60
2 Experiments in Pebble Flows
by their neighbors, which makes the neighboring pebbles move collectively. For these
reasons, the diffusion among pebbles is confined to be limited so that the two-region
arrangement can form and maintain the configuration during running, as well as the
mixing zone can be constrained to a small size.
The average streamline curves depicted in Fig. 2.11b are smooth and precisely
symmetrical against the central axis of the vessel. The average streamlines of the
pebbles clinging to the radial wall of the vessel are considered to be the boundary of
the stagnant zones in the pebble bed. The size of the stagnant zones is determined by
the size of the regions enclosed by the streamlines and the vessel wall. The average
streamlines are different and related to the radial positions of the pebbles, but they
are all parabolic curves except for the central position. It is considered that the
motion path of a pebble in the pebble bed is not a single “streamline” but a statistical
“stream tube” composed of many “streamlines”. The central line of the “stream tube”
is the average of the “streamlines” shown in Fig. 2.11b, and the size of the tube is
determined by the motion paths shown in Fig. 2.11a. The size of the tube is related
to the radial and axis positions of the pebble.
2.3.4 Equilibrium Conditions and Flow Characteristics
An attempt is made to ascertain whether the two-region arrangement has been in an
equilibrium state. Three terms are considered as equilibrium conditions. First, the
amount of black and colorless pebbles remaining in the vessel is approximately invariable. Second, the shape and the size of the two regions mainly remain unchanged.
Third, the size of the mixing zone is acceptable. A variable r , calculated at intervals,
is defined as the amount ratio of the discharged colorless pebbles to the discharged
black pebbles. Thus, the first equilibrium condition could be validated by the time
variation of r , since the discharge rate is set equal to the summation of the loading
rates of the black and the colorless pebbles. If r , equal to the ratio of the loading
rates, is related to the colorless pebbles and the black pebbles, the amount of black
and colorless pebbles draining out would be equal to that inserted. The loading rate
ratio of the colorless pebbles to the black pebbles is set to be 28:144 (0.23) in the
experiment. In other words, if r reaches and maintains the value of 0.23, the number
of the two types of pebbles remaining in the vessel is considered invariable, and an
equilibrium state for the two-region arrangement is reached. Figure 2.12 plots the
time-variation curve of r .
The flow of the pebble bed in the pebble-bed reactor core is categorized as a
granular flow. It is incredibly complicated, and the mechanism is not comprehensively
understood. This section will describe the general characteristics of the pebble flow
observed in the experiments. Since the discharge rate of the pebbles is low, the flow
of the pebbles is very slow and the pebbles are in a static equilibrium most of the time.
Firstly, the motion of the pebble bed is activated at the orifice of the vessel. Pebbles
right above the orifice move out of the vessel leaving the voids they occupied, and
pebbles neighboring the voids flow into the voids and leave the voids they filled. The
2 Experiments in Pebble Flows
by their neighbors, which makes the neighboring pebbles move collectively. For these
reasons, the diffusion among pebbles is confined to be limited so that the two-region
arrangement can form and maintain the configuration during running, as well as the
mixing zone can be constrained to a small size.
The average streamline curves depicted in Fig. 2.11b are smooth and precisely
symmetrical against the central axis of the vessel. The average streamlines of the
pebbles clinging to the radial wall of the vessel are considered to be the boundary of
the stagnant zones in the pebble bed. The size of the stagnant zones is determined by
the size of the regions enclosed by the streamlines and the vessel wall. The average
streamlines are different and related to the radial positions of the pebbles, but they
are all parabolic curves except for the central position. It is considered that the
motion path of a pebble in the pebble bed is not a single “streamline” but a statistical
“stream tube” composed of many “streamlines”. The central line of the “stream tube”
is the average of the “streamlines” shown in Fig. 2.11b, and the size of the tube is
determined by the motion paths shown in Fig. 2.11a. The size of the tube is related
to the radial and axis positions of the pebble.
2.3.4 Equilibrium Conditions and Flow Characteristics
An attempt is made to ascertain whether the two-region arrangement has been in an
equilibrium state. Three terms are considered as equilibrium conditions. First, the
amount of black and colorless pebbles remaining in the vessel is approximately invariable. Second, the shape and the size of the two regions mainly remain unchanged.
Third, the size of the mixing zone is acceptable. A variable r , calculated at intervals,
is defined as the amount ratio of the discharged colorless pebbles to the discharged
black pebbles. Thus, the first equilibrium condition could be validated by the time
variation of r , since the discharge rate is set equal to the summation of the loading
rates of the black and the colorless pebbles. If r , equal to the ratio of the loading
rates, is related to the colorless pebbles and the black pebbles, the amount of black
and colorless pebbles draining out would be equal to that inserted. The loading rate
ratio of the colorless pebbles to the black pebbles is set to be 28:144 (0.23) in the
experiment. In other words, if r reaches and maintains the value of 0.23, the number
of the two types of pebbles remaining in the vessel is considered invariable, and an
equilibrium state for the two-region arrangement is reached. Figure 2.12 plots the
time-variation curve of r .
The flow of the pebble bed in the pebble-bed reactor core is categorized as a
granular flow. It is incredibly complicated, and the mechanism is not comprehensively
understood. This section will describe the general characteristics of the pebble flow
observed in the experiments. Since the discharge rate of the pebbles is low, the flow
of the pebbles is very slow and the pebbles are in a static equilibrium most of the time.
Firstly, the motion of the pebble bed is activated at the orifice of the vessel. Pebbles
right above the orifice move out of the vessel leaving the voids they occupied, and
pebbles neighboring the voids flow into the voids and leave the voids they filled. The