III. Verification of STREAM3D for APR1400 Reactor Core Benchmark
3.4 Control Rod Worth
APR1400 core is controlled by a total of 7 types control rod bank. Figure 14 indicates the 7 types of control rod banks. The seven control rods consist of 4-fingers (bank A, B, 1, 2) and 12-fingers (bank 2, 3, 4, 5). Additionally, 1, 2, 3, 4, and 5 are regulating banks. B, A are shutdown bank. The control rod group insertion order is 5-4-3-2-1-B-A [8]. All condition of problems is that fuel is 600K, the moderator is 600K, cladding is 600K, and boron concentration is 0 ppm.
Table 15 appears the reactivity error and RMS error of assembly power compared to McCARD for 3D core. Table 16 proffers the reactivity error and RMS error of assembly power compared to MCS for 3D core. In both cases, the reactivity error is greatest when all control rod banks are inserted, and RMS error of assembly power is largest when groups 5, 4, 3, 2, 1, and B are inserted. Table 17 contains the accumulated worth and group worth compared to McCARD for STREAM3D. The greatest error appears when group 2 is inserted. As shown in Table 17, the largest group worth is about 5.81%. Table 18 provides the control rod worth compared to MCS. The largest group worth is about 6.77%. In all control rod cases, control rod worth differences compared to McCARD and MCS indicate excellent agreement within about 3%, except when group 2 is inserted. Figure 15 presents 3D core radial power distribution for STREAM3D and reactivity error compared to McCARD and MCS. Figure 16 compares the axial power distribution of STREAM3D, McCARD, and MCS, and it shows that the three codes appear a similar shape. Table 19 summarizes the RMS error of axial power. The largest RMS error of axial power compared to McCARD is about 2.24%. Compared to MCS, the maximum RMS error of axial power is about 1.96%. When all control rod banks are inserted, RMS error of axial power tends to be the greatest.
Figure 14. Control rod bank [8]
39
Table 15. Reactivity error and RMS error of assembly power compared to McCARD for 3D core
3D CORE Bank
Inserted
McCARD STREAM 3D RMS
error of assembly
power [%]
k-inf std.
[pcm] k-inf
Reactivity error [pcm]
APR04V02 ARO 1.13941 4 1.13931 -8 1.07
APR05V01 5 1.13463 4 1.13462 -1 1.32
APR05V02 5-4 1.13044 4 1.13052 6 0.85
APR05V03 5-4-3 1.11786 4 1.11803 14 0.73
APR05V04 5-4-3-2 1.10487 4 1.10429 -48 1.01
APR05V05 5-4-3-2-1 1.08072 4 1.08052 -17 0.92
APR05V06 5-4-3-2-1-B 1.03458 4 1.03459 1 3.40
APR05V07 5-4-3-2-1-B-A 0.96248 5 0.96408 172 2.69
40
Table 16. Reactivity error and RMS error of assembly power compared to MCS for 3D core
3D CORE Bank
Inserted
MCS STREAM 3D RMS
error of assembly
power [%]
k-inf std.
[pcm] k-inf
Reactivity error [pcm]
APR04V02 ARO 1.13921 4 1.13931 8 1.88
APR05V01 5 1.13438 4 1.13462 19 0.55
APR05V02 5-4 1.13025 4 1.13052 21 0.64
APR05V03 5-4-3 1.11762 4 1.11803 33 0.84
APR05V04 5-4-3-2 1.10475 4 1.10429 -38 0.85
APR05V05 5-4-3-2-1 1.08071 4 1.08052 -16 1.09
APR05V06 5-4-3-2-1-B 1.03440 4 1.03459 18 2.49
APR05V07 5-4-3-2-1-B-A 0.96248 5 0.96408 172 2.18
41
Table 17. Control rod worth compared to McCARD
Bank Inserted
McCARD STREAM3D
Accum.
Diff [%]
Group Diff [%]
Accum.
worth [pcm]
Group worth [pcm]
Accum.
worth [pcm]
Group worth [pcm]
ARO - - - -
5 369.74 369.74 362.81 362.81 -1.87 -1.87
5-4 696.41 326.67 682.45 319.64 -2.01 -2.15 5-4-3 1691.92 995.51 1670.61 988.17 -1.26 -0.74 5-4-3-2 2743.67 1051.75 2783.50 1112.88 1.45 5.81 5-4-3-2-1 4766.18 2022.52 4775.61 1992.11 0.20 -1.50 5-4-3-2-1-B 8892.86 4126.68 8884.22 4108.61 -0.10 -0.44 5-4-3-2-1-B-A 16133.54 7240.68 15953.41 7069.19 -1.12 -2.37
42
Table 18. Control rod worth compared to MCS
Bank Inserted
MCS STREAM3D
Accum.
