

Figure 8: Diving path of the ring-type particle
after being pushed down into the basin from a
position below the liquid surface (particle center
position at impact t = 0 is 0 mm) color indicatestime starting in blue

Figure 9: Rotational speed of the particle during its dive, shown asa black profile. Depth position of the particle over the measurement
duration is shown in red (particle center position at impact t = 0 is0 mm).

The sphere’s rapid increase and decrease of rotational speed needs further examination of the details of the flow aroundthe particle. Two exemplary velocity fields are displayed in figure 10 and 11 together with the surface of the particle todemonstrate the flow situation as well as the particle/flow interaction.

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

Figure 10: 3D velocity field around the particle att = 0.17 s after impact. At this position the particle still
dives into the basin. The rotational speed of the particle
increases.

Figure 11: 3D velocity field around the particle att = 0.35 s after impact. At this position the particle is nearits bottom dead center and the hole is aligned with thevertical. The rotational speed of the particle has decreased.

Figure 10 shows the flow at time t=0.17s after the beginning of the measurement. At this position the ring-type particle
still moves downward into the basin while the rotational speed of the particle increases. At the front part of the outersurface of the ring the flow shows the behavior of a plain displacement flow. However, flow in the cross section of thesphere indicates that the lower half of the ring acts like an airfoil in pitching motion. In the hole on the left side of theparticle a large leading vortex is induced while on the right-hand side of the ring a trailing vortex has shed into thewake. This causes a lift force (FL) on the front part of the particle. Since, the load application point is located at thelower part of the ring and not on the particle’s center of gravity it induces a torque on the particle. This torque enforces
the rotation of the ring (see the sketch in figure 12). Furthermore, the particle rotation induces another force on theparticle, the Magnus-force (FM). This force also contributes to the particle’s lateral motion to the left.

Figure 12: Left: sketch of the flow behavior in the cross section of the catalyst particle at time step 23 (t = 0.17s). The
lower half of the ring works like an airfoil in pitching motion causing generation of a leading and a trailing edge vortex.
As seen on the right with a visualisation of the Lambda 2 criteria
Because of continuing rotation of the particle the angle of attack for the half of the ring increases similar to an airfoil inpitching motion. Suddenly, lift force drops sharply when the leading edge vortex in the hole starts to detach (t > 0.35 s).
The particle’s hole is yet positioned almost vertical and bottom dead center is reached. As a consequence of thedeceleration of the particle, the fluid in the wake behind the ring starts to overtake the ring at the inner and outer side. A
larger part of the wake fluid attached to the aft part of the particle is guided through the hole towards the front and leads
to a jet-like flow as visualized in figure 11. Furthermore, on the right-hand sight of the measurement volume a second
strong flow current enters the measurement volume. From figure 13 on the right side, it can be identified as part of the
far wake region of the ring which now starts to interact with the particle, as the iso-contour of the Lambda 2 kirteria
indicates. This counter flow on the particle’s right-hand side causes a velocity gradient along the particle. Accordingly,10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13
Delft, The Netherlands, July 2-4, 2013

it induces a Saffman force (FS) on the particle while moving upwards causing the change of direction of the lift force
after path reversal (see figure 13).

Figure 13: Left: sketch of the flow behavior in the cross section of the ring-type particle at time step 46 (t = 0.17 s).
overtaking the particle itself causing a gradient in the flow field. Right: iso conturs Lambda 2 indicating the incoming
wake that starts to interact with the particles motion. The vectors on the y-slice also show the two vortices
The Proper Orthogonal Decomposition is one common method to perform a modal reduction of a snapshot series ofobservables (e.g. velocity field). For more information the reader is referred to (Berkooz et al. 1993) and (Andrianne etal. 2011). In fluid dynamics it is used to extract dominant flow characteristics by identifying coherent structures. The
mean flow field is subtracted from each snapshot to achieve a time series of fluctuations on which the decomposition isapplied. Figure 14 shows the temporal averaged flow field, which characterizes the displacement flow generated by the
diving particle. The POD-technique ranks the spatial structures according their fluctuation energy. In figure 15 theenergy distribution is illustrated, showing an exponential decrease within the first 10 POD-modes, which cover 94.1 %of the mode energy.

