Transcript COMPARATIVE ANALYSIS OF DIFFERENT METHODS OF MODELING TRANSIENTS
COMPARATIVE ANALYSIS OF DIFFERENT METHODS OF MODELING OF MOST LOADED FUEL PIN IN TRANSIENTS
Y.Ovdiyenko, V.Khalimonchuk, M. Ieremenko
State Scientific and Technical Centre on Nuclear and Radiation Safety (SSTC N&RS)
Stusa st. 35-37, 03142 Kyiv, Ukraine [email protected]
17th SYMPOSIUM of AER on VVER Reactor Physics and Reactor Safety September 24 - 28, 2007, Yalta, Ukraine
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
THREE METHODS OF MODELLING OF MOST LOADED FUEL PIN ARE CONSIDERED: • • • Pin-by-pin calculation by using of coupled codes DYN3D/DERAB; power distribution reconstruction inside of fuel assembly “hot channel” methodology used by DYN3D code.
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 2
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
PIN-BY-PIN CALCULATION BY USING OF COUPLED CODES DYN3D/DERAB : • • • • • • Most accurate method of modelling of single fuel pin from among used in frame of the given work.
DERAB - fine-mesh finite-difference program intended for neutron flux calculation with two-group diffusion approximation in hexagonal fuel assembly cross-section with triangular fuel lattice.
Two-group neutron diffusion equation is solved in region composed of central assembly and six half of surrounding assemblies.
Fine-mesh calculation is performed with setting of boundary conditions from DYN3D code.
Pin burnup distribution is taking into account in every node by taking stock of history of previous fuel campaigns.
Requires too much resource.
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 3
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
• • POWER DISTRIBUTION RECONSTRUCTION : neutron flux is reconstructed by an analytical solution of the two dimensional diffusion equation in each layer of the assembly ; pin power reconstruction is performed on base of average value of fuel burnup in considered node that will cause some error during modelling of most loaded fuel pin • • • “HOT CHANNEL” METHODOLOGY : Axial power distribution for each “hot channel” is defined by multiplication of axial power distribution of average loaded pin of considered fuel assembly by some coefficient.
Axial profile of relative power of “hot channel” will be corresponding to profile of connected core channel.
Doesn’t allow determining change of position of most loaded element, and also change of axial and radial profiles inside of fuel assembly during transient.
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 4
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
INITIAL CONDITIONS: • • • • • • reactor power corresponds to rated value 3000 MW; beginning of the reactor campaign (most high power peeking factors) working group of CPS control rods is located at position of Н10 =177 cm from bottom of core ( lowest regulation position); temperature of coolant at inlet of core is 287 С; non-uniform equilibrium poisoning with Xe and Sm.
ejection of cluster from fuel assembly №85 for time 0.1s is considered in the presented transient.
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 5
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
158 0.30
159 0.66
160 1.00
161 1.00
162 0.67
163 0.33
Fig. 1 – Relative assembly powers (Kq) at the beginning of transient September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine
149
6
0.33
150 0.58
151 1.20
152 1.30
153 0.98
154 1.30
155 1.20
156 0.58
157 0.30
139 0.67
140 1.20
141 1.33
142 1.27
143 0.94
144 0.94
145 1.27
146 1.33
147 1.20
148 0.66
128 1.00
129 1.30
130 1.27
131 1.05
132 1.10
133 1.27
134 1.10
135 1.05
136 1.27
137 1.30
138 1.00
116 1.00
117 0.98
118 0.94
119 1.10
120 1.09
121 0.96
122 0.96
123 1.09
124 1.10
125 0.94
126 0.98
127 1.00
103 0.66
104 1.30
105 0.94
106 1.27
107 0.96
108 1.02
109 1.24
110 1.02
111 0.96
112 1.27
113 0.94
114 1.30
115 0.67
89 0.30
90 1.20
91 1.27
92 1.10
93 0.96
94 1.24
95 1.00
96 1.00
97 1.24
98 0.96
99 1.10
100 1.27
101 1.20
102 0.33
76 0.58
62 0.33
49 0.67
63 1.20
50 1.30
64 1.27
51 0.94
65 1.10
52 1.27
66 0.96
53 0.96
67 1.24
54 1.02
68 1.00
55 1.24
69 1.00
56 1.02
70 1.24
57 0.96
71 0.96
58 1.27
72 1.10
59 0.94
73 1.27
60 1.30
74 1.20
61 0.66
75 0.30
37 1.00
77 1.33
38 0.98
78 1.05
39 0.94
79 1.09
40 1.10
80 1.02
41 1.09
81 1.00
42 0.96
82 0.73
43 0.96
83 1.00
44 1.09
84 1.02
45 1.10
85 1.09
46 0.94
86 1.05
47 0.98
87 1.33
48 1.00
88 0.58
26 1.00
27 1.30
28 1.27
29 1.05
30 1.10
31 1.27
32 1.10
33 1.05
34 1.27
35 1.30
36 1.00
16 0.66
17 1.20
18 1.33
19 1.27
20 0.94
21 0.94
22 1.27
23 1.33
24 1.20
25 0.67
7 0.30
8 0.58
9 1.20
10 1.30
11 0.98
12 1.30
13 1.20
14 0.58
15 0.33
1 0.33
2 0.67
3 1.00
4 1.00
5 0.66
6 0.30
31-05-2007 15:27 system:WindowsXP_juri
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
Three fuel pins are considered : • • • most loaded fuel pin peripheral fuel pin №266 of assembly №101; №266 of assembly №85, from which ejection of partial inserted cluster is considered; fuel pin №206 of assembly №85, that situated near to inserted cluster.
