Cross-validation of 3D particle tracking velocimetry
for the study of granular
flows down rotating chutes
S.S. Shirsath
a, J.T. Padding
a,n, H.J.H. Clercx
b,c, J.A.M. Kuipers
a aMultiphase Reactors, Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands bDepartment of Physics and J.M. Burgers Center for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands c
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
H I G H L I G H T S
A 3D particle tracking technique is cross-validated against independent methods.
Granular particles are flowing down a rotating chute.
Surface particle velocities and parti-cle bed height are obtained simulta-neously.
Discrete Element Model simulations are validated.
G R A P H I C A L A B S T R A C T
a r t i c l e i n f o
Article history:
Received 29 August 2014 Received in revised form 9 April 2015
Accepted 1 May 2015 Available online 11 May 2015 Keywords: 3D-PTV PIV Granularflows Rotating chute Coriolis force DEM
a b s t r a c t
Three-dimensional particle tracking velocimetry (3D-PTV) is a promising technique to study the behavior of granularflows. The aim of this paper is to cross-validate 3D-PTV against independent or more established techniques, such as particle image velocimetry (PIV), electronic ultrasonic sensor measurements for bed height, and the discrete element model (DEM), for the complicating circumstance in which granular particles areflowing down a rotating chute. 3D-PTV was used to gain access to Lagrangian trajectory data of surface particles in suchflows, from which independent measurements of both the surface velocity and the bed height in the chute were derived. The 3D-PTV method was based on imaging and tracking colored tracer particles that were introduced in the granular material, which are viewed from three directions. The three cameras collected consecutive frames a known time interval apart and the PTV algorithm for locating and tracking particles was used to determine particle trajectories and velocities. We found that the 3D-PTV results are in good agreement with PIV results with regard to the streamwise and spanwise surface velocity of particles in the rotating chute. The particle bed height obtained from 3D-PTV was also found to be in good agreement with data from an ultrasonic bed-height sensor. The experimentalfindings from PTV for the non-rotating case were used to tune the friction coefficient in our DEM simulations. The simulation method was validated by the good agreement between experimentalfindings and simulations at all rotation rates studied.
& 2015 Elsevier Ltd. All rights reserved.
1. Introduction
Experimental studies of granularflows are difficult to perform due to the opaque nature of such materials. Nevertheless, insight has been generated through use of magnetic resonance imaging Contents lists available atScienceDirect
journal homepage:www.elsevier.com/locate/ces
Chemical Engineering Science
http://dx.doi.org/10.1016/j.ces.2015.05.005
0009-2509/& 2015 Elsevier Ltd. All rights reserved. nCorresponding author.
(Kawaguchi, 2010; Hill et al., 1997), digital imaging (Guler et al.,
1999; Capart et al., 2002; Bonamy et al., 2002), particle image
velocimetry (PIV) applied to 2D granular flows (Bokkers et al.,
2004; Laverman et al., 2008; Zeilstra et al., 2008) and particle
tracking velocimetry (PTV) (Chou and Lee, 2009; Yang and Hsiau, 2006; Liao and Hsiau, 2009; Jasti and Higgs, 2008; Veje et al.,
1999; Jain et al., 2002). In the past a large amount of experimental
work has been performed on granular flows through inclined channels, see e.g. Augenstein and Hogg (1978), Brennen et al.
(1983), Campbell and Brennen (1985), Johnson et al. (1990),
Holyoake (2011), Ottino and Khakhar (2000), Khakhar et al.
(1999), Savage and Lun (1988), Pouliquen and Renaut (1996),
Silbert (2001), Ancey (2001), Barbolini et al. (2005), and Baran
et al. (2006).
Most of the above experimental studies are focused onfixed chutes. However, in some applications such as in the operation of blast furnaces in the metallurgical industry, the chutes are rotat-ing. The chutes may even rotate at such high rates that Coriolis and centrifugal forces start to play a significant role, leading to flows and particle distributions deviating considerably from those in non-rotating chutes. Reliable measurements are essential to obtain a detailed understanding of such granularflows in rotating chutes. Three-dimensional particle tracking velocimetry is a promising technique, because it can potentially deliver with high spatial and temporal resolution the particle bed height and 3D velocity profile. The bed height can also be obtained by using ultrasonic height sensors, but the resolution of such sensors is lower, while the experimental procedure is much more labour intensive or expen-sive (a new experiment needs to be performed for each measure-ment position, or a large number of sensors needs to be used). The velocity profile can also be obtained by using particle image velocimetry, but usually only in two dimensions.
In this paper we will focus on cross-validation of the 3D-PTV technique, for applications of granularflows in chutes rotating at significant rotation rates. Note that by ‘cross-validation’ we do not mean the statistical technique of estimating the performance of a predictive model. Rather we mean the practice of confirming experimental findings from one technique by repeating the experiments using independent other techniques.
The 3D-PTV technique is aflexible non intrusive image analysis technique forflow measurements. It was first introduced byChang
et al. (1984)and was further developed byRacca and Dewey (1988).
