From ba42547eb3a0bb06c83094f5b21f26530eaf3098 Mon Sep 17 00:00:00 2001 From: Sam Shaner Date: Tue, 23 Aug 2016 15:26:24 -0400 Subject: [PATCH] added tally-arithmetic.ipynb with six-factor formula --- .../pythonapi/examples/tally-arithmetic.ipynb | 533 ++++++++++++------ openmc/filter.py | 18 +- 2 files changed, 360 insertions(+), 191 deletions(-) diff --git a/docs/source/pythonapi/examples/tally-arithmetic.ipynb b/docs/source/pythonapi/examples/tally-arithmetic.ipynb index dfd493f16..088af07b3 100644 --- a/docs/source/pythonapi/examples/tally-arithmetic.ipynb +++ b/docs/source/pythonapi/examples/tally-arithmetic.ipynb @@ -136,8 +136,8 @@ "max_x = openmc.XPlane(x0=+0.63, boundary_type='reflective')\n", "min_y = openmc.YPlane(y0=-0.63, boundary_type='reflective')\n", "max_y = openmc.YPlane(y0=+0.63, boundary_type='reflective')\n", - "min_z = openmc.ZPlane(z0=-0.63, boundary_type='reflective')\n", - "max_z = openmc.ZPlane(z0=+0.63, boundary_type='reflective')" + "min_z = openmc.ZPlane(z0=-100., boundary_type='vacuum')\n", + "max_z = openmc.ZPlane(z0=+100., boundary_type='vacuum')" ] }, { @@ -264,7 +264,7 @@ "settings_file.output = {'tallies': True}\n", "\n", "# Create an initial uniform spatial source distribution over fissionable zones\n", - "bounds = [-0.63, -0.63, -0.63, 0.63, 0.63, 0.63]\n", + "bounds = [-0.63, -0.63, -100., 0.63, 0.63, 100.]\n", "uniform_dist = openmc.stats.Box(bounds[:3], bounds[3:], only_fissionable=True)\n", "settings_file.source = openmc.source.Source(space=uniform_dist)\n", "\n", @@ -339,7 +339,7 @@ "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAD6AgMAAAD1grKuAAAABGdBTUEAALGPC/xhBQAAACBjSFJN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\nP2X7EAAAAABJRU5ErkJggg==\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAD6AgMAAAD1grKuAAAABGdBTUEAALGPC/xhBQAAACBjSFJN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\nfBSvLgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] @@ -410,7 +410,32 @@ "tally.filters.append(energy_filter)\n", "tally.scores = ['absorption', 'total']\n", "tally.nuclides = [o16, h1]\n", - "tallies_file.append(tally)" + "tallies_file.append(tally)\n", + "\n", + "# Instantiate a tally mesh \n", + "mesh = openmc.Mesh(mesh_id=1)\n", + "mesh.type = 'regular'\n", + "mesh.dimension = [1, 1, 1]\n", + "mesh.lower_left = [-0.63, -0.63, -100.]\n", + "mesh.width = [1.26, 1.26, 200.]\n", + "mesh_filter = openmc.Filter(type='mesh', bins=[mesh.id])\n", + "mesh_filter.mesh = mesh\n", + "\n", + "# Instantiate thermal, fast, and total leakage tallies\n", + "leak = openmc.Tally(name='leakage')\n", + "leak.filters = [mesh_filter]\n", + "leak.scores = ['current']\n", + "tallies_file.append(leak)\n", + "\n", + "thermal_leak = openmc.Tally(name='thermal leakage')\n", + "thermal_leak.filters = [mesh_filter, openmc.Filter(type='energy', bins=[0., 0.625e-6])]\n", + "thermal_leak.scores = ['current']\n", + "tallies_file.append(thermal_leak)\n", + "\n", + "fast_leak = openmc.Tally(name='fast leakage')\n", + "fast_leak.filters = [mesh_filter, openmc.Filter(type='energy', bins=[0.625e-6, 20.])]