Neutron Fast Pulse

The first test is the simple fission decay heat modelling. This test based on experiment of deacay heat measurements after short thermal neutrons pulse on samples with uranium-235. The calculatation will be conducted through two steps with external neutron field (short pulse during 1.0 sec) and without it (during ‘cooling time’ 100 sec). First of all we need to prepare Configure.xml input file. To get result as faster as we can let’s use a chebyshev method with 16th order for 1.0 second (description in sections <timestep> and <timerecord> are equal in this example) for 10 calculation steps.

<configure>
  <chain>./examples/chain_endfb71.xml</chain>
  <nuclides>./examples/nuclides.xml</nuclides>
  <impxslibs>
    <impxslib>./examples/XMAS172.xml</impxslib>
  </impxslibs>
  <inpmaterials>./examples/U235thn_1sec/materialsi.xml</inpmaterials>
  <reaction>./examples/U235thn_1sec/reactions.xml</reaction>
  <outmaterials>./examples/U235thn_1sec/materialso.xml</outmaterials>
  <filters>
    <filter type="exnuclide">U238 U239 U235 Pu238 Pu239 Pu240 Pu241 Pu242 Am241 Am242_m1</filter>
  </filters>
  <numbers>10</numbers>
  <timestep>1</timestep>
  <!-- IT IS  equivalent time description
  timerecord year="0" month="0" day="0.0" hour="0" minute="0" second="1"/-->
  <method>chebyshev</method>
  <epb>1.e-3</epb>
  <decaykey>false</decaykey>
  <uncertanties>false</uncertanties>
  <decay_print>false</decay_print>
  <cram_order>16</cram_order>
</configure>

We made references to path with chain file based on nuclear data library endfb; to path with imported cross-section XMAS172 with 172 energy multigroup cross-sections library. Materials description is quite simple for the test.

<materials>
  <material name="u235" volume="1.0" mass="1.0" power="1.0">
    <namenuclides>U235</namenuclides>
    <conc>1.00000</conc>
  </material>
</materials>

As first calculation are provided under neutron external source we need a Reactions.xml file:

<compositions>
  <composit name="u235">
    <energy ng="4">0.0252 2.15 1000.0 800000.0 20000000.0</energy>
    <energy ng="1">0.0252 20000000.0</energy>
    <xslibs ng="1" typex="rxs">
      <xslib name="U235" ng="1" reaction="fission">1.7528e+16</xslib>
      <xslib name="Pu239" ng="1" reaction="fission">2.9496e+15</xslib>
    </xslibs>
    <flux ng="4">1.0 0.0 0.0 0.0</flux>
    <dflux ng="4">0.1 0.0 0.0 0.0</dflux>
  </composit>
</compositions>
Note: It is very important that name of composit should be match with

name of according material.

To right calculation of neutron fission product yields it is important to describe a flux. It is sufficient one value to according energy:

<energy ng="4">0.0252 2.15 1000.0 800000.0 20000000.0</energy>
<flux ng="4">1.0 0.0 0.0 0.0</flux>

After successfull calculation of the first part of the test we just need to modify our Configure.xml. The key <decaykey> should be switched on to perform simulation without external field, meantime the key <decay_print> should be switched on too for decay heat values printing. Then we need to change time and step numbers parametres:

<numbers>100</numbers>
<timestep>100</timestep>
<inpmaterials>./examples/U235thn_1sec/materialso.xml</inpmaterials>

Input materials file name should be equal to name of output materials file from the first part of calculation. As we calculate decay heat from the fission products we must exclude actinides using filters section:

<filters>
  <filter type="exnuclide">U238 U239 U235 Pu238 Pu239 Pu240 Pu241 Pu242 Am241 Am242_m1</filter>
</filters>

Finally we get outlog.csv file.