This technique has a history of development for more than a decade at the Institute of Geodesy and Photogrammetry (IGP) and at the Institute for Hydrodynamics and Water Resources Management (IHW) both at the Swiss Federal Institute (ETH) Zurich (Maas, 1991;
Malik et al., 1993; Maas, 1995; Maas et al., 2002). In a previous paper
we used the PIV technique to measure the surface particle velocity and an electronic ultrasonic sensor to measure the bed height in a rotating chute (Shirsath, 2013). In contrast to PIV, PTV is able to track individual particles in theflow and provides both the Lagrangian and the Eulerian representation of theflow field (Willneff, 2002). To be able to track individual particles instead of providing a global (Eulerian) flow field, PTV requires three cameras to detect the position of the particle in the three dimensional domain. The cameras capture images of the flow from different angles. From these images, it is possible to determine the position of an individual particle and compute its trajectory. In PTV it is necessary to make a clear distinction between the particles which are actually tracked and all other particles. Therefore, tracer particles are introduced in the granularflow. Obviously, the concentration of tracer particles may not be too high, otherwise it becomes difficult to distinguish individual tracer particles, and the method becomes less accurate
(Prasad, 2000).
We perform our analysis on a system of monodisperse 3 mm spherical glass particles,flowing down a rectangular plexiglass
chute inclined at 301 and rotating at various rotation rates. The mass rate used is 3.2 kg/s. In our previous paper (Shirsath, 2014), we published a discrete element method (DEM) validation using experimental results of surface velocity obtained by PIV and bed height from an ultrasonic sensor, using a lower mass rate of 1.6 kg/s.
Besides the primary goal of assessing the ability of the 3D-PTV technique to provide surface information such as surface velocity of particle and particle bed height, as a secondary goal we will use the results of this work to further validate our DEM simulations
(Shirsath, 2014). Recently, a number of papers focusing on DEM
simulations of granularflows in the blast furnace charging process have appeared (Mio et al., 2008, 2009, 2010, 2012; Ho et al., 2009; Zhou et al., 2011; Yu and Saxén, 2010, 2011; Yu, 2013; Yu and Saxén, 2013; Wu et al., 2013; Bhattacharya and McCarthy, 2014;
Akashi et al., 2008; Zhang et al., 2014). Given its popularity, it is
crucial that the DEM method is properly validated against precise experiments, including cases in which the process equipment is rotating.
The paper is organized as follows. InSection 2we present the experimental set-up and its procedure. InSection 3, the measure-ment techniques using PIV, PTV and the electronic ultrasonic sensor are presented. In Section 4, the numerical model is explained briefly. In Section 5, we present our post-processing methods to obtain data from the numerical model which are similar in spirit to the experimental measurements. InSection 6, we present the experimental results, including a repeatability study of the PTV experiments for bed height and streamwise surface particle velocity. We compare the bed height from PTV with independent measurements using an ultrasonic height sen-sor, and compare the surface velocity from PTV with independent measurements using PIV. In Section 7, we validate our DEM simulations by comparing with the experimental findings of bed height, streamwise velocity and spanwise velocity for different rotation rates of the chute. We end with our conclusions.
2. Experimental setup and procedure
In this section we describe the hardware of the 3D-PTV system, consisting of the rotating table facility, camera system and illumi-nation facility.
2.1. Experimental setup
The experimental equipment includes a plexiglass chute, a hopper for storage of particles, and a collection tank. A dynamic weighing scale was used to measure the mass rate, and PTV, PIV and an electronic ultrasonic sensor were used to measure surface information such as particle bed height and the surface particle velocityfield.
The granular particles were deposited onto a rectangular plexiglas chute straight from the hopper mouth. The bottom wall of the chute was white to achieve a better contrast in the photographs for detecting tracer particles. The whole chute was fixed at its bottom to a strong metal plate of 1 cm thickness to minimize vibrations caused by the particles poured from the hopper mouth to the chute surface at the inlet. The inclination angle of the chute was adjustable between 0 and 701 with respect to the horizontal. At the end of the chute, a collection tank received the granular particles. This tank was placed on a dynamic weighing scale to measure the exit massflow rate.
The whole setup was mounted on a rotating table, so that the flow was measured in the non-inertial frame of reference. All the hardware, constituting the focusing system and the measurement system, was located on the top of the table or surface below it as
shown inFig. 1. The equipment was remotely controlled from an adjacent room for safety precautions during the rotating experi-ments. Details of the rotating table and camera system are described in the next subsections.
2.1.1. Rotating table
The rotating table at the Fluid Dynamics Laboratory (Depart-ment of Applied Physics, TU/e) used in this research was designed to support heavy constructions up to a weight of 1000 kg. Furthermore, the table has the ability to spin at a constant angular velocity in the range of 0.01–10 rad/s, with an accuracy of 0.005
Ω
.del Castello and Clercx (2013) and van Bokhoven et al. (2009)
employed this rotating table facility for rotating turbulence stu-dies. They did several experiments and tests to determine the exact stability and accuracy of the table.
In our experiments we chose a particular range of rotation rates between 0 and 24 rotations per minute (0 and 2.51 rad/s) because we expected a transition in the behavior occurring within this range. The dimensionless Rossby number and Froude numbers for the experimental setup, based on the rotation rates and maximum particle velocity at the end of chute, are given inTable 1. Since the PIV and PTV measurements are highly sensitive for camera move-ments during the experiment, a stable rotational operation was absolutely necessary.
