diff --git a/include/interfacekernels/ADMatInterfaceReactionYHxPCT_LowPressure.h b/include/interfacekernels/ADMatInterfaceReactionYHxPCT_LowPressure.h new file mode 100644 index 000000000..33ce3ae00 --- /dev/null +++ b/include/interfacekernels/ADMatInterfaceReactionYHxPCT_LowPressure.h @@ -0,0 +1,50 @@ +/************************************************************/ +/* DO NOT MODIFY THIS HEADER */ +/* TMAP8: Tritium Migration Analysis Program, Version 8 */ +/* */ +/* Copyright 2021 - 2025 Battelle Energy Alliance, LLC */ +/* ALL RIGHTS RESERVED */ +/************************************************************/ + +#pragma once + +#include "ADInterfaceKernel.h" + +/** + * + * Implements a reactio n to establish ReactionRate=k_f*u-k_b*v to compute the surface H + * concentration in YHx from the temperature and partial pressure based on the PCT curves with u the + * concentration in the solid and v (neighbor) the concentration in the gas. + * + * The original data is from C. E. Lundin, J. P. Blackledge, Pressure-Temperature-Composition + * Relationships of the Yttrium-Hydrogen System, Journal of The Electrochemical Society 109 (9) + * (1962) 838–5. + * The fits are from Matthews et al., Metal Hydride Simulations Using SWIFT, LANL technical report + * LA-UR-21-27538, 2021. + */ + +class ADMatInterfaceReactionYHxPCT_LowPressure : public ADInterfaceKernel +{ +public: + static InputParameters validParams(); + + ADMatInterfaceReactionYHxPCT_LowPressure(const InputParameters & parameters); + +protected: + virtual ADReal computeQpResidual(Moose::DGResidualType type) override; + + /// Coupled temperature variable + const GenericVariableValue & _neighbor_temperature; + + /// Density of the solid + const ADMaterialProperty & _density; + + /// Forward reaction rate coefficient + const ADMaterialProperty & _kf; + + /// Backward reaction rate coefficient + const ADMaterialProperty & _kb; + + /// Flag to silence correlation out of bound warnings + const bool _silence_warnings; +}; diff --git a/src/interfacekernels/ADMatInterfaceReactionYHxPCT_LowPressure.C b/src/interfacekernels/ADMatInterfaceReactionYHxPCT_LowPressure.C new file mode 100644 index 000000000..89bb027a4 --- /dev/null +++ b/src/interfacekernels/ADMatInterfaceReactionYHxPCT_LowPressure.C @@ -0,0 +1,101 @@ +/************************************************************/ +/* DO NOT MODIFY THIS HEADER */ +/* TMAP8: Tritium Migration Analysis Program, Version 8 */ +/* */ +/* Copyright 2021 - 2025 Battelle Energy Alliance, LLC */ +/* ALL RIGHTS RESERVED */ +/************************************************************/ + +#include "ADMatInterfaceReactionYHxPCT_LowPressure.h" + +#include "PhysicalConstants.h" + +registerMooseObject("TMAP8App", ADMatInterfaceReactionYHxPCT_LowPressure); + +InputParameters +ADMatInterfaceReactionYHxPCT_LowPressure::validParams() + +{ + InputParameters params = ADInterfaceKernel::validParams(); + params.addClassDescription( + "Implements a reaction to establish ReactionRate=k_f*u-k_b*v to compute the surface H " + "concentration in YHx from the temperature and partial pressure based on the PCT curves with " + "u the co nc entration in the solid and v (neighbor) the concentration in the gas in " + "mol/m^3."); + params.addRequiredCoupledVar( + "neighbor_temperature", + "The variable on the other side of the interface for temperature (K)."); + params.addParam("density", "density", "Density of the solid in (mol/m^3)."); + params.addParam( + "forward_rate", "kf", "Forward reaction rate coefficient (1/s)."); + params.addParam( + "backward_rate", "kb", "Backward reaction rate coefficient (1/s)."); + params.addParam( + "silence_warnings", false, "Whether to silence correlation out of bound warnings"); + return params; +} + +ADMatInterfaceReactionYHxPCT_LowPressure::ADMatInterfaceReactionYHxPCT_LowPressure( + const InputParameters & parameters) + : ADInterfaceKernel(parameters), + _neighbor_temperature(this->template coupledGenericValue("neighbor_temperature")), + _density(getADMaterialProperty("density")), + _kf(getADMaterialProperty("forward_rate")), + _kb(getNeighborADMaterialProperty("backward_rate")), + _silence_warnings(getParam("silence_warnings")) +{ +} + +ADReal +ADMatInterfaceReactionYHxPCT_LowPressure::computeQpResidual(Moose::DGResidualType type) +{ + ADReal r = 0; + + // Calculate the equilibrium concentration value based on PCT curve + // (/2 because two atoms for a molecule) (pressure in Pa) + auto neighbor_pressure = + PhysicalConstants::ideal_gas_constant * _neighbor_temperature[_qp] * _neighbor_value[_qp] / 2; + + // Calculate the value of the pressures for the phase transition plateau (pressure in Pa) + auto limit_pressure = std::exp(-26.1 + 3.88e-2 * _neighbor_temperature[_qp] - + 9.7e-6 * Utility::pow<2>(_neighbor_temperature[_qp])); + + // return warning if the PCT curves is used out of bounds (pressure in Pa) + if (!_silence_warnings && ((neighbor_pressure < limit_pressure) || (neighbor_pressure > 1.e6))) + mooseDoOnce(mooseWarning("In YHxPCT: pressure ", + neighbor_pressure, + "Pa and temperature ", + _neighbor_temperature[_qp], + "K are outside the bounds of the atomic fraction correlation. See " + "documentation for YHxPCT material.")); + + // Calculate the atomic fraction based on the PCT curve + auto atomic_fraction = + 5.0e-01 - + std::pow(1.0e-03 + + std::exp(-89.3906 + 7.5958e-02 * _neighbor_temperature[_qp] + + (1.1924 - 4.4124e-03 * _neighbor_temperature[_qp]) * + (std::log(std::max(limit_pressure - neighbor_pressure, 1e-10)))), + -1); + + // Convert to concentration + auto _surface_equilibrium_concentration = atomic_fraction * _density[_qp]; + + switch (type) + { + // Move all the terms to the LHS to get residual, for primary domain + // Residual = kf*u - kb*v + // Weak form for primary domain is: (test, kf*u - kb*v) + case Moose::Element: + r = _test[_i][_qp] * (_kf[_qp] * _u[_qp] - _kb[_qp] * _surface_equilibrium_concentration); + break; + + // Similarly, weak form for secondary domain is: -(test, kf*u - kb*v), + // flip the sign because the direction is opposite. + case Moose::Neighbor: + r = -_test_neighbor[_i][_qp] * + (_kf[_qp] * _u[_qp] - _kb[_qp] * _surface_equilibrium_concentration); + break; + } + return r; +} diff --git a/test/tests/yttrium_hydrogen_system/YHx_PCT_LowPressure.i b/test/tests/yttrium_hydrogen_system/YHx_PCT_LowPressure.i new file mode 100644 index 000000000..702028e84 --- /dev/null +++ b/test/tests/yttrium_hydrogen_system/YHx_PCT_LowPressure.i @@ -0,0 +1,333 @@ +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant from PhysicalConstants.h +N_a = '${units 6.02214076e23 1/mol}' # Avogadro's number from PhysicalConstants.h +boltzmann_constant = '${units 1.380649e-23 J/K}' # Boltzmann constant from PhysicalConstants.h + +# Simulation conditions and material properties +temperature = '${units 1323 K}' +density_Y = '${units 48605 mol/m^3}' +initial_pressure_H2_enclosure_1 = '${units 2e02 Pa}' +initial_concentration_H_enclosure_1 = '${units ${fparse 2*initial_pressure_H2_enclosure_1 / (R*temperature)} mol/m^3}' +initial_atomic_fraction = 0.2# (-) +initial_concentration_H_enclosure_2 = '${units ${fparse initial_atomic_fraction*density_Y} mol/m^3}' + +# diffusivity from Majer et al., Journal of Alloys and Compounds 330-332 (2002) 