The results of calculation

dt

Act, sec-1

Q, Mev

dAct, sec-1

dQ, Mev

u235

1

2.87807e+15

1.0377e+16

8.88746e+13

3.0786e+14

2

2.18948e+15

7.60349e+15

6.96329e+13

2.30963e+14

3

1.77375e+15

6.00587e+15

5.71852e+13

1.84742e+14

4

1.49139e+15

4.95996e+15

4.81608e+13

1.528e+14

5

1.28575e+15

4.21881e+15

4.12684e+13

1.29225e+14

6

1.12879e+15

3.66398e+15

3.58373e+13

1.11111e+14

7

1.00485e+15

3.23177e+15

3.14602e+13

9.67793e+13

8

9.04417e+14

2.88495e+15

2.7868e+13

8.51753e+13

9

8.21365e+14

2.60027e+15

2.48749e+13

7.55998e+13

10

7.51538e+14

2.36238e+15

2.23482e+13

6.75728e+13

11

6.92016e+14

2.16071e+15

2.01911e+13

6.07554e+13

12

6.40687e+14

1.9877e+15

1.83316e+13

5.49021e+13

13

5.95986e+14

1.83782e+15

1.67154e+13

4.98311e+13

14

5.56726e+14

1.70689e+15

1.53006e+13

4.54051e+13

15

5.21993e+14

1.5917e+15

1.40545e+13

4.1518e+13

16

4.91069e+14

1.48973e+15

1.29514e+13

3.80868e+13

17

4.63382e+14

1.39898e+15

1.19704e+13

3.50447e+13

18

4.38472e+14

1.31782e+15

1.10946e+13

3.23376e+13

19

4.1596e+14

1.24493e+15

1.03102e+13

2.9921e+13

20

3.95534e+14

1.1792e+15

9.60538e+12

2.77577e+13

21

3.76935e+14

1.11972e+15

8.97047e+12

2.58161e+13

22

3.59942e+14

1.06571e+15

8.39711e+12

2.40696e+13

23

3.44367e+14

1.0165e+15

7.87816e+12

2.24952e+13

24

3.30052e+14

9.71539e+14

7.40749e+12

2.10731e+13

25

3.16857e+14

9.30334e+14

6.97974e+12

1.9786e+13

26

3.04664e+14

8.92467e+14

6.59028e+12

1.8619e+13

27

2.93369e+14

8.57574e+14

6.23501e+12

1.75588e+13

28

2.8288e+14

8.25336e+14

5.91035e+12

1.6594e+13

29

2.73117e+14

7.95476e+14

5.61316e+12

1.57144e+13

30

2.64011e+14

7.67751e+14

5.34064e+12

1.4911e+13

31

2.555e+14

7.41947e+14

5.09031e+12

1.41758e+13

32

2.47528e+14

7.17874e+14

4.85999e+12

1.3502e+13

33

2.40046e+14

6.95367e+14

4.6477e+12

1.28832e+13

34

2.33012e+14

6.74278e+14

4.45173e+12

1.2314e+13

35

2.26386e+14

6.54476e+14

4.27051e+12

1.17893e+13

36

2.20133e+14

6.35844e+14

4.10265e+12

1.13049e+13

37

2.14224e+14

6.1828e+14

3.94692e+12

1.08569e+13

38

2.08629e+14

6.01692e+14

3.80219e+12

1.04418e+13

39

2.03324e+14

5.85996e+14

3.66748e+12

1.00564e+13

40

1.98286e+14

5.71118e+14

3.54189e+12

9.69806e+12

41

1.93495e+14

5.56994e+14

3.42461e+12

9.36423e+12

42

1.88932e+14

5.43562e+14

3.31492e+12

9.0527e+12

43

1.84581e+14

5.30771e+14

3.21217e+12

8.76147e+12

44

1.80427e+14

5.18571e+14

3.11576e+12

8.48877e+12

45

1.76456e+14

5.06919e+14

3.02516e+12

8.23297e+12

46

1.72656e+14

4.95776e+14

2.9399e+12

7.99263e+12

47

1.69015e+14

4.85106e+14

2.85955e+12

7.76645e+12

48

1.65523e+14

4.74876e+14

2.7837e+12

7.55325e+12

49

1.6217e+14

4.65058e+14

2.712e+12

7.35198e+12

50

1.58948e+14

4.55625e+14

2.64414e+12

7.16166e+12

51

1.55849e+14

4.46552e+14

2.57981e+12

6.98144e+12

52

1.52865e+14

4.37816e+14

2.51875e+12

6.81054e+12

53

1.4999e+14

4.29399e+14

2.46071e+12

6.64823e+12

54

1.47217e+14

4.2128e+14

2.40548e+12

6.49388e+12

55

1.44541e+14

4.13442e+14

2.35286e+12

6.34689e+12

56

1.41957e+14

4.05871e+14

2.30265e+12

6.20674e+12

57

1.39459e+14

3.98551e+14

2.2547e+12

6.07294e+12

58

1.37044e+14

3.91468e+14

2.20885e+12

5.94504e+12

59

1.34707e+14

3.84612e+14

2.16496e+12