2.1.2. Camera system
Three high speed cameras were situated above the chute, used to capture the images that were used for the optical measurement techniques particle image velocimetry (PIV) and particle tracking velocimetry (PTV). PIV was used to measure the surface velocity of the granularflow, whereas PTV was used to measure the trajec-tories of the individual particles along the length of the chute. For PIV only one camera was needed to capture images of the granular flow. It was positioned perpendicular above the center of the chute at a distance of 1.6 m (the middle camera). For PTV three cameras are needed, one of which has the same position as for PIV, while the two other cameras were placed at an up and downstream position, respectively, and were slightly tilted, seeFig. 1. From the three different angles the position of particles can be determined and subsequently the trajectory of individual particles. A Nikon 28 mm f/2.8 lens was used to cover the entire length of the chute for all three cameras. The image magnification was 1:55, i.e. each
Fig. 1. The experimental setup with rotating table facility at the Fluid Dynamics Laboratory (Department of Applied Physics, TU/e) and PTV cameras.
Table 1
Dimensionless numbers for simulations and experiments.
Rotation rate (rpm) Rossby number Froude number
Ω ¼ 8 1.879 0.055
Ω ¼ 16 0.939 0.218
3 mm particle was imaged to a size of 55
μ
m on the camera sensor. Given the pixel size of 17μ
m, this corresponds to 3.2 pixels for a particle. The three cameras were synchronized so that images were captured at the same time from all cameras. The high speed cameras (Photron FastcamX-1024PCI) have an internal memory of 12 GB RAM to save up to 60,000 images, which is equal to a saving time of roughly 30 seconds when using a frame rate of 2000 frames per second and a resolution of 128 1024 pixels. This saving time of 30 s is sufficient to execute a single experiment, since the maximum experimental time was 9 seconds (total weight granular material was 30 kg;flow rate was 3.2 kg/s). To be able to save the captured images and to run the PIV/PTV software, a computer system was needed. After each experiment, the images were transferred from the internal memory of the cameras to this computer system. From there on, the images can be processed using the specific PIV and PTV software.2.1.3. Illumination system
The high frame rate of the cameras implies a very short exposure time. Therefore, the illumination system had to be strong and homogeneous enough for the cameras to see the light reflected by the granular particles, including the tracer particles, in every part of the measurementfield. The LED light was supplied by Ledlight Group, Germany, and is using a LED light power supply of 95 W max (Vout: 30–350 V DC, Lout: 350 mA-constant current,
power factor correction (PFC): 0.98.) Four LED lights were used to illuminate the whole chute. Each LED Light contains 72 small lights (CrystalLed TM 72 LED). Two lights arefixed at each side of the chute, taking care that they do not block thefield of view of the cameras, as shown inFig. 1.
2.1.4. Tracer particles
To properly visualize the granular in the rotating chute for 3D-PTV it has to be seeded with tracer particles. The physical properties of these particles should be close to the properties of the flowing granular particles to guarantee that they properly represent theflow behavior. In our experiments we used 3 mm blue spherical glass spheres, which have the same collision properties as the other transparent glass particles. We mixed 1 kg of these tracer particles into 30 kg of glass particles. 2.1.5. Calibration plate
InFig. 2(bottomfigure), the top view of the calibration plate
used for the experiments is shown. The calibration plate had a thickness of 0.009 m and was 0.08 m wide and 1 m long, which was sufficient to cover the entire area of the chute. The calibration plate contained 5 62 calibration points. The calibration points had a diameter of 4 mm and the distance from the center of one calibration point to the next was 16 mm. Furthermore, three calibration points had a larger diameter, to identify the center and orientation of the calibration plate during processing of the calibration phase.
2.2. Experimental procedure
During the start-up of the experiments, the following steps were performed. First, the particles werefilled in the hopper. Then the rotating table was accelerated until it reached a steady rotation rate. Then an experiment was started by opening the outlet of the hopper by remote control. Measurements were made continuously until the hopper was depleted. The time range during which steady-state flow conditions apply was determined after the experiment by analyzing the time dependence of mass, height and velocity measurements.
3. Measurement techniques 3.1. Ultrasonic height sensor
We used an electronic ultrasonic sensor LRS3, provided by Formate Messtechnik GmbH (Germany), to measure the particle bed height at selected locations in the chute. For more detailed information about this technique we refer toShirsath (2013). 3.2. Particle image velocimetry
Particle image velocimetry (PIV) is an optical, non-invasive measuring technique that was used to obtain the instantaneous 2D velocityfield. PIV was originally developed in the field of experi-mental fluid dynamics to study the flow of single phase fluids
(Westerweel, 1997). In this work PIV has been applied to obtained
surface velocity of the granular flow in the rotating chute. For more detailed information, we refer toShirsath (2013).
InSection 5.3we will describe the post-processing, to obtain a
time-averaged particle velocityfield from the sequence of instan-taneous velocity fields. To measure the time-averaged velocity profiles, more than 3000 PIV image pairs were taken.
