From 941074178f02a97a1872f7c02d063c39bf92ae28 Mon Sep 17 00:00:00 2001 From: Adam Nelson Date: Sun, 19 Mar 2017 17:34:44 -0400 Subject: [PATCH] Forgot to include the notebook --- docs/source/examples/search.ipynb | 238 ++++++++++++++++++++++++++++++ docs/source/examples/search.rst | 13 ++ 2 files changed, 251 insertions(+) create mode 100644 docs/source/examples/search.ipynb create mode 100644 docs/source/examples/search.rst diff --git a/docs/source/examples/search.ipynb b/docs/source/examples/search.ipynb new file mode 100644 index 0000000000..92c885edb3 --- /dev/null +++ b/docs/source/examples/search.ipynb @@ -0,0 +1,238 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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", + "\n", + "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", + "\n", + "This notebook will first create that function, and then, run the search.\n", + "\n", + "\n", + "# Create Parametrized Model" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "import openmc\n", + "import openmc.model\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To use the search functionality of `openmc.KeffSearch`, we require a function which creates an `openmc.model.Model` object. The first parameter of this function will be modified during the search process for our critical eigenvalue.\n", + "\n", + "Our model will be a pin-cell from the [Multi-Group Mode Part II](./mg-mode-part-ii.rst) assembly, except this time the entire model building process will be contained within a function, and the Boron concentration will be parametrized." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Create the model. `ppm_Boron` will be the parametric variable.\n", + "\n", + "def build_model(ppm_Boron):\n", + " # Create the pin materials\n", + " fuel = openmc.Material(name='1.6% Fuel')\n", + " fuel.set_density('g/cm3', 10.31341)\n", + " fuel.add_element('U', 1., enrichment=1.6)\n", + " fuel.add_element('O', 2.)\n", + "\n", + " zircaloy = openmc.Material(name='Zircaloy')\n", + " zircaloy.set_density('g/cm3', 6.55)\n", + " zircaloy.add_element('Zr', 1.)\n", + "\n", + " water = openmc.Material(name='Borated Water')\n", + " water.set_density('g/cm3', 0.741)\n", + " water.add_element('H', 2.)\n", + " water.add_element('O', 1.)\n", + "\n", + " # Include the amount of boron in the water based on the ppm,\n", + " # neglecting the other constituents of boric acid\n", + " water.add_element('B', ppm_Boron * 1E-6)\n", + " \n", + " # Instantiate a Materials object\n", + " materials = openmc.Materials((fuel, zircaloy, water))\n", + " \n", + " # Create cylinders for the fuel and clad\n", + " fuel_outer_radius = openmc.ZCylinder(R=0.39218)\n", + " clad_outer_radius = openmc.ZCylinder(R=0.45720)\n", + "\n", + " # Create boundary planes to surround the geometry\n", + " min_x = openmc.XPlane(x0=-0.63, boundary_type='reflective')\n", + " 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", + "\n", + " # Create