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 7
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
1.01
1.04
1.06
1.09
1.12
1.15
1.17
1.20
1.23
1.25
1.28
1.31
1.34
1.36
1.39
1.42
1.45
Fig. 3 – Relative pin powers (Kr) at FA №101 at the beginning of transient September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine
266 1.50
245 1.45
224 1.45
203 1.45
182 1.46
161 1.46
140 1.46
119 1.45
98 1.44
77 1.43
56 1.45
277 1.47
256 1.35
235 1.33
214 1.38
193 1.40
172 1.42
151 1.42
130 1.40
109 1.37
88 1.31
67 1.32
46 1.41
287 1.47
267 1.33
246 0.43
225 1.30
204 1.37
183 1.40
162 1.41
141 1.40
120 1.37
99 1.30
78 0.43
57 1.30
37 1.40
296 1.47
278 1.37
257 1.29
236 1.29
215 1.35
194 1.39
173 1.44
8
304 1.46
288 1.39
268 1.35
247 1.35
226 1.39
205 1.40
184 1.41
152 1.44
131 1.40
110 1.36
89 1.29
68 1.28
47 1.34
29 1.39
142 1.45
121 1.44
100 1.41
79 1.35
58 1.34
38 1.35
22 1.38
311 1.44
297 1.38
279 1.37
258 1.37
237 1.41
90 1.42
69 1.37
48 1.35
30 1.34
16 1.36
195 1.35
174 1.36
153 1.43
132 1.45
317 1.41
305 1.36
289 1.36
269 1.40
248 1.42
227 1.41
206 1.34
185 0.43
164 1.35
143 1.43
122 1.44
101 1.44
80 1.42
59 1.39
39 1.33
23 1.32
11 1.34
238 1.41
217 1.39
196 1.33
175 1.34
49 1.36
31 1.30
17 1.28
7 1.30
322 1.38
312 1.32
298 1.32
280 1.38
133 1.43
112 1.41
91 1.42
Maximal value 1. FP # 266 Maximal value 2. FP # 1 326 1.33
318 1.27
306 1.27
290 1.31
270 1.38
249 1.39
228 1.40
329 1.30
323 1.18
313 1.17
299 1.24
281 1.33
260 1.36
239 1.36
218 1.38
197 1.38
176 1.39
155 1.39
134 1.38
186 1.38
165 1.39
144 1.41
123 1.40
102 1.39
81 1.38
60 1.36
40 1.29
24 1.24
12 1.22
4 1.26
92 1.34
71 1.33
50 1.30
32 1.22
18 1.15
8 1.14
2 1.23
145 1.36
124 1.33
103 1.26
82 1.24
41 1.24
25 1.12
13 0.37
5 1.12
1 1.23
331 1.28
327 1.16
319 0.37
307 1.15
291 1.27
93 0.38
72 1.19
51 1.22
33 1.15
19 1.09
9 1.09
3 1.18
198 1.31
177 1.33
156 1.33
135 1.31
114 1.23
250 1.34
229 1.34
208 1.35
187 1.37
330 1.21
324 1.11
314 1.11
300 1.18
282 1.26
261 1.29
240 1.29
321 1.13
309 1.10
293 1.11
273 1.15
252 1.15
231 1.11
210 1.12
189 1.19
168 1.21
147 1.20
126 1.20
105 1.19
84 1.17
63 1.15
43 1.10
27 1.09
15 1.12
230 1.20
209 1.21
188 1.27
167 1.29
146 1.29
328 1.18
320 1.13
308 1.14
292 1.18
272 1.24
251 1.24
325 1.15
315 1.12
301 1.14
283 1.19
241 1.15
220 0.37
199 1.17
104 1.19
83 1.17
62 1.20
42 1.15
26 1.12
14 1.11
6 1.16
52 1.17
34 1.12
20 1.11
10 1.14
157 1.25
136 1.25
115 1.22
94 1.20
95 1.13
74 1.08
53 1.07
35 1.06
21 1.09
200 1.14
179 1.17
158 1.17
137 1.17
316 1.10
302 1.07
284 1.07
263 1.08
242 1.11
310 1.07
294 1.03
274 1.02
253 1.02
232 1.07
211 1.09
190 1.12
148 1.12
127 1.11
106 1.08
85 1.03
64 1.02
44 1.03
28 1.06
96 0.94
75 0.93
54 0.97
36 1.02
303 1.03
285 0.98
264 0.94
243 0.94
222 1.00
201 1.03
180 1.07
159 1.07
138 1.03
117 1.00
295 0.99
275 0.91
254 0.30
233 0.91
212 0.96
191 0.99
170 0.99
149 0.99
128 0.96
107 0.91
86 0.30
65 0.90
45 0.98
276 0.94
255 0.93
234 0.93
213 0.94
192 0.95
171 0.95
150 0.94
129 0.94
108 0.92
87 0.92
66 0.94
160 0.95
139 0.94
118 0.92
97 0.87
76 0.88
55 0.95
286 0.95
265 0.88
244 0.88
223 0.92
202 0.94