3.3. Particle tracking velocimetry
The software code used for postprocessing is based on the ETH-code mentioned above, which is modified and adapted for this setup by specialists of the Fluid Dynamics Laboratory at the Department of Applied Physics (TU/e). The code forms the basis of the PTV system with which the image sequences from the three cameras are processed and the 4D-coordinates {x, y, z, t} of the tracer particles are reconstructed. The software code is freely available for non-commercial use. The processing basically con-sists of three phases: calibration of the camera system on a known target body, reconstruction of 3D-positions from image to object space, and temporal tracking (Castello, 2010).
The calibration procedure adopted in our setup is explained in detail in the following section. Once calibrated and synchronized, the camera system continuously records the tracer particle posi-tions. The two-dimensional coordinates of all tracer particles in the image are detected for all cameras and all time instants using image processing and image analysis techniques. After assignment of corresponding particle images from different views it is possible
Fig. 2. Raw images of granularflow in a chute rotating at 24 rpm, captured by 3 PTV cameras at the same time instant. The group of tracer particles circled in the three images represents the same particles as seen by the different cameras. The bottomfigure shows the top view of the calibration plate used in the experiments.
to determine the 3D position in the object space by forward intersection. Using epipolar constraints, homologous image points can be detected and the 3D object coordinate of each particle can be determined. Finally, temporal matching is performed to deter-mine trajectories of each tracer particle.
With the present setup, up to 400 particles per time step were tracked on average. This number is not a hard limit of the method. In a larger setup, e.g. when using a wider chute, a much larger number of tracer particles could have been tracked. The limitation in this number lies entirely in the requirement of having a sufficiently low seeding density to ensure a large separation (relative to the diameter) between the visible tracer particles.
Details of the algorithms used in our code can be found in the literature: for calibration and 3D positioning algorithms we refer
toMaas et al. (1993); for the temporal tracking algorithm toMalik
et al. (1993); and for the latest developments of the tracking
routine toWillneff (2002, 2003),Willneff et al. (2012). Below we will discuss the most important steps.
3.3.1. Calibration of the camera system
Calibration of the camera means determining the extrinsic and intrinsic parameters using a set of image points with known world coordinates. A multi-planar calibration method is used, in which multiple images are captured of the same planar calibration plate at different heights within the experimental volume. The accuracy of the calibration is highly dependent on the correct positioning of the plate (Castello, 2010). For this reason, special care has been taken to accurately position the calibration plate throughout the measurement volume, to minimize the disadvantage of the multi-planar calibration method. The larger the volume covered by the calibration plate, the smaller are interpolation and extrapolation errors of the calibration functions (Castello, 2010).
To create the calibration functions which correlate the pixel information of each camera to the world coordinates, recordings of the calibration unit have been carried out with the same orienta-tion: the calibration plate plane is parallel to the chute base. Translation in the coordinate direction perpendicular to the calibration plate plane is carried out. The recordings of the calibration plate are registered in 4 different positions, at a height of 9 mm, 19 mm, 34 mm and 54 mm, with typical positioning error of less than 0.5 mm. With the information of the pixel size of the camera sensors, and the diameter of the circular voids, 3rd order polynomials relate the pixel information to the physical dimen-sions of the calibration plate. Linear interpolations and extrapola-tions of the generated polynomials are extended to the whole measurement volume.
3.3.2. Three-dimensional positioning of the particles
The second important phase of 3D-PTV processing is the three-dimensional positioning of particles in space from the raw images.
Fig. 2 shows an example of the raw images simultaneously
generated by the three cameras.
Several processing steps are required to obtain the particle position from the captured images. The first two steps are preprocessing steps, namely high pass filtering, and particle detection and location of the particles. High pass filtering is necessary to remove non-uniformities in the background illumi-nation (Willneff, 2002). For the detected and located particles in the preprocessing stage, the corresponding particles for all cam-eras are established. Since the corresponding particles are detected by all cameras, subsequently the 3D coordinates of these particles can be determined with the obtained calibration data from thefirst phase. The resulting error in the particle position is 0.5 mm in the horizontal plane and 1.0 mm in the depth direction.
From the 3D coordinates, the particles can be tracked in the object and image space.
3.3.3. Particle trajectory reconstruction
After obtaining the 3D coordinates of each particle, a particle trajectory is constructed by comparing the positions of particles in consecutive image frames. For each frame, the software tries to find an individual particle based on the position of that particular particle in the previous frame(s). Later the displacement of an individual particle between two frames (a single time step) is evaluated. In order to find such a displacement, at least two cameras are needed. The trajectory of a particle that is detected by an individual camera can be imaged as a two-dimensional path, also called epipolar lines. If a second camera detects the same particle trajectory, a three-dimensional path can be determined from both two-dimensional pathways. In PTV practice, three or even four cameras are used. The redundant information is used to improve the accuracy of the method. In this research, only trajectories of particles which are detected by all three cameras were used for further analysis. Furthermore, because particle trajectories with just a few number of positions have a higher probability of being false than trajectories with a large number of positions, we only used trajectories with a minimum number of positions. This procedure has proven very useful to remove unrealistic particle trajectories. Elimination of particle trajectories comprising less than 10 spatial positions has been found to be adequate in our work.
