diff --git a/doc/content/bib/tmap8.bib b/doc/content/bib/tmap8.bib index f3e8dd35..6201bc9d 100644 --- a/doc/content/bib/tmap8.bib +++ b/doc/content/bib/tmap8.bib @@ -287,3 +287,14 @@ @article{li2010analytical year={2010}, publisher={American Society of Civil Engineers} } + +@article{meschini2023modeling, + title={Modeling and analysis of the tritium fuel cycle for ARC-and STEP-class DT fusion power plants}, + author={Meschini, Samuele and Ferry, Sara E and Delaporte-Mathurin, R{\'e}mi and Whyte, Dennis G}, + journal={Nuclear Fusion}, + volume={63}, + number={12}, + pages={126005}, + year={2023}, + publisher={IOP Publishing} +} diff --git a/doc/content/verification_and_validation/figures/comparison_fuel_cycle_benchmark.py b/doc/content/verification_and_validation/figures/comparison_fuel_cycle_benchmark.py new file mode 120000 index 00000000..190954b4 --- /dev/null +++ b/doc/content/verification_and_validation/figures/comparison_fuel_cycle_benchmark.py @@ -0,0 +1 @@ +../../../../test/tests/fuel_cycle_benchmark/comparison_fuel_cycle_benchmark.py \ No newline at end of file diff --git a/doc/content/verification_and_validation/fuel_cycle_benchmarking.md b/doc/content/verification_and_validation/fuel_cycle_benchmarking.md new file mode 100644 index 00000000..1b27d15d --- /dev/null +++ b/doc/content/verification_and_validation/fuel_cycle_benchmarking.md @@ -0,0 +1,132 @@ +# Fuel Cycle Benchmarking + +## Case and Model Description + +This benchmarking case is taken from [!cite](meschini2023modeling) to simulate a fuel cycle model using resident time method. The model only assign a resident time to simulate the tritium flow for each system in fuel energy plant. The model avoid the complex techinical detail and the un finished technical. The model help us to understand the challenges and potential solutions to lowering the requirement for the tritium inventory and accelerate the development of fusion energy. + +In the model, we have 11 systems to finish the tritium recycling in fuel cycle. The detail and corresponding ODE for each system are listed in below: + +!table id=tritsystems caption=Systems and labels used in this example. +| System Name | System number | Tritium inventory variable| system equation | +| --- | --- | --- | --- | +| Breeding Blanket | 1 | `T_01_BB` | [eqn:t1] | +| Tritium Extraction System | 2 | `T_02_TES` | [eqn:t2] | +| First Wall | 3 | `T_03_FW` | [eqn:t3] | +| Divertor | 4 | `T_04_DIV` | [eqn:t4] | +| Heat Exchanger | 5 | `T_05_HX` | [eqn:t5] | +| Detritiation System | 6 | `T_06_DS` | [eqn:t6] | +| Vaccum Pump | 7 | `T_07_vacuum` | [eqn:t7] | +| Fuel Clean-up | 8 | `T_08_FCU` | [eqn:t8] | +| Isotope Separation System | 9 | `T_09_ISS` | [eqn:t9] | +| Storage and Management | 10 | `T_10_storage` | [eqn:t10] | +| Fueling System | 11 | - | - | +| Tritium Separation Membrane | 12 | `T_11_membrane` | [eqn:t11] | + +!alert note title=The fuel cycle of Tritium in Fueling System is ignored +Fueling system only injects fresh fuel in the vacuum chamber and is not modeled in the fuel cycle to simplify the model. Instead, an outflux equal to the tritium fueling rate is added to the equation describing the storage and management system. + + + +\begin{equation} +\label{eqn:t1} +\frac{dI_1}{dt} = TBR \cdot \dot{N}_{T,burn} + \frac{I_3}{\tau_3} + \frac{I_4}{\tau_4} + f_{5-1} \frac{I_5}{\tau_5} - \frac{I_1}{\tau_1}- \frac{I_1\varepsilon_1}{\tau_1} - I_1\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t2} +\frac{dI_2}{dt} = \frac{I_1}{\tau_1} - \frac{I_2}{\tau_2} - \frac{I_2\varepsilon_2}{\tau_2} - I_2\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t3} +\frac{dI_3}{dt} = f_{p-3} \frac{ \dot{N}_{T,burn} }{TBE} + f_{5-3}\frac{I_5}{\tau_5} - \frac{I_3}{\tau_3} - \frac{I_3\varepsilon_3}{\tau_3} - I_3\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t4} +\frac{dI_4}{dt} = f_{p-4}\frac{\dot{N}_{T,burn}}{TBE} + f_{5-4}\frac{I_5}{\tau_5} - \frac{I_4}{\tau_4} - \frac{I_4\varepsilon_4}{\tau_4} - I_4\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t5} +\frac{dI_5}{dt} = (1 - \eta_2)\frac{I_2}{\tau_2} - \frac{I_5}{\tau_5} -\frac{I_5\varepsilon_5}{\tau_5} - I_5\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t6} +\frac{dI_6}{dt} = f_{5-6}\frac{I_5}{\tau_5} + f_{9-6}\frac{I_9}{\tau_9} - \frac{I_6}{\tau_6} - \frac{I_6\varepsilon_6}{\tau_6} - I_6\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t7} +\frac{dI_7}{dt} = (1- TBE - f_{p-3} - f_{p-4}) \frac{\dot{N}_{T,burn}}{TBE} - \frac{I_7}{\tau_7} - \frac{I_7\varepsilon_7}{\tau_7} - I_7\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t8} +\frac{dI_8}{dt} = (1 - f_{DIR}) \frac{I_7}{\tau_7} - \frac{I_8}{\tau_8} - \frac{I_8\varepsilon_8}{\tau_8} - I_8\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t9} +\frac{dI_9}{dt} = \frac{I_6}{\tau_6} + \frac{I_8}{\tau_8} - \frac{I_9\varepsilon_9}{\tau_9} - \frac{I_9}{\tau_9} - I_9\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t10} +\frac{dI_{10}}{dt} = (1 - f_{9-6}) \frac{I_9}{\tau_9} + f_{DIR} \frac{I_7}{\tau_7} + \frac{I_{11}}{\tau_{11}} - \frac{\dot{N}_{T,burn}}{TBE} - I_{10}\lambda , +\end{equation} + +\begin{equation} +\label{eqn:t11} +\frac{dI_{11}}{dt} = \eta_2 \frac{I_2}{\tau_2} - \frac{I_{11}}{\tau_{11}} - \frac{I_{11}\varepsilon_{11}}{\tau_{11}} - I_{11}\lambda , +\end{equation} + +where $TBE$, the tritium burn efficiency, is defined as: + +\begin{equation} +\label{eqn:TBE} +TBE = \eta_f f_b +\end{equation} + + +## Case and Model Parameters + +We use the ScalarKernels in MOOSE to calculate the ODEs from 11 systems. All the model parameters are listed in [fuel_cycle_benchmark_table2]: + +!table id=fuel_cycle_benchmark_table2=Values of material properties. +| Parameter | Description | Value | Units | +| --------- | ------------------------------------ | ----------------------------------------------------------- | --------------------- | +| TBR | Tritium breeding ratio | 1.067 | - | +| TBE | Tritium burn efficiency in plasma | 0.025 | - | +| AF | Availability factor | 0.75 | - | +| $\varepsilon_i$ | Fraction of tritium lost from non-radioactive phenomena in the $i$th component | 1e-4 except for FW and DIV system | - | +| $\eta_f$ | Fueling efficiency | 0.25 | - | +| $f_b$ | Tritium burn fraction in the plasma | 0.10 | - | +| $\eta_2$ | Tritium extraction efficiency | 0.7 | - | +| $f_{DIR}$ | Direct internal recycling fraction | 0.5 | - | +| $I_i$ | Tritium inventory in the $i$th component | - | kg | +| $\dot{N}_{T,burn}$ | Tritium burn rate | 8.99e-7 | - | +| $\lambda$ | Tritium decay rate | 1.73e-9 | s$^{-1}$ | +| $t$ | time | - | s | +| $\tau_i$ | Tritium residence time in the $i$th component | 4500 in $\tau_1$, 86400 in $\tau_2$, 1000 in $\tau_3$, $\tau_4$, $\tau_5$, 3600 in $\tau_6$, 600 in $\tau_7$, 585 in $\tau_8$, 22815 in $\tau_9$, 100 in $\tau_11$ | s | + + + +## Results + +We compare results from TMAP8 with MatLab results from [!cite](meschini2023modeling) in [comparison_fuel_cycle_benchmarking]. The agreements between the four chosen systems are quite good. + +!media comparison_fuel_cycle_benchmark.py + image_name=fuel_cycle_comparison.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=fuel_cycle_comparison + caption=Comparison of TMAP8 calculation with the MatLab data on the fuel cycle model. + +## Input files + +!style halign=left +The input file for this case can be found at [/fuel_cycle_benchmark/fuel_cycle.i]. The input file is different from the input file used as test in TMAP8. To limit the computational costs of the test case, the test runs a version of the file with fewer time steps. More information about the changes can be found in the test specification file for this case, namely [/fuel_cycle_benchmark/tests]. + + +!bibtex bibliography diff --git a/doc/content/verification_and_validation/index.md b/doc/content/verification_and_validation/index.md index ffde74a3..c4a4cc0d 100644 --- a/doc/content/verification_and_validation/index.md +++ b/doc/content/verification_and_validation/index.md @@ -41,6 +41,7 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how | Case | Title | | ------- | ---------------------------------------------------------------------------------- | | ver-1fc | [Conduction in Composite Structure with Constant Surface Temperatures](ver-1fc.md) | +| fuel cycle | [Tritium fuel cycle in fusion energy plant](fuel_cycle_benchmarking.md) | # List of validation cases diff --git a/test/tests/fuel_cycle_benchmark/comparison_fuel_cycle_benchmark.py b/test/tests/fuel_cycle_benchmark/comparison_fuel_cycle_benchmark.py new file mode 100644 index 00000000..2518a331 --- /dev/null +++ b/test/tests/fuel_cycle_benchmark/comparison_fuel_cycle_benchmark.py @@ -0,0 +1,116 @@ +import matplotlib.pyplot as plt +import numpy as np +from matplotlib import gridspec +import pandas as pd +from scipy import special +import os + +# Changes working directory to script directory (for consistent MooseDocs usage) +script_folder = os.path.dirname(__file__) +os.chdir(script_folder) + +# ================================= Functions ================================ # +def interpolation_on_expected_input(date_x, data_y, expected_input): + """Get new numerical solution based on the experimental input data points + + Args: + expected_input (float): expected input data points + date_x (float, ndarray): numerical input data points + data_y (float, ndarray): numerical output data points + + Returns: + float: updated expected output based on the data points in expected_input + """ + left_limit = np.argwhere((np.diff(date_x < expected_input)))[0][0] + right_limit = left_limit + 1 + return (expected_input - date_x[left_limit]) / (date_x[right_limit] - date_x[left_limit]) * (data_y[right_limit] - data_y[left_limit]) + data_y[left_limit] + + +def read_csv_from_TMAP8(file_name, parameter_names): + # Read simulation data + if "/TMAP8/doc/" in script_folder: # if in documentation folder + csv_folder = f"../../../../test/tests/fuel_cycle/gold/{file_name}" + else: # if in test folder + csv_folder = f"./gold/{file_name}" + simulation_data = pd.read_csv(csv_folder) + simulation_results = [] + for i in range(len(parameter_names)): + simulation_results.append(simulation_data[parameter_names[i]]) + simulation_results = np.array(simulation_results) + return simulation_results + +# ================================ parameters ================================ # +# reserve inventory +time_unit = 3600 * 24 # time unit - days +two_year = 3600 * 24 * 365 * 2 # double time +tritium_burn_rate = 8.99e-7 # kg/s +TBE = 0.02 +q = 0.25 +t_res = 24 * 3600 # s +initial_inventory = 1.14 # kg +AF = 0.7 +reserve_inventory = tritium_burn_rate / TBE * q * t_res * AF +print(f"Required reserve inventory = {reserve_inventory} kg") + +# =========================== TMAP8 data extraction ========================== # +file_name = "fuel_cycle_out.csv" +parameter_names = ['time','T_01_BZ','T_02_TES','T_09_ISS','T_10_storage'] +simulation_results = read_csv_from_TMAP8(file_name, parameter_names) # read csv file +simulation_results[parameter_names.index('time')] = simulation_results[parameter_names.index('time')] / time_unit # update time unit + +# inflection point +inflection_y = np.min(simulation_results[parameter_names.index('T_10_storage')]) +inflection_x = simulation_results[parameter_names.index('time')][np.argmin(simulation_results[parameter_names.index('T_10_storage')])] +print(f"TMAP8_base: Inflection time = {round(inflection_x,5)} days, and inventory = {round(inflection_y,5)} kg") + +# end inventory +end_inventory = interpolation_on_expected_input(simulation_results[parameter_names.index('time')], + simulation_results[parameter_names.index('T_10_storage')], + two_year / time_unit) +print(f"TMAP8_base: End inventory = {round(end_inventory,5)} ({round(end_inventory / initial_inventory, 