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NEA 3-D Kinetics Group Withdrawal benchmark
Detailed problem specifications may be found in (/6).
The table of configurations list the possible core configurations
ig encountered in each problem case and the figure after sketches the composition upper limits vs time.
Axial reflectors are simulated by means of equivalent log boundary conditions clogbc and cloghc.
Composition ig=1 is an unaltered bottom layer of unrodded, unpoisoned (by pyrex burnable poison) fuel.
"aro" stands for "All Rods Out", unrodded, but poisoned, composition.
Case a covers the withdrawal of initially inserted D group of 1400e-5 reactivity.
Parentheses around a composition indicates the rod groups undergoing withdrawal.
Rod group withdrawal speed is 3.673/188 m/s for all cases.
When scram moment sec_au is reached, all the rods drop at a constant speed 3.673/2 m/s.
Case b and c differ from each other only by the specification of clad/coolant heat exchange coefficient.
Initial steady state
At sec=0, the core is filled by configurations 1 and 3.
The characteristics to be calculated in the benchmark exercise are specified in table 1.
The selected benchmark reference/6 for steady state and transient results are Nuclear Electric results generated by a detailed (3x3 nodes per assembly and 48 axial nodes) 3-d Panther program calculation. See (/6) for detailed benchmark results.
Initial results for case a
input dat: gwzp_a.dat (download)
Original 2-group diffusion neutronic data (values and their derivatives) are specified for each composition data.
They are firstly collapsed , in each configuration, to 1-group SAFPWR configuration data format by means of the standard method.
Initial steady state results
They are detailed in
lines B1 through B6 of table.
For each item, we indicate the triplet initial steady sate/reference.
Case C which barely differs from case B is skipped.
Discussion of results.
The agreement vs benchmark reference for global items (B1,B2) is quite good.
Actually, this agreement validates here the initial reference calculation model /3 rather than that of the SAFPWR model itself, since, by construction, ini, core adjusts the initial SAFPWR core representation on the reference "design" model
Hot channel items B3,B4,B5 are all about a ratio 1.148 higher than the ref, whilst B2 (axial power profile) is ok.
This could only been explained by a different definition for Fxy.
The hot channel model assumes conservatively that the hot channels of each configuration (where max Fxy is observed) are aligned with the hot channel, and this should result in an overestimation of average power in it. ("piling" effect)
Except for the thin bottom layer, the core is occupied by configuration 3 only, and the flux solution is thus expected to be well separable and the hot channel corrected represented .
Actually, if we infer the ref fxyk values from the ref B4 an B5 and SAFPWR B2 profile, we get B4/ref=1.149, B5/ref=1.148, B3/ref=1.147 and B6/ref=1.153.
All fxy type items appear thus overestimated by about 15%.
If the Fxy were redefined in terms of assembly power, then the agreement for Fxy would become good.
The SAFPWR assembly-wise Fq should be about
2.167/1.15 =1.88, also in agreement with the ref.
These observation should be kept in mind when comparing Fxy-dependent items.
It is further observed that KWU Fq result is also overestimated by about the same amount. This could explain why our agreement with KWU will consistently be better for such items, and for all the cases.
Average transient results.
(chart a1) The reactivity ramp before power peak is about 17e-5/s. For such a slow rate, a first "Doppler" feedback-controlled power peak (here, rather a "bend") is observed at about 2 s after core reactivity
rc has reached (at 70 s) its peak, just below
beta= 760e-5, but at a power level still under the indicated power trip level of
.35 fnc.
Thus, the power keeps increasing, but at a slower rate due to the Doppler feedback, and reaches eventually the trip level of .35 at
sec_au_f2c= 81.3;
the rods start dropping
dsecau=.6 s later, which causes immediate reduction of all safety related items.
Occurrence of this singular double peak pattern was not anticipated, but revealed itself as a severe test for the benchmarking exercise.
At power peak time, configuration 2 and 3 occupy about half of core.(
chart 2)
Examination of lines C1:4 in table and direct comparison with the published benchmark results indicates that SAFPWR results are well within the dispersion range of the best benchmark contributions, except however for a tendency to overestimation, mainly for hot channel heating items, which was expected.
(
chart a3)
C1 (
f2c/fnc) and C2 (
q2c/fnc) peaks are well predicted.
(
chart a2)
C3 (
t2ck(16) peaks at about 3 K above ref.
Hot pellet transient results
(
chart a5)
D1 (
f2c/fnc Fqc) is higher by 7%, which is consistent with the overestimation of
Fq (
B6) at initial condition. The agreement with KWU is better.
D2 is not available.
(
chart a6) D3 (
t2c7k(16)) is 1.5 K high.
D4 is not available.
(
chart a7)
D5 (
hu2c7 accumulated from initial value) is overestimated by ratio
7/6.2= 1.13, which is about the ratio observed on initial value of
Fq .