\n", + "fast_leak.scores = ['current']\n", + "tallies_file.append(fast_leak)" ] }, { @@ -484,12 +509,12 @@ "outputs": [], "source": [ "# Instantiate energy filter to illustrate Tally slicing\n", - "energy_filter = openmc.Filter(type='energy', bins=np.logspace(np.log10(1e-8), np.log10(20), 10))\n", + "fine_energy_filter = openmc.Filter(type='energy', bins=np.logspace(np.log10(1e-8), np.log10(20), 10))\n", "\n", "# Instantiate flux Tally in moderator and fuel\n", "tally = openmc.Tally(name='need-to-slice')\n", "tally.filters = [openmc.Filter(type='cell', bins=[fuel_cell.id, moderator_cell.id])]\n", - "tally.filters.append(energy_filter)\n", + "tally.filters.append(fine_energy_filter)\n", "tally.scores = ['nu-fission', 'scatter']\n", "tally.nuclides = [h1, u238]\n", "tallies_file.append(tally)" @@ -541,9 +566,10 @@ "\n", " Copyright: 2011-2016 Massachusetts Institute of Technology\n", " License: http://openmc.readthedocs.io/en/latest/license.html\n", - " Version: 0.7.1\n", - " Git SHA1: 3d68c07625e33cd64188df03ee03e9c31b3d4b74\n", - " Date/Time: 2016-07-22 21:39:46\n", + " Version: 0.8.0\n", + " Git SHA1: 93862cea249e4441beb714e719120da3bd2b7d0a\n", + " Date/Time: 2016-08-23 15:24:53\n", + " MPI Processes: 1\n", "\n", " ===========================================================================\n", " ========================> INITIALIZATION <=========================\n", @@ -553,12 +579,12 @@ " Reading geometry XML file...\n", " Reading cross sections XML file...\n", " Reading materials XML file...\n", - " Reading U235.71c from /home/romano/openmc/data/nndc_hdf5/U235_71c.h5\n", - " Reading U238.71c from /home/romano/openmc/data/nndc_hdf5/U238_71c.h5\n", - " Reading O16.71c from /home/romano/openmc/data/nndc_hdf5/O16_71c.h5\n", - " Reading H1.71c from /home/romano/openmc/data/nndc_hdf5/H1_71c.h5\n", - " Reading B10.71c from /home/romano/openmc/data/nndc_hdf5/B10_71c.h5\n", - " Reading Zr90.71c from /home/romano/openmc/data/nndc_hdf5/Zr90_71c.h5\n", + " Reading U235.71c from /Users/sam/git/openmc-sam/data/nndc_hdf5/U235_71c.h5\n", + " Reading U238.71c from /Users/sam/git/openmc-sam/data/nndc_hdf5/U238_71c.h5\n", + " Reading O16.71c from /Users/sam/git/openmc-sam/data/nndc_hdf5/O16_71c.h5\n", + " Reading H1.71c from /Users/sam/git/openmc-sam/data/nndc_hdf5/H1_71c.h5\n", + " Reading B10.71c from /Users/sam/git/openmc-sam/data/nndc_hdf5/B10_71c.h5\n", + " Reading Zr90.71c from /Users/sam/git/openmc-sam/data/nndc_hdf5/Zr90_71c.h5\n", " Maximum neutron transport energy: 20.0000 MeV for U235.71c\n", " Reading tallies XML file...\n", " Building neighboring cells lists for each surface...\n", @@ -570,26 +596,26 @@ "\n", " Bat./Gen. k Average k \n", " ========= ======== ==================== \n", - " 1/1 1.03471 \n", - " 2/1 1.03257 \n", - " 3/1 1.00600 \n", - " 4/1 1.04547 \n", - " 5/1 1.02287 \n", - " 6/1 1.05752 \n", - " 7/1 1.04283 1.05017 +/- 0.00734\n", - " 8/1 1.05189 1.05074 +/- 0.00428\n", - " 9/1 1.01645 1.04217 +/- 0.00909\n", - " 10/1 1.04978 1.04369 +/- 0.00721\n", - " 11/1 1.03459 1.04218 +/- 0.00608\n", - " 12/1 1.04019 1.04189 +/- 0.00514\n", - " 13/1 1.05985 1.04414 +/- 0.00499\n", - " 14/1 1.02111 1.04158 +/- 0.00509\n", - " 15/1 1.04774 1.04219 +/- 0.00459\n", - " 16/1 1.00733 1.03902 +/- 0.00523\n", - " 17/1 1.02224 1.03763 +/- 0.00497\n", - " 18/1 1.03263 1.03724 +/- 0.00459\n", - " 19/1 1.01611 1.03573 +/- 0.00451\n", - " 20/1 1.04692 1.03648 +/- 0.00426\n", + " 1/1 0.96168 \n", + " 2/1 0.96651 \n", + " 3/1 1.00678 \n", + " 4/1 0.98773 \n", + " 5/1 1.01883 \n", + " 6/1 1.02959 \n", + " 7/1 0.99859 1.01409 +/- 0.01550\n", + " 8/1 1.03441 1.02086 +/- 0.01123\n", + " 9/1 1.06097 1.03089 +/- 0.01279\n", + " 10/1 1.06094 1.03690 +/- 0.01159\n", + " 11/1 1.04687 1.03856 +/- 0.00961\n", + " 12/1 1.02982 1.03731 +/- 0.00821\n", + " 13/1 1.03520 1.03705 +/- 0.00712\n", + " 14/1 0.99508 1.03239 +/- 0.00782\n", + " 15/1 1.03973 1.03312 +/- 0.00703\n", + " 16/1 1.03807 1.03357 +/- 0.00638\n", + " 17/1 1.03091 1.03335 +/- 0.00583\n", + " 18/1 1.01421 1.03188 +/- 0.00556\n", + " 19/1 0.99339 1.02913 +/- 0.00583\n", + " 20/1 1.04827 1.03040 +/- 0.00558\n", " Creating state point statepoint.20.h5...