5.82265e+12

60

1.32443e+14

3.77969e+14

2.1229e+12

5.70539e+12

61

1.3025e+14

3.71529e+14

2.08255e+12

5.59293e+12

62

1.28124e+14

3.65283e+14

2.04381e+12

5.48495e+12

63

1.26062e+14

3.59221e+14

2.00656e+12

5.38118e+12

64

1.24061e+14

3.53335e+14

1.97074e+12

5.28135e+12

65

1.22119e+14

3.47617e+14

1.93624e+12

5.18522e+12

66

1.20231e+14

3.42058e+14

1.90299e+12

5.09258e+12

67

1.18397e+14

3.36653e+14

1.87091e+12

5.00322e+12

68

1.16614e+14

3.31395e+14

1.83995e+12

4.91696e+12

69

1.1488e+14

3.26277e+14

1.81005e+12

4.83361e+12

70

1.13193e+14

3.21295e+14

1.78113e+12

4.75303e+12

71

1.1155e+14

3.16441e+14

1.75316e+12

4.67507e+12

72

1.09951e+14

3.11712e+14

1.72608e+12

4.59959e+12

73

1.08393e+14

3.07102e+14

1.69984e+12

4.52645e+12

74

1.06874e+14

3.02608e+14

1.67441e+12

4.45556e+12

75

1.05395e+14

2.98224e+14

1.64975e+12

4.38678e+12

76

1.03952e+14

2.93946e+14

1.62581e+12

4.32003e+12

77

1.02544e+14

2.89772e+14

1.60257e+12

4.25521e+12

78

1.01171e+14

2.85696e+14

1.57999e+12

4.19223e+12

79

9.98308e+13

2.81716e+14

1.55804e+12

4.131e+12

80

9.85226e+13

2.77829e+14

1.5367e+12

4.07145e+12

81

9.72451e+13

2.74031e+14

1.51594e+12

4.01351e+12

82

9.59974e+13

2.70319e+14

1.49573e+12

3.9571e+12

83

9.47783e+13

2.6669e+14

1.47605e+12

3.90217e+12

84

9.35871e+13

2.63143e+14

1.45688e+12

3.84865e+12

85

9.24227e+13

2.59673e+14

1.43819e+12

3.79649e+12

86

9.12843e+13

2.56279e+14

1.41998e+12

3.74564e+12

87

9.01711e+13

2.52958e+14

1.40221e+12

3.69604e+12

88

8.90822e+13

2.49709e+14

1.38488e+12

3.64764e+12

89

8.8017e+13

2.46528e+14

1.36797e+12

3.60041e+12

90

8.69746e+13

2.43415e+14

1.35146e+12

3.55429e+12

91

8.59544e+13

2.40366e+14

1.33533e+12

3.50925e+12

92

8.49557e+13

2.3738e+14

1.31958e+12

3.46526e+12

93

8.39779e+13

2.34455e+14

1.30419e+12

3.42226e+12

94

8.30203e+13

2.3159e+14

1.28915e+12

3.38024e+12

95

8.20824e+13

2.28782e+14

1.27444e+12

3.33916e+12

96

8.11635e+13

2.26031e+14

1.26006e+12

3.29898e+12

97

8.02633e+13

2.23334e+14

1.24599e+12

3.25968e+12

98

7.9381e+13

2.2069e+14

1.23222e+12

3.22123e+12

99

7.85162e+13

2.18098e+14

1.21875e+12

3.1836e+12

100

7.76685e+13

2.15556e+14

1.20557e+12

3.14677e+12

Results proceeding

This test are based on experiment to decay head measurement conducted by [Dickens] ORNL. We can compare our results with experiment. Let us consider new function F are defined as follows:

(1)\[F = \frac{Q*t}{R_{fission}};\]

where Q is our decay heat (Mev); t is a current time and Rfissionis a number of fissions during 1.0 sec pulse, it means just a reaction-rate values for U235 from reactions.xml. Given results are presented on the next graph:

../_images/graph_u235_100sec.png

Total decay heat from thermal pulse on U235.

As you can see in Total decay heat from thermal pulse on U235. our calculation result has a good agreement with experimental data especially after of 20 sec of the cooling time.

References

Dickens

J. K. Dickens, J. F. Emery, T. A. Love, J. W. McConnell ,K.J.Northcutt ,R. W. Peelle, and H. Weaver, “Fission Product Energy Release for Times Following Thermal-Neutron Fission of U235 Between 2 and 14000 Seconds,” Tech. Rep. ORNL/NUREG-14, Oak Ridge National Laboratory, 1979.