openmc.deplete.CECMIntegrator

class openmc.deplete.CECMIntegrator(operator: TransportOperator, timesteps: Sequence[float] | Sequence[tuple[float, str]], power: float | Sequence[float] | None = None, power_density: float | Sequence[float] | None = None, source_rates: float | Sequence[float] | None = None, timestep_units: str = 's', solver: str = 'cram48', continue_timesteps: bool = False)[source]

Deplete using the CE/CM algorithm.

Implements the second order CE/CM predictor-corrector algorithm.

“CE/CM” stands for constant extrapolation on predictor and constant midpoint on corrector. This algorithm is mathematically defined as:

\[\begin{aligned} \mathbf{n}_{i+1/2} &= \exp \left (\frac{h}{2}\mathbf{A}(\mathbf{n}_i) \right) \mathbf{n}_i \\ \mathbf{n}_{i+1} &= \exp \left(h \mathbf{A}(\mathbf{n}_{i+1/2}) \right) \mathbf{n}_i. \end{aligned} \]

Parameters:

operator (openmc.deplete.abc.TransportOperator) – Operator to perform transport simulations
timesteps (iterable of float or iterable of tuple) – Array of timesteps. Note that values are not cumulative. The units are specified by the timestep_units argument when timesteps is an iterable of float. Alternatively, units can be specified for each step by passing an iterable of (value, unit) tuples.
power (float or iterable of float, optional) – Power of the reactor in [W]. A single value indicates that the power is constant over all timesteps. An iterable indicates potentially different power levels for each timestep. For a 2D problem, the power can be given in [W/cm] as long as the “volume” assigned to a depletion material is actually an area in [cm^2]. Either power, power_density, or source_rates must be specified.
power_density (float or iterable of float, optional) – Power density of the reactor in [W/gHM]. It is multiplied by initial heavy metal inventory to get total power if power is not specified.
source_rates (float or iterable of float, optional) –
Source rate in [neutron/sec] or neutron flux in [neutron/s-cm^2] for each interval in timesteps

Added in version 0.12.1.
timestep_units ({'s', 'min', 'h', 'd', 'a', 'MWd/kg'}) – Units for values specified in the timesteps argument. ‘s’ means seconds, ‘min’ means minutes, ‘h’ means hours, ‘a’ means Julian years and ‘MWd/kg’ indicates that the values are given in burnup (MW-d of energy deposited per kilogram of initial heavy metal).
solver (str or callable, optional) –
If a string, must be the name of the solver responsible for solving the Bateman equations. Current options are:
- cram16 - 16th order IPF CRAM
- cram48 - 48th order IPF CRAM [default]
If a function or other callable, must adhere to the requirements in solver.

Added in version 0.12.
continue_timesteps (bool, optional) –
Whether or not to treat the current solve as a continuation of a previous simulation. Defaults to False. When False, the depletion steps provided are appended to any previous steps. If True, the timesteps provided to the Integrator must exacly match any that exist in the prev_results passed to the Operator. The power, power_density, or source_rates must match as well. The method of specifying power, power_density, or source_rates should be the same as the initial run.

Added in version 0.15.1.

Variables:

operator (openmc.deplete.abc.TransportOperator) – Operator to perform transport simulations
chain (openmc.deplete.Chain) – Depletion chain
timesteps (iterable of float) – Size of each depletion interval in [s]
source_rates (iterable of float) – Source rate in [W] or [neutron/sec] for each interval in timesteps
solver (callable) –
Function that will solve the Bateman equations \(\frac{\partial}{\partial t}\vec{n} = A_i\vec{n}_i\) with a step size \(t_i\). Can be configured using the solver argument. User-supplied functions are expected to have the following signature: solver(A, n0, t) -> n1 where
- A is a scipy.sparse.csc_matrix making up the depletion matrix
- n0 is a 1-D numpy.ndarray of initial compositions for a given material in atoms/cm3
- t is a float of the time step size in seconds, and
- n1 is a numpy.ndarray of compositions at the next time step. Expected to be of the same shape as n0
transfer_rates (openmc.deplete.TransferRates) –
Transfer rates for the depletion system used to model continuous removal/feed between materials.