\n", "\n", " ===========================================================================\n", @@ -599,28 +625,28 @@ "\n", " =======================> TIMING STATISTICS <=======================\n", "\n", - " Total time for initialization = 3.5600E-01 seconds\n", - " Reading cross sections = 2.3400E-01 seconds\n", - " Total time in simulation = 1.8333E+01 seconds\n", - " Time in transport only = 1.8325E+01 seconds\n", - " Time in inactive batches = 2.6950E+00 seconds\n", - " Time in active batches = 1.5638E+01 seconds\n", - " Time synchronizing fission bank = 1.0000E-03 seconds\n", - " Sampling source sites = 0.0000E+00 seconds\n", + " Total time for initialization = 5.4300E-01 seconds\n", + " Reading cross sections = 3.5400E-01 seconds\n", + " Total time in simulation = 1.8555E+01 seconds\n", + " Time in transport only = 1.8464E+01 seconds\n", + " Time in inactive batches = 2.4600E+00 seconds\n", + " Time in active batches = 1.6095E+01 seconds\n", + " Time synchronizing fission bank = 1.1000E-02 seconds\n", + " Sampling source sites = 4.0000E-03 seconds\n", " SEND/RECV source sites = 1.0000E-03 seconds\n", " Time accumulating tallies = 0.0000E+00 seconds\n", - " Total time for finalization = 1.0000E-03 seconds\n", - " Total time elapsed = 1.8711E+01 seconds\n", - " Calculation Rate (inactive) = 4638.22 neutrons/second\n", - " Calculation Rate (active) = 2398.00 neutrons/second\n", + " Total time for finalization = 3.0000E-03 seconds\n", + " Total time elapsed = 1.9120E+01 seconds\n", + " Calculation Rate (inactive) = 5081.30 neutrons/second\n", + " Calculation Rate (active) = 2329.92 neutrons/second\n", "\n", " ============================> RESULTS <============================\n", "\n", - " k-effective (Collision) = 1.03296 +/- 0.00669\n", - " k-effective (Track-length) = 1.03648 +/- 0.00426\n", - " k-effective (Absorption) = 1.03431 +/- 0.00702\n", - " Combined k-effective = 1.03621 +/- 0.00456\n", - " Leakage Fraction = 0.00000 +/- 0.00000\n", + " k-effective (Collision) = 1.02791 +/- 0.00553\n", + " k-effective (Track-length) = 1.03040 +/- 0.00558\n", + " k-effective (Absorption) = 1.02011 +/- 0.00491\n", + " Combined k-effective = 1.02461 +/- 0.00398\n", + " Leakage Fraction = 0.01677 +/- 0.00109\n", "\n" ] }, @@ -674,8 +700,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We have a tally of the total fission rate and the total absorption rate, so we can calculate k-infinity as:\n", - "$$k_\\infty = \\frac{\\langle \\nu \\Sigma_f \\phi \\rangle}{\\langle \\Sigma_a \\phi \\rangle}$$\n", + "We have a tally of the total fission rate and the total absorption rate, so we can calculate k-eff as:\n", + "$$k_{eff} = \\frac{\\langle \\nu \\Sigma_f \\phi \\rangle}{\\langle \\Sigma_a \\phi \\rangle + \\langle L \\rangle}$$\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." ] }, @@ -704,17 +730,17 @@ " \n", " 0\n", " total\n", - " (nu-fission / absorption)\n", - " 1.038387\n", - " 0.006141\n", + " (nu-fission / (absorption + current))\n", + " 1.02431\n", + " 0.00704\n", " \n", " \n", "\n", "" ], "text/plain": [ - " nuclide score mean std. dev.\n", - "0 total (nu-fission / absorption) 1.04e+00 6.14e-03" + " nuclide score mean std. dev.