diff --git a/docs/source/methods/depletion.rst b/docs/source/methods/depletion.rst index edcf2c3f534..ecdfb9531c6 100644 --- a/docs/source/methods/depletion.rst +++ b/docs/source/methods/depletion.rst @@ -339,3 +339,56 @@ where: Note that mass conservation is guaranteed by transferring the number of atoms directly. + +--------------------- +External Source Rates +--------------------- + +OpenMC allows the addition of external source rates to the depletion matrix. +This is useful for modeling the feed or removal of fixed amounts of nuclides +to or from a depletable material. Rates are specified as a mass flow (default +units of [g/s]) and converted to [atom/s] source terms for the nuclides in the +composition vector. A positive rate corresponds to feed and a negative rate to +removal. + +Mathematically, this is represented as an external source term :math:`S_i` to +the depletion equation: + +.. math:: + + \frac{dN_i}{dt} = \sum_j A_{ij} N_j + S_i + +The resulting linear system is non-homogeneous but can be recast in homogeneous +form by augmenting the nuclide vector with a constant component equal to unity: + +.. math:: + + \frac{d}{dt}\begin{bmatrix}\mathbf{n}\\ 1\end{bmatrix} = + \begin{bmatrix} + \mathbf{A} & \mathbf{s}\\ + \mathbf{0} & 0 + \end{bmatrix} + \begin{bmatrix} + \mathbf{n}\\ + 1 + \end{bmatrix} + +where :math:`\mathbf{s}` is the vector of external source rates in [atom/s]. The +resulting system can be solved with the same integration algorithms that are +used in the absence of the external source term. + +External source rates with transfer rates coupling materials +------------------------------------------------------------ + +In the presence of external source rates and coupled transfer rates between +materials, the off-diagonal transfer blocks must match the dimensions of the +corresponding diagonal blocks. Using the transfer example above, if an external +source rate is applied to material 1 (the losing material), the coupling matrix +:math:`\mathbf{T_{21}}` is extended with an additional column of zeroes so that +its column count matches the augmented :math:`\mathbf{A_{11}}`. If the external +source is applied to material 2 (the receiving material), +:math:`\mathbf{T_{21}}` instead receives an additional row of zeroes so that its +row count matches the augmented :math:`\mathbf{A_{22}}`. + + + diff --git a/docs/source/usersguide/depletion.rst b/docs/source/usersguide/depletion.rst index 9a22adf0160..4e52fefde6a 100644 --- a/docs/source/usersguide/depletion.rst +++ b/docs/source/usersguide/depletion.rst @@ -450,6 +450,67 @@ to transfer xenon from one material to another, you'd use:: integrator.add_transfer_rate(mat1, ['Xe'], 0.1, destination_material=mat2) +External Source Rates +===================== + +External source rates define a fixed mass feed or removal of nuclides to or +from a depletable material. Unlike transfer rates, which are proportional to +the instantaneous nuclide inventory, external source rates add a constant +source term to the depletion equations. This can be useful to model batch +refueling, makeup fuel addition, or fixed-rate off-gas removal. + +External source rates are defined by calling the +:meth:`~openmc.deplete.abc.Integrator.add_external_source_rate()` method +directly from one of the Integrator classes:: + + ... + integrator = openmc.deplete.PredictorIntegrator(op, time_steps, power) + integrator.add_external_source_rate(...) + +Defining external source rates +------------------------------ + +The :meth:`~openmc.deplete.abc.Integrator.add_external_source_rate()` method +requires a :class:`~openmc.Material` instance (or a material ID or the name) as +the depletable material, a composition dictionary giving the relative weight +fractions of elements and/or nuclides in the feed or removal stream, and a mass +flow rate. + +.. caution:: + + Make sure you set the rate value with the right sign. A positive rate + corresponds to feed, while a negative rate corresponds to removal. This is + the opposite convention used for transfer rates. + +The ``rate_units`` argument specifies the units for the mass flow rate. The +default is ``g/s``, but ``g/min``, ``g/h``, ``g/d``, and ``g/a`` are also valid +options. + +For example, to feed U235 into a material at 10 g/day, you'd use:: + + mat = openmc.Material() + ... + + integrator = openmc.deplete.PredictorIntegrator(op, time_steps, power) + composition = {'U235': 1.0} + integrator.add_external_source_rate(mat1, composition, 10, rate_units='g/d') + +Composition keys may be nuclides (e.g., ``'U235'``) or naturally abundant +elements (e.g., ``'U'``). When an element is specified, the mass flow is +distributed across its naturally occurring isotopes according to their natural +abundances. + +The optional ``timesteps`` argument restricts the external source rate to +specific depletion step indices. If omitted, the rate is applied at every step. + +Combining with transfer rates +----------------------------- + +External source rates can be used together with transfer rates, including +transfers between materials via ``destination_material``. See +:ref:`methods_depletion` for the augmented-matrix formulation used when both +features are active. + Comparing to