4.2 Gravity-Driven Flow Regime Characterization
201
slowest flow in this analysis for F6 also displays the tiny intermittency when C
equals to 0.1048.
4.2.4.5 Criteria of Flow Regime Categorization
The multi-fractal and fluctuation analysis of the time-velocity series provides a quantitative way to characterize the regime of dense pebble flows. Data of the C−RFKE
has been collected for the dense pebble flow with different mean velocities and more
details are shown in Fig. 4.24. Concerning the slow pebble flow in Cases F1 and F2,
the pebble flow indicates the strongly intermittent or non-consistent characteristic
with C > 0.5. Meanwhile, the larger RFKE around 0.9 means the larger magnitude
of the burst motion events. On the contrary, the pebble flow for F5 and F6 behave
more like a consistent liquid-like flow with smaller intermittency and fluctuation.
There is a large fluctuation with RFKE > 10% and small intermittency with C < 0.5
for the middle-level recirculation flow rates.
It is necessary to offer some physical interpretation for the two characteristic
parameters, namely the intermittency index C and the relative fluctuating kinetic
energy (RFKE). C is a dimensionless parameter describing the intermittency and
self-similarity characteristics of the velocity signals from the point of multi-fractal
analysis. C = 0 when the signal is a constant function, and C = 1 when the signal is
an impulse function (Fig. 4.24a). In other words, C indicates the uniformity of timevelocity distribution. Dense pebble flows with large C will keep steady or uniform
motion state most of the time between two burst motion events. For instance, the very
slow dense pebble flow can keep quiescent for a long period before the burst motion
events happen. The burst motion events are induced by the irregular voids propagation
process. The liquid-like dense granular flow with almost constant velocity keeps the
steady discharging state for all the time with a small number of the burst motion
Fig. 4.24 a Two extreme cases for the intermittency index C. b The parameter analysis for categorizing the dense pebble flow
201
slowest flow in this analysis for F6 also displays the tiny intermittency when C
equals to 0.1048.
4.2.4.5 Criteria of Flow Regime Categorization
The multi-fractal and fluctuation analysis of the time-velocity series provides a quantitative way to characterize the regime of dense pebble flows. Data of the C−RFKE
has been collected for the dense pebble flow with different mean velocities and more
details are shown in Fig. 4.24. Concerning the slow pebble flow in Cases F1 and F2,
the pebble flow indicates the strongly intermittent or non-consistent characteristic
with C > 0.5. Meanwhile, the larger RFKE around 0.9 means the larger magnitude
of the burst motion events. On the contrary, the pebble flow for F5 and F6 behave
more like a consistent liquid-like flow with smaller intermittency and fluctuation.
There is a large fluctuation with RFKE > 10% and small intermittency with C < 0.5
for the middle-level recirculation flow rates.
It is necessary to offer some physical interpretation for the two characteristic
parameters, namely the intermittency index C and the relative fluctuating kinetic
energy (RFKE). C is a dimensionless parameter describing the intermittency and
self-similarity characteristics of the velocity signals from the point of multi-fractal
analysis. C = 0 when the signal is a constant function, and C = 1 when the signal is
an impulse function (Fig. 4.24a). In other words, C indicates the uniformity of timevelocity distribution. Dense pebble flows with large C will keep steady or uniform
motion state most of the time between two burst motion events. For instance, the very
slow dense pebble flow can keep quiescent for a long period before the burst motion
events happen. The burst motion events are induced by the irregular voids propagation
process. The liquid-like dense granular flow with almost constant velocity keeps the
steady discharging state for all the time with a small number of the burst motion
Fig. 4.24 a Two extreme cases for the intermittency index C. b The parameter analysis for categorizing the dense pebble flow