Fission rate in transient simulations

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anaantunes
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Fission rate in transient simulations

Post by anaantunes » Thu Jul 15, 2021 4:22 pm

Greetings!

I was hoping you guys could help me with transient simulations. I read a lot of stuff here but I don't think there are any posts covering my questions.

I am running C5G7 benchmark simulations. The benchmark is supercritical by definition (k_eff=1.17129); so in order to run the transients I have to limit them and I decided to do it by using gcut. As it turns out, depending on which gcut value I use, I get different fission rate values. You can see below the fission rate values I got for a 0.01s transient without any changes to the initial state (initial fission rate was 3.05E+10 ± 8.20E-06):

gcut / fission rate
15 / 1.40E+08 ± 0.00317
30 / 1.45E+09 ± 0.00754
45 / 1.23E+10 ± 0.03956
60 / 1.05E+11 ± 0.05976


I then increased the boron content to try and run a subcritical transient simulation (k_eff=0.98631) so I wouldn't have to limit it with gcut, and once again I got a weird value: initial fission rate was 3.04E+10 ± 1.80E-06 and the transient fission rate was 1.01012E+08 ± 0.01073. Again, no changes were made on the geometry/materials.

I also tried increasing population for all the cases, which didn't affect the fission rate. I used in all inputs:

Code: Select all

set delnu 1
set bala 1
set gcu  -1 
set impl 0 0 0  
I appreciate any help I can get on this.

Ville Valtavirta
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Re: Fission rate in transient simulations

Post by Ville Valtavirta » Thu Jul 15, 2021 4:36 pm

Hi,

it's probably better to use one of these approaches: The first one if you do not need to concern yourself with the delayed neutron source and the second one if you need to include the delayed neutron source.

What happens with gcut, I assume is that you are simply modelling the first 15 to 60 prompt generations instead of a 0.01 s transient. If your prompt generation time is in the 10s of microseconds there are hundreds of prompt generations in every 0.01 seconds.

-Ville

anaantunes
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Re: Fission rate in transient simulations

Post by anaantunes » Mon Jul 19, 2021 10:37 pm

Hi Ville, thank you for your answer.

I am using the second approach as delayed neutrons are important in this case. It is still problematic: the fission rate is around twice the value of the steady-state case.

Here is the input I used for source generation:

Code: Select all

% --- INPUT C5G7 Ana Antunes
set title "C5G7 2-D source generation"

% --- Cross section library file path: 

set acelib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80u.xsdata" 
set declib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80.dec" 
set nfylib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80.nfy" 
set sfylib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80.sfy"

set savesrc "./source" [0.2 1 1 1 1] 

% ------------------------------------------------------------

% --- Material definitions:

% UO2 
mat UO2  sum  tmp 293.15
92235.06c   8.6500E-4
92238.06c   2.2250E-2
8016.06c    4.6220E-2


% MOX 4.3 wt % enrichment
mat MOX4  sum tmp 293.15
92235.06c   5.0000E-5
92238.06c   2.2100E-2
94238.06c   1.5000E-5
94239.06c   5.8000E-4
94240.06c   2.4000E-4
94241.06c   9.8000E-5
94242.06c   5.4000E-5
95241.06c   1.3000E-5
8016.06c    4.6300E-2

% MOX 7.0 wt % enrichment
mat MOX7  sum tmp 293.15
92235.06c   4.7493E-5
92238.06c   2.1462E-2
94238.06c   2.4452E-5
94239.06c   9.5151E-4
94240.06c   4.0069E-4
94241.06c   1.5682E-4
94242.06c   8.7024E-5
95241.06c   1.9724E-5
8016.06c    4.6300E-2

% MOX 8.7 wt % enrichment
mat MOX8  sum tmp 293.15
92235.06c   4.7052E-5
92238.06c   2.1063E-2
94238.06c   3.0390E-5
94239.06c   1.1800E-3
94240.06c   5.0056E-4
94241.06c   1.9490E-4
94242.06c   1.0816E-4
95241.06c   2.5645E-5
8016.06c    4.6300E-2


% --- Al Clad
mat ALCLAD  sum tmp 293.15
13027.06c    6.0000E-2

% --- Zr Clad
mat ZRCLAD  sum tmp 293.15
40090.06c   2.21235E-2
40091.06c   4.82460E-3
40092.06c   7.37450E-3
40094.06c   7.47340E-3
40096.06c   1.20400E-3

% --- Control rods
mat CR   sum  tmp 293.15
47107.06c   2.27105E-2
47109.06c   2.27105E-2
49115.06c   8.00080E-3
48113.06c   2.72410E-3

