464
7 Applications: Pebble Flow Optimizations
7.3.4.2 Vertical Standard Deviation— D v
In the previous section, pre-filled stripes were employed to highlight the vertical
movement of the pebble flow. In this part, features of a horizontal pebble-stripe can
be used to reflect the radial flow uniformity. One stripe of differently colored pebbles
is tracked from the beginning, and their location data is collected over the simulation
time. For instance, in a radial-uniform flow field, one initially located pebble-stripe
can remain horizontal and concentrate in a thin layer during the running process like
a mass flow pattern shown in Fig. 7.12a. However, in a flow field with bad radial
uniformity, a pebble-stripe would curve and disperse because of changing vertical
velocity along the radius, as shown in Fig. 7.12b. The standard deviation of the
pebble-stripe’s vertical coordinates (D v ), which reflects the extent of dispersion in
the vertical direction, can be regarded as the indication of radial uniformity. The
uniform field can keep D v as small as its initial value even when the marked pebblestripe enters the lower bin. The value of D v will increase sharply in the non-uniform
field. The inconstant vertical velocity profile, especially in the lower bin (refer to
Fig. 7.13), is responsible for the significant vertical dispersion.
From what is depicted in Fig. 7.18b, there is a big difference between two beds
on changing D v representing the stripe initially located at 70–75 cm (namely the top
stripe in Figs. 7.12 and 7.16). The normal bed presents a rapidly increasing profile
over 100s time from 0.014 at 20 s to 0.082 at 120 s, while the modified bed with the
insert keeps its value at the bottom level and only experiences a very slight rise from
0.014 to 0.016. The pebble-stripe in the normal bed sees a more significant vertical
dispersion than that in the bed with the insert, and the reason is the non-uniform
distribution of vertical velocity along the radius. In the normal bed, the middle part of
the stripe belonging to the dominating central flow can move down fast and smoothly,
but with side parts of the stripe left far behind. This leads to a visual curved stripe
and a rising value of D v . Nevertheless, after being equipped with the insert, the flow
field becomes consistently tiny, D v , and this proves a much-improved radial flow
uniformity in the bed. This bed can hold the overall pebble flow field as a uniform
and simultaneously moving entirety with little unexpected dispersion because vertical
velocity remains constant in the radial direction. Excellent radial flow uniformity is
an essential feature of mass flow patterns, and it is also one of the points to distinguish
mass flow from funnel flow. A modified bed with an insert, which can provide better
radial flow uniformity, has an advantage in the HTGR application.
7.3.4.3 Mean Sequence Value—S M and Its Descending Profile
Flow pattern in a reactor core should follow the first-in first-out rule, which aims
at ensuring the correct discharging sequence. To put it simply, fuel pebbles at the
lower layer always get out of the bed before those at the upper layer, ensuring the
discharging sequence the same as the loading sequence. Only this way can make sure
that each fuel pebble has a similar staying time within the core as well as a similar
burn-up level when they are drained out .
7 Applications: Pebble Flow Optimizations
7.3.4.2 Vertical Standard Deviation— D v
In the previous section, pre-filled stripes were employed to highlight the vertical
movement of the pebble flow. In this part, features of a horizontal pebble-stripe can
be used to reflect the radial flow uniformity. One stripe of differently colored pebbles
is tracked from the beginning, and their location data is collected over the simulation
time. For instance, in a radial-uniform flow field, one initially located pebble-stripe
can remain horizontal and concentrate in a thin layer during the running process like
a mass flow pattern shown in Fig. 7.12a. However, in a flow field with bad radial
uniformity, a pebble-stripe would curve and disperse because of changing vertical
velocity along the radius, as shown in Fig. 7.12b. The standard deviation of the
pebble-stripe’s vertical coordinates (D v ), which reflects the extent of dispersion in
the vertical direction, can be regarded as the indication of radial uniformity. The
uniform field can keep D v as small as its initial value even when the marked pebblestripe enters the lower bin. The value of D v will increase sharply in the non-uniform
field. The inconstant vertical velocity profile, especially in the lower bin (refer to
Fig. 7.13), is responsible for the significant vertical dispersion.
From what is depicted in Fig. 7.18b, there is a big difference between two beds
on changing D v representing the stripe initially located at 70–75 cm (namely the top
stripe in Figs. 7.12 and 7.16). The normal bed presents a rapidly increasing profile
over 100s time from 0.014 at 20 s to 0.082 at 120 s, while the modified bed with the
insert keeps its value at the bottom level and only experiences a very slight rise from
0.014 to 0.016. The pebble-stripe in the normal bed sees a more significant vertical
dispersion than that in the bed with the insert, and the reason is the non-uniform
distribution of vertical velocity along the radius. In the normal bed, the middle part of
the stripe belonging to the dominating central flow can move down fast and smoothly,
but with side parts of the stripe left far behind. This leads to a visual curved stripe
and a rising value of D v . Nevertheless, after being equipped with the insert, the flow
field becomes consistently tiny, D v , and this proves a much-improved radial flow
uniformity in the bed. This bed can hold the overall pebble flow field as a uniform
and simultaneously moving entirety with little unexpected dispersion because vertical
velocity remains constant in the radial direction. Excellent radial flow uniformity is
an essential feature of mass flow patterns, and it is also one of the points to distinguish
mass flow from funnel flow. A modified bed with an insert, which can provide better
radial flow uniformity, has an advantage in the HTGR application.
7.3.4.3 Mean Sequence Value—S M and Its Descending Profile
Flow pattern in a reactor core should follow the first-in first-out rule, which aims
at ensuring the correct discharging sequence. To put it simply, fuel pebbles at the
lower layer always get out of the bed before those at the upper layer, ensuring the
discharging sequence the same as the loading sequence. Only this way can make sure
that each fuel pebble has a similar staying time within the core as well as a similar
burn-up level when they are drained out .