4. Simulation model 4.1. Discrete element model
The results of this work will be used to further validate the discrete element method (DEM) presented in our previous work
(Shirsath, 2014). DEM can be used to parametrically investigate the
role of particle interactions on the granularflow, as well as to gain access to properties which are not readily available from experi-ments. The DEM used in our work is based on the linear spring/ dashpot soft-sphere model, originally developed byCundall and
Strack (1979).
In our previous work (Shirsath, 2014) we introduced the particles in a rectangular area with a bcc-lattice arrangement of the particles, parallel to the chute bottom wall, where the initial velocity is set by the required mass rate. We then found that the resulting bed height and particle velocity profiles were indepen-dent of the exact manner of introducing the particles after a distance of approximately 0.2 m from the inlet. To reproduce the experiments somewhat more closely, in this work we introduce the particles parallel to gravity, but still using the bcc-lattice arrangement for convenience.Fig. 3shows a snapshot of introdu-cing particles at the inlet in this manner. We determined thefirst length wise position at which the bed height and surface flow velocity match between experiment and simulation for a non-rotating chute at an angle of inclination of 301, and subsequently placed the axis of rotation in our simulations at the same distance from this location as in the experiments to ensure the same centrifugal forces are felt by the particles.
4.2. Simulation settings
The physical properties of the spherical glass particles, the chute dimensions, and theflow conditions in our DEM simulations are kept the same as in our lab-scale experiments, as shown in
Table 2. In the simulation, the chute is initially empty, as is the case
constant massflow rate at the inlet of the chute. We introduce the particles with a massflow rate of 3.2 kg/s, which is equal to the massflow rate of the experiments. With this mass flow rate, the total number of particles in the chute is typically 55,000.
The simulations were carried out on a single core of an Intel Xeon E5520 processor (at 2.27 GHz). In general each simulation required 60 h of calculation time for each 6 s of simulation.
5. Postprocessing of experimental and simulation data 5.1. Calculation of bed height from experimental PTV data
To obtain the particle bed height at different positions in the chute from the PTV data, a postprocessing step is necessary. We assume that the bed surface can be defined as the height at which the visible track density (in the height direction) is highest. This is better than using an envelope around the top-most tracks, because such a measure would be dominated by positions of stray particles. To determine the local track density, the chute volume was first divided into computational cells. For each cell, the number of tracks that pass through it was calculated, where tracks with a length of more than 10 positions were used. Subsequently, for each column of cells the local maximum of the track density
was ascertained, and thus the height of the bed surface is known. We divided the entire chute in 250 (length) 16 (width) 200 (height)¼800,000 cells. This division was chosen to strike the best balance between a small cell size in the height direction and a sufficiently large number of tracks per cell. The resulting error on the estimated bed height is typically the same as the error on the determination of the vertical (depth) position of the particles, i.e. 1.0 mm.
Fig. 4(blue line) shows an example of the bed height obtained
in this manner for a non-rotating chute, as a function of stream-wise position and averaged over the width of the chute. Note that the measurements are still somewhat noisy. Therefore, a Gaussian filter of width 0.07 m was used to smooth the curve as shown in
Fig. 4(blue circles). Thisfilter width is large enough to significantly
smooth the data, yet small enough to still resolve the dependence of bed height on streamwise position.
5.2. Calculation of bed height in simulations
In the DEM simulations, the bed height was calculated via the center of mass (COM) height. In an ideal situation of homogenous packing, the bed height is exactly twice the center of mass height. However, we note that the bed height obtained from PTV mea-surements is basically a result of tracking the centers of particles. To enable a fair comparison between experiments and simulations, we should therefore base the bed height on the average height of the centers of the surface particles. As explained inFig. 5, the bed height (h) can be obtained by subtracting half a particle diameter from twice the COM height.
5.3. Calculation of experimental surface velocity using PIV
We used particle image velocimetry (PIV) to determine the average two-dimensional velocity field of the visible surface particles. Pairs of images were postprocessed using the commer-cial software package Davis 8.0.3. A multipass algorithm was used with an initial interrogation area size of 32 32 pixels and a final non-overlapping interrogation area size of 16 16 pixels, which yielded an approximate displacement error of O(0.1) pixels. Due to the very high seeding density (particles per interrogation area) there were practically no outliers. Any remaining outliers were removed with a standard median filter. For rotating chute flow, there may be a significant sideways motion and parts of the chute may fall “dry”, meaning that only stray particles are present in
Fig. 3. Snapshot of particle introduction at the inlet of the chute.
Table 2
Computational conditions (equal to experimental conditions).
