-Experiments in FluidsIndirect measurements of streamwise solid fraction variations of granular flows accelerating
down a smooth rectangular chute
L. T. Sheng,1 C. Y. Kuo,2 Y. C. Tai,3 and S. S. Hsiaua)1
1)
Department of Mechanical Engineering, National Central University, Taiwan 320, ROC
2)
3)
Research Center for Applied Sciences, Academia Sinica, Taiwan 115, ROC
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Taiwan 701, ROC
Supplementary Fig.1 Two-dimensional average solid fraction distributions in the depth-wise
direction. Two inclination 30° and 36° are calculated. The flow images are divided into seven layers
in the depth direction. The total numbers in each layer within the imaging window (stream-wise) are
counted using the PTV (Capart et al., 2002) method. We can calculate the total two-dimensional
occupation area of the particles within each layer. Then we infer the depth-wise ratio of the
occupation area. It is speculated that this distribution is somewhat proportional to the volume fraction.
The results in the figures above represent the averaging of 500 image frames. From these figures, we
can conclude that the volume fraction profiles have a rather uniform distribution.
30°
36°
Supplementary Fig.2 Dependence of the solid fraction on the power law farther downstream of the
original imaging zone for the 30° and 36° inclinations (red markers). The 30° inclination results
show that the discrepancies become larger at positions with larger values of x, but they asymptote
remain at a constant level. The 36° inclination results keep almost the same as the original data. Near
x = 90 cm, the flow almost reaches the end of the chute (x =100 cm).
a)
Author to whom correspondence should be addressed. Electronic mail: sshsiau@cc.ncu.edu.tw.