\n", + "0 total (nu-fission / (absorption + current)) 1.02e+00 7.04e-03" ] }, "execution_count": 24, @@ -723,10 +749,17 @@ } ], "source": [ - "# Compute k-infinity using tally arithmetic\n", + "# Get the fission and absorption rate tallies\n", "fiss_rate = sp.get_tally(name='fiss. rate')\n", "abs_rate = sp.get_tally(name='abs. rate')\n", - "keff = fiss_rate / abs_rate\n", + "\n", + "# Get the leakage tally\n", + "leak = sp.get_tally(name='leakage')\n", + "leak = leak.summation(filter_type='surface', remove_filter=True)\n", + "leak = leak.summation(filter_type='mesh', remove_filter=True)\n", + "\n", + "# Compute k-infinity using tally arithmetic\n", + "keff = fiss_rate / (abs_rate + leak)\n", "keff.get_pandas_dataframe()" ] }, @@ -734,9 +767,9 @@ "cell_type": "markdown", "metadata": {}, "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", + "Notice that even though the neutron production rate, absorption rate, and current are separate tallies, we still get a first-order estimate of the uncertainty on the quotient of them automatically!\n", "\n", - "Often in textbooks you'll see k-infinity represented using the four-factor formula $$k_\\infty = p \\epsilon f \\eta.$$ Let's analyze each of these factors, starting with the resonance escape probability which is defined as $$p=\\frac{\\langle\\Sigma_a\\phi\\rangle_T}{\\langle\\Sigma_a\\phi\\rangle}$$ where the subscript $T$ means thermal energies." + "Often in textbooks you'll see k-eff represented using the six-factor formula $$k_{eff} = p \\epsilon f \\eta P_{FNL} P_{TNL}.$$ Let's analyze each of these factors, starting with the resonance escape probability which is defined as $$p=\\frac{\\langle\\Sigma_a\\phi\\rangle_T + \\langle L \\rangle_T}{\\langle\\Sigma_a\\phi\\rangle + \\langle L \\rangle_T}$$ where the subscript $T$ means thermal energies." ] }, { @@ -768,17 +801,20 @@ " 0.0\n", " 6.250000e-07\n", " total\n", - " absorption\n", - " 0.693337\n", - " 0.004109\n", + " (absorption + current)\n", + " 0.695303\n", + " 0.005091\n", " \n", " \n", "\n", "" ], "text/plain": [ - " energy low [MeV] energy high [MeV] nuclide score mean std. dev.\n", - "0 0.00e+00 6.25e-07 total absorption 6.93e-01 4.11e-03" + " energy low [MeV] energy high [MeV] nuclide score \\\n", + "0 0.00e+00 6.25e-07 total (absorption + current) \n", + "\n", + " mean std. dev. \n", + "0 6.95e-01 5.09e-03 " ] }, "execution_count": 25, @@ -789,7 +825,10 @@ "source": [ "# Compute resonance escape probability using tally arithmetic\n", "therm_abs_rate = sp.get_tally(name='therm. abs. rate')\n", - "res_esc = therm_abs_rate / abs_rate\n", + "thermal_leak = sp.get_tally(name='thermal leakage')\n", + "thermal_leak = thermal_leak.summation(filter_type='surface', remove_filter=True)\n", + "thermal_leak = thermal_leak.summation(filter_type='mesh', remove_filter=True)\n", + "res_esc = (therm_abs_rate + thermal_leak) / (abs_rate + thermal_leak)\n", "res_esc.get_pandas_dataframe()" ] }, @@ -831,8 +870,8 @@ " 6.250000e-07\n", " total\n", " nu-fission\n", - " 1.203042\n", - " 0.0076\n", + " 1.202639\n", + " 0.010348\n", " \n", " \n", "\n", @@ -840,7 +879,7 @@ ], "text/plain": [ " energy low [MeV] energy high [MeV] nuclide score mean std. dev.