3)} I_startup)") + +# ======================== Experiment data extraction ======================== # +file_name = "inventory_paper.csv" +parameter_names_experiment = ['time [s]','blanket inventory [kg]','TES inventory [kg]','ISS inventory [kg]','storage inventory [kg]'] +experiment_results = read_csv_from_TMAP8(file_name, parameter_names_experiment) # read csv file +experiment_results[parameter_names_experiment.index('time [s]')] = experiment_results[parameter_names_experiment.index('time [s]')] / time_unit # update time unit + +# inflection point +inflection_y = np.min(experiment_results[parameter_names_experiment.index('storage inventory [kg]')]) +inflection_x = experiment_results[parameter_names_experiment.index('time [s]')][np.argmin(experiment_results[parameter_names_experiment.index('storage inventory [kg]')])] +print(f"experiment: Inflection time = {round(inflection_x,5)} days, and inventory = {round(inflection_y,5)} kg") +# end inventory +end_inventory = interpolation_on_expected_input(experiment_results[parameter_names_experiment.index('time [s]')], + experiment_results[parameter_names_experiment.index('storage inventory [kg]')], + two_year / time_unit) +print(f"experiment: End inventory = {round(end_inventory,5)} ({round(end_inventory / initial_inventory, 3)} I_startup)") + +figure_base = 'fuel_cycle_comparison' +# =================================== Plot =================================== # +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +for i in range(len(parameter_names)-1): + if i==0: + ax.plot(simulation_results[parameter_names.index('time')], simulation_results[i+1], linestyle='-', label=r"TMAP8", c='tab:grey') + ax.plot(experiment_results[parameter_names_experiment.index('time [s]')], experiment_results[i+1], '--', label=r"MatLab", c='tab:blue') + else: + ax.plot(simulation_results[parameter_names.index('time')], simulation_results[i+1], linestyle='-', c='tab:grey') + ax.plot(experiment_results[parameter_names_experiment.index('time [s]')], experiment_results[i+1], '--', c='tab:blue') +ax.text(10, 5.5e-3, 'BZ',fontweight='bold') +ax.text(10, 1e-1, 'TES',fontweight='bold') +ax.text(10, 2.05e-1, 'ISS',fontweight='bold') +ax.text(10, 9.5e-1, 'storage',fontweight='bold') + +ax.set_xlabel(u'time (days)') +ax.set_ylabel(u"Tritium Inventory (kg)") +ax.legend(loc="best",ncols=3) +ax.set_ylim(bottom=0.001,top=1e2) +ax.set_xlim(left=0.1) +plt.xscale('log') +plt.yscale('log') +plt.grid(visible=True, which='major', color='0.65', linestyle='--', alpha=0.3) +ax.minorticks_on() +plt.savefig(f'{figure_base}.png', bbox_inches='tight', dpi=300) +plt.close(fig) diff --git a/test/tests/fuel_cycle_benchmark/fuel_cycle.i b/test/tests/fuel_cycle_benchmark/fuel_cycle.i new file mode 100644 index 00000000..e7937b6f --- /dev/null +++ b/test/tests/fuel_cycle_benchmark/fuel_cycle.i @@ -0,0 +1,556 @@ +# This input file re-creates the deuterium-tritium fuel cycle model +# described by Meschini et al (2023). +# "Modeling and analysis of the tritium fuel cycle for ARC- and STEP-class D-T +# fusion power plants." S Meschini & S E Ferry & R Delaporte-Mathurin +# & D G Whyte Nucl. Fusion 63 (2023) https://doi.org/10.1088/1741-4326/acf3fc + +# The mesh is completely ignored, but TMAP/MOOSE will complain without it. If high-fidelity +# models of specific components are required, the scalar variables can be coupled to +# "Field" variables which can vary spatially across the mesh, or could be co-ordinated +# with sub-apps. + +pulse_time = '${units 1800 s}' +initial_inventory = '${units 1.14 kg}' +accuracy_time = '${units 94608000 s}' # 864000 s} +time_interval_middle = '${units 1e6 s}' +simulation_time = '${units 94608000 s}' # 3 years + +# Modeling parameters +resident_time_1 = '${units 4500 s}' +resident_time_2 = '${units 86400 s}' +resident_time_3 = '${units 1000 s}' +resident_time_4 = '${units 1000 s}' +resident_time_5 = '${units 1000 s}' +resident_time_6 = '${units 3600 s}' +resident_time_7 = '${units 600 s}' +resident_time_8 = '${units 585 s}' +resident_time_9 = '${units 22815 s}' +resident_time_11 = '${units 100 s}' +epsilon_low = 0 # - +epsilon = 1e-4 # - +f_5to1 = 0.33 # - +f_5to3 = 0.33 # - +f_5to6 = 1e-4 # - +f_9to6 = 0.1 # - +f_Pto3 = 1e-4 # - +f_Pto4 = 1e-4 # - +f_DIR = 0.5 # - +eta_2 = 0.7 # - +TBR_value = 1.067 # - +AF_value = 0.75 # - +t_decay = '${units 1.73e-9 1/s}' +TBE_value = 0.025 # - +tritium_burn_rate_value = 8.99e-7 # - + +[Mesh] + type = GeneratedMesh + dim = 1 + xmin = 0 + xmax = 1 + nx = 1 +[] + +# One variable for each inventory of tritium is generated. All variables +# are defined as "SCALAR", meaning that they are a single value and are +# disconnected from any specific geometry + +[Variables] + [T_01_BZ] + family = SCALAR + [] + [T_02_TES] + family = SCALAR + [] + [T_03_FW] + family = SCALAR + [] + [T_04_DIV] + family = SCALAR + [] + [T_05_HX] + family = SCALAR + [] + [T_06_DS] # Detritiation system + family = SCALAR + [] + [T_07_vacuum] + family = SCALAR + [] + [T_08_FCU] + family = SCALAR + [] + [T_09_ISS] + family = SCALAR + [] + [T_10_storage] + family = SCALAR + initial_condition = ${initial_inventory} + [] + [T_11_membrane] # Tritium separation membrane + family = SCALAR + [] +[] + +# Tritium burn fraction is going to be small. Much +# will be lost to the scrape-off-layer (SOL) and +# recycled. + +# TES - tritium extraction system pulls tritium from +# the blanket + +# CPS - Coolant purification system pulls tritium from +# the coolant (CPS is signored in ARC reactor) +# Ignored in ARC due to liquid FLiBe + +# An ODE is defined in TMAP8 such that all of the terms must +# be on the left hand side. The terms can be split +# across multiple "ScalarKernels", which are additive, +# so that we have one ODETimeDerivative for each tritium +# inventory and a ParsedODEKernel for the rest of the +# terms. These equations should reflect those described +# in Appendix A of the paper (A.1-A.13), with negation +# on the ParsedODEKernels due to moving the terms to the +# left hand side. + +[ScalarKernels] + [I1t] + type = ODETimeDerivative + variable = T_01_BZ + [] + [I2t] + type = ODETimeDerivative + variable = T_02_TES + [] + [I3t] + type = ODETimeDerivative + variable = T_03_FW + [] + [I4t] + type = ODETimeDerivative + variable = T_04_DIV + [] + [I5t] + type = ODETimeDerivative + variable = T_05_HX + [] + [I6t] + type = ODETimeDerivative + variable = T_06_DS + [] + [I7t] + type = ODETimeDerivative + variable = T_07_vacuum + [] + [I8t] + type = ODETimeDerivative + variable = T_08_FCU + [] + [I9t] + type = ODETimeDerivative + variable = T_09_ISS + [] + [I10t] + type = ODETimeDerivative + variable = T_10_storage + [] + [I11t] + type = ODETimeDerivative + variable = T_11_membrane + [] + [I1] # Breeding Zone + type = ParsedODEKernel + expression = '-(breeder_pulse + T_03_FW / residence3 + T_04_DIV / residence4 + HX_BZ_leak_fraction * T_05_HX / residence5 - T_01_BZ / residence1 - T_01_BZ * epsilon1 / residence1 - T_01_BZ * tdecay)' + variable = 'T_01_BZ' + coupled_variables = 'T_03_FW T_04_DIV T_05_HX' + postprocessors = 'breeder_pulse HX_BZ_leak_fraction residence1 residence3 residence4 residence5 tdecay epsilon1' + [] + [I2] #Tritium Extraction System + type = ParsedODEKernel + expression = '-(T_01_BZ / residence1 - T_02_TES / residence2 - T_02_TES * epsilon2 / residence2 - T_02_TES * tdecay)' + variable = 'T_02_TES' + coupled_variables = 'T_01_BZ' + postprocessors = 'residence1 residence2 tdecay epsilon2' + [] + [I3] #First Wall + type = ParsedODEKernel + expression = '-(P_FW_leak_fraction * burn_pulse + HX_FW_leak_fraction * T_05_HX / residence5 + - T_03_FW / residence3 - T_03_FW * epsilon3 / residence3 - T_03_FW * tdecay)' + variable = 'T_03_FW' + coupled_variables = 'T_05_HX' + postprocessors = 'P_FW_leak_fraction HX_FW_leak_fraction burn_pulse residence5 residence3 tdecay epsilon3' + [] + # TBE = tritium_burn_fraction * tritium_fueling_efficiency + [I4] #Divertor + type = ParsedODEKernel + expression = '-(P_DIV_leak_fraction * burn_pulse + (1 - HX_BZ_leak_fraction - HX_DS_leak_fraction - HX_FW_leak_fraction) * T_05_HX / residence5 + - T_04_DIV * epsilon4 / residence4 - T_04_DIV / residence4 - T_04_DIV * tdecay)' + variable = 'T_04_DIV' + coupled_variables = 'T_05_HX' + postprocessors = 'P_DIV_leak_fraction HX_BZ_leak_fraction HX_DS_leak_fraction HX_FW_leak_fraction burn_pulse residence5 residence4 tdecay epsilon4' + [] + [I5] #Heat eXchanger + type = ParsedODEKernel + expression = '-((1 - TES_efficiency) * T_02_TES / residence2 - T_05_HX / residence5 - T_05_HX * epsilon5 / residence5 - T_05_HX * tdecay)' + variable = 'T_05_HX' + coupled_variables = 'T_02_TES' + postprocessors = 'TES_efficiency residence2 residence5 tdecay epsilon5' + [] + [I6] #Detritiation system + type = ParsedODEKernel + expression = '-(HX_DS_leak_fraction * T_05_HX / residence5 + ISS_DS_leak_fraction * T_09_ISS / residence9 - T_06_DS / residence6 - T_06_DS * epsilon6 / residence6 - T_06_DS * tdecay)' + variable = 'T_06_DS' + coupled_variables = 'T_05_HX T_09_ISS' + postprocessors = 'HX_DS_leak_fraction ISS_DS_leak_fraction residence5 residence9 residence6 tdecay epsilon6' + [] + [I7] #Vacuum Pump + type = ParsedODEKernel + expression = '-((1 - TBE - P_FW_leak_fraction - P_DIV_leak_fraction) * burn_pulse + - T_07_vacuum / residence7 - T_07_vacuum * epsilon7 / residence7 - T_07_vacuum * tdecay)' + variable = 'T_07_vacuum' + postprocessors = 'TBE burn_pulse P_FW_leak_fraction P_DIV_leak_fraction residence7 tdecay epsilon7' + [] + [I8] #Fuel clean-up + type = ParsedODEKernel + expression = '-((1 - DIR_fraction) * T_07_vacuum / residence7 - T_08_FCU / residence8 - T_08_FCU * epsilon8 / residence8 - T_08_FCU * tdecay)' + variable = 'T_08_FCU' + coupled_variables = 'T_07_vacuum' + postprocessors = 'DIR_fraction residence7 residence8 tdecay epsilon8' + [] + [I9] #Isotope Separation System + type = ParsedODEKernel + expression = '-(T_06_DS / residence6 + T_08_FCU / residence8 - T_09_ISS / residence9 - T_09_ISS * epsilon9 / residence9 - T_09_ISS*tdecay)' + variable = 'T_09_ISS' + coupled_variables = 'T_06_DS T_08_FCU' + postprocessors = 'residence6 residence8 residence9 tdecay epsilon9' + [] + [I10] #Storage and Management (STO) + type = ParsedODEKernel + expression = '-((1 - ISS_DS_leak_fraction) * T_09_ISS / residence9 + DIR_fraction * T_07_vacuum / residence7 + T_11_membrane / residence11 - burn_pulse - T_10_storage * tdecay)' + variable = 'T_10_storage' + coupled_variables = 'T_09_ISS T_07_vacuum T_11_membrane' + postprocessors = 'ISS_DS_leak_fraction DIR_fraction burn_pulse residence9 residence7 residence11 tdecay AF' + [] + [I11] #Tritium Separation Membrane (TSM) + type = ParsedODEKernel + expression = '-(TES_efficiency * T_02_TES/residence2 - T_11_membrane / residence11 - T_11_membrane * epsilon11 / residence11 - T_11_membrane * tdecay)' + variable = 'T_11_membrane' + coupled_variables = 'T_02_TES' + postprocessors = 'TES_efficiency residence2 residence11 tdecay epsilon11' + [] +[] + +[Functions] + [breeder_pulse_function] + type = ParsedFunction + symbol_names = 'AF tritium_burn_rate TBR' + symbol_values = 'AF tritium_burn_rate TBR' + expression = 'if(t > ${accuracy_time}, AF * tritium_burn_rate * TBR, + if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate * TBR, 0))' + [] + [burn_pulse_function] + type = ParsedFunction + symbol_names = 'AF tritium_burn_rate TBE' + symbol_values = 'AF tritium_burn_rate TBE' + expression = 'if(t > ${accuracy_time}, AF * tritium_burn_rate / TBE, + if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate / TBE, 0))' + [] + [dt_function] + type = ParsedFunction + symbol_names = 'AF' + symbol_values = 'AF' + expression = 'if(t > ${accuracy_time}, ${time_interval_middle}, + if(t % ${pulse_time} < AF * ${pulse_time}, AF * ${pulse_time} - t % ${pulse_time} + 0.01, + if(t % ${pulse_time} < ${pulse_time}, ${pulse_time} - t % ${pulse_time} + 0.01, 2)))' + [] +[] + +# These postprocessors define the constants referenced in +# the equations above. The value of any of these constants +# could be informed by more detailed models (using sub-apps +# and transfers), but it is important that the postprocessor +# is evaluated before the executioner attempts to solve the +# ODE, which is not the default behavior. +[Postprocessors] + [burn_pulse] + type = FunctionValuePostprocessor + function = burn_pulse_function + execute_on = 'initial timestep_end' + [] + [breeder_pulse] + type = FunctionValuePostprocessor + function = breeder_pulse_function + execute_on = 'initial timestep_end' + [] + [HX_BZ_leak_fraction] #f_{5-1} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to1} + [] + [HX_FW_leak_fraction] #f_{5-3} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to3} + [] + [HX_DS_leak_fraction] #f_{5-6} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to6} + [] + [ISS_DS_leak_fraction] #f_{9-6} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_9to6} + [] + [P_DIV_leak_fraction] #f_{P-4} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_Pto4} + [] + [P_FW_leak_fraction] #f_{P-3} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_Pto3} + [] + [TES_efficiency] #eta_2 from Abdou et al. 2020 + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${eta_2} + [] + [TBR] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${TBR_value} # for t_d = 2 yrs + [] + [DIR_fraction] #f_DIR + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_DIR} # (0.1 - 0.9) + [] + [AF] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${AF_value} # (0.75 from Meschini) + [] + [tdecay] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${t_decay} # (from Meschini) 1.7828336471961835e-9 (from Abdou) + [] + [TBE] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${TBE_value} # (0.005 - 0.1) Meschini + [] + [tritium_burn_rate] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${tritium_burn_rate_value} # (5.3125e-6 from Abdou) (9.3e-7 Kg/s from Meschini paper) (8.99e-7 Kg/s from Meschini matlab) + [] + [epsilon1] #BZ + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon2] #TES + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon3] #FW + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon_low} + [] + [epsilon4] #DIV + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon_low} + [] + [epsilon5] #HX + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon6] #DS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon7] #Vac + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon8] #FCU + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon9] #ISS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon11] #TSM + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [residence1] #BZ + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_1} # s 1.25 h, (Meschini) and (Ferrero et al) T_BZ = 3 g, 864000 # s 10 days + [] + [residence2] #TES + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_2} # s Meschini + #value = 1 h - 240 h Riva + [] + [residence3] #FW + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_3} # s Riva + [] + [residence4] #DIV + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_4} # s Riva + [] + [residence5] #HX + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_5} # s Abdou 2021 paper chosen for analysis + [] + [residence6] #DS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_6} # s Meschini + [] + [residence7] #Vac + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_7} # s + [] + [residence8] #FCU + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_8} # 0.1625 h 3600 # s 1 h Meschini + # value = 0.1 - 1 h Meschini + #value = 5 h Coleman + #value = 8640 Abdou + #value = 86400 Abdou + [] + [residence9] #ISS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_9} # s 6.3375 h Meschini + #value = 0.9 - 11 h # (for four hour