Fig. 14: Mean flow field showing the displacement
flow of the diving ring-type particle when pushed
down into the basin

Fig. 15: Energy distribution of the POD-modes
showing an exponential decrease within the first 10
POD-modes. The main four POD-modes are labeled.

The applied POD-algorithm results in orthogonal structures (Topos or POD-Modes) and their temporal behavior(Chronos or temporal POD-coefficents). The coefficients are generated by projecting each orthogonal structure onto
each snapshot. Thus, a snapshot can be reconstructed by summing the mean flow field and all modes multiplied by thecoefficient of the particular snapshot. An overview of the first four POD-modes (Topos), their corresponding temporalcoefficients (Chronos) and the associated energy fractions are shown in Fig.16.
The resulting modes of the POD analysis are used to identify the most energetic flow structures and to distinguish thedifferent phases of the dive. The first four resulting modes together with their temporal development and their ratio of
the total energy are shown in figure 16. Note that these modes already represent over 80 % of the flow energy,
indicating their importance to the flow field. Here mode #1 is the most important, containing over 40 % of the totalenergy. Looking at its temporal formation, it starts playing a major role only after time step 40 (t > 0.45s). This is when

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

the fluid in the wake of the particle starts to overtake the ring along the outer side. Mode #2 is of importance between
time step 40 and 70 (0.3s < t < 0.53s). The particle has reversed its vertical motion and starts to rise while interactingwith its former wake. Both flow features can be clearly seen in the modes. Mode #3 still contains about 13 % of theexperiment’s fluctuation energy and represents the displacement flow at dive and rise. The last mode still contains
nearly 7 % of the energy fluctuation. Here the flow field indicates a larger vortex with high velocities on the left side of
the measurement volume. During the particle’s downward movement this is the position of the leading-edge vortex
induced into the hole between time step 20 and 40 (0.15s < t < 0.3s).

Figure 16: The first four POD-modes and their temporal development

Disscussion
This work shows the complex path of a ring-type catalyst particle when interacting with its surrounding flow in a dive.
The particle is represented by a silicone sphere with a longitudinal hole which is pushed into a refractive index matchedwater glycerin mixture. The time-trace of the trajectory of the particle as well as its rotation is analyzed. A single
camera setup together with a polygonal scanner is used to reconstruct the 3D measurement volume by the so called
stacking technique (Hess et al. 2011). Afterwards, the velocity fields are calculated via a 3D least squares matchingalgorithm. The results demonstrate that the front part of the ring acts as an airfoil when the hole inside is aligned
perpendicular to the relative flow. This causes a self-enforcing instability similar to a pitching motion of an airfoil. As aresults, a lateral drift as well as a torque is imposed on the particle motion. On the other hand, once the longitudinal holealigned close to the flow direction, the rotational motion of the particle diminished and the path stabilized. Decelerationof the particle due to buoyancy caused the wake to overtake the particle during path reversal laterally at one side, thus

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

inducing Saffman forces that lead to lateral drift anew. Overall the experiments showed a complex interaction between
the motion of the particle and the surrounding flow. Even under laboratory conditions the particles trajectory as well as
the surrounding flow fluctuated between the measurements. Hence, the results are only examples of the possible flow
situations in industrial applications. In case of particle swarms and clusters, additional particle interaction might
increase the degree of possible interactions. It needs to be further investigated whether such catalyst particles at higher
void fractions still align with the main flow direction. As a consequence, total heat transfer may largely differ
depending on the number and size of such catalyst particles in the flow.
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. 3Dvisualization was supported by the eScience Network Saxony.

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