184
4 Numerical Methods and Simulation for Pebble Flows
Fig. 4.14 Probability density distributions of E(t) at different circulating rates
the data points representing the long static period will concentrate on the small order
of the magnitude, resulting in a higher peak probability density. These “single-peak”
statistical distributions have profiles of the same pattern but different shapes and
quantitative values, which will be discussed further in the next section. Two characteristic parameters can be calculated from each distribution, and they will present
the flow features and help quantitatively distinguishing gravity-driven dense particle
flows from a macroscopic time-energy perspective Fig. 4.14.
4.2.3.5 Criteria for Subdividing Gravity-Driven Dense Particle Flow
The “single-peak” distribution rule of log 10 E(t) provides a quantitative method to
characterize the time-energy distribution feature of gravity-driven dense particle
flows. Two characteristic parameters based on the distribution pattern are proposed
for the sake of defining quantitative criteria: the standard deviation (σ ) and the span
of energy magnitude (E span ). The geometric meanings of these two parameters refer
to Fig. 4.15.
It is necessary to offer some physical interpretation for these two parameters.
The standard deviation (σ ) of log 10 E(t) indicates the uniformity of time-energy
distribution. Dense particle flows with a small value of σ must maintain steady
and uniform motion state most of the time. For instance, completely static particle
4 Numerical Methods and Simulation for Pebble Flows
Fig. 4.14 Probability density distributions of E(t) at different circulating rates
the data points representing the long static period will concentrate on the small order
of the magnitude, resulting in a higher peak probability density. These “single-peak”
statistical distributions have profiles of the same pattern but different shapes and
quantitative values, which will be discussed further in the next section. Two characteristic parameters can be calculated from each distribution, and they will present
the flow features and help quantitatively distinguishing gravity-driven dense particle
flows from a macroscopic time-energy perspective Fig. 4.14.
4.2.3.5 Criteria for Subdividing Gravity-Driven Dense Particle Flow
The “single-peak” distribution rule of log 10 E(t) provides a quantitative method to
characterize the time-energy distribution feature of gravity-driven dense particle
flows. Two characteristic parameters based on the distribution pattern are proposed
for the sake of defining quantitative criteria: the standard deviation (σ ) and the span
of energy magnitude (E span ). The geometric meanings of these two parameters refer
to Fig. 4.15.
It is necessary to offer some physical interpretation for these two parameters.
The standard deviation (σ ) of log 10 E(t) indicates the uniformity of time-energy
distribution. Dense particle flows with a small value of σ must maintain steady
and uniform motion state most of the time. For instance, completely static particle