8
1 Introduction
pebbles discharged from the bed bottom. The loading rate is precisely equal to the
discharging rate, so the total number of the fuel pebbles in the core remains constant
during the operation.
Different from other types of granular flow, the flow rate of the pebbles in the
reactor is slow that the equivalent flow velocity in HTGR is lower than most granular
flows in several orders. In most applications, it can be viewed as a pebble system
composed of the equivalent stagnant pebbles. This is a new flow regime of extremely
slow pebble flow. Granular flow is an attractively simple and yet surprisingly complex
subject [45]. To date, the detailed understanding of the slow and dense granular
flows has not been obtained and remains one of the critical challenges in the fields
of the granular science and technology. In general, the fast and dilute flows can be
analyzed by the classical hydrodynamics. In contrast, the slow and dense flows pose
a considerable challenge to theorists in terms of the complex many-body interactions
and non-thermal fluctuations. Moreover, the slow granular flows have many important
engineering applications [46], e.g., the new pebble-bed nuclear reactors [47], whose
efficiency and safety depend on the degree of the mixing in prolonged granular
drainage (<1 pebble per min) [48]. Thus, the physics of the slow pebble flow is a
significant but poorly understood topic.
1.3.3 Pebble Flow Intermittency
The understanding of granular flow is hampered by their singular behavior. For
instance, the flow behaves like a solid, liquid or gas depending on the mechanical
energy. Some interesting phenomena, e.g., avalanches, convection, arching, and so
on, were observed [49–51].
It is needed to define a measure for analyzing intermittency quantitatively. Over the
past decades, many investigations have been devoted to the unresolved fundamental
problems on the physics of slow and dense pebble flows, such as flow jamming [52]
or intermittency [53]. It is important to know that the mechanisms on when and
where the jamming is formed and how the overall granular flow field is influenced
by flow intermittency. To reach this goal, quantitative analyses on the flow jamming
and intermittency events are essential.
The intermittency measure is an essential issue in quantitative analyses of the
intermittent pebble flow. However, few studies have been reported on the intermittency measure of the slow and dense granular flow in the silo bed. With regards to
the relevant research fields, Brereton and Grace [54], characterized the mesoscale
transient flow by devising measures for the flow intermittency, which describes the
variability or heterogeneity of time-dependent signals from multiphase flow systems.
Besides, an intermittency index has been proposed to capture the global behavior of
the measured signal. The index was defined as the ratio of the standard deviation
of density fluctuations under the selected conditions to the standard deviations of
fully segregated flow. Johnsson [55] calculated the values of the kurtosis from the
time-series of absolute pressure fluctuations. The kurtosis is a measure of the “peak”
1 Introduction
pebbles discharged from the bed bottom. The loading rate is precisely equal to the
discharging rate, so the total number of the fuel pebbles in the core remains constant
during the operation.
Different from other types of granular flow, the flow rate of the pebbles in the
reactor is slow that the equivalent flow velocity in HTGR is lower than most granular
flows in several orders. In most applications, it can be viewed as a pebble system
composed of the equivalent stagnant pebbles. This is a new flow regime of extremely
slow pebble flow. Granular flow is an attractively simple and yet surprisingly complex
subject [45]. To date, the detailed understanding of the slow and dense granular
flows has not been obtained and remains one of the critical challenges in the fields
of the granular science and technology. In general, the fast and dilute flows can be
analyzed by the classical hydrodynamics. In contrast, the slow and dense flows pose
a considerable challenge to theorists in terms of the complex many-body interactions
and non-thermal fluctuations. Moreover, the slow granular flows have many important
engineering applications [46], e.g., the new pebble-bed nuclear reactors [47], whose
efficiency and safety depend on the degree of the mixing in prolonged granular
drainage (<1 pebble per min) [48]. Thus, the physics of the slow pebble flow is a
significant but poorly understood topic.
1.3.3 Pebble Flow Intermittency
The understanding of granular flow is hampered by their singular behavior. For
instance, the flow behaves like a solid, liquid or gas depending on the mechanical
energy. Some interesting phenomena, e.g., avalanches, convection, arching, and so
on, were observed [49–51].
It is needed to define a measure for analyzing intermittency quantitatively. Over the
past decades, many investigations have been devoted to the unresolved fundamental
problems on the physics of slow and dense pebble flows, such as flow jamming [52]
or intermittency [53]. It is important to know that the mechanisms on when and
where the jamming is formed and how the overall granular flow field is influenced
by flow intermittency. To reach this goal, quantitative analyses on the flow jamming
and intermittency events are essential.
The intermittency measure is an essential issue in quantitative analyses of the
intermittent pebble flow. However, few studies have been reported on the intermittency measure of the slow and dense granular flow in the silo bed. With regards to
the relevant research fields, Brereton and Grace [54], characterized the mesoscale
transient flow by devising measures for the flow intermittency, which describes the
variability or heterogeneity of time-dependent signals from multiphase flow systems.
Besides, an intermittency index has been proposed to capture the global behavior of
the measured signal. The index was defined as the ratio of the standard deviation
of density fluctuations under the selected conditions to the standard deviations of
fully segregated flow. Johnsson [55] calculated the values of the kurtosis from the
time-series of absolute pressure fluctuations. The kurtosis is a measure of the “peak”