\n", - "0 0.00e+00 6.25e-07 total nu-fission 1.20e+00 7.60e-03" + "0 0.00e+00 6.25e-07 total nu-fission 1.20e+00 1.03e-02" ] }, "execution_count": 26, @@ -896,8 +935,8 @@ " 10000\n", " total\n", " absorption\n", - " 0.748413\n", - " 0.004723\n", + " 0.749349\n", + " 0.006731\n", " \n", " \n", "\n", @@ -905,10 +944,10 @@ ], "text/plain": [ " energy low [MeV] energy high [MeV] cell nuclide score mean \\\n", - "0 0.00e+00 6.25e-07 10000 total absorption 7.48e-01 \n", + "0 0.00e+00 6.25e-07 10000 total absorption 7.49e-01 \n", "\n", " std. dev. \n", - "0 4.72e-03 " + "0 6.73e-03 " ] }, "execution_count": 27, @@ -927,7 +966,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The final factor is the number of fission neutrons produced per absorption in fuel, calculated as $$\\eta = \\frac{\\langle \\nu\\Sigma_f\\phi \\rangle_T}{\\langle \\Sigma_a \\phi \\rangle^F_T}$$" + "The next factor is the number of fission neutrons produced per absorption in fuel, calculated as $$\\eta = \\frac{\\langle \\nu\\Sigma_f\\phi \\rangle_T}{\\langle \\Sigma_a \\phi \\rangle^F_T}$$" ] }, { @@ -962,8 +1001,8 @@ " 10000\n", " total\n", " (nu-fission / absorption)\n", - " 1.663385\n", - " 0.011253\n", + " 1.663736\n", + " 0.015707\n", " \n", " \n", "\n", @@ -974,7 +1013,7 @@ "0 0.00e+00 6.25e-07 10000 total \n", "\n", " score mean std. dev. \n", - "0 (nu-fission / absorption) 1.66e+00 1.13e-02 " + "0 (nu-fission / absorption) 1.66e+00 1.57e-02 " ] }, "execution_count": 28, @@ -992,7 +1031,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can calculate $k_\\infty$ using the product of the factors form the four-factor formula." + "There are two leakage factors to account for fast and thermal leakage. The fast non-leakage probability is computed as $$P_{FNL} = \\frac{\\langle \\Sigma_a\\phi \\rangle + \\langle L \\rangle_T}{\\langle \\Sigma_a \\phi \\rangle + \\langle L \\rangle}$$" ] }, { @@ -1001,6 +1040,130 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/html": [ + "
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energy low [MeV]energy high [MeV]nuclidescoremeanstd. dev.
00.06.250000e-07total(absorption + current)0.9851020.005855
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" + ], + "text/plain": [ + " energy low [MeV] energy high [MeV] nuclide score \\\n", + "0 0.00e+00 6.25e-07 total (absorption + current) \n", + "\n", + " mean std. dev. \n", + "0 9.85e-01 5.86e-03 " + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p_fnl = (abs_rate + thermal_leak) / (abs_rate + leak)\n", + "p_fnl.get_pandas_dataframe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The final factor is the thermalnon-leakage probability and is computed as $$P_{TNL} = \\frac{\\langle \\Sigma_a\\phi \\rangle_T}{\\langle \\Sigma_a \\phi \\rangle_T + \\langle L \\rangle_T}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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energy low [MeV]energy high [MeV]nuclidescoremeanstd. dev.
00.06.250000e-07total(absorption / (absorption + current))0.9974070.008492
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" + ], + "text/plain": [ + " energy low [MeV] energy high [MeV] nuclide \\\n", + "0 0.00e+00 6.25e-07 total \n", + "\n", + " score mean std. dev. \n", + "0 (absorption / (absorption + current)) 9.97e-01 8.49e-03 " + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p_tnl = therm_abs_rate / (therm_abs_rate + thermal_leak)\n", + "p_tnl.get_pandas_dataframe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can calculate $k_{eff}$ using the product of the factors form the four-factor formula." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -1026,9 +1189,9 @@ " 6.250000e-07\n", " 10000\n", " total\n", - " (((absorption * nu-fission) * absorption) * (n...\n", - " 1.038387\n", - " 0.01316\n", + " ((((((absorption + current) * nu-fission) * ab...