Other Codes ======================== diff --git a/openmc/deplete/abc.py b/openmc/deplete/abc.py index 66bd7148d33..3e70b5fa726 100644 --- a/openmc/deplete/abc.py +++ b/openmc/deplete/abc.py @@ -1028,11 +1028,6 @@ def add_transfer_rate( self.transfer_rates = TransferRates( self.operator, materials, len(self.timesteps)) - if self.external_source_rates is not None and destination_material: - raise ValueError('Currently is not possible to set a transfer rate ' - 'with destination matrial in combination with ' - 'external source rates.') - self.transfer_rates.set_transfer_rate( material, components, transfer_rate, transfer_rate_units, timesteps, destination_material) @@ -1074,11 +1069,6 @@ def add_external_source_rate( self.external_source_rates = ExternalSourceRates( self.operator, materials, len(self.timesteps)) - if self.transfer_rates is not None and self.transfer_rates.index_transfer: - raise ValueError('Currently is not possible to set an external ' - 'source rate in combination with transfer rates ' - 'with destination matrial.') - self.external_source_rates.set_external_source_rate( material, composition, rate, rate_units, timesteps) diff --git a/openmc/deplete/pool.py b/openmc/deplete/pool.py index 19ad0ada503..35d000ca36e 100644 --- a/openmc/deplete/pool.py +++ b/openmc/deplete/pool.py @@ -6,10 +6,10 @@ from multiprocessing import Pool import numpy as np -from scipy.sparse import hstack +from scipy.sparse import hstack, vstack from openmc.mpi import comm -from .._sparse_compat import block_array +from .._sparse_compat import block_array, csc_array # Configurable switch that enables / disables the use of # multiprocessing routines during depletion @@ -41,6 +41,29 @@ def _distribute(items): return items[j:j + chunk_size] j += chunk_size + +def _add_external_source( + matrices, n, chain, external_source_rates, current_timestep +): + """Augment depletion matrices and nuclide vectors with external sources.""" + sources = map(chain.form_ext_source_term, repeat(external_source_rates), + repeat(current_timestep), external_source_rates.local_mats) + matrices = [ + hstack([matrix, source]) + for matrix, source in zip(matrices, sources) + ] + n_solve = [arr.copy() for arr in n] + + # Homogenize the augmented matrices and nuclide vectors + for i, matrix in enumerate(matrices): + if matrix.shape[0] + 1 == matrix.shape[1]: + matrices[i] = vstack( + [matrix, csc_array((1, matrix.shape[1]))]) + n_solve[i] = np.append(n_solve[i], 1.0) + + return matrices, n_solve + + def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, transfer_rates=None, external_source_rates=None, substeps=1, *matrix_args): @@ -62,7 +85,7 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, Time in [s] to deplete for current_timestep : int Current timestep index - maxtrix_func : callable, optional + matrix_func : callable, optional Function to form the depletion matrix after calling ``matrix_func(chain, rates, fission_yields)``, where ``fission_yields = {parent: {product: yield_frac}}`` Expected to return the depletion matrix required by @@ -87,7 +110,6 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, list contains the number of [atom] of each nuclide. """ - fission_yields = chain.fission_yields if len(fission_yields) == 1: fission_yields = repeat(fission_yields[0]) @@ -103,8 +125,14 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, matrices = map(matrix_func, repeat(chain), rates, fission_yields, *matrix_args) - if (transfer_rates is not None and - current_timestep in transfer_rates.external_timesteps): + # Determine if transfer rates or external source rates are active + transfer_active = transfer_rates is not None and \ + current_timestep in transfer_rates.external_timesteps + external_active = external_source_rates is not None and \ + current_timestep in external_source_rates.external_timesteps + + n_solve = n + if transfer_active: # Calculate transfer rate terms as diagonal matrices transfers = map(chain.form_rr_term, repeat(transfer_rates), repeat(current_timestep), transfer_rates.local_mats) @@ -120,10 +148,16 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, transfer_rates.redox[mat_id][0], transfer_rates.redox[mat_id][1]) + # Add external sources if present + if external_active: + matrices, n_solve = _add_external_source( + matrices, n, chain, external_source_rates, current_timestep) + + # Set transfer rate terms with destination material if present if current_timestep in transfer_rates.index_transfer: # Gather all on comm.rank 0 matrices = comm.gather(matrices) - n = comm.gather(n) + n = comm.gather(n_solve) if comm.rank == 0: # Expand lists @@ -132,20 +166,27 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, # Calculate transfer rate terms as diagonal matrices transfer_pair = {} - for mat_pair in transfer_rates.index_transfer[current_timestep]: + for mat_pair in dict.fromkeys(transfer_rates.index_transfer[current_timestep]): transfer_matrix = chain.form_rr_term(transfer_rates, current_timestep, mat_pair) - # check if destination material has a redox control if mat_pair[0] in transfer_rates.redox: transfer_matrix = chain.add_redox_term(transfer_matrix, transfer_rates.redox[mat_pair[0]][0], transfer_rates.redox[mat_pair[0]][1]) + # Add external