% --- Water:

mat water   sum tmp 293.15 moder lwe6 1001
1001.06c    6.70000E-02
8016.06c    3.35000E-02
5010.06c    5.53220E-06
5011.06c    2.22678E-05

therm lwe6  lwe6.00t

% --- Fission chamber:

mat FC   sum tmp 293.15 
1001.06c    6.70000E-02
8016.06c    3.35000E-02
92235.06c   1.00000E-08
5010.06c    5.53220E-06
5011.06c    2.22678E-05


% ------------------------------------------------------------

% --- Parameters ("param block"):

set gcu  -1     
set impl 0 0 0  

% --- Set power level

set power 1.0

% --- Neutron population and criticality cycles:

set pop 8000 8000 200 1.0 100

% --- Boundary conditions

set usym 0 3 2 0.0 0.0 0 90

% ------------------------------------------------------------

% --- Geometry ("geom block"): 

% --- UO2 fuel pin
pin 1
UO2    0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- 4.3 MOX fuel pin
pin 2
MOX4   0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- 7.0 MOX fuel pin
pin 3
MOX7   0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- 8.7 MOX fuel pin
pin 4
MOX8   0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- CR guide tube 
pin 5
water   0.3400
ALCLAD  0.5400
water

% --- fission chamber/central guide tube 
pin 6
FC   0.3400
ALCLAD  0.5400
water


% --- UOX-assembly ("unit 100"):

surf  1000  sqc  0.0 0.0 10.71 

cell 100  100  fill 110   -1000
cell 101  100  water       1000

% --- MOX-assembly ("unit 200"):

surf  2000  sqc  0.0 0.0 10.71

cell 200  200  fill 210   -2000
cell 201  200  water       2000

% --- Core lattice ("global unit 0"):

surf  3000  sqc  0.0 0.0 64.26

cell 300   0  fill 300   -3000
cell 301   0  outside     3000


% --- Water reflector:

surf 4000 sqc 0.0 0.0 10.71

cell 400 400 water -4000
cell 401 400 water 4000

% ------------------------------------------------------------

% --- Lattices ("array block"):

% --- UO2 pin lattice:

lat 110  1  0.0 0.0 17 17  1.26

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 2
1 1 1 1 1 5 1 1 5 1 1 5 1 1 1 1 1   % 3
1 1 1 5 1 1 1 1 1 1 1 1 1 5 1 1 1   % 4
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 5
1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1   % 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 7
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 8
1 1 5 1 1 5 1 1 6 1 1 5 1 1 5 1 1   % 9
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 10
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 11
1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1   % 12
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 13
1 1 1 5 1 1 1 1 1 1 1 1 1 5 1 1 1   % 14
1 1 1 1 1 5 1 1 5 1 1 5 1 1 1 1 1   % 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 16
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 17

% --- MOX pin lattice:

lat 210  1  0.0 0.0 17 17  1.26

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2   % 18
2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2   % 19
2 3 3 3 3 5 3 3 5 3 3 5 3 3 3 3 2   % 20
2 3 3 5 3 4 4 4 4 4 4 4 3 5 3 3 2   % 21
2 3 3 3 4 4 4 4 4 4 4 4 4 3 3 3 2   % 22
2 3 5 4 4 5 4 4 5 4 4 5 4 4 5 3 2   % 23
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 24
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 25
2 3 5 4 4 5 4 4 6 4 4 5 4 4 5 3 2   % 26
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 27
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 28
2 3 5 4 4 5 4 4 5 4 4 5 4 4 5 3 2   % 29
2 3 3 3 4 4 4 4 4 4 4 4 4 3 3 3 2   % 30
2 3 3 5 3 4 4 4 4 4 4 4 3 5 3 3 2   % 31
2 3 3 3 3 5 3 3 5 3 3 5 3 3 3 3 2   % 32
2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2   % 33
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2   % 34

% --- Core lattice:

lat 300  1  0.0 0.0 6 6  21.42

400 400 400 400 400 400
400 400 400 400 400 400
400 400 400 400 400 400
400 400 400 100 200 400
400 400 400 200 100 400
400 400 400 400 400 400

% ------------------------------------------------------------

% --- Detectors:

det pinfr dr -6 void dx 0 42.841 34 dy 0 42.84 34
And here is the input I am using for the transient:

Code: Select all

% --- INPUT C5G7 Ana Antunes

set title "C5G7 2-D transient"


% --- Cross section library file path: 

set acelib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80u.xsdata" 
set declib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80.dec" 
set nfylib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80.nfy" 
set sfylib "/cm/shared/apps/ncsu/SERPENT/xsdata/endfb80/sss_endfb80.sfy"


