2.5 Particle Velocimetry Measurements
81
Fig. 2.23 (a) Shear rates in different height obtained by the slope of the average velocity curves;
(b). The contour map of modulus of the shear rate (
1
s )
• For C 2 in the conical zone: the contractive configuration of the pebble bed makes
less distance between the streamlines, and the particles near the outlet are discharged at constant flow rates. As a result, the intermittencies between the streamlines become close to each other, and stay around the value of 0.3.
2.5.3.7 The Relation of Autocorrelation and Intermittency
This section will further discuss the relation between autocorrelation time τ c and the
intermittent index C 2 . The radial distribution of the autocorrelation time (Fig. 2.20)
presents a positive correlation with intermittency. For example, the longer intervals
over the significant motion events near the wall dominate the larger autocorrelation
time, whereas the short intervals in the center indicate the small τ c . Similar relationships are shown in the streamlines Nos. 2–4 in the vertical direction. In contrast, the
particles correlate less with their previous velocities near the outlet on the streamline
No. 1. The bulk motion events take place increasingly frequently or fluctuate quickly.
As the paper reported before [4, 38], the stagnant zone can be found in the low
corners, or in the bottom of the conical base of the experimental vessels near the
wall under some conditions [15] (see Fig. 2.15 for the sketch map of the stagnant
zone between the streamline No. 5 and the right wall of the vessel). The particles in
the stagnant region flow very slowly, or remain stationary, or even take about one
hundred hours to be discharged through the outlet.
To investigate the autocorrelation and intermittency in the stagnant zones, herein,
two typical cases are analyzed. Case 1 focuses on the rectangular zones on streamline
No. 5, while case 2 is for the stagnant zones fixed at x = 30d (Fig. 2.24) with different
heights. Although τ c decreases with a height reduction in the two situations, in case 2,
the zones closer to the wall show smaller autocorrelation than in case 1, which differs
81
Fig. 2.23 (a) Shear rates in different height obtained by the slope of the average velocity curves;
(b). The contour map of modulus of the shear rate (
1
s )
• For C 2 in the conical zone: the contractive configuration of the pebble bed makes
less distance between the streamlines, and the particles near the outlet are discharged at constant flow rates. As a result, the intermittencies between the streamlines become close to each other, and stay around the value of 0.3.
2.5.3.7 The Relation of Autocorrelation and Intermittency
This section will further discuss the relation between autocorrelation time τ c and the
intermittent index C 2 . The radial distribution of the autocorrelation time (Fig. 2.20)
presents a positive correlation with intermittency. For example, the longer intervals
over the significant motion events near the wall dominate the larger autocorrelation
time, whereas the short intervals in the center indicate the small τ c . Similar relationships are shown in the streamlines Nos. 2–4 in the vertical direction. In contrast, the
particles correlate less with their previous velocities near the outlet on the streamline
No. 1. The bulk motion events take place increasingly frequently or fluctuate quickly.
As the paper reported before [4, 38], the stagnant zone can be found in the low
corners, or in the bottom of the conical base of the experimental vessels near the
wall under some conditions [15] (see Fig. 2.15 for the sketch map of the stagnant
zone between the streamline No. 5 and the right wall of the vessel). The particles in
the stagnant region flow very slowly, or remain stationary, or even take about one
hundred hours to be discharged through the outlet.
To investigate the autocorrelation and intermittency in the stagnant zones, herein,
two typical cases are analyzed. Case 1 focuses on the rectangular zones on streamline
No. 5, while case 2 is for the stagnant zones fixed at x = 30d (Fig. 2.24) with different
heights. Although τ c decreases with a height reduction in the two situations, in case 2,
the zones closer to the wall show smaller autocorrelation than in case 1, which differs