\n", + " 1.02431\n", + " 0.02062\n", " \n", " \n", "\n", @@ -1039,16 +1202,16 @@ "0 0.00e+00 6.25e-07 10000 total \n", "\n", " score mean std. dev. \n", - "0 (((absorption * nu-fission) * absorption) * (n... 1.04e+00 1.32e-02 " + "0 ((((((absorption + current) * nu-fission) * ab... 1.02e+00 2.06e-02 " ] }, - "execution_count": 29, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "keff = res_esc * fast_fiss * therm_util * eta\n", + "keff = res_esc * fast_fiss * therm_util * eta * p_fnl * p_tnl\n", "keff.get_pandas_dataframe()" ] }, @@ -1063,7 +1226,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 32, "metadata": { "collapsed": false, "scrolled": true @@ -1079,7 +1242,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 33, "metadata": { "collapsed": false }, @@ -1109,8 +1272,8 @@ " 6.250000e-07\n", " (U238 / total)\n", " (nu-fission / flux)\n", - " 6.636968e-07\n", - " 4.132875e-09\n", + " 6.662479e-07\n", + " 6.039323e-09\n", " \n", " \n", " 1\n", @@ -1119,8 +1282,8 @@ " 6.250000e-07\n", " (U238 / total)\n", " (scatter / flux)\n", - " 2.099856e-01\n", - " 1.232455e-03\n", + " 2.099897e-01\n", + " 1.843251e-03\n", " \n", " \n", " 2\n", @@ -1129,8 +1292,8 @@ " 6.250000e-07\n", " (U235 / total)\n", " (nu-fission / flux)\n", - " 3.552458e-01\n", - " 2.252681e-03\n", + " 3.568130e-01\n", + " 3.255144e-03\n", " \n", " \n", " 3\n", @@ -1139,8 +1302,8 @@ " 6.250000e-07\n", " (U235 / total)\n", " (scatter / flux)\n", - " 5.554345e-03\n", - " 3.265385e-05\n", + " 5.555326e-03\n", + " 4.893022e-05\n", " \n", " \n", " 4\n", @@ -1149,8 +1312,8 @@ " 2.000000e+01\n", " (U238 / total)\n", " (nu-fission / flux)\n", - " 7.126668e-03\n", - " 5.296883e-05\n", + " 7.215044e-03\n", + " 4.968448e-05\n", " \n", " \n", " 5\n", @@ -1159,8 +1322,8 @@ " 2.000000e+01\n", " (U238 / total)\n", " (scatter / flux)\n", - " 2.277460e-01\n", - " 1.003558e-03\n", + " 2.273966e-01\n", + " 8.969811e-04\n", " \n", " \n", " 6\n", @@ -1169,8 +1332,8 @@ " 2.000000e+01\n", " (U235 / total)\n", " (nu-fission / flux)\n", - " 8.010911e-03\n", - " 6.802256e-05\n", + " 7.969615e-03\n", + " 5.374119e-05\n", " \n", " \n", " 7\n", @@ -1179,8 +1342,8 @@ " 2.000000e+01\n", " (U235 / total)\n", " (scatter / flux)\n", - " 3.367794e-03\n", - " 1.443644e-05\n", + " 3.362798e-03\n", + " 1.286767e-05\n", " \n", " \n", "\n", @@ -1198,17 +1361,17 @@ "7 10000 6.25e-07 2.00e+01 (U235 / total) \n", "\n", " score mean std. dev. \n", - "0 (nu-fission / flux) 6.64e-07 4.13e-09 \n", - "1 (scatter / flux) 2.10e-01 1.23e-03 \n", - "2 (nu-fission / flux) 3.55e-01 2.25e-03 \n", - "3 (scatter / flux) 5.55e-03 3.27e-05 \n", - "4 (nu-fission / flux) 7.13e-03 5.30e-05 \n", - "5 (scatter / flux) 2.28e-01 1.00e-03 \n", - "6 (nu-fission / flux) 8.01e-03 6.80e-05 \n", - "7 (scatter / flux) 3.37e-03 1.44e-05 " + "0 (nu-fission / flux) 6.66e-07 6.04e-09 \n", + "1 (scatter / flux) 2.10e-01 1.84e-03 \n", + "2 (nu-fission / flux) 3.57e-01 3.26e-03 \n", + "3 (scatter / flux) 5.56e-03 4.89e-05 \n", + "4 (nu-fission / flux) 7.22e-03 4.97e-05 \n", + "5 (scatter / flux) 2.27e-01 8.97e-04 \n", + "6 (nu-fission / flux) 7.97e-03 5.37e-05 \n", + "7 (scatter / flux) 3.36e-03 1.29e-05 " ] }, - "execution_count": 31, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -1227,7 +1390,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -1236,11 +1399,11 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[[ 6.63696783e-07]\n", - " [ 3.55245846e-01]]\n", + "[[[ 6.66247898e-07]\n", + " [ 3.56812954e-01]]\n", "\n", - " [[ 7.12666800e-03]\n", - " [ 8.01091088e-03]]]\n" + " [[ 