source rates if present + if external_active: + if len(external_source_rates.get_components(mat_pair[0], current_timestep)) > 0: + transfer_matrix = vstack([transfer_matrix, + csc_array((1, transfer_matrix.shape[1]))]) + if len(external_source_rates.get_components(mat_pair[1], current_timestep)) > 0: + transfer_matrix = hstack([transfer_matrix, + csc_array((transfer_matrix.shape[0], 1))]) transfer_pair[mat_pair] = transfer_matrix - # Combine all matrices together in a single matrix of matrices - # to be solved in one go + # Combine all matrices together in a single block matrix of matrices + # to be solved on one rank n_rows = n_cols = len(transfer_rates.burnable_mats) rows = [] for row in range(n_rows): @@ -171,37 +212,25 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, # Split back the nuclide vector result into the original form n_result = np.split(n_result, np.cumsum([len(i) for i in n])[:-1]) - else: n_result = None - # Braodcast result to other ranks + # Broadcast result to other MPI ranks and then distribute n_result = comm.bcast(n_result) - # Distribute results across MPI n_result = _distribute(n_result) - return n_result - - if (external_source_rates is not None and - current_timestep in external_source_rates.external_timesteps): - # Calculate external source term vectors - sources = map(chain.form_ext_source_term, repeat(external_source_rates), - repeat(current_timestep), external_source_rates.local_mats) + # Remove extra values based on the materials local to each rank + if external_active: + external_source_rates.reformat_nuclide_vectors(n_result) - # stack vector column at the end of the matrix - matrices = [ - hstack([matrix, source]) - for matrix, source in zip(matrices, sources) - ] + return n_result - # Add a last row of zeroes to the matrices and append 1 to the last row - # of the nuclide vectors - for i, matrix in enumerate(matrices): - if not np.equal(*matrix.shape): - matrix.resize(matrix.shape[1], matrix.shape[1]) - n[i] = np.append(n[i], 1.0) + # If only external source rates are present + elif external_active: + matrices, n_solve = _add_external_source( + matrices, n, chain, external_source_rates, current_timestep) - inputs = zip(matrices, n, repeat(dt), repeat(substeps)) + inputs = zip(matrices, n_solve, repeat(dt), repeat(substeps)) if USE_MULTIPROCESSING: with Pool(NUM_PROCESSES) as pool: @@ -209,10 +238,8 @@ def deplete(func, chain, n, rates, dt, current_timestep=None, matrix_func=None, else: n_result = list(starmap(func, inputs)) - # Remove extra value at the end of the nuclide vectors - if (external_source_rates is not None and - current_timestep in external_source_rates.external_timesteps): - external_source_rates.reformat_nuclide_vectors(n) + # Remove extra value at the end of the nuclide vectors if external source rates are present + if external_active: external_source_rates.reformat_nuclide_vectors(n_result) return n_result diff --git a/tests/regression_tests/deplete_with_transfer_rates/ref_depletion_with_ext_source_and_transfer.h5 b/tests/regression_tests/deplete_with_transfer_rates/ref_depletion_with_ext_source_and_transfer.h5 new file mode 100644 index 00000000000..d13d210139f Binary files /dev/null and b/tests/regression_tests/deplete_with_transfer_rates/ref_depletion_with_ext_source_and_transfer.h5 differ diff --git a/tests/regression_tests/deplete_with_transfer_rates/test.py b/tests/regression_tests/deplete_with_transfer_rates/test.py index 461287f6e6f..1597eb31bd7 100644 --- a/tests/regression_tests/deplete_with_transfer_rates/test.py +++ b/tests/regression_tests/deplete_with_transfer_rates/test.py @@ -126,3 +126,38 @@ def test_external_source_rates(run_in_tmpdir, model, rate, power, ref_result): assert_atoms_equal(res_ref, res_test, tol=1e-3) assert_reaction_rates_equal(res_ref, res_test, tol=1e-3) + +@pytest.mark.parametrize("external_source_rate, transfer_rate, power, ref_result", [ + (1e-1, 1e-1, 174., 'depletion_with_ext_source_and_transfer'), +]) +def test_external_source_rates_with_transfer_rates(run_in_tmpdir, model, external_source_rate, + transfer_rate, power, ref_result): + """Tests external_rates depletion class with external source rates and transfer rates""" + + chain_file = Path(__file__).parents[2] / 'chain_simple.xml' + + external_source_vector = {'U': 1} + + op = CoupledOperator(model, chain_file) + op.round_number = True + integrator = openmc.deplete.PredictorIntegrator( + op, [1], power, timestep_units='d') + integrator.add_external_source_rate('f', external_source_vector, external_source_rate) + integrator.add_transfer_rate('f', ['U235'], transfer_rate, destination_material='w') + integrator.integrate() + + # Get path to test and reference results + path_test = op.output_dir / 'depletion_results.h5' + path_reference = Path(__file__).with_name(f'ref_{ref_result}.h5') + + # If updating results, do so and return + if config['update']: + shutil.copyfile(str(path_test), str(path_reference)) + return + + # Load the reference/test results + res_ref = openmc.deplete.Results(path_reference) + res_test = openmc.deplete.Results(path_test) + + assert_atoms_equal(res_ref, res_test, tol=1e-3) + assert_reaction_rates_equal(res_ref, res_test, tol=1e-3) \ No newline at end of file