% ------------------------------------------------------------

% --- Material definitions:

% UO2 
mat UO2  sum  tmp 293.15
92235.06c   8.6500E-4
92238.06c   2.2250E-2
8016.06c    4.6220E-2


% MOX 4.3 wt % enrichment
mat MOX4  sum tmp 293.15
92235.06c   5.0000E-5
92238.06c   2.2100E-2
94238.06c   1.5000E-5
94239.06c   5.8000E-4
94240.06c   2.4000E-4
94241.06c   9.8000E-5
94242.06c   5.4000E-5
95241.06c   1.3000E-5
8016.06c    4.6300E-2

% MOX 7.0 wt % enrichment
mat MOX7  sum tmp 293.15
92235.06c   4.7493E-5
92238.06c   2.1462E-2
94238.06c   2.4452E-5
94239.06c   9.5151E-4
94240.06c   4.0069E-4
94241.06c   1.5682E-4
94242.06c   8.7024E-5
95241.06c   1.9724E-5
8016.06c    4.6300E-2

% MOX 8.7 wt % enrichment
mat MOX8  sum tmp 293.15
92235.06c   4.7052E-5
92238.06c   2.1063E-2
94238.06c   3.0390E-5
94239.06c   1.1800E-3
94240.06c   5.0056E-4
94241.06c   1.9490E-4
94242.06c   1.0816E-4
95241.06c   2.5645E-5
8016.06c    4.6300E-2


% --- Al Clad
mat ALCLAD  sum tmp 293.15
13027.06c    6.0000E-2

% --- Zr Clad
mat ZRCLAD  sum tmp 293.15
40090.06c   2.21235E-2
40091.06c   4.82460E-3
40092.06c   7.37450E-3
40094.06c   7.47340E-3
40096.06c   1.20400E-3

% --- Control rods
mat CR   sum  tmp 293.15
47107.06c   2.27105E-2
47109.06c   2.27105E-2
49115.06c   8.00080E-3
48113.06c   2.72410E-3

% --- Water:

mat water   sum tmp 293.15 moder lwe6 1001
1001.06c    6.70000E-02
8016.06c    3.35000E-02
5010.06c    5.53220E-06
5011.06c    2.22678E-05

therm lwe6  lwe6.00t

% --- Fission chamber:

mat FC   sum tmp 293.15 
1001.06c    6.70000E-02
8016.06c    3.35000E-02
92235.06c   1.00000E-08
5010.06c    5.53220E-06
5011.06c    2.22678E-05


% ------------------------------------------------------------

set usym 0 3 2 0.0 0.0 0 90

set gcu  -1     

set impl 0 0 0  

set delnu 1

set bala 1

set power 1

set opti 3

set memfrac 1

set nbuf 5000
set pbuf 5000

set nps 130000 10 simutime
tme simutime 2 50 0 0.001

set tcut 0.001

% --- Link source (use point-wise precursor tracking)

set dynsrc "./source" 1


% ------------------------------------------------------------

% --- Geometry ("geom block"): 

% --- UO2 fuel pin
pin 1
UO2    0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- 4.3 MOX fuel pin
pin 2
MOX4   0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- 7.0 MOX fuel pin
pin 3
MOX7   0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- 8.7 MOX fuel pin
pin 4
MOX8   0.4095
void   0.4180
ZRCLAD 0.4750
void   0.4800
ALCLAD 0.5400
water

% --- CR guide tube 
pin 5
water   0.3400
ALCLAD  0.5400
water

% --- fission chamber/central guide tube 
pin 6
FC   0.3400
ALCLAD  0.5400
water


% --- UOX-assembly ("unit 100"):

surf  1000  sqc  0.0 0.0 10.71 

cell 100  100  fill 110   -1000
cell 101  100  water       1000

% --- MOX-assembly ("unit 200"):

surf  2000  sqc  0.0 0.0 10.71

cell 200  200  fill 210   -2000
cell 201  200  water       2000

% --- Core lattice ("global unit 0"):

surf  3000  sqc  0.0 0.0 64.26

cell 300   0  fill 300   -3000
cell 301   0  outside     3000


% --- Water reflector:

surf 4000 sqc 0.0 0.0 10.71

cell 400 400 water -4000
cell 401 400 water 4000

% ------------------------------------------------------------

% --- Lattices ("array block"):