fuel Cell\n", + " fuel_cell = openmc.Cell(name='1.6% Fuel')\n", + " fuel_cell.fill = fuel\n", + " fuel_cell.region = -fuel_outer_radius\n", + "\n", + " # Create a clad Cell\n", + " clad_cell = openmc.Cell(name='1.6% Clad')\n", + " clad_cell.fill = zircaloy\n", + " clad_cell.region = +fuel_outer_radius & -clad_outer_radius\n", + "\n", + " # Create a moderator Cell\n", + " moderator_cell = openmc.Cell(name='1.6% Moderator')\n", + " moderator_cell.fill = water\n", + " moderator_cell.region = +clad_outer_radius & (+min_x & -max_x & +min_y & -max_y)\n", + "\n", + " # Create root Universe\n", + " root_universe = openmc.Universe(name='root universe', universe_id=0)\n", + " root_universe.add_cells([fuel_cell, clad_cell, moderator_cell])\n", + "\n", + " # Create Geometry and set root universe\n", + " geometry = openmc.Geometry(root_universe)\n", + " \n", + " # Finish with the settings file\n", + " settings = openmc.Settings()\n", + " settings.batches = 300\n", + " settings.inactive = 20\n", + " settings.particles = 1000\n", + " settings.run_mode = 'eigenvalue'\n", + "\n", + " # Create an initial uniform spatial source distribution over fissionable zones\n", + " bounds = [-0.63, -0.63, -10, 0.63, 0.63, 10.]\n", + " uniform_dist = openmc.stats.Box(bounds[:3], bounds[3:], only_fissionable=True)\n", + " settings.source = openmc.source.Source(space=uniform_dist)\n", + "\n", + " # We dont need a tallies file so dont waste the disk input/output time\n", + " settings.output = {'tallies': False}\n", + " \n", + " model = openmc.model.Model(geometry, materials, settings)\n", + " \n", + " return model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Search for the Critical Boron Concentration\n", + "\n", + "To perform the search we will initialize the `openmc.KeffSearch` object by passing it the model building function (`build_model`) and a bracketed range for the expected critical Boron concentration (1,000 to 2,500 ppm). We could also 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, a bisection method will be used for the search.\n", + "\n", + "We will also set the `print_iterations` attribute of `openmc.KeffSearch` to `True` so we can display the iteration progress." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration: 0; Guess of 1.00E+03 produced a keff of 1.08721 +/- 0.00158\n", + "Iteration: 1; Guess of 2.50E+03 produced a keff of 0.95263 +/- 0.00147\n", + "Iteration: 2; Guess of 1.75E+03 produced a keff of 1.01466 +/- 0.00163\n", + "Iteration: 3; Guess of 2.12E+03 produced a keff of 0.98475 +/- 0.00167\n", + "Iteration: 4; Guess of 1.94E+03 produced a keff of 0.99954 +/- 0.00154\n", + "Iteration: 5; Guess of 1.84E+03 produced a keff of 1.00428 +/- 0.00162\n", + "Iteration: 6; Guess of 1.89E+03 produced a keff of 1.00633 +/- 0.00166\n", + "Iteration: 7; Guess of 1.91E+03 produced a keff of 1.00388 +/- 0.00166\n", + "Iteration: 8; Guess of 1.93E+03 produced a keff of 0.99813 +/- 0.00142\n", + "Critical Boron Concentration: 1926 ppm\n" + ] + } + ], + "source": [ + "# Initialize our searching object\n", + "searcher = openmc.KeffSearch(build_model, bracket=[1000., 2500.])