crp/OpenMC
1
0
Fork 0
mirror of https://github.com/openmc-dev/openmc.git synced 2026-07-26 05:05:30 -04:00
Code Issues Projects Releases Packages Wiki Activity Actions

Update tally arithmetic notebook to fix an error in thermal flux

Browse source 
utilization. Also make equations prettier.
This commit is contained in:
Paul Romano 2015-08-10 13:26:12 +07:00
parent 8fff5b1810
commit 0d75cbf8c1
1 changed files with 32 additions and 25 deletions
Download patch file Download diff file Expand all files Collapse all files

57
docs/source/pythonapi/examples/tally-arithmetic.ipynb
View file

@ -572,7 +572,7 @@
" Copyright: 2011-2015 Massachusetts Institute of Technology\n",
" License: http://mit-crpg.github.io/openmc/license.html\n",
" Version: 0.6.2\n",
" Date/Time: 2015-08-10 06:51:18\n",
" Date/Time: 2015-08-10 13:21:32\n",
" MPI Processes: 4\n",
"\n",
" ===========================================================================\n",
@ -628,20 +628,20 @@
"\n",
" =======================> TIMING STATISTICS <=======================\n",
"\n",
" Total time for initialization = 8.9900E-01 seconds\n",
" Reading cross sections = 2.5700E-01 seconds\n",
" Total time in simulation = 9.5070E+00 seconds\n",
" Time in transport only = 8.6890E+00 seconds\n",
" Time in inactive batches = 1.0080E+00 seconds\n",
" Time in active batches = 8.4990E+00 seconds\n",
" Time synchronizing fission bank = 7.8300E-01 seconds\n",
" Sampling source sites = 4.4000E-02 seconds\n",
" SEND/RECV source sites = 0.0000E+00 seconds\n",
" Time accumulating tallies = 3.0000E-03 seconds\n",
" Total time for initialization = 1.4260E+00 seconds\n",
" Reading cross sections = 3.8800E-01 seconds\n",
" Total time in simulation = 9.0700E+00 seconds\n",
" Time in transport only = 8.3270E+00 seconds\n",
" Time in inactive batches = 1.4110E+00 seconds\n",
" Time in active batches = 7.6590E+00 seconds\n",
" Time synchronizing fission bank = 6.7300E-01 seconds\n",
" Sampling source sites = 1.1000E-02 seconds\n",
" SEND/RECV source sites = 2.0000E-03 seconds\n",
" Time accumulating tallies = 1.0000E-03 seconds\n",
" Total time for finalization = 2.0000E-03 seconds\n",
" Total time elapsed = 1.0410E+01 seconds\n",
" Calculation Rate (inactive) = 12400.8 neutrons/second\n",
" Calculation Rate (active) = 4412.28 neutrons/second\n",
" Total time elapsed = 1.0500E+01 seconds\n",
" Calculation Rate (inactive) = 8858.97 neutrons/second\n",
" Calculation Rate (active) = 4896.20 neutrons/second\n",
"\n",
" ============================> RESULTS <============================\n",
"\n",
@ -726,7 +726,8 @@
"metadata": {},
"source": [
"We have a tally of the total fission rate and the total absorption rate, so we can calculate k-infinity as:\n",
"$$k_\\infty = \\frac{\\nu \\Sigma_f \\phi}{\\Sigma_a \\phi}$$"
"$$k_\\infty = \\frac{\\langle \\nu \\Sigma_f \\phi \\rangle}{\\langle \\Sigma_a \\phi \\rangle}$$\n",
"In this notation, $\\langle \\cdot \\rangle^a_b$ represents an OpenMC that is integrated over region $a$ and energy range $b$. If $a$ or $b$ is not reported, it means the value represents an integral over all space or all energy, respectively."
]
},
{
@ -794,7 +795,7 @@
"source": [
"Notice that even though the neutron production rate and absorption rate are separate tallies, we still get a first-order estimate of the uncertainty on the quotient of them automatically!\n",
"\n",
"Now, let's analyze of few of the classic factors in the four-factor formula, starting with the resonance escape probability, which we'll define as $$p=\\frac{\\Sigma_{a,thermal}\\phi}{\\Sigma_a\\phi}$$"
"Now, let's analyze of few of the classic factors in the four-factor formula, starting with the resonance escape probability, which we'll define as $$p=\\frac{\\langle\\Sigma_a\\phi\\rangle_T}{\\langle\\Sigma_a\\phi\\rangle}$$ where the subscript $T$ means thermal energies."
]
},
{
@ -860,7 +861,7 @@
"metadata": {},
"source": [
"The fast fission factor can be calculated as\n",
"$$\\epsilon=\\frac{\\Sigma_f\\phi}{\\Sigma_{f,thermal}\\phi}$$"
"$$\\epsilon=\\frac{\\langle\\Sigma_f\\phi\\rangle}{\\langle\\Sigma_f\\phi\\rangle_T}$$"
]
},
{
@ -927,8 +928,8 @@
"metadata": {},
"source": [
"The thermal flux utilization is calculated as\n",
"$$f=\\frac{\\Sigma_{a,thermal}^F\\phi}{\\Sigma_a\\phi}$$\n",
"where $F$ denotes fuel."
"$$f=\\frac{\\langle\\Sigma_a\\phi\\rangle^F_T}{\\langle\\Sigma_a\\phi\\rangle_T}$$\n",
"where the superscript $F$ denotes fuel."
]
},
{
@ -946,6 +947,8 @@
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>energy [MeV]</th>\n",
" <th>cell</th>\n",
" <th>nuclide</th>\n",
" <th>score</th>\n",
" <th>mean</th>\n",
@ -957,24 +960,28 @@
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.0e+00 - 6.2e-01</td>\n",
" <td>10000</td>\n",
" <td>total</td>\n",
" <td>absorption</td>\n",
" <td>0.769263</td>\n",
" <td>0.004172</td>\n",
" <td>0.802094</td>\n",
" <td>0.004432</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" nuclide score mean std. dev.\n",
"bin \n",
"0 total absorption 0.769263 0.004172"
" energy [MeV] cell nuclide score mean std. dev.\n",
"bin \n",
"0 0.0e+00 - 6.2e-01 10000 total absorption 0.802094 0.004432"
]
},
"execution_count": 29,
@ -985,7 +992,7 @@
"source": [
"# Compute thermal flux utilization factor using tally arithmetic\n",
"fuel_therm_abs_rate = sp.get_tally(name='fuel therm. abs. rate')\n",
"therm_util = fuel_therm_abs_rate / abs_rate\n",
"therm_util = fuel_therm_abs_rate / therm_abs_rate\n",
"therm_util.get_pandas_dataframe()"
]
},