4.2 Gravity-Driven Flow Regime Characterization
165
law divergence in the intermittent flow regime. Moreover, instead of the hysteretic
transition, Fischer et al. [35], observed temporal intermittency in the rotating drum
with spontaneous, erratic switches from discontinuous to continuous flow regime.
Such intermittent feature has also been found in other types of flows, such as a
collection of rigid frictional disks inside a narrow vertical pipe [36], where the intermittent flow is composed of alternating phases of creep motions when the pressure
at the bottom of the particle assembly rises nonlinearly with time and sudden slip.
In relation to the specific avalanche characteristic of particle materials, Silbert [23],
demonstrated the prevalence of intermittency in gravity-driven, dense particle flows
down an inclined plane, etc.
With regards to flow regimes, it can be qualitatively categorized into three principal regimes: a gas-like (rapid flow), a liquid-like (slow flow), and a plastic flow (very
slow or quasi-static flow [33]). These categorizations are always taken to be rather
empirical or ideal (asymptotic regime classification based on theoretical dimensional
analysis [37]). The analysis of the fundamental mechanisms in the quantitative categorization of the flow regimes remains to be investigated. Rapid flow has been
extensively studied and described by gas-kinetic theories [37, 38]. Nevertheless, few
insights have been given into the characteristics of slow particle flows, as well as
their flow regime characterizations.
The particle flow is fairly slow inside the pebble-bed reactor core which belongs
to a typical slow flow regime. This section aims to provide the underlying complex
mechanisms of slow particle flows, as well as some important issues on flow regime
characterization, via exploring the intermittency characteristics of a slow particle flow
comparing to a fast dense flow. For this purpose, the flow behavior characteristics
of a gravity-driven dense particle flow in a particle bed with a contracted drainage
orifice are quantitatively analyzed based on the discrete element method simulation.
Three values of discharging rates, ranging from relatively fast to slow dense flows, are
investigated. Time variations and derivatives of mean forces and velocities, as well
as their respective correlations, are analyzed to depict the characteristics of particle
flow regimes. The auto-correlation functions and its Fourier spectrum are utilized to
show the differences of the mechanisms of the slow and the fast particle flows.
4.2.1.1 Numerical Setup and Conditions
The dimension of numerical setup is set based on the configurations of an experimental test facility built at the Institute of Nuclear and New Energy Technology
(INET) of Tsinghua University [39], which is 40 × 800 × 1000 mm in depth (x),
width (y), and height (z), respectively. The bed is filled with 15,210 spherical particles of uniform diameter d p = 12 mm (Fig. 4.2). The bottom of the bed is contracted
to a drainage orifice with a conical base angle of 30
◦ . A discharging hole of 120 mm
in width is located in the bottom center. The setup runs at a recirculation mode.
For each case, the pebbles are removed through the bottom hole at a fixed rate, and
simultaneously reloaded at the same rate on the top to keep the number of pebbles
stable. The parameters are listed in Table 4.1.
165
law divergence in the intermittent flow regime. Moreover, instead of the hysteretic
transition, Fischer et al. [35], observed temporal intermittency in the rotating drum
with spontaneous, erratic switches from discontinuous to continuous flow regime.
Such intermittent feature has also been found in other types of flows, such as a
collection of rigid frictional disks inside a narrow vertical pipe [36], where the intermittent flow is composed of alternating phases of creep motions when the pressure
at the bottom of the particle assembly rises nonlinearly with time and sudden slip.
In relation to the specific avalanche characteristic of particle materials, Silbert [23],
demonstrated the prevalence of intermittency in gravity-driven, dense particle flows
down an inclined plane, etc.
With regards to flow regimes, it can be qualitatively categorized into three principal regimes: a gas-like (rapid flow), a liquid-like (slow flow), and a plastic flow (very
slow or quasi-static flow [33]). These categorizations are always taken to be rather
empirical or ideal (asymptotic regime classification based on theoretical dimensional
analysis [37]). The analysis of the fundamental mechanisms in the quantitative categorization of the flow regimes remains to be investigated. Rapid flow has been
extensively studied and described by gas-kinetic theories [37, 38]. Nevertheless, few
insights have been given into the characteristics of slow particle flows, as well as
their flow regime characterizations.
The particle flow is fairly slow inside the pebble-bed reactor core which belongs
to a typical slow flow regime. This section aims to provide the underlying complex
mechanisms of slow particle flows, as well as some important issues on flow regime
characterization, via exploring the intermittency characteristics of a slow particle flow
comparing to a fast dense flow. For this purpose, the flow behavior characteristics
of a gravity-driven dense particle flow in a particle bed with a contracted drainage
orifice are quantitatively analyzed based on the discrete element method simulation.
Three values of discharging rates, ranging from relatively fast to slow dense flows, are
investigated. Time variations and derivatives of mean forces and velocities, as well
as their respective correlations, are analyzed to depict the characteristics of particle
flow regimes. The auto-correlation functions and its Fourier spectrum are utilized to
show the differences of the mechanisms of the slow and the fast particle flows.
4.2.1.1 Numerical Setup and Conditions
The dimension of numerical setup is set based on the configurations of an experimental test facility built at the Institute of Nuclear and New Energy Technology
(INET) of Tsinghua University [39], which is 40 × 800 × 1000 mm in depth (x),
width (y), and height (z), respectively. The bed is filled with 15,210 spherical particles of uniform diameter d p = 12 mm (Fig. 4.2). The bottom of the bed is contracted
to a drainage orifice with a conical base angle of 30
◦ . A discharging hole of 120 mm
in width is located in the bottom center. The setup runs at a recirculation mode.
For each case, the pebbles are removed through the bottom hole at a fixed rate, and
simultaneously reloaded at the same rate on the top to keep the number of pebbles
stable. The parameters are listed in Table 4.1.