7.21504433e-03]\n", + " [ 7.96961502e-03]]]\n" ] } ], @@ -1259,7 +1422,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 35, "metadata": { "collapsed": false }, @@ -1268,9 +1431,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[[ 0.00555435]]\n", + "[[[ 0.00555533]]\n", "\n", - " [[ 0.00336779]]]\n" + " [[ 0.0033628 ]]]\n" ] } ], @@ -1283,7 +1446,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 36, "metadata": { "collapsed": false }, @@ -1292,8 +1455,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[[ 0.22774598]\n", - " [ 0.00336779]]]\n" + "[[[ 0.22739657]\n", + " [ 0.0033628 ]]]\n" ] } ], @@ -1314,7 +1477,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -1345,7 +1508,7 @@ " U238\n", " nu-fission\n", " 0.000002\n", - " 7.473789e-09\n", + " 1.057199e-08\n", " \n", " \n", " 1\n", @@ -1354,8 +1517,8 @@ " 6.250000e-07\n", " U235\n", " nu-fission\n", - " 0.861547\n", - " 4.131310e-03\n", + " 0.856784\n", + " 5.730044e-03\n", " \n", " \n", " 2\n", @@ -1364,8 +1527,8 @@ " 2.000000e+01\n", " U238\n", " nu-fission\n", - " 0.082356\n", - " 5.560461e-04\n", + " 0.082495\n", + " 5.176027e-04\n", " \n", " \n", " 3\n", @@ -1374,8 +1537,8 @@ " 2.000000e+01\n", " U235\n", " nu-fission\n", - " 0.092574\n", - " 7.315442e-04\n", + " 0.091123\n", + " 5.574052e-04\n", " \n", " \n", "\n", @@ -1383,19 +1546,19 @@ ], "text/plain": [ " cell energy low [MeV] energy high [MeV] nuclide score mean \\\n", - "0 10000 0.00e+00 6.25e-07 U238 nu-fission 1.61e-06 \n", - "1 10000 0.00e+00 6.25e-07 U235 nu-fission 8.62e-01 \n", - "2 10000 6.25e-07 2.00e+01 U238 nu-fission 8.24e-02 \n", - "3 10000 6.25e-07 2.00e+01 U235 nu-fission 9.26e-02 \n", + "0 10000 0.00e+00 6.25e-07 U238 nu-fission 1.60e-06 \n", + "1 10000 0.00e+00 6.25e-07 U235 nu-fission 8.57e-01 \n", + "2 10000 6.25e-07 2.00e+01 U238 nu-fission 8.25e-02 \n", + "3 10000 6.25e-07 2.00e+01 U235 nu-fission 9.11e-02 \n", "\n", " std. dev. \n", - "0 7.47e-09 \n", - "1 4.13e-03 \n", - "2 5.56e-04 \n", - "3 7.32e-04 " + "0 1.06e-08 \n", + "1 5.73e-03 \n", + "2 5.18e-04 \n", + "3 5.57e-04 " ] }, - "execution_count": 35, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } @@ -1408,7 +1571,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -1438,8 +1601,8 @@ " 1.080060e-07\n", " H1\n", " scatter\n", - " 4.599225\n", - " 0.015973\n", + " 4.547947\n", + " 0.028000\n", " \n", " \n", " 1\n", @@ -1448,8 +1611,8 @@ " 1.166529e-06\n", " H1\n", " scatter\n", - " 2.037260\n", - " 0.011236\n", + " 2.003068\n", + " 0.008587\n", " \n", " \n", " 2\n", @@ -1458,8 +1621,8 @@ " 1.259921e-05\n", " H1\n", " scatter\n", - " 1.662552\n", - " 0.010280\n", + " 1.647225\n", + " 0.011136\n", " \n", " \n", " 3\n", @@ -1468,8 +1631,8 @@ " 1.360790e-04\n", " H1\n", " scatter\n", - " 1.872201\n", - " 0.012136\n", + " 1.831367\n", + " 0.010196\n", " \n", " \n", " 4\n", @@ -1478,8 +1641,8 @@ " 1.469734e-03\n", " H1\n", " scatter\n", - " 2.080459\n", - " 0.013155\n", + " 2.039613\n", + " 0.008059\n", " \n", " \n", " 5\n", @@ -1488,8 +1651,8 @@ " 1.587401e-02\n", " H1\n", " scatter\n", - " 2.154996\n", - " 0.011975\n", + " 2.137523\n", + " 0.012885\n", " \n", " \n", " 6\n", @@ -1498,8 +1661,8 @@ " 1.714488e-01\n", " H1\n", " scatter\n", - " 2.218740\n", - " 0.008528\n", + " 2.170725\n", + " 0.012669\n", " \n", " \n", " 7\n", @@ -1508,8 +1671,8 @@ " 1.851749e+00\n", " H1\n", " scatter\n", - " 2.010517\n", - " 0.009187\n", + " 2.002724\n", + " 0.010768\n", " \n", " \n", " 8\n", @@ -1518,8 +1681,8 @@ " 2.000000e+01\n", " H1\n", " scatter\n", - " 