% --- UO2 pin lattice:

lat 110  1  0.0 0.0 17 17  1.26

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 2
1 1 1 1 1 5 1 1 5 1 1 5 1 1 1 1 1   % 3
1 1 1 5 1 1 1 1 1 1 1 1 1 5 1 1 1   % 4
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 5
1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1   % 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 7
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 8
1 1 5 1 1 5 1 1 6 1 1 5 1 1 5 1 1   % 9
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 10
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 11
1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1   % 12
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 13
1 1 1 5 1 1 1 1 1 1 1 1 1 5 1 1 1   % 14
1 1 1 1 1 5 1 1 5 1 1 5 1 1 1 1 1   % 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 16
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   % 17

% --- MOX pin lattice:

lat 210  1  0.0 0.0 17 17  1.26

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2   % 18
2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2   % 19
2 3 3 3 3 5 3 3 5 3 3 5 3 3 3 3 2   % 20
2 3 3 5 3 4 4 4 4 4 4 4 3 5 3 3 2   % 21
2 3 3 3 4 4 4 4 4 4 4 4 4 3 3 3 2   % 22
2 3 5 4 4 5 4 4 5 4 4 5 4 4 5 3 2   % 23
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 24
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 25
2 3 5 4 4 5 4 4 6 4 4 5 4 4 5 3 2   % 26
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 27
2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 2   % 28
2 3 5 4 4 5 4 4 5 4 4 5 4 4 5 3 2   % 29
2 3 3 3 4 4 4 4 4 4 4 4 4 3 3 3 2   % 30
2 3 3 5 3 4 4 4 4 4 4 4 3 5 3 3 2   % 31
2 3 3 3 3 5 3 3 5 3 3 5 3 3 3 3 2   % 32
2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2   % 33
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2   % 34

% --- Core lattice:

lat 300  1  0.0 0.0 6 6  21.42

400 400 400 400 400 400
400 400 400 400 400 400
400 400 400 400 400 400
400 400 400 100 200 400
400 400 400 200 100 400
400 400 400 400 400 400

% ------------------------------------------------------------

% --- Detectors:

det pinfr dr -6 void dx 0 42.841 34 dy 0 42.84 34

% --- Plotters ("plot block"):

% --- Geometry and mesh plots:

% plot 3 1000 1000 [ 0.0 -70 70 -70 70 ]
% plot 2 1200 1200
% mesh 3 500 500

% ------------------------------------------------------------


Any thoughts?

Ana Jambrina
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Re: Fission rate in transient simulations

Post by Ana Jambrina » Mon Jul 19, 2021 10:58 pm

How did you determine the time cut-off? The population grows exponentially in super-critical systems and, thus, the number of events can be very sensitive to the time cut-off, and its effect. Is it a converging population? Aside from that, killing neutrons always have a side effect. Might it have a major impact in this case (where do those take place)?
- Ana

Ville Valtavirta
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Re: Fission rate in transient simulations

Post by Ville Valtavirta » Tue Jul 20, 2021 10:14 am

Could you explain a bit more about the transient you want to model. What kind of conditions do you want to begin the transient from? What kind of initial distributions do you want to use for delayed neutron precursors?

You cannot generate physical initial delayed neutron precursor distributions from your current model as your model is not critical.

From the important notes in the transient simulations page:
The system should be as close to criticality as possible as any deviations result in errors in the live neutron source (due to the k-eigenvalue iteration only being accurate in critical systems) and in the precursor source (since the stable concentrations are calculated assuming steady state).
BTW: No need to use brackets [] in your "set savesrc" command, they are simply used to indicate optional parameters as is done in the Serpent Input Syntax Manual.

-Ville

anaantunes
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Re: Fission rate in transient simulations

Post by anaantunes » Tue Aug 10, 2021 10:47 pm

Greetings all,

I appreciate all of your help. I have some answers after I got some help.

First, in order to force criticality, I added the following line to the transient input:

Code: Select all

set keff 1.17129
that divides the keff value by this parameter (in this case 1.17129), making the model critical and eliminating the need for a time cutoff.

Dr. Fridman's paper is a good reference for dynamic simulation, and reactivity calculation in the transient is well explained: 10.1016/j.anucene.2020.107707

It was also important to remember that the transient detectors have different units than the steady state detectors, i.e., they are time-integrated.

Ana Jambrina
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Re: Fission rate in transient simulations

Post by Ana Jambrina » Wed Aug 11, 2021 6:22 pm

For reference of the ‘set keff’ option use, check: viewtopic.php?f=25&t=2864&p=8544&hilit= ... ient#p8559 (from Serpent 2.1.31 on, the option scales both prompt and delayed neutron precursor production, nubar).
Note, a detector provides the flux (or response) integrated over space, energy and direction (and time).
- Ana

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