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Fix error in equation in depletion user docs

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Paul Romano 2022-08-16 16:38:21 -05:00
parent d31b083685
commit 282c8115df
1 changed files with 13 additions and 13 deletions
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docs/source/usersguide/depletion.rst
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@ -14,7 +14,7 @@ are requested.
The depletion module is designed such that the reaction rate solution (the
transport "operator") is completely isolated from the solution of the
transmutation equations and the method used for advancing time.
transmutation equations and the method used for advancing time.
:mod:`openmc.deplete` supports multiple time-integration methods for determining
material compositions over time. Each method appears as a different class.
@ -40,7 +40,7 @@ time::
Note that the coupling between the reaction rate solver and the transmutation
solver happens in-memory rather than by reading/writing files on disk. OpenMC
has two categories of transport operators for obtaining transmutation reaction
rates.
rates.
.. _coupled-depletion:
@ -65,7 +65,7 @@ Any material that contains a fissionable nuclide is depleted by default, but
this can behavior can be changed with the :attr:`Material.depletable` attribute.
.. important::
The volume must be specified for each material that is depleted by setting
the :attr:`Material.volume` attribute. This is necessary in order to
calculate the proper normalization of tally results based on the source rate.
@ -198,8 +198,8 @@ Transport-independent depletion
===============================
.. warning::
This feature is still under heavy development and has yet to be rigorously
This feature is still under heavy development and has yet to be rigorously
verified. API changes and feature additions are possible and likely in
the near future.
@ -237,7 +237,7 @@ object::
'U236': 4.57e18,
'O16': 4.64e22,
'O17': 1.76e19}
volume = 0.5
volume = 0.5
op = openmc.deplete.IndependentOperator.from_nuclides(volume,
nuclides,
micro_xs,
@ -250,8 +250,8 @@ transport-depletion calculation and follow the same steps from there.
.. note::
Ideally, one-group cross section data should be available for every
reaction in the depletion chain. If a nuclide that has a reaction
associated with it in the depletion chain is present in the `nuclides`
reaction in the depletion chain. If a nuclide that has a reaction
associated with it in the depletion chain is present in the `nuclides`
parameter but not the cross section data, that reaction will not be
simulated.
@ -289,7 +289,7 @@ or from data arrays::
.. important::
Both :meth:`~openmc.deplete.MicroXS.from_csv()` and
:meth:`~openmc.deplete.MicroXS.from_array()` assume the cross section values
:meth:`~openmc.deplete.MicroXS.from_array()` assume the cross section values
provided are in barns by defualt, but have no way of verifying this. Make
sure your cross sections are in the correct units before passing to a
:class:`~openmc.deplete.IndependentOperator` object.
@ -315,11 +315,11 @@ normalizing reaction rates:
the cross-sections by the ``source-rate``.
2. ``fission-q`` normalization, which uses the ``power`` or ``power_density``
provided by the time integrator to obtain reaction rates by computing a value
for the flux based on this power. The general equation for the flux is
for the flux based on this power. The general equation for the flux is
.. math::
\phi = \frac{P}{V \cdot \sum_i (Q_i \cdot \sigma^f_i \cdot \n_i)}
\phi = \frac{P}{V \cdot \sum\limits_i (Q_i \cdot \sigma^f_i \cdot n_i)}
where :math:`\sum_i` is the sum over all nuclides :math:`i`. This equation
makes the same assumptions and issues as discussed in
@ -328,13 +328,13 @@ normalizing reaction rates:
However, there is a method to converge to a more accurate value for flux by
using substeps during time integration.
`This paper <https://doi.org/10.1016/j.anucene.2016.05.031>`_ provides a
good discussion of this method.
good discussion of this method.
.. warning::
The accuracy of results when using ``fission-q`` is entirely dependent on
your depletion chain. Make sure it has sufficient data to resolve the
dynamics of your particular scenario.
dynamics of your particular scenario.
Multiple Materials
~~~~~~~~~~~~~~~~~~