0.372022\n", - " 0.003196\n", + " 0.371624\n", + " 0.002959\n", " \n", " \n", "\n", @@ -1527,29 +1690,29 @@ ], "text/plain": [ " cell energy low [MeV] energy high [MeV] nuclide score mean \\\n", - "0 10002 1.00e-08 1.08e-07 H1 scatter 4.60e+00 \n", - "1 10002 1.08e-07 1.17e-06 H1 scatter 2.04e+00 \n", - "2 10002 1.17e-06 1.26e-05 H1 scatter 1.66e+00 \n", - "3 10002 1.26e-05 1.36e-04 H1 scatter 1.87e+00 \n", - "4 10002 1.36e-04 1.47e-03 H1 scatter 2.08e+00 \n", - "5 10002 1.47e-03 1.59e-02 H1 scatter 2.15e+00 \n", - "6 10002 1.59e-02 1.71e-01 H1 scatter 2.22e+00 \n", - "7 10002 1.71e-01 1.85e+00 H1 scatter 2.01e+00 \n", + "0 10002 1.00e-08 1.08e-07 H1 scatter 4.55e+00 \n", + "1 10002 1.08e-07 1.17e-06 H1 scatter 2.00e+00 \n", + "2 10002 1.17e-06 1.26e-05 H1 scatter 1.65e+00 \n", + "3 10002 1.26e-05 1.36e-04 H1 scatter 1.83e+00 \n", + "4 10002 1.36e-04 1.47e-03 H1 scatter 2.04e+00 \n", + "5 10002 1.47e-03 1.59e-02 H1 scatter 2.14e+00 \n", + "6 10002 1.59e-02 1.71e-01 H1 scatter 2.17e+00 \n", + "7 10002 1.71e-01 1.85e+00 H1 scatter 2.00e+00 \n", "8 10002 1.85e+00 2.00e+01 H1 scatter 3.72e-01 \n", "\n", " std. dev. \n", - "0 1.60e-02 \n", - "1 1.12e-02 \n", - "2 1.03e-02 \n", - "3 1.21e-02 \n", - "4 1.32e-02 \n", - "5 1.20e-02 \n", - "6 8.53e-03 \n", - "7 9.19e-03 \n", - "8 3.20e-03 " + "0 2.80e-02 \n", + "1 8.59e-03 \n", + "2 1.11e-02 \n", + "3 1.02e-02 \n", + "4 8.06e-03 \n", + "5 1.29e-02 \n", + "6 1.27e-02 \n", + "7 1.08e-02 \n", + "8 2.96e-03 " ] }, - "execution_count": 36, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -1565,21 +1728,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 2", "language": "python", - "name": "python3" + "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 3 + "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.2" + "pygments_lexer": "ipython2", + "version": "2.7.12" } }, "nbformat": 4, diff --git a/openmc/filter.py b/openmc/filter.py index 9b4eb67dd..771d40401 100644 --- a/openmc/filter.py +++ b/openmc/filter.py @@ -781,12 +781,18 @@ class Filter(object): filter_bins = np.repeat(self.bins, self.stride) tile_factor = data_size / len(filter_bins) filter_bins = np.tile(filter_bins, tile_factor) - filter_bins = [x if x != 1 else 'x-min' for x in filter_bins] - filter_bins = [x if x != 2 else 'x-max' for x in filter_bins] - filter_bins = [x if x != 3 else 'y-min' for x in filter_bins] - filter_bins = [x if x != 4 else 'y-max' for x in filter_bins] - filter_bins = [x if x != 5 else 'z-min' for x in filter_bins] - filter_bins = [x if x != 6 else 'z-max' for x in filter_bins] + filter_bins = [x if x != 1 else 'x-min out' for x in filter_bins] + filter_bins = [x if x != 2 else 'x-max out' for x in filter_bins] + filter_bins = [x if x != 3 else 'y-min out' for x in filter_bins] + filter_bins = [x if x != 4 else 'y-max out' for x in filter_bins] + filter_bins = [x if x != 5 else 'z-min out' for x in filter_bins] + filter_bins = [x if x != 6 else 'z-max out' for x in filter_bins] + filter_bins = [x if x != 7 else 'x-min in' for x in filter_bins] + filter_bins = [x if x != 8 else 'x-max in' for x in filter_bins] + filter_bins = [x if x != 9 else 'y-min in' for x in filter_bins] + filter_bins = [x if x != 10 else 'y-max in' for x in filter_bins] + filter_bins = [x if x != 11 else 'z-min in' for x in filter_bins] + filter_bins = [x if x != 12 else 'z-max in' for x in filter_bins] df = pd.concat([df, pd.DataFrame({self.type : filter_bins})]) # universe, material, surface, cell, and cellborn filters