Property Value
Length of chute 0.9 m
Width of chute 0.08 m
Height of chute 0.09 m
Inclination of chute 301
Massflow rate 3.2 kg/s
Particle type Spherical glass
Particle diameter 3 mm
Particle density 2550 kg/m3
Coefficient of normal restitution en;pp¼ en;pw¼ 0:96 Coefficient of tangential restitution et;pp¼ et;pw¼ 0:33 Coefficient of friction μpp¼ 0:10; μpw¼ 0:22
Total simulation time 6.0 s
Time step 2:5 10 6s
Fig. 4. Experimental particle bed height defined by the highest track density from PTV, for a non-rotating and rotating chute. The blue line represents the raw data from the post-processing, the blue circles, the smoothed bed height profile. Note that the smoothing was performed on all data, including positions near the inlet for zo0. The much larger bed height near the inlet explains the apparent increase of the smoothed data in the range between 0 and 0.03 m. (For interpretation of the references to color in thisfigure caption, the reader is referred to the web version of this paper.)
some regions. Masking was performed on these dry regions, meaning that no cross correlation analysis was applied in the masked region of the chute. After post-processing, a time-averaged velocityfield was obtained from a sequence of instanta-neous velocityfields obtained over a time interval during which theflow was steady. We found that the error in this velocity field was 0.2%, which is relatively small.
5.4. Calculation of experimental surface velocity using PTV
Similar to PIV, it is possible to determine the surface velocity profile using the PTV technique. From the known positions of tracer particle tracks at different time instances and the time difference in between two frames, we derived the velocity profile. Although PTV is a 3D technique, in these dense granularflows it is limited to tracking surface particles (those visible from the top). Thus the results (for the streamwise and spanwise components) are expected to match the surface particle velocity obtained from the PIV technique.
The procedure for obtaining Eulerian velocity profiles from the Lagrangian PTV tracks was as follows. (1) The tracks were smoothed using a (Matlab) loess filter to avoid irregularities. (2) The domain was divided into 250 (length) 9 (width) columns. Coordinates of tracks inside each column were identified. (3) The distance between each consecutive point of a track in a column was found, and multiplied by the frame rate to obtain the velocity of that track section. (4) The average velocity for each column was calculated to obtain the surface velocity profile as a function of spanwise and streamwise position.
Each individual velocity measurement had a relatively high error of 1.0 m/s due to the uncertainty of 0.5 mm in particle position combined with the frame rate of 2000 Hz. However, the error in the estimate of the average velocity was much smaller. Treating each velocity measurement as an independent measure-ment, and using approximately 400–500 individual velocity mea-surements per column, we arrived at an error in the estimated average velocity of 0.05 m/s.
Note that the 3D-PTV technique also delivers information about the depthwise velocity component of the surface particles, which cannot be obtained from the current PIV experiments. Although another PIV camera could be installed viewing the chute perpendicularly from the side, this would still make it very difficult, if not impossible, to obtain the dependence of the depthwise velocity of the surface particles on their spanwise position inside the chute. As we will show, this is very relevant for rotating chuteflows. Another option would be to use stereo-PIV (Sstereo-PIV), which is routinely used influid dynamics experiments using a laser sheet to highlight a particular section in afluid flow
(Wieneke, 2005; Dreyer et al., 2014). However, this is not easily
extensible to granular flows, leaving PTV as the best option to obtain the desired data.
5.5. Calculation of surface velocity in simulations
To enable a direct comparison between experimental and simulated surface velocity, a particle velocity field is calculated also in our simulations. It is important to only include those particles that would be optically visible from above the chute, because in the experiments the camera was mounted perpendi-cularly above the chute at a large distance. Specifically, in our simulations, the surface velocity is calculated by time-averaging the velocity of the topmost 6 particles in each streamwise and spanwise column of 5 mm 6 mm. The choice for this number of particles was made because at the given particle diameter of 3 mm, it is expected that at most 6 particles will be visible from above the chute in each of the computational columns. We have checked the dependence of the surface velocity measurements on the number of topmost particles used, and found only a negligible influence for particle numbers ranging from 3 to 12.
6. Experimental results and discussion 6.1. Repeatability of PTV experiments
To investigate the repeatability of the PTV measurements, as well as to rule out possible effects of wear and tear of the glass particles, some experiments have been performed twice: once at the start of our experimental series, and once near the end.
Fig. 6(a) shows the average streamwise surface particle velocity
along the centerline of the chute as a function of the streamwise position, for a non-rotating and rotating chute.Fig. 6(b) shows the average bed height along the centerline of the chute as a function of the streamwise position, for a non-rotating chute.
Fig. 5. For comparison with PTV data, the bed height in our simulations is calculated as twice the center of mass (COM) height minus half a particle diameter.
Fig. 6. Repeatability of measurements from PTV for a non-rotating and rotating chute inclined at 301. These results have been obtained at the start and end of our experimental series, respectively. (a) Streamwise surface velocity, and (b) bed height along the center-line of the chute.
The results show that the repeatability of our PTV experiments is satisfactory.
6.2. Comparison of bed height using PTV and the ultrasonic sensor
Fig. 7 shows the bed height as measured in a non-rotating
chute using PTV measurements (blue symbols) and the electronic ultrasonic sensor (red symbols) for a non-rotating chute. These experiments were performed with an interval of 4 months. As explained in Section 5.1, the bed height calculated in the PTV experiments is based on the maximum density of visible tracks in the height direction, whereas the ultrasonic sensor measures the bed height over a circular area of 28 mm in diameter. To enable an honest comparison, we have averaged the PTV data over the same area. We note that in the initial section, up to 0.2 m from the chute entrance, the electronic height sensor measurements were some-what affected by the noise (sound) generated by particles drop-ping from the hopper onto the chute surface. This may explain the deviations in the initial section. In the remaining section of the chute, the electronic height sensor measurements follow the PTV measurements quite closely, with an off-set of the order of one particle radius (1.5 mm). This bias can be explained by the fact that sound waves scatter off the top of the particles, while PTV is tracking the centers of particles, as explained inFig. 5. Overall, the agreement between the two independent experimental techni-ques is very satisfactory.