Diff [%]
Group Diff [%]
Accum.
worth [pcm]
Group worth [pcm]
Accum.
worth [pcm]
Group worth [pcm]
ARO - - - -
5 373.75 373.75 362.81 362.81 -2.93 -2.93
5-4 695.87 322.12 682.45 319.64 -1.93 -0.77
5-4-3 1695.72 999.85 1670.61 988.17 -1.48 -1.17
5-4-3-2 2738.09 1042.37 2783.50 1112.88 1.66 6.77 5-4-3-2-1 4751.63 2013.54 4775.61 1992.11 0.50 -1.06 5-4-3-2-1-B 8894.27 4142.64 8884.22 4108.61 -0.11 -0.82 5-4-3-2-1-B-A 16118.13 7223.86 15953.41 7069.19 -1.02 -2.14
43
44
Figure 15. Radial power distribution and relative error for 3D core
45
Figure 16. Axial power distribution for 3D core
46
Table 19. RMS error of axial power
3D CORE
RMS error [%]
McCARD MCS
APR05V01 1.64 1.55
APR05V02 1.93 1.69
APR05V03 1.38 1.51
APR05V04 1.47 1.69
APR05V05 1.57 1.46
APR05V06 1.77 1.49
APR05V07 2.24 1.96
47 3.5 3D Core Depletion with Hot Full Power Condition.
This section describes a 3D core depletion problem. 3D whole core depletion problem is calculated by HFP condition. Operating conditions for thermal-hydraulic feedback calculation are given in Table 20 [8]. There is no McCARD reference result. Therefore, in this thesis, STREAM3D compares to nTRACER and MPACT. Figure 17 presents the CBC (Critical Boron Concentration) search for each burnup step. STREAM3D reaches 17 MWD/kgU. The first burnup step is calculated without xenon.
Table 21 summarizes numerical changes in boron concentration at each step. The largest difference between the three codes occurs at 8 MWD/kgU. There are many reasons for this difference at 8 MWD/kgU, one thing is that the timing of gad burning out different from code to code. In addition, there are reasons for options or library version and so on. Figure 18 indicates the difference in boron concentration at each burnup step. The maximum difference compared to MPACT is about 46.62 ppm.
Compared to nTRACER, the maximum difference is about 71.58 ppm large numerical value relatively.
STREAM3D result is closer to MPACT result than nTRACER result.
Table 20. Depletion problem condition
Parameter Value
Pressure 15.51315MPa
Core thermal power 3983 MWt
Coolant lnlet temperature 563.75K
Coolant outlet temperature 597.05K
Coolant mass flow rate 75.6 x
106kg/hrControl rod state All rod out
48
Figure 17. The result of 3D core depletion
Figure 18. The difference of boron concentration by burnup step
49
Table 21. CBC of STREAM3D, MPACT, and nTRACER by burnup step
Burnup
[MWD/kgU]
STREAM3D CBC [ppm]
MPACT CBC [ppm]
nTRACER CBC [ppm]
Difference from MPACT
Difference from nTRACER
0 1096.36 1083.5 1085.05 -12.86 -11.31
0.05 832.28 804.13 804.85 -28.15 -27.43
0.5 767.42 753.12 745.33 -14.30 -22.09
1 769.28 758.04 760.32 -11.24 -8.96
2 755.59 755.54 759.79 -0.05 4.20
3 727.48 735.58 748.58 8.10 21.10
4 696.92 710.47 727.85 13.55 30.93
5 665.36 686.32 707.17 20.96 41.81
6 637.17 666.70 690.03 29.53 52.86
7 614.34 654.05 680.34 39.71 66.00
8 598.17 644.79 669.75 46.62 71.58
9 585.00 622.80 639.88 37.80 54.88
10 562.13 579.05 586.93 16.92 24.80
11 516.20 519.56 519.66 3.36 3.46
12 452.57 451.16 444.04 -1.41 -8.53
13 377.85 377.69 362.94 -0.16 -14.91
14 299.27 301.01 281.73 1.74 -17.54
15 216.64 221.85 192.45 5.21 -24.19
50
16 134.41 140.83 105.68 6.42 -28.73
17 47.59 58.76 15.43 11.17 -32.16
18 0 0 0 0 0
Figure 19 shows the radial power distribution at BOC (Beginning of Cycle), MOC (Middle of Cycle), and EOC (End of Cycle). There is no conspicuous power change by cycle. But axial power distribution can observe change. Figure 20 presents the STREAM3D axial power shape at BOC, MOC, and EOC.
At the BOC, the highest power is located in the middle of the core. Therefore, the fuel burnup in middle region is higher than the other regions. This phenomenon led to the result of relatively lower power in that region. For this reason, the axial power shape is flatter in the middle region than in another cycle at the end of the cycle [13]. For another reason, the accumulation of fission products can affect this phenomenon [14].
Figure 19. STREAM 3D radial power distribution at BOC, MOC, EOC in cycle 1
51
Figure 20. STREAM 3D axial power shape at BOC, MOC, EOC in cycle 1
52