438-442. +diffusivity_Do = '${units 1.e-8 m^2/s}' +diffusivity_Ea = '${units 0.38 eV -> J}' +diffusivity_ratio_gas_YHx = '${fparse initial_concentration_H_enclosure_2 / initial_concentration_H_enclosure_1 * 10}' # this ratio is large and helps InterfaceDiffusion due to the ratio of concentrations +# Surface reaction rate from P. W. Fisher, M. Tanase, Journal of Nuclear Materials 122-123 (1984) 1536-1540. +reaction_rate_0 = '${units 4.95e5 1/s}' +reaction_rate_Ea = '${units 1.52 eV -> J}' + +# Domain size and mesh parameters +domain_length = '${units 1 m}' +num_nodes = 8 + +# time +simulation_time = '${units 1e5 s}' +dt_max = '${fparse simulation_time/100}' +dt_init = '${units 1e-5 s}' +tau_constant_BC = '${fparse dt_init*2e-2}' # the smaller, the faster the up-ramp for the pressure BC + +# convergence parameters +lower_value_threshold_concentration_enclosure_1 = 1e-20 +lower_value_threshold_concentration_enclosure_2 = 1e-20 + +# file base +output_file_base = 'YHx_PCT_out' + +[Mesh] + [generated] + type = GeneratedMeshGenerator + dim = 1 + nx = ${num_nodes} + xmax = ${domain_length} + [] + [enclosure_1] + type = SubdomainBoundingBoxGenerator + input = generated + block_id = 1 + bottom_left = '0 0 0' + top_right = '${fparse 1/2 * domain_length} 0 0' + [] + [enclosure_2] + type = SubdomainBoundingBoxGenerator + input = enclosure_1 + block_id = 2 + bottom_left = '${fparse 1/2 * domain_length} 0 0' + top_right = '${fparse domain_length} 0 0' + [] + [interface] + type = SideSetsBetweenSubdomainsGenerator + input = enclosure_2 + primary_block = 1 + paired_block = 2 + new_boundary = interface + [] + [interface_2] + type = SideSetsBetweenSubdomainsGenerator + input = interface + primary_block = 2 + paired_block = 1 + new_boundary = interface_2 + [] +[] + +[Variables] + [concentration_H_enclosure_1] + block = 1 + initial_condition = '${initial_concentration_H_enclosure_1}' + [] + [concentration_H_enclosure_2] + block = 2 + initial_condition = '${initial_concentration_H_enclosure_2}' + [] +[] + +[Bounds] + # To prevent negative concentrations + [concentration_H_enclosure_1_lower_bound] + type = ConstantBounds + variable = bounds_dummy_concentration_H_enclosure_1 + bounded_variable = concentration_H_enclosure_1 + bound_type = lower + bound_value = ${lower_value_threshold_concentration_enclosure_1} + [] + [concentration_H_enclosure_2_lower_bound] + type = ConstantBounds + variable = bounds_dummy_concentration_H_enclosure_2 + bounded_variable = concentration_H_enclosure_2 + bound_type = lower + bound_value = ${lower_value_threshold_concentration_enclosure_2} + [] +[] + +[BCs] + [concentration_H_enclosure_1_fixed] + type = FunctionDirichletBC + variable = concentration_H_enclosure_1 + boundary = left + function = 'function_BC_concentration_H_enclosure_1' + [] +[] + +[Functions] + [function_BC_concentration_H_enclosure_1] + type = ParsedFunction + expression = 'exp(-${tau_constant_BC}/t)* ${initial_concentration_H_enclosure_1}' + [] +[] + +[Kernels] + # Diffusion equation for H in enclosure 1 + [H_time_derivative_enclosure_1] + type = TimeDerivative + variable = concentration_H_enclosure_1 + block = '1' + [] + [H_diffusion_enclosure_1] + type = MatDiffusion + variable = concentration_H_enclosure_1 + diffusivity = diffusivity_gas + block = '1' + [] + # Diffusion equation for H in enclosure 2 + [H_time_derivative_enclosure_2] + type = TimeDerivative + variable = concentration_H_enclosure_2 + block = '2' + [] + [H_diffusion_enclosure_2] + type = MatDiffusion + variable = concentration_H_enclosure_2 + diffusivity = diffusivity_YHx + block = '2' + [] +[] + +[AuxVariables] + [temperature] + initial_