6.3. Comparison of streamwise velocity using PTV and PIV
Fig. 8shows the averaged streamwise surface velocity along the
center-line of the chute using PTV measurements (blue) and PIV measurements (green), for a non-rotating chute (lines) and a chute rotating at 24 rpm (circles). As observed in our previous work
(Shirsath, 2013), the granularflow decelerates roughly in the first
half of the chute and accelerates in the second half (both relative to the non-rotating case), which we attributed to a changing balance between Coriolis and centrifugal forces. For the purpose of this paper, it is encouraging to see that the two independent measurement techniques, one based on Lagrangian tracking of tracer particles and the other based on spatiotemporal correlations of all particles, are in good mutual agreement.
In the next section we will show more detailed comparisons between PTV and PIV measurements, but also include our DEM simulation results to validate the simulation method.
7. Validation of DEM using experimental measurements Having performed a cross-validation of independent experi-mental measurements, we now use these measurements to validate our discrete element model.
Fig. 9shows from a top view: the experiment, the PIV velocity
field, a collection of PTV particle tracks, and the simulation, respectively, for monodisperse glass particles in a non-rotating chute (left) and a chute rotating at 24 rpm (right). All results are in qualitative agreement with each other. The major effect of chute rotation is a sideways deflection of the particle stream due to Coriolis forces present in the frame of reference co-rotating with the chute. In the next sections we will present a detailed quantitative comparison.
7.1. Bed surface height
Fig. 10shows the full bed surface as a collection of PTV particle
tracks (left) and the full bed surface obtained from our DEM simula-tions (right) for non-rotating (top) and rotating (bottom) chutes.
Fig. 11provides a more detailed comparison, showing the bed
surface height as a function of position along the length of the chute, for a chute rotating at various rotation rates. The bed height is averaged over 5 mm wide sections of the chute, for three different width-wise positions in the chute (on the left, center and right-hand side). The simulation results (lines) are compared with the PTV experimental results (symbols). For the non-rotating chute, the bed height continuously decreases along the length of the chute, and the results are nearly indistinguishable for the different width-wise positions. As the rotation rate of the chute increases, the bed height increases on the right side of the chute and decreases on the left side. Moreover, at higher rotation rates we observe a maximum in the height as a function of streamwise position at the right side of the chute. Deviations between simulation and experiments are observed at the right side of the chute (blue lines) at higher rotation rates. This is consistent with our previous observation that the precise manner of particle introduction is important for the first section (approximately 0.2 m) of the chute. Given the experimental error of approximately half a particle diameter, these simulation results are in good agreement with the experimental measurements.
Fig. 7. Bed height obtained from PTV measurements (blue line) and electronic height sensor measurements (green symbols) for a non-rotating chute (0 rpm). Note that the electronic height sensor measures the bed height from the top surface of the particles, whereas PTV measures bed height based on the centers of the particles. This explains the bias of half a diameter (1.5 mm) between the two types of measurements. Close to the inlet, acoustic noise from the particles dropping onto the particle bed is confusing the ultrasonic signals, explaining the initial deviation. (For interpretation of the references to color in thisfigure caption, the reader is referred to the web version of this paper.)
Fig. 8. Averaged streamwise surface particle velocity along the center-line obtained from PTV and PIV measurements for a non-rotating chute (0 rpm) and a rotating chute (24 rpm). Note that the PIV measurements stop at 0.66 m for the rotating case because of masking (see main text). (For interpretation of the references to color in thisfigure, the reader is referred to the web version of this paper.)
7.2. Streamwise surface particle velocity
Fig. 12 shows the streamwise surface particle velocity as a
function of width-wise position at four different streamwise positions, for rotation rates 0 rpm (non-rotating chute), 8 rpm, 16 rpm and 24 rpm. The streamwise positions are at z¼0.0 m,
0.2 m, 0.4 m and 0.6 m. The simulation results (lines) are com-pared with the experimental results of PIV (filled symbols) and PTV (open symbols). Generally wefind good agreement between the simulations and both sets of experimental results. Some deviations between the PIV and PTV measurements are visible at higher rotation rates. This is caused by the sideways motion of the
Fig. 9. Top view of the experiment, the PIV velocityfield, a collection of PTV particle tracks, and a snapshot from the simulation (color scale indicates particle velocity), respectively. (a) Non-rotating chute. (b) Chute rotating at 24 rpm. (For interpretation of the references to color in thisfigure, the reader is referred to the web version of this paper.)