181 0.95
13-09-2007 16:59 system:WindowsXP_juri 1.50
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
1.01
1.04
1.06
1.09
1.12
1.15
1.17
1.20
1.23
1.25
1.28
1.31
1.34
1.36
1.39
1.42
1.45
Fig. 2 – Relative pin powers (Kr) at FA №85 at the beginning of transient September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine
266 1.07
245 1.04
224 1.04
203 1.04
182 1.04
161 1.03
140 1.03
119 1.03
98 1.03
77 1.03
56 1.05
277 1.06
256 1.02
235 1.01
214 1.02
193 1.03
172 1.03
151 1.03
130 1.02
109 1.01
88 1.00
67 1.01
46 1.04
287 1.06
267 1.02
246 0.67
225 1.00
204 1.02
183 1.03
162 1.04
141 1.03
120 1.02
99 1.00
78 0.73
57 1.01
37 1.04
296 1.07
278 1.04
257 1.01
236 1.01
215 1.03
194 1.05
173 1.05
152 1.05
131 1.05
110 1.03
89 1.01
68 1.00
47 1.02
29 1.04
304
9
1.07
288 1.05
268 1.04
247 1.04
226 1.06
205 1.07
184 1.08
142 1.07
121 1.06
100 1.04
79 1.03
58 1.02
38 1.03
22 1.04
311 1.08
297 1.06
279 1.06
258 1.07
237 1.08
90 1.06
69 1.05
48 1.03
30 1.04
16 1.05
195 1.10
174 1.10
153 1.10
132 1.09
Maximal value 1. FP # 276 Maximal value 2. FP # 1 317 1.09
305 1.07
289 1.07
269 1.08
248 1.10
227 1.11
206 1.11
185 1.10
164 1.11
143 1.11
122 1.10
101 1.09
80 1.08
59 1.06
39 1.04
23 1.04
11 1.05
238 1.12
217 1.13
196 1.13
175 1.13
49 1.06
31 1.04
17 1.04
7 1.05
322 1.09
312 1.07
298 1.07
280 1.09
133 1.12
112 1.10
91 1.10
326 1.09
318 1.06
306 1.06
290 1.08
270 1.11
249 1.13
228 1.14
186 1.15
165 1.15
144 1.14
123 1.13
102 1.12
81 1.11
60 1.09
40 1.06
24 1.03
12 1.04
4 1.06
329 1.10
323 1.04
313 1.02
299 1.07
281 1.10
260 1.13
239 1.13
218 1.15
197 1.16
176 1.15
155 1.14
134 1.15
92 1.12
71 1.11
50 1.08
32 1.05
18 1.02
8 1.03
2 1.07
41 1.07
25 1.03
13 0.69
5 1.04
1 1.10
145 1.15
124 1.15
103 1.14
82 1.12
331 1.14
327 1.05
319 0.54
307 1.03
291 1.09
250 1.14
229 1.15
208 1.16
187 1.15
93 1.12
72 1.12
51 1.09
33 1.06
19 1.03
9 1.04
3 1.09
198 1.17
177 1.16
156 1.16
135 1.16
114 1.15
330 1.12
324 1.05
314 1.03
300 1.08
282 1.12
261 1.15
240 1.16
321 1.14
309 1.11
293 1.11
273 1.13
252 1.15
231 1.16
210 1.16
189 1.17
168 1.17
147 1.14
126 1.15
105 1.14
84 1.12
63 1.10
43 1.09
27 1.09
15 1.10
230 1.16
209 1.17
188 1.17
167 1.17
146 1.17
328 1.12
320 1.08
308 1.08
292 1.11
272 1.14
251 1.16
325 1.13
315 1.10
301 1.10
283 1.13
241 1.16
220 1.15
199 1.17
104 1.14
83 1.13
62 1.11
42 1.08
26 1.06
14 1.06
6 1.09
52 1.09
34 1.08
20 1.08
10 1.10
157 1.17
136 1.16
115 1.15
94 1.14
95 1.12
74 1.10
53 1.09
35 1.09
21 1.11
200 1.16
179 1.16
158 1.16
137 1.15
316 1.15
302 1.12
284 1.11
263 1.12
242 1.14
310 1.15
294 1.11
274 1.09
253 1.09
232 1.12
211 1.14
190 1.15
148 1.14
127 1.13
106 1.10
85 1.08
64 1.08
44 1.09
28 1.12
295 1.15
275 1.07
254 0.50
233 1.05
212 1.09
191 1.11
170 1.12
149 1.11
128 1.09
107 1.05
86 0.57
65 1.06
45 1.12
96 1.05
75 1.04
54 1.08
36 1.12
303 1.15
285 1.10
264 1.05
243 1.05
222 1.10
201 1.12
180 1.13
159 1.13
138 1.11
117 1.09
276 1.19
255 1.16
234 1.15
213 1.15
192 1.16
171 1.15
150 1.15
129 1.14
108 1.14
87 1.14
66 1.16
160 1.12
139 1.11
118 1.10
97 1.07
76 1.08
55 1.13
286 1.16
265 1.09
244 1.07
223 1.10
202 1.12