overall residence time in inner loop) + [] + [residence11] #TSM + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_11} # (from Meschini) 1958.25 # s (1899.50 m / 0.97 m/s = 1958.25) (from Papa et al. 2021) + [] + # These postprocessors exist to sum up the tritium inventory + # across the entirety of the system + [T_BZ] + type = ScalarVariable + variable = T_01_BZ + execute_on = TIMESTEP_END + [] + [T_TES] + type = ScalarVariable + variable = T_02_TES + execute_on = TIMESTEP_END + [] + [T_FW] + type = ScalarVariable + variable = T_03_FW + execute_on = TIMESTEP_END + [] + [T_DIV] + type = ScalarVariable + variable = T_04_DIV + execute_on = TIMESTEP_END + [] + [T_HX] + type = ScalarVariable + variable = T_05_HX + execute_on = TIMESTEP_END + [] + [T_DS] + type = ScalarVariable + variable = T_06_DS + execute_on = TIMESTEP_END + [] + [T_VAC] + type = ScalarVariable + variable = T_07_vacuum + execute_on = TIMESTEP_END + [] + [T_FCU] + type = ScalarVariable + variable = T_08_FCU + execute_on = TIMESTEP_END + [] + [T_ISS] + type = ScalarVariable + variable = T_09_ISS + execute_on = TIMESTEP_END + [] + [T_STO] + type = ScalarVariable + variable = T_10_storage + execute_on = TIMESTEP_END + [] + [T_TSM] + type = ScalarVariable + variable = T_11_membrane + execute_on = TIMESTEP_END + [] + [total_tritium] + type = SumPostprocessor + values = 'T_BZ T_TES T_FW T_DIV T_HX T_DS T_VAC T_FCU T_ISS T_STO T_TSM' + [] +[] +[UserObjects] + [terminator] + type = Terminator + expression = 'T_STO < 0' + fail_mode = 'HARD' + message = 'Tritium in storage has been depleted' + [] + [terminator2] + type = Terminator + expression = 'total_tritium < 0' + fail_mode = 'HARD' + message = 'Tritium in system has been depleted' + [] +[] + +[Executioner] + type = Transient + start_time = 0 + dtmin = 1 + end_time = ${simulation_time} + [TimeStepper] + type = FunctionDT + function = dt_function + [] + solve_type = 'PJFNK' + nl_rel_tol = 1e-08 + nl_abs_tol = 1e-14 +[] + +[Outputs] + hide = "AF breeder_pulse burn_pulse HX_BZ_leak_fraction HX_FW_leak_fraction HX_DS_leak_fraction " + "ISS_DS_leak_fraction P_DIV_leak_fraction P_FW_leak_fraction TES_efficiency TBR " + "DIR_fraction T_BZ T_DS T_DIV T_TSM T_FCU T_FW T_HX T_ISS T_STO T_TES T_VAC epsilon1 " + "epsilon11 epsilon2 epsilon3 epsilon4 epsilon5 epsilon6 epsilon7 epsilon8 epsilon9 " + "residence1 residence11 residence2 residence3 residence4 residence5 residence6 residence7 " + "residence8 residence9 tdecay TBE tritium_burn_rate" + file_base = 'fuel_cycle_out' + csv = true + console = false +[] diff --git a/test/tests/fuel_cycle_benchmark/gold/fuel_cycle_out.csv b/test/tests/fuel_cycle_benchmark/gold/fuel_cycle_out.csv new file mode 100644 index 00000000..49d06c9d --- /dev/null +++ b/test/tests/fuel_cycle_benchmark/gold/fuel_cycle_out.csv @@ -0,0 +1,105122 @@ +time,total_tritium,T_01_BZ,T_02_TES,T_03_FW,T_04_DIV,T_05_HX,T_06_DS,T_07_vacuum,T_08_FCU,T_09_ISS,T_10_storage,T_11_membrane +0,0,0,0,0,0,0,0,0,0,0,1.14,0 +1350.1,1.1400741420681,0.001000887113278,0.00029566708290417,2.1776545857869e-06,2.1810087145568e-06,5.8974575325856e-07,4.6504442317739e-05,0.01456012591155,0.0049518977568636,0.010806187376151,1.1084077009709,2.2300514116263e-07 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[fuel_cycle_benchmarking_csvdiff] + type = CSVDiff + input = 'fuel_cycle.i' + cli_args = 'accuracy_time="${units 864000 s}" Outputs/file_base=fuel_cycle_limited_out' + csvdiff = fuel_cycle_limited_out.csv + requirement = 'The system shall be able to model tritium fuel cycle from Meschini et al. (2023).' + [] + [fuel_cycle_benchmarking_comparison] + type = RunCommand + command = 'python3 comparison_fuel_cycle_benchmark.py' + requirement = 'The system shall be able to generate comparison plots between the simulated solution from TMAP8 and Meschini et al. (2023), modeling tritium fuel cycle.' + required_python_packages = 'matplotlib numpy pandas scipy os' + [] +[]