\n", + "# Perform the search with a tolerance that is larger in magnitude to the eigenvalue uncertainty we expect\n", + "searcher.print_iterations = True\n", + "crit_ppm = searcher.search(tol=1.E-2, bracketed_method='bisect')\n", + "\n", + "print('Critical Boron Concentration: {:4.0f} ppm'.format(crit_ppm))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, the `openmc.KeffSearch` object was storing our critical boron concentration guesses and the corresponding eigenvalue from OpenMC. Let's use that information to make a quick plot of the value of keff versus the boron concentration." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ZmfUbSfMjoqOn5XwHPTMzs5JzsjczMys5J3szM7OSG9rsAMzMzMrutgXLmT5n\nCSvWrGdUextTJx7E5MOr7zNXHCd7MzOzAt22YDnTZi9i/YZNACxfs55psxcB9FvCdze+mZlZgabP\nWbI50Ves37CJ6XOW9FsMTvZmZmYFWrFm/TaVF8HJ3szMrECj2tu2qbwITvZmZmYFmjrxINqGbfng\n1rZhQ5g68aB+i8ED9MzMzApUGYTn0fhmZmYlNvnw0f2a3Ku5G9/MzKzknOzNzMxKzsnezMys5Jzs\nzczMSs7J3szMrOSc7M3MzErOyd7MzKzknOzNzMxKrtBkL2mSpCWSlkq6qEb9fpLukbRQ0lxJY6rq\nh0taLunqIuM0MzMrs8KSvaQhwDXAycA44ExJ46oWuwKYFRGHApcCl1XVfxG4r6gYzczMBoMiz+yP\nApZGxNMR8SfgJuDUqmXGAfek6Xvz9ZLeBuwF3FVgjGZmZqVXZLIfDSzLzXelsrxHgNPT9HuBXSXt\nKWkH4KvA1ALjMzMzGxSKTPaqURZV8xcCJ0haAJwALAc2Ah8H7oiIZXRD0hRJnZI6V69e3Rcxm5mZ\nlU6RT73rAvbJzY8BVuQXiIgVwGkAknYBTo+ItZKOBY6T9HFgF2BHSesi4qKq9WcAMwA6Ojqqv0iY\nmZkZxSb7B4EDJO1Pdsb+QeBD+QUkjQBejIhXgGnATICIOCu3zLlAR3WiNzMzs8YU1o0fERuBC4A5\nwOPAzRGxWNKlkt6TFpsALJH0BNlgvC8VFY+ZmdlgpYhy9H53dHREZ2dns8MwMzPrN5LmR0RHT8v5\nDnpmZmYl52RvZmZWck72ZmZmJedkb2ZmVnJO9mZmZiXnZG9mZlZypfnpnaTVwK/6eLMjgOf7eJsD\ngdvVWtyu1uJ2tZ5Wbtt+ETGyp4VKk+yLIKmzkd8vthq3q7W4Xa3F7Wo9ZW5bhbvxzczMSs7J3szM\nrOSc7Ls3o9kBFMTtai1uV2txu1pPmdsG+Jq9mZlZ6fnM3szMrOQGVbKXNFPSKkmP5sr2kHS3pCfT\nv7unckm6StJSSQslHZFb55y0/JOSzmlGW/LqtGu6pP9Osd8qqT1XNy21a4mkibnySalsqaSL+rsd\ntdRqW67uQkkhaUSab+ljlso/kY7BYkmX58pb4pjV+VscL+l+SQ9L6pR0VCpvieMlaR9J90p6PB2X\n/53Ky/DZUa9tLf35Ua9dufqW/ezotYgYNC/geOAI4NFc2eXARWn6IuArafoU4E5AwDHAA6l8D+Dp\n9O/uaXqpn5qZAAAItElEQVT3Adiuk4ChaforuXaNAx4BXgPsDzwFDEmvp4A3ADumZcYNxGOWyvcB\n5pDdW2FESY7ZO4EfA69J869rtWNWp113ASfnjtHcVjpewN7AEWl6V+CJdEzK8NlRr20t/flRr11p\nvqU/O3r7GlRn9hExD3ixqvhU4IY0fQMwOVc+KzL3A+2S9gYmAndHxIsR8VvgbmBS8dHXV6tdEXFX\nRGxMs/cDY9L0qcBNEfFyRDwDLAWOSq+lEfF0RPwJuCkt21R1jhnA14C/BfKDTlr6mAF/A/xTRLyc\nllmVylvmmNVpVwDD0/RuwIo03RLHKyJWRsRDafr3wOPAaMrx2VGzba3++dHNMYMW/+zorUGV7OvY\nKyJWQvYHArwulY8GluWW60pl9coHsg+TfWuFErRL0nuA5RHxSFVVq7ftQOA4SQ9Iuk/Skam81dv1\nKWC6pGXAFcC0VN5y7ZI0FjgceICSfXZUtS2vpT8/8u0q8WdHj4Y2O4ABTDXKopvyAUnSxcBG4NuV\nohqLBbW/+A24dkl6LXAxWTfjVtU1ylrpmA0l6yo8BjgSuFnSG2jxY0bWY/HpiPiepA8A3wDeTYsd\nL0m7AN8DPhURv5NqhZktWqNswLYLtm5brrylPz/y7SJrR1k/O3rkM3t4LnXXkP6tdJ12kV3bqRhD\n1v1Yr3zASYNJ/hw4K9IFKFq/XW8ku1b4iKRnyeJ8SNLraf22dQGzU1fiL4FXyO7Z3ertOgeYnaa/\nS9blCy3ULknDyJLGtyOi0pZSfHbUaVvLf37UaFeZPzt61uxBA/39Asay5eCh6Ww5yObyNP1nbDlg\n45fx6oCNZ8jOwHZP03sMwHZNAh4DRlYtdzBbDrB5mmxwzdA0vT+vDrA5uNntqtW2qrpneXWQTasf\ns48Bl6bpA8m6D9Vqx6xGux4HJqTpdwHzW+l4pfhmAVdWlbf8Z0c3bWvpz4967apapmU/O3r1njQ7\ngH7+A7gRWAlsIPvG9hFgT+Ae4Mn07x65P5ZryEaYLgI6ctv5MNnAlKXAeQO0XUvJksXD6XVtbvmL\nU7uWkEZJp/JTyEatPgVc3Ox21WtbVX3+P2yrH7MdgW8BjwIPASe22jGr0653APNTAngAeFsrHa8U\nfwALc/+fTinJZ0e9trX050e9dlUt05KfHb19+Q56ZmZmJedr9mZmZiXnZG9mZlZyTvZmZmYl52Rv\nZmZWck72ZmZmJedkb9ZLkjalJ7k9IukhSW9vQgxnS3o0PdnrMUkX9ncMVfGMl3RKL9YbK+lDufkO\nSVf1UUyV4zSqL7bXzX6+LelFSe8rcj9mveFkb9Z76yNifEQcRna/98saXVHSkO3duaSTyW4DelJE\nHEz2tLm127vd7TSe7PfWW5HU3e25xwKbk31EdEbEJ/sopspxKvTOZxFxFnB7kfsw6y0ne7O+MRz4\nLWx+Nvb0dMa9SNIZqXxCesb2f5LduANJn0nLPSrpU6lsbHoO93XpjP0uSW019jkNuLCSxCLijxFx\nXdpG5RnyleeRV561PlfSVyT9UtITko5L5UMkXZHiXSjpE6n8bemhPPMlzcndHnar7UjaEbgUOCOd\nSZ8h6QuSZki6C5iV2vbT1BOS7w35J7KHAD0s6dPpvfpB2tcekm5Lcd0v6dBU/gVJM1MsT0tq6MuB\npHWSvpr2f4+kkbk2XSnp5+l4HJXbzw3pODwr6TRJl6f36kfptqxmA1uz7+rjl1+t+gI2kd2Z67/J\nzqgrd4Y7nexRmEOAvYBfkz1fewLwB2D/tNzbyJL+zsAuwGKyp3ONJXtox/i03M3AX9bY/4vAbnVi\nWwickKYvJd02FJgLfDVNnwL8OE3/Ddl9xCvPMN8DGAb8nHTLVOAMYGYP2zkXuDoXxxfI7p7XluZf\nC+yUpg8AOtP0BOAHufU2zwP/AlySpk8EHs5t++dkt24dAbwADKvxXqyrmg+y+70DfL4Sb2rTdWn6\neNItf9N+/iu9H4cBL5HuHAfcCkzObft64H3N/tv0y6/ql596Z9Z76yNiPICkY8nOXN9KdqvOGyNi\nE9nDUu4je4rd78juuf1MWv8dwK0R8Ye0jdnAcWRdwc9ExMNpuflkXwAaImk3oD0i7ktFN5A9gKai\n8rCT/HbfTXZL1I0AEfFiastbgbuVPeFtCNmtcLvbTi23R8T6ND0MuFrSeLIvSwc20KR3kH2BIiJ+\nImnP1EaAH0bEy8DLklaRfbnq6mF7rwDfSdPfyrUDstv9EhHzJA2X1J7K74yIDZIWkb0PP0rli9iG\nY2PWLE72Zn0gIn4haQQwktqPxaz4Q266u+Vezk1vAmp14y8m6x34SaNxVm17E69+BoitH90pYHFE\nHLsN26kl3+ZPA8+RnSHvAPyxgXi7e8xo9fvUm8+0qDO91X4i4hVJGyKiUv5KL/dp1q98zd6sD0h6\nM9kZ3wvAPLLr1kPS9eDjgV/WWG0eMFnSayXtDLwX+Ok27PYy4HJlj+hE0mskfTIi1gK/rVyPB/4X\ncF+9jSR3AR+rDKKTtAfZg05Gpl4LJA2TdHAP2/k9sGs39bsBKyPilRRXZaBid+vNA85KMUwAno/c\nM9d7YQegMmL+Q2Rd9BWV8RXvANam99Ks5fkbqVnvtUmqdLULOCciNkm6FTiW7ClvAfxtRPwmfSHY\nLCIeknQ9r34R+PeIWCBpbCM7j4g7JO0F/FhZP3sAM1P1OcC1kl5L9ujR83rY3L+TdakvlLSB7Nr1\n1cp+RnZV6jYfClxJ1qNQz73ARel9qfXrhH8Fvifp/WnZyln/QmCjpEfIrnsvyK3zBeCbkhaSXS8/\np4e29OQPwMGS5pONtTgjV/dbST8nG3D54e3cj9mA4afemVmpSVoXEbvUm8+VzyX7dUPnduzrerKB\nhbf0dhtmRXA3vpmV3e/UTzfVAU6gsXEIZv3KZ/ZmZmYl5zN7MzOzknOyNzMzKzknezMzs5Jzsjcz\nMys5J3szM7OSc7I3MzMruf8PsJgBT1rI6FgAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 4.5))\n", + "plt.title('Eigenvalue versus Boron Concentration')\n", + "plt.scatter(searcher.guesses, searcher.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": "3.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/source/examples/search.rst b/docs/source/examples/search.rst new file mode 100644 index 0000000000..9bb75b5830 --- /dev/null +++ b/docs/source/examples/search.rst @@ -0,0 +1,13 @@ +.. _notebook_search: + +================== +Criticality Search +================== + +.. only:: html + + .. notebook:: search.ipynb + +.. only:: latex + + IPython notebooks must be viewed in the online HTML documentation.