2.5 Particle Velocimetry Measurements
97
left, center, right inlet tubes, respectively. 3). Meanwhile, the pebbles are discharged
from the outlet hole at a rate of 150 pebbles per minute. Thus, the total number of
pebbles in the vessel remains constant. This recirculation mode is different from the
previous experiment, where the drained pebbles flow freely[1].
In addition, much more detail about the experimental setup, properties of the glass
beads, and the method to control the constant discharge rate of the pebbles has been
provided in the previous papers [1, 40, 49].
2.5.4.2 Particle Tracking Technique
The polished stainless black glass balls are chosen to ensure the necessary resolutions
in snapshots [27]. In the images, every pebble diameter occupies about d=50 pixels.
Due to a total number of 70,000 pebbles in the bed, the circulating rate of 2.5 particles
per second produces a very slow velocity of the pebble flow. The discharged particles
per second make up 0.0035 % of the total particles in the setup. On average, the
particles move less than 0.01d per second. Then, the snapshots with a 0.1-second
interval can ensure recording motions of the moving pebbles comprehensively [44].
Several time intervals (0.05s, 0.1s, 0.5s, 1s) are chosen to compare with each other.
It has fewer effects.
The particle tracking velocimetry method is used here, which incorporates the
Relaxation Method (RM) [11]. In this algorithm, the locations of the pebbles are
identified by the Dynamical Threshold Binarization (DTB), where the threshold
level is detected particle by particle. The DTB is better than the Single-Threshold
Binarization (STB) using a uniform threshold level to detect particles [15].
The basic concept of this particle tracking algorithm is to find the most probable
link of a reference particle with similar displacements among its neighbors. In the
iterative process, the correct linking probability converges toward unity while the
other probabilities decrease to zero. The scheme of this particle tracking method is
shown in Fig. 2.32 and can be expressed as follows. A particle i in the 1
st frame has
a number of N p possible matchings to the particles in the 2
nd frame which follow
the relation:
y j − y
i
< R s ,
(2.20)
where y
i is the predicted location of particle i in the second frame considering the
mean velocity, and R s is the search radius. Meanwhile, the radius R n is used to select
the N n neighbor particles of particle i (Fig. 2.32). The threshold R q is the radius of
the relaxation area where the neighbor particles x k show a similar movement to the
particle x i , and the deviation from parallel motion is allowed. A weighting parameter
Q i jkl is defined to indicate whether or not a neighbor link satisfies the quasi-rigidity
condition [16]. The d i j stands for the displacement vector from particle x i to y j , and
d kl from particle x k to y l .
97
left, center, right inlet tubes, respectively. 3). Meanwhile, the pebbles are discharged
from the outlet hole at a rate of 150 pebbles per minute. Thus, the total number of
pebbles in the vessel remains constant. This recirculation mode is different from the
previous experiment, where the drained pebbles flow freely[1].
In addition, much more detail about the experimental setup, properties of the glass
beads, and the method to control the constant discharge rate of the pebbles has been
provided in the previous papers [1, 40, 49].
2.5.4.2 Particle Tracking Technique
The polished stainless black glass balls are chosen to ensure the necessary resolutions
in snapshots [27]. In the images, every pebble diameter occupies about d=50 pixels.
Due to a total number of 70,000 pebbles in the bed, the circulating rate of 2.5 particles
per second produces a very slow velocity of the pebble flow. The discharged particles
per second make up 0.0035 % of the total particles in the setup. On average, the
particles move less than 0.01d per second. Then, the snapshots with a 0.1-second
interval can ensure recording motions of the moving pebbles comprehensively [44].
Several time intervals (0.05s, 0.1s, 0.5s, 1s) are chosen to compare with each other.
It has fewer effects.
The particle tracking velocimetry method is used here, which incorporates the
Relaxation Method (RM) [11]. In this algorithm, the locations of the pebbles are
identified by the Dynamical Threshold Binarization (DTB), where the threshold
level is detected particle by particle. The DTB is better than the Single-Threshold
Binarization (STB) using a uniform threshold level to detect particles [15].
The basic concept of this particle tracking algorithm is to find the most probable
link of a reference particle with similar displacements among its neighbors. In the
iterative process, the correct linking probability converges toward unity while the
other probabilities decrease to zero. The scheme of this particle tracking method is
shown in Fig. 2.32 and can be expressed as follows. A particle i in the 1
st frame has
a number of N p possible matchings to the particles in the 2
nd frame which follow
the relation:
y j − y
i
< R s ,
(2.20)
where y
i is the predicted location of particle i in the second frame considering the
mean velocity, and R s is the search radius. Meanwhile, the radius R n is used to select
the N n neighbor particles of particle i (Fig. 2.32). The threshold R q is the radius of
the relaxation area where the neighbor particles x k show a similar movement to the
particle x i , and the deviation from parallel motion is allowed. A weighting parameter
Q i jkl is defined to indicate whether or not a neighbor link satisfies the quasi-rigidity
condition [16]. The d i j stands for the displacement vector from particle x i to y j , and
d kl from particle x k to y l .