7.3 Flow-Corrective Insert Optimization
465
The method to evaluate the discharging sequence is by first marking each pebble with a value (sequence value S) based on its initial vertical location. Then the
sequence is recording the mean value (mean sequence value S M ) of those marked
pebbles that have not been discharged out yet. Pebbles, whose heights range 0.2–
0.7 m, were chosen and values linearly varying from 1 to 0 were assigned to them:
Sequence value S = 1 −
(y(i) − 0.2)
(0.7 − 0.2)
(7.3)
where y(i) represents the vertical coordinate of pebble i. When the simulation starts,
pebbles located at the lower layer with larger values are expected to be discharged
first, and then those upper ones marked with smaller values will be discharged next. So
if the right order is strictly obeyed, the mean value of the remaining marked pebbles
(S M ) would decline in the fastest way because the pebble being discharged always
has the largest sequence value at that moment. The theoretical descending profile of
S M for the fastest way can be calculated, and it has been depicted in Fig. 7.12c. The
theoretical profile is the steepest-decent one only depending on the discharging rate
and the sum of marked pebbles:
S M (t) =
((C R t)
2
− 2N C R t + N
2
)
2N (N − C R t)
(7.4)
where C R represents the discharging rate (120 pebbles/s), and N represents the total
number of marked pebbles (20,383).
The descending profile of S M is determined by the pebble-bed geometry when
pebble properties are specific. A pebble bed with a relatively fast descending profile
of S M is created because it indicates thousands of fuel pebbles can circulate (being
loaded, discharged, and reloaded) with an ordered and stable sequence. It is about the
most critical points in HTGR running in terms of safety and efficiency. Descending
profiles of S M in a normal bed and modified bed with an insert are both illustrated
in Fig. 7.12c.
Descending profile in the modified bed with the insert is much closer to the
theoretical profile: worse than the ideal situation, but much improved for that of a
normal bed. It is the proper insert that creates a well-organized pebble flow field and
relieves the disorder happening in a normal bed. Hence, in consideration of the flow
sequence, the insert-corrective pebble bed is also a better option.
7.3.5 Insert Design
Previous sections prove that the placement of a proper insert can improve flow performance of a pebble bed from several aspects, which are crucial to HTGR running:
stagnant rate, radial flow uniformity, and flow sequence. For applying the flowcorrective insert technique to the dense, very slow, and discharge-controlled process
465
The method to evaluate the discharging sequence is by first marking each pebble with a value (sequence value S) based on its initial vertical location. Then the
sequence is recording the mean value (mean sequence value S M ) of those marked
pebbles that have not been discharged out yet. Pebbles, whose heights range 0.2–
0.7 m, were chosen and values linearly varying from 1 to 0 were assigned to them:
Sequence value S = 1 −
(y(i) − 0.2)
(0.7 − 0.2)
(7.3)
where y(i) represents the vertical coordinate of pebble i. When the simulation starts,
pebbles located at the lower layer with larger values are expected to be discharged
first, and then those upper ones marked with smaller values will be discharged next. So
if the right order is strictly obeyed, the mean value of the remaining marked pebbles
(S M ) would decline in the fastest way because the pebble being discharged always
has the largest sequence value at that moment. The theoretical descending profile of
S M for the fastest way can be calculated, and it has been depicted in Fig. 7.12c. The
theoretical profile is the steepest-decent one only depending on the discharging rate
and the sum of marked pebbles:
S M (t) =
((C R t)
2
− 2N C R t + N
2
)
2N (N − C R t)
(7.4)
where C R represents the discharging rate (120 pebbles/s), and N represents the total
number of marked pebbles (20,383).
The descending profile of S M is determined by the pebble-bed geometry when
pebble properties are specific. A pebble bed with a relatively fast descending profile
of S M is created because it indicates thousands of fuel pebbles can circulate (being
loaded, discharged, and reloaded) with an ordered and stable sequence. It is about the
most critical points in HTGR running in terms of safety and efficiency. Descending
profiles of S M in a normal bed and modified bed with an insert are both illustrated
in Fig. 7.12c.
Descending profile in the modified bed with the insert is much closer to the
theoretical profile: worse than the ideal situation, but much improved for that of a
normal bed. It is the proper insert that creates a well-organized pebble flow field and
relieves the disorder happening in a normal bed. Hence, in consideration of the flow
sequence, the insert-corrective pebble bed is also a better option.
7.3.5 Insert Design
Previous sections prove that the placement of a proper insert can improve flow performance of a pebble bed from several aspects, which are crucial to HTGR running:
stagnant rate, radial flow uniformity, and flow sequence. For applying the flowcorrective insert technique to the dense, very slow, and discharge-controlled process