(
chart a8)
D6 (
u2c7), counted from initial level, is also high by ratio
410/346= 1.18.
(
(chart a10)) plots
hu2c7 (hot pellet average value) in relation to
u2c7 ( at pellet center) for the hot pellet.
The ref point
(61660 J/kg, 345 K) falls unexplainly 23 K under this plot.
This may be due to how the centerline temp is calculated:
chart a11 shows how the center temp relates to average ring temperatures for a typical pellet. Center temp appears to be well aligned with ring temp.
On the other hand
chart a12 compares the fuel rods enthalpy increase with the value taken from heat balance
SUM(dsec(f-q))/vuc : the agreement is perfect, as anticipated.
D7 (clad outer temp) is not available but could easily calculated by extending the xurc7(1:6) vector to xurc7(1:9) in order to include the average and edge points of the clad.
E3 (Fxy) is 12% high, E4 11% high and E5 -8% low.
E6 (Fq) is 11% high, like the initial value, but close to KWU.
Sensitivity studies.
(charts a14:a15) portray the effect of initial power:
using 10e-6 instead of 10e-13 has no significant effect on the peaks: it just advances them by about .3 s.
Case B results.
(cf: gwzp_b.dat (download wgzp_b.123)
Steady state.
Same remark as for case A: all the Fxy- dependent items (B2 to B6) are about 4% high.
If Fxy is expressed in terms of assembly power, the agreement is good.
(
chart b1) The reactivity insertion rate (
d rc/d sec) before peak is about
68e-5/s (
17e-5/s for case
A). Here,
rc peaks at 809e-5
above beta, at 31.34 s, which results in a faster power increase. Power trip level is reached right after, at 31.4 s.
(chart b4) Power peak is checked by rapid
u2c (Doppler temp) rise, which in only stopped when rods start dropping. Thus, the trip delay
dsec_au is critical.
(
chart b3)
C1 shape and peak compare well with the ref, except that power rise starts some 3 s earlier. This anticipation does not, in any way, affect the safety related levels.
The anticipation effect, which was at first attributed to rod cusping (effect of reactivity transition at rod edge) seems rather due to a slight topwards skewness of flux profile (representation effect of reflectors?)
C2 is 25% high, but again close to KWU.
C3 an
C4 (
chart b4) are slightly overestimated, still close to KWU.
(
chart b5)
D1 in underestimated, but this peak has no much meaning because it is very sharp; the covered energy only is important.
(
chart b7)
D5 and
D6: we observe the same "anomaly" as for case a:
D5 (
hu2c7) is barely overestimated whereas the corresponding
D6 (
u2c7) is unexplainly higher.
(
chart b8) shows the configuration positions at critical times
(
chart b9) compares hot pellet average and center temperatures evolutions.
(
chart b10) illustrates the effect of pellet effective temperature definition.
xurc= .3, 4*0, .7 corresponds to benchmark specification.
xurc= 0, 4*.25, 0 amounts to using average pellet temperature.
The effect on hot pellet center temp is not negligible!
Case D results.
Steady state: same as case b
(gwzp_d.dat) (download)
Transient results.
The reactivity rate before peak (chart d02) is now 65e-5/s.
(
chart d01) Max
rc, reached at 35.2 s overrides
beta by 40e-5.
C1 (
f2c/fnc) peaks .2 s later.
Trip power level is reached at
sec_au_f2c= 35.47 s.
Rods start dropping .6 s later at 36.05 s, which stops the
q2c (
chart d4) and
u2c (
chart d5) raise.
As for case b,
f2c peak is reached earlier (about 2 s) than ref.
(
chart d04)
C1 is 6% high.
C2 (
q2c/fnc) is 28% high (8% vs KWU).
(
ch d05)
C3 (
u2ck(16)) is only .8 K above ref.
C4 (
u2c, C) .4 K high.
(
chart d07)
D3 is 1 K high.
D5 (
hu2c7) is 2% high,whereas
D6 (
u2c7, C) (
chart d10)is 33 K high (18 K vs KWU).
It is also observed (
chart d08) that the (
hu2c7-hu0c7,
u2c7-u0c7) point falls below the SAFPWR curve by about 30 K. Here again, this could only be explained by higher center peaking of the pellet radial temp distribution, for the same average value.
(
chart d09)
Fxy-dependent items
E3 to
E6 are about 7% high which is consistent with the overestimation of the corresponding steady state values.
(
Chart d03) Close examination of shows that the PJA is only disabled between 30 an 37 s and that the automatic time-step adjustment performs well, except around 36.1, around the
q2c peak where it should be tightened to better describe the u2c peak.
This could be achieved by using a lower epsom criterion level.
Execution time is only about 1 s!