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352 lines
25 KiB
Text
352 lines
25 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This Notebook illustrates the usage of the OpenMC Python API's generic eigenvalue search capability. In this Notebook, we will do a critical boron concentration search of a typical PWR pin cell.\n",
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"\n",
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"To use the search functionality, we must create a function which creates our model according to the input parameter we wish to search for (in this case, the boron concentration). \n",
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"\n",
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"This notebook will first create that function, and then, run the search."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Initialize third-party libraries and the OpenMC Python API\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"\n",
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"import openmc\n",
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"import openmc.model\n",
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"\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Create Parametrized Model\n",
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"\n",
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"To perform the search we will use the `openmc.search_for_keff` function. This function requires a different function be defined which creates an parametrized model to analyze. This model is required to be stored in an `openmc.model.Model` object. The first parameter of this function will be modified during the search process for our critical eigenvalue.\n",
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"\n",
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"Our model will be a pin-cell from the [Multi-Group Mode Part II](http://docs.openmc.org/en/latest/examples/mg-mode-part-ii.html) assembly, except this time the entire model building process will be contained within a function, and the Boron concentration will be parametrized."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Create the model. `ppm_Boron` will be the parametric variable.\n",
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"\n",
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"def build_model(ppm_Boron):\n",
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" # Create the pin materials\n",
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" fuel = openmc.Material(name='1.6% Fuel')\n",
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" fuel.set_density('g/cm3', 10.31341)\n",
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" fuel.add_element('U', 1., enrichment=1.6)\n",
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" fuel.add_element('O', 2.)\n",
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"\n",
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" zircaloy = openmc.Material(name='Zircaloy')\n",
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" zircaloy.set_density('g/cm3', 6.55)\n",
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" zircaloy.add_element('Zr', 1.)\n",
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"\n",
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" water = openmc.Material(name='Borated Water')\n",
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" water.set_density('g/cm3', 0.741)\n",
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" water.add_element('H', 2.)\n",
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" water.add_element('O', 1.)\n",
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"\n",
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" # Include the amount of boron in the water based on the ppm,\n",
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" # neglecting the other constituents of boric acid\n",
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" water.add_element('B', ppm_Boron * 1e-6)\n",
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" \n",
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" # Instantiate a Materials object\n",
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" materials = openmc.Materials([fuel, zircaloy, water])\n",
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" \n",
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" # Create cylinders for the fuel and clad\n",
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" fuel_outer_radius = openmc.ZCylinder(r=0.39218)\n",
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" clad_outer_radius = openmc.ZCylinder(r=0.45720)\n",
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"\n",
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" # Create boundary planes to surround the geometry\n",
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" min_x = openmc.XPlane(x0=-0.63, boundary_type='reflective')\n",
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" max_x = openmc.XPlane(x0=+0.63, boundary_type='reflective')\n",
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" min_y = openmc.YPlane(y0=-0.63, boundary_type='reflective')\n",
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" max_y = openmc.YPlane(y0=+0.63, boundary_type='reflective')\n",
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"\n",
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" # Create fuel Cell\n",
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" fuel_cell = openmc.Cell(name='1.6% Fuel')\n",
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" fuel_cell.fill = fuel\n",
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" fuel_cell.region = -fuel_outer_radius\n",
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"\n",
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" # Create a clad Cell\n",
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" clad_cell = openmc.Cell(name='1.6% Clad')\n",
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" clad_cell.fill = zircaloy\n",
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" clad_cell.region = +fuel_outer_radius & -clad_outer_radius\n",
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"\n",
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" # Create a moderator Cell\n",
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" moderator_cell = openmc.Cell(name='1.6% Moderator')\n",
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" moderator_cell.fill = water\n",
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" moderator_cell.region = +clad_outer_radius & (+min_x & -max_x & +min_y & -max_y)\n",
