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Update depletion-related documentation
This commit is contained in:
Paul Romano
parent
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commit
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3 changed files with 67 additions and 122 deletions
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@ -33,12 +33,11 @@ material compositions over time. Each method appears as a different class.
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For example, :class:`openmc.deplete.CECMIntegrator` runs a depletion calculation
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using the CE/CM algorithm (deplete over a timestep using the middle-of-step
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reaction rates). An instance of :class:`openmc.deplete.Operator` is passed to
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one of these functions along with the power level and timesteps::
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one of these functions along with the timesteps and power level::
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power = 1200.0e6
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days = 24*60*60
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timesteps = [10.0*days, 10.0*days, 10.0*days]
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openmc.deplete.CECMIntegrator(op, power, timesteps).integrate()
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power = 1200.0e6 # watts
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timesteps = [10.0, 10.0, 10.0] # days
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openmc.deplete.CECMIntegrator(op, timesteps, power, timestep_units='d').integrate()
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The coupled transport-depletion problem is executed, and once it is done a
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``depletion_results.h5`` file is written. The results can be analyzed using the
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@ -67,7 +66,7 @@ the energy deposited during a transport calculation will be lower than expected.
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This causes the reaction rates to be over-adjusted to hit the user-specific power,
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or power density, leading to an over-depletion of burnable materials.
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There are some remedies. First, the fission Q values can be directly set in a
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There are some remedies. First, the fission Q values can be directly set in a
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variety of ways. This requires knowing what the total fission energy release should
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be, including indirect components. Some examples are provided below::
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@ -99,11 +98,11 @@ Local Spectra and Repeated Materials
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------------------------------------
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It is not uncommon to explicitly create a single burnable material across many locations.
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From a pure transport perspective, there is nothing wrong with creating a single
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From a pure transport perspective, there is nothing wrong with creating a single
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3.5 wt.% enriched fuel ``fuel_3``, and placing that fuel in every fuel pin in an assembly
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or even full core problem. This certainly expedites the model making process, but can pose
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issues with depletion.
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Under this setup, :mod:`openmc.deplete` will deplete a single ``fuel_3`` material using
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issues with depletion.
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Under this setup, :mod:`openmc.deplete` will deplete a single ``fuel_3`` material using
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a single set of reaction rates, and produce a single new composition for the next time
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step. This can be problematic if the same ``fuel_3`` is used in very different regions
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of the problem.
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@ -1,25 +1,7 @@
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import openmc
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import openmc.deplete
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import numpy as np
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import matplotlib.pyplot as plt
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###############################################################################
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# Simulation Input File Parameters
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###############################################################################
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# OpenMC simulation parameters
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batches = 100
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inactive = 10
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particles = 1000
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# Depletion simulation parameters
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time_step = 1*24*60*60 # s
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final_time = 5*24*60*60 # s
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time_steps = np.full(final_time // time_step, time_step)
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chain_file = './chain_simple.xml'
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power = 174 # W/cm, for 2D simulations only (use W for 3D)
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###############################################################################
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# Load previous simulation results
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###############################################################################
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@ -37,31 +19,34 @@ previous_results = openmc.deplete.ResultsList("depletion_results.h5")
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###############################################################################
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# Instantiate a Settings object, set all runtime parameters
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settings_file = openmc.Settings()
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settings_file.batches = batches
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settings_file.inactive = inactive
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settings_file.particles = particles
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settings = openmc.Settings()
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settings.batches = 100
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settings.inactive = 10
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settings.particles = 10000
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# Create an initial uniform spatial source distribution over fissionable zones
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bounds = [-0.62992, -0.62992, -1, 0.62992, 0.62992, 1]
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uniform_dist = openmc.stats.Box(bounds[:3], bounds[3:], only_fissionable=True)
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settings_file.source = openmc.source.Source(space=uniform_dist)
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settings.source = openmc.source.Source(space=uniform_dist)
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entropy_mesh = openmc.RegularMesh()
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entropy_mesh.lower_left = [-0.39218, -0.39218, -1.e50]
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entropy_mesh.upper_right = [0.39218, 0.39218, 1.e50]
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entropy_mesh.dimension = [10, 10, 1]
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settings_file.entropy_mesh = entropy_mesh
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settings.entropy_mesh = entropy_mesh
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###############################################################################
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# Initialize and run depletion calculation
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###############################################################################
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op = openmc.deplete.Operator(geometry, settings_file, chain_file,
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previous_results)
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# Create depletion "operator"
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chain_file = './chain_simple.xml'
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op = openmc.deplete.Operator(geometry, settings, chain_file, previous_results)
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# Perform simulation using the predictor algorithm
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integrator = openmc.deplete.PredictorIntegrator(op, time_steps, power)
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time_steps = [1.0, 1.0, 1.0, 1.0, 1.0] # days