Added in version 0.14.0.
external_source_rates (openmc.deplete.ExternalSourceRates) –
External source rates for the depletion system.

Added in version 0.15.3.

__call__(n, rates, dt, source_rate, _i=None)[source]

Integrate using CE/CM

Parameters:

n (list of numpy.ndarray) – List of atom number arrays for each material. Each array in the list contains the number of [atom] of each nuclide.
rates (openmc.deplete.ReactionRates) – Reaction rates from operator
dt (float) – Time in [s] for the entire depletion interval
source_rate (float) – Power in [W] or source rate in [neutron/sec]
_i (int, optional) – Current iteration count. Not used

Returns:

proc_time (float) – Time spent in CRAM routines for all materials in [s]
n_end (list of numpy.ndarray) – Concentrations at end of interval

__iter__(): Return pair of time step in [s] and source rate in [W] or [neutron/sec]

__len__(): Return integer number of depletion intervals

add_external_source_rate(material: str | int | Material, composition: dict[str, float], rate: float, rate_units: str = 'g/s', timesteps: Sequence[int] | None = None)

Add external source rates to depletable material.

Parameters:

material (openmc.Material or str or int) – Depletable material
composition (dict of str to float) – External source rate composition vector, where key can be an element or a nuclide and value the corresponding weight percent.
rate (float) – External source rate in units of mass per time. A positive or negative value corresponds to a feed or removal rate, respectively.
units ({'g/s', 'g/min', 'g/h', 'g/d', 'g/a'}) – Units for values specified in the rate argument. ‘s’ for seconds, ‘min’ for minutes, ‘h’ for hours, ‘a’ for Julian years.
timesteps (list of int, optional) – List of timestep indices where to set external source rates. Defaults to None, which means the external source rate is set for all timesteps.

add_redox(material, buffer, oxidation_states, timesteps=None)

Add redox control to depletable material.

Parameters:

material (openmc.Material or str or int) – Depletable material
buffer (dict) – Dictionary of buffer nuclides used to maintain redox balance. Keys are nuclide names (strings) and values are their respective fractions (float) that collectively sum to 1.
oxidation_states (dict) – User-defined oxidation states for elements. Keys are element symbols (e.g., ‘H’, ‘He’), and values are their corresponding oxidation states as integers (e.g., +1, 0).
timesteps (list of int, optional) – List of timestep indices where to set external source rates. Defaults to None, which means the external source rate is set for all timesteps.

Add transfer rates to depletable material.

Parameters:

material (openmc.Material or str or int) – Depletable material
components (list of str) – List of strings of elements and/or nuclides that share transfer rate. A transfer rate for a nuclide cannot be added to a material alongside a transfer rate for its element and vice versa.
transfer_rate (float) – Rate at which elements are transferred. A positive or negative values set removal of feed rates, respectively.
transfer_rate_units ({'1/s', '1/min', '1/h', '1/d', '1/a'}) – Units for values specified in the transfer_rate argument. ‘s’ means seconds, ‘min’ means minutes, ‘h’ means hours, ‘a’ means Julian years.
timesteps (list of int, optional) – List of timestep indices where to set external source rates. Defaults to None, which means the external source rate is set for all timesteps.
destination_material (openmc.Material or str or int, Optional) – Destination material to where nuclides get fed.

integrate(final_step: bool = True, output: bool = True, path: str | PathLike = 'depletion_results.h5', write_rates: bool = False)

Perform the entire depletion process across all steps

Parameters:

final_step (bool, optional) –
Indicate whether or not a transport solve should be run at the end of the last timestep.

Added in version 0.12.1.
output (bool, optional) –
Indicate whether to display information about progress

Added in version 0.13.1.
path (PathLike) –
Path to file to write. Defaults to ‘depletion_results.h5’.

Added in version 0.15.0.
write_rates (bool, optional) –
Whether reaction rates should be written to the results file for each step. Defaults to False to reduce file size.

Added in version 0.15.3.