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"\n",
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" # Create root Universe\n",
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" root_universe = openmc.Universe(name='root universe', universe_id=0)\n",
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" root_universe.add_cells([fuel_cell, clad_cell, moderator_cell])\n",
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"\n",
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" # Create Geometry and set root universe\n",
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" geometry = openmc.Geometry(root_universe)\n",
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" \n",
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" # Finish with the settings file\n",
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" settings = openmc.Settings()\n",
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" settings.batches = 300\n",
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" settings.inactive = 20\n",
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" settings.particles = 1000\n",
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" settings.run_mode = 'eigenvalue'\n",
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"\n",
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" # Create an initial uniform spatial source distribution over fissionable zones\n",
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" bounds = [-0.63, -0.63, -10, 0.63, 0.63, 10.]\n",
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" uniform_dist = openmc.stats.Box(bounds[:3], bounds[3:], only_fissionable=True)\n",
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" settings.source = openmc.source.Source(space=uniform_dist)\n",
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"\n",
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" # We dont need a tallies file so dont waste the disk input/output time\n",
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" settings.output = {'tallies': False}\n",
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" \n",
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" model = openmc.model.Model(geometry, materials, settings)\n",
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" \n",
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" return model"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Search for the Critical Boron Concentration\n",
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"\n",
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"To perform the search we imply call the `openmc.search_for_keff` function and pass in the relvant arguments. For our purposes we will be passing in the model building function (`build_model` defined above), a bracketed range for the expected critical Boron concentration (1,000 to 2,500 ppm), the tolerance, and the method we wish to use. \n",
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"\n",
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"Instead of the bracketed range we could have used a single initial guess, but have elected not to in this example. Finally, due to the high noise inherent in using as few histories as are used in this example, our tolerance on the final keff value will be rather large (1.e-2) and a bisection method will be used for the search."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 1; Guess of 1.00e+03 produced a keff of 1.08853 +/- 0.00158\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 2; Guess of 2.50e+03 produced a keff of 0.95372 +/- 0.00148\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 3; Guess of 1.75e+03 produced a keff of 1.01328 +/- 0.00169\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 4; Guess of 2.12e+03 produced a keff of 0.98150 +/- 0.00158\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 5; Guess of 1.94e+03 produced a keff of 0.99886 +/- 0.00146\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 6; Guess of 1.84e+03 produced a keff of 1.00759 +/- 0.00162\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 7; Guess of 1.89e+03 produced a keff of 1.00063 +/- 0.00166\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 8; Guess of 1.91e+03 produced a keff of 0.99970 +/- 0.00150\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/romano/openmc/openmc/mixin.py:71: IDWarning: Another Universe instance already exists with id=0.\n",
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" warn(msg, IDWarning)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration: 9; Guess of 1.90e+03 produced a keff of 0.99935 +/- 0.00164\n",
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"Critical Boron Concentration: 1902 ppm\n"
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]
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}
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],
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"source": [
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"# Perform the search\n",
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"crit_ppm, guesses, keffs = openmc.search_for_keff(build_model, bracket=[1000., 2500.],\n",
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" tol=1e-2, bracketed_method='bisect',\n",
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" print_iterations=True)\n",
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"\n",
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"print('Critical Boron Concentration: {:4.0f} ppm'.format(crit_ppm))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Finally, the `openmc.search_for_keff` function also provided us with `List`s of the guesses and corresponding keff values generated during the search process with OpenMC. Let's use that information to make a quick plot of the value of keff versus the boron concentration."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 576x324 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(8, 4.5))\n",
|
|
"plt.title('Eigenvalue versus Boron Concentration')\n",
|
|
"# Create a scatter plot using the mean value of keff\n",
|
|
"plt.scatter(guesses, [keffs[i].nominal_value for i in range(len(keffs))])\n",
|
|
"plt.xlabel('Boron Concentration [ppm]')\n",
|
|
"plt.ylabel('Eigenvalue')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"source": [
|
|
"We see a nearly linear reactivity coefficient for the boron concentration, exactly as one would expect for a pure 1/v absorber at small concentrations."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.7.0"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|