181 1.12
13-09-2007 16:54 system:WindowsXP_juri 1.50
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
t=0 300 DYN3D - flux reconstraction DYN3D - hot channel DYN3D/DERAB 200 100 0 0 100 200 linear power, W/cm 300 400 Fig. 4 – Linear power at pin № 266 of assembly №101, t=0 September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 10
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
t=0 300 DYN3D/DERAB DYN3D - hot channel DYN3D - flux reconstruction 200 100 September 24 - 28, 2007 0 0 100 200 300 linear power, W/cm Fig. 5 – Linear power at pin № 206 of assembly №85, t=0
17th SYMPOSIUM of AER, Yalta, Ukraine 11
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
t=0 300 DYN3D/DERAB DYN3D - hot channel DYN3D - flux reconstruction 200 100 September 24 - 28, 2007 0 0 100 200 300 linear power, W/cm Fig. 6 – Linear power at pin № 266 of assembly №85, t=0
17th SYMPOSIUM of AER, Yalta, Ukraine 12
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
t=0.1s
300 200 100 DYN3D/DERAB DYN3D - hot channel DYN3D - flux reconstruction 0 100 200 300 400 linear power, W/cm Fig. 7 – Linear power at pin № 266 of assembly №101, t=0.1s
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 13
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
t=0.1s
300 200 100 DYN3D/DERAB DYN3D - hot channel DYN3D - flux reconstruction September 24 - 28, 2007 0 100 150 200 250 linear power, W/cm 300 350 Fig. 8 – Linear power at pin № 206 of assembly №85, t=0.1s
17th SYMPOSIUM of AER, Yalta, Ukraine 14
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
t=0.1s
300 200 100 DYN3D/DERAB DYN3D - hot channel DYN3D - flux reconstruction 0 100 150 200 250 linear power, W/cm 300 350 Fig. 9 – Linear power at pin № 266 of assembly №85, t=0.1s
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 15
State Scientific and Technical Centre on Nuclear and Radiation Safety of Ukraine
CONCLUSIONS • Significant differences of linear power calculation by use of “hot channel” and power reconstruction in comparison to pin-by-pin calculation are • observed in the part of fuel assembly with inserted cluster.
In the part of fuel assembly without inserted cluster all three methods • demonstrate the enough close results (3%) of axial linear power.
Underestimation ≈3% of the absolute value of linear power obtained by power reconstruction is observed, because microstructure of fuel assembly isn’t taken into account during flux reconstruction (namely presence of water • gap).
Modeling with use of “hot channel” method is preferably for application for safety analysis of accidents with use of conservative approaches. This • method gives more conservative results.
Model with use of power reconstruction, which partially takes into account deformation of power field inside of fuel assembly, is more applicable to so called «best estimated» calculations. But for this purpose it must be modified in part of taking into account of inner microstructure of fuel assembly and influence of spatial distribution of fuel pin burnup.
September 24 - 28, 2007
17th SYMPOSIUM of AER, Yalta, Ukraine 16