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power = 174 # W/cm, for 2D simulations only (use W for 3D)
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integrator = openmc.deplete.PredictorIntegrator(op, time_steps, power, timestep_units='d')
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integrator.integrate()
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###############################################################################
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@ -77,27 +62,28 @@ time, keff = results.get_eigenvalue()
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# Obtain U235 concentration as a function of time
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time, n_U235 = results.get_atoms('1', 'U235')
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# Obtain Xe135 absorption as a function of time
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time, Xe_gam = results.get_reaction_rate('1', 'Xe135', '(n,gamma)')
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# Obtain Xe135 capture reaction rate as a function of time
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time, Xe_capture = results.get_reaction_rate('1', 'Xe135', '(n,gamma)')
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###############################################################################
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# Generate plots
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###############################################################################
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days = 24*60*60
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plt.figure()
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plt.plot(time/(24*60*60), keff, label="K-effective")
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plt.plot(time/days, keff, label="K-effective")
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plt.xlabel("Time (days)")
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plt.ylabel("Keff")
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plt.show()
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plt.figure()
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plt.plot(time/(24*60*60), n_U235, label="U 235")
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plt.plot(time/days, n_U235, label="U 235")
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plt.xlabel("Time (days)")
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plt.ylabel("n U5 (-)")
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plt.show()
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plt.figure()
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plt.plot(time/(24*60*60), Xe_gam, label="Xe135 absorption")
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plt.plot(time/days, Xe_capture, label="Xe135 capture")
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plt.xlabel("Time (days)")
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plt.ylabel("RR (-)")
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plt.show()
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@ -1,47 +1,31 @@
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from math import pi
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import openmc
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import openmc.deplete
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import numpy as np
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import matplotlib.pyplot as plt
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###############################################################################
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# Simulation Input File Parameters
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###############################################################################
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# OpenMC simulation parameters
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batches = 100
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inactive = 10
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particles = 1000
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# Depletion simulation parameters
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time_step = 1*24*60*60 # s
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final_time = 5*24*60*60 # s
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time_steps = np.full(final_time // time_step, time_step)
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chain_file = './chain_simple.xml'
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power = 174 # W/cm, for 2D simulations only (use W for 3D)
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###############################################################################
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# Define materials
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###############################################################################
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# Instantiate some Materials and register the appropriate Nuclides
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uo2 = openmc.Material(material_id=1, name='UO2 fuel at 2.4% wt enrichment')
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uo2 = openmc.Material(name='UO2 fuel at 2.4% wt enrichment')
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uo2.set_density('g/cm3', 10.29769)
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uo2.add_element('U', 1., enrichment=2.4)
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uo2.add_element('O', 2.)
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uo2.depletable = True
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helium = openmc.Material(material_id=2, name='Helium for gap')
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helium = openmc.Material(name='Helium for gap')
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helium.set_density('g/cm3', 0.001598)
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helium.add_element('He', 2.4044e-4)
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zircaloy = openmc.Material(material_id=3, name='Zircaloy 4')
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zircaloy = openmc.Material(name='Zircaloy 4')
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zircaloy.set_density('g/cm3', 6.55)
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zircaloy.add_element('Sn', 0.014 , 'wo')
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zircaloy.add_element('Sn', 0.014, 'wo')
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zircaloy.add_element('Fe', 0.00165, 'wo')
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zircaloy.add_element('Cr', 0.001 , 'wo')
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zircaloy.add_element('Cr', 0.001, 'wo')
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zircaloy.add_element('Zr', 0.98335, 'wo')
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borated_water = openmc.Material(material_id=4, name='Borated water')
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borated_water = openmc.Material(name='Borated water')
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borated_water.set_density('g/cm3', 0.740582)
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borated_water.add_element('B', 4.0e-5)
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borated_water.add_element('H', 5.0e-2)
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@ -52,87 +36,62 @@ borated_water.add_s_alpha_beta('c_H_in_H2O')
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# Create geometry
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###############################################################################
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# Instantiate ZCylinder surfaces
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fuel_or = openmc.ZCylinder(surface_id=1, x0=0, y0=0, r=0.39218, name='Fuel OR')
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clad_ir = openmc.ZCylinder(surface_id=2, x0=0, y0=0, r=0.40005, name='Clad IR')
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clad_or = openmc.ZCylinder(surface_id=3, x0=0, y0=0, r=0.45720, name='Clad OR')
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left = openmc.XPlane(surface_id=4, x0=-0.62992, name='left')
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right = openmc.XPlane(surface_id=5, x0=0.62992, name='right')
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bottom = openmc.YPlane(surface_id=6, y0=-0.62992, name='bottom')
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top = openmc.YPlane(surface_id=7, y0=0.62992, name='top')
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# Define surfaces
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pitch = 1.25984
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fuel_or = openmc.ZCylinder(r=0.39218, name='Fuel OR')
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clad_ir = openmc.ZCylinder(r=0.40005, name='Clad IR')
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clad_or = openmc.ZCylinder(r=0.45720, name='Clad OR')
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box = openmc.model.rectangular_prism(pitch, pitch, boundary_type='reflective')
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left.boundary_type = 'reflective'
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right.boundary_type = 'reflective'
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top.boundary_type = 'reflective'
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bottom.boundary_type = 'reflective'
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# Define cells
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fuel = openmc.Cell(fill=uo2, region=-fuel_or)
