"This notebook shows the how tallies can be combined (added, subtracted, multiplied, etc.) using the Python API in order to create derived tallies. Since no covariance information is obtained, it is assumed that tallies are completely independent of one another when propagating uncertainties. The target problem is a simple pin cell.\n",
"\n",
"**Note:** that this Notebook was created using the latest Pandas v0.16.1. Everything in the Notebook will wun with older versions of Pandas, but the multi-indexing option in >v0.15.0 makes the tables look prettier."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%load_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import glob\n",
"from IPython.display import Image\n",
"import numpy as np\n",
"\n",
"import openmc\n",
"from openmc.statepoint import StatePoint\n",
"from openmc.summary import Summary\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate Input Files"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we need to define materials that will be used in the problem. Before defining a material, we must create nuclides that are used in the material."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Instantiate some Nuclides\n",
"h1 = openmc.Nuclide('H-1')\n",
"b10 = openmc.Nuclide('B-10')\n",
"o16 = openmc.Nuclide('O-16')\n",
"u235 = openmc.Nuclide('U-235')\n",
"u238 = openmc.Nuclide('U-238')\n",
"zr90 = openmc.Nuclide('Zr-90')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the nuclides we defined, we will now create three materials for the fuel, water, and cladding of the fuel pin."
"With our three materials, we can now create a materials file object that can be exported to an actual XML file."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Instantiate a MaterialsFile, add Materials\n",
"materials_file = openmc.MaterialsFile()\n",
"materials_file.add_material(fuel)\n",
"materials_file.add_material(water)\n",
"materials_file.add_material(zircaloy)\n",
"materials_file.default_xs = '71c'\n",
"\n",
"# Export to \"materials.xml\"\n",
"materials_file.export_to_xml()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's move on to the geometry. Our problem will have three regions for the fuel, the clad, and the surrounding coolant. The first step is to create the bounding surfaces -- in this case two cylinders and six reflective planes."
"OpenMC requires that there is a \"root\" universe. Let us create a root cell that is filled by the pin cell universe and then assign it to the root universe."
"We now must create a geometry that is assigned a root universe, put the geometry into a geometry file, and export it to XML."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Create Geometry and set root Universe\n",
"geometry = openmc.Geometry()\n",
"geometry.root_universe = root_universe"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Instantiate a GeometryFile\n",
"geometry_file = openmc.GeometryFile()\n",
"geometry_file.geometry = geometry\n",
"\n",
"# Export to \"geometry.xml\"\n",
"geometry_file.export_to_xml()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the geometry and materials finished, we now just need to define simulation parameters. In this case, we will use 5 inactive batches and 15 active batches each with 2500 particles."
"Let us also create a plot file that we can use to verify that our pin cell geometry was created successfully."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Instantiate a Plot\n",
"plot = openmc.Plot(plot_id=1)\n",
"plot.filename = 'materials-xy'\n",
"plot.origin = [0, 0, 0]\n",
"plot.width = [1.26, 1.26]\n",
"plot.pixels = [250, 250]\n",
"plot.color = 'mat'\n",
"\n",
"# Instantiate a PlotsFile, add Plot, and export to \"plots.xml\"\n",
"plot_file = openmc.PlotsFile()\n",
"plot_file.add_plot(plot)\n",
"plot_file.export_to_xml()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the plots.xml file, we can now generate and view the plot. OpenMC outputs plots in .ppm format, which can be converted into a compressed format like .png with the convert utility."
"As we can see from the plot, we have a nice pin cell with fuel, cladding, and water! Before we run our simulation, we need to tell the code what we want to tally. The following code shows how to create a variety of tallies."
"Our simulation ran successfully and created a statepoint file with all the tally data in it. We begin our analysis here loading the statepoint file and 'reading' the results. By default, the tally results are not read into memory because they might be large, even large enough to exceed the available memory on a computer."
"You may have also noticed we instructed OpenMC to create a summary file with lots of geometry information in it. This can help to produce more sensible output from the Python API, so we will use the summary file to link against."
"\u001b[1;32m<ipython-input-25-3cd87b8121ef>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;31m# Load the summary file and link with statepoint\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[0msu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mSummary\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'summary.h5'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0msp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlink_with_summary\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msu\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[1;32m/usr/local/lib/python2.7/dist-packages/openmc-0.7.0-py2.7.egg/openmc/statepoint.pyc\u001b[0m in \u001b[0;36mlink_with_summary\u001b[1;34m(self, summary)\u001b[0m\n\u001b[0;32m 610\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mtally_id\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtally\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtallies\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 611\u001b[0m \u001b[1;31m# Get the Tally name from the summary file\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 612\u001b[1;33m \u001b[0mtally\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mname\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msummary\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtallies\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mtally_id\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 613\u001b[0m \u001b[0mtally\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwith_summary\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 614\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\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."
"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",
"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."
"The final factor is the number of fission neutrons produced per absorption in fuel, calculated as $$\\eta = \\frac{\\langle \\nu\\Sigma_f\\phi \\rangle_T}{\\langle \\Sigma_a \\phi \\rangle^F_T}$$"
"We see that the value we've obtained here has exactly the same mean as before. However, because of the way it was calculated, the standard deviation appears to be larger.\n",
"\n",
"Let's move on to a more complicated example now. Before we set up tallies to get reaction rates in the fuel and moderator in two energy groups for two different nuclides. We can use tally arithmetic to divide each of these reaction rates by the flux to get microscopic multi-group cross sections."
"We see that when the two tallies with multiple bins were divided, the derived tally contains the outer product of the combinations. If the filters/scores are the same, no outer product is needed. The `get_values(...)` method allows us to obtain a subset of tally scores. In the following example, we obtain just the neutron production microscopic cross sections."
"A more advanced method is to use `get_slice(...)` to create a new derived tally that is a subset of an existing tally. This has the benefit that we can use `get_pandas_dataframe()` to see the tallies in a more human-readable format."