Fig. 10. Surface plot for monodisperse particleflows down a nonrotating chute (a and b) and a chute rotating with a rate of 24 rpm (c and d). Left (a and c): particle tracks from PTV experiments. Right (b and d): bed surface from DEM simulations. Note that for clarity we have chosen a view in which theflow is from right to left.
granular particles, leaving one side of the chute empty with occasional stray particles. These stray particle regions are masked out from our PIV analysis, while the stray particles are still processed up by our PTV analysis. The observed deviations there-fore correspond to velocities of very low number of particles. 7.3. Spanwise surface particle velocity
Fig. 13shows the spanwise surface particle velocity along the
width of the chute at different cross sections in the length of the chute. The simulation results are compared with the experimental results for different rotation rates of the chute. We observe that the magnitude of the spanwise velocityfirst increases and then decreases for consecutive streamwise positions. This corresponds to the process of sideways motion induced by Coriolis forces, which isfinally stopped by the compaction of the granular flow
against the side wall. The maximum spanwise velocity increases with increasing rotation rate. Some deviations between simulation and experiments are observed at the start of the chute (for zr0:2 m) because the way of introducing particles in the simula-tions is different from experiments. In all other cases, a rather good agreement is found between experiments and simulations. Note that previously we estimated the error in the average velocity obtained from PTV to be of the order of 0.05 m/s. This is consistent with thefluctuations observed in the PTV data, especially for the non-rotating case where no sideways velocity is expected. 7.4. Depthwise surface particle velocity
Fig. 14shows the depthwise surface particle velocity along the
length of the chute for different spanwise sections of the chute, as obtained from the PTV experiments. Note that for the non-rotating
Fig. 11. Bed height as a function of stream-wise position (along the length of the chute) for three different width-wise positions in a chute rotating with rates of 0 rpm, 8 rpm, 16 rpm and 24 rpm, respectively. Small circles are PTV experiments and lines are simulations. (For interpretation of the references to color in thisfigure, the reader is referred to the web version of this paper.)
Fig. 12. Streamwise particle velocity along the width of the chute for rotation rates of 0 rpm, 8 rpm, 16 rpm and 24 rpm. Filled symbols are PIV measurements, open symbols are PTV measurements, and lines are simulation measurements.
chute, the depthwise velocity is high near the inlet of the chute and gradually decreases to zero. For rotating chutes, there is a marked difference between relatively small depthwise velocities measured at the left side of the chute (blue lines) and relatively large depthwise velocities at the start of the right side of the chute (red lines). This is consistent with the observed bed height profiles from our simulations and PTV tracks. We confirmed that the slope of the bed height is consistent with the ratio of streamwise to depthwise velocity (not shown). This confirms that the particles move parallel to the bed surface.
8. Conclusions
In this paper, a three-dimensional particle tracking technique was applied to study bed height and surface particle velocities of granularflows in rotating chutes. The 3D-PTV experiments show
very good repeatability. A cross-validation of the particle bed height and the two dimensional velocityfield was performed by comparing with independent results obtained using an electronic ultrasonic height sensor and particle image velocimetry. All experimental results are in good mutual agreement.
The 3D-PTV technique has several advantages over other existing techniques. The advantages relative to the use of an electronic height sensor for the measurement of the bed height are,first, a better spatial resolution of the bed height profile and, second, a great reduction of the number of necessary experiments (unless a large number of height sensors is used). The advantage of 3D-PTV relative to the use of particle image velocimetry (PIV) is the measurement of the third (depthwise) component of the surface particle velocity. An overall advantage of 3D-PTV is that it can provide the measurements of particle bed height and surface particle velocityfield within one and the same experiment.
We have used the experimental results to further validate our discrete element model. We have shown that the simulation
Fig. 13. Spanwise particle velocity along the width of the chute for rotation rates of 0 rpm, 8 rpm, 16 rpm and 24 rpm. Open symbols are PTV measurements, closed symbols are PIV measurements, and lines are simulation measurements. Different colors represent different streamwise positions: 0.0 m (black), 0.2 m (red), 0.4 m (green) and 0.6 m (blue). (For interpretation of the references to color in thisfigure caption, the reader is referred to the web version of this paper.)
0 0.2 0.4 0.6 0.8 −0.1 −0.05 0 0.05 0.1 Chute length (m) = 0 rpm
Depthwise surface particle velocity (m/s)
x = 0.02 m x = 0.04 m x = 0.06 m 0 0.2 0.4 0.6 0.8 −0.1 −0.05 0 0.05 0.1 = 8 rpm 0 0.2 0.4 0.6 0.8 −0.1 −0.05 0 0.05 0.1 = 16 rpm 0 0.2 0.4 0.6 0.8 −0.1 −0.05 0 0.05 0.1 = 24 rpm
Fig. 14. Depth wise particle velocity along the width of the chute as measured by PTV for rotation rates of 0 rpm, 8 rpm, 16 rpm and 24 rpm. Measurements at the left side (blue), center (green) and right side (red) of the chute. (For interpretation of the references to color in thisfigure caption, the reader is referred to the web version of this paper.)
model is capable of predicting the evolution of the granularflow both qualitatively and quantitatively.
Acknowledgements
The authors wish to acknowledge STW forfinancial support. We thank L. McAlpine, A.P.C. Holten and G. Oerlemans for their technical support during this project. We thank O. Bokhove, A.R. Thornton, D.R. Tunuguntla, and T.W.J. Peeters for stimulating discussions.
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