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gap = openmc.Cell(fill=helium, region=+fuel_or & -clad_ir)
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clad = openmc.Cell(fill=zircaloy, region=+clad_ir & -clad_or)
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water = openmc.Cell(fill=borated_water, region=+clad_or & box)
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# Instantiate Cells
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fuel = openmc.Cell(cell_id=1, name='cell 1')
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gap = openmc.Cell(cell_id=2, name='cell 2')
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clad = openmc.Cell(cell_id=3, name='cell 3')
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water = openmc.Cell(cell_id=4, name='cell 4')
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# Use surface half-spaces to define regions
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fuel.region = -fuel_or
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gap.region = +fuel_or & -clad_ir
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clad.region = +clad_ir & -clad_or
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water.region = +clad_or & +left & -right & +bottom & -top
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# Register Materials with Cells
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fuel.fill = uo2
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gap.fill = helium
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clad.fill = zircaloy
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water.fill = borated_water
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# Instantiate Universe
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root = openmc.Universe(universe_id=0, name='root universe')
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# Register Cells with Universe
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root.add_cells([fuel, gap, clad, water])
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# Instantiate a Geometry, register the root Universe
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geometry = openmc.Geometry(root)
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# Define overall geometry
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geometry = openmc.Geometry([fuel, gap, clad, water])
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###############################################################################
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# Set volumes of depletable materials
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###############################################################################
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# Compute cell areas
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area = {}
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area[fuel] = np.pi * fuel_or.coefficients['r'] ** 2
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# Set materials volume for depletion. Set to an area for 2D simulations
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uo2.volume = area[fuel]
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# Set material volume for depletion. For 2D simulations, this should be an area.
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uo2.volume = pi * fuel_or.r**2
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###############################################################################
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# Transport calculation settings
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###############################################################################
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# Instantiate a Settings object, set all runtime parameters, and export to XML
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settings_file = openmc.Settings()
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settings_file.batches = batches
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settings_file.inactive = inactive
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settings_file.particles = particles
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settings = openmc.Settings()
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settings.batches = 100
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settings.inactive = 10
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settings.particles = 1000
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# Create an initial uniform spatial source distribution over fissionable zones
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bounds = [-0.62992, -0.62992, -1, 0.62992, 0.62992, 1]
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uniform_dist = openmc.stats.Box(bounds[:3], bounds[3:], only_fissionable=True)
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settings_file.source = openmc.source.Source(space=uniform_dist)
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settings.source = openmc.source.Source(space=uniform_dist)
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entropy_mesh = openmc.RegularMesh()
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entropy_mesh.lower_left = [-0.39218, -0.39218, -1.e50]
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entropy_mesh.upper_right = [0.39218, 0.39218, 1.e50]
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entropy_mesh.dimension = [10, 10, 1]
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settings_file.entropy_mesh = entropy_mesh
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settings.entropy_mesh = entropy_mesh
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###############################################################################
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# Initialize and run depletion calculation
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###############################################################################
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op = openmc.deplete.Operator(geometry, settings_file, chain_file)
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# Create depletion "operator"
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chain_file = './chain_simple.xml'
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op = openmc.deplete.Operator(geometry, settings, chain_file)
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# Perform simulation using the predictor algorithm
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integrator = openmc.deplete.PredictorIntegrator(op, time_steps, power)
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time_steps = [1.0, 1.0, 1.0, 1.0, 1.0] # days
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power = 174 # W/cm, for 2D simulations only (use W for 3D)
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integrator = openmc.deplete.PredictorIntegrator(op, time_steps, power, timestep_units='d')
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integrator.integrate()
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###############################################################################
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@ -148,27 +107,28 @@ time, keff = results.get_eigenvalue()
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# Obtain U235 concentration as a function of time
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time, n_U235 = results.get_atoms('1', 'U235')
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# Obtain Xe135 absorption as a function of time
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time, Xe_gam = results.get_reaction_rate('1', 'Xe135', '(n,gamma)')
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# Obtain Xe135 capture reaction rate as a function of time
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time, Xe_capture = results.get_reaction_rate('1', 'Xe135', '(n,gamma)')
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###############################################################################
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# Generate plots
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###############################################################################
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days = 24*60*60
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plt.figure()
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plt.plot(time/(24*60*60), keff, label="K-effective")
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plt.plot(time/days, keff, label="K-effective")
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plt.xlabel("Time (days)")
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plt.ylabel("Keff")
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plt.show()
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plt.figure()
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plt.plot(time/(24*60*60), n_U235, label="U 235")
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plt.plot(time/days, n_U235, label="U235")
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plt.xlabel("Time (days)")
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plt.ylabel("n U5 (-)")
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plt.show()
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plt.figure()
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plt.plot(time/(24*60*60), Xe_gam, label="Xe135 absorption")
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plt.plot(time/days, Xe_capture, label="Xe135 capture")
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plt.xlabel("Time (days)")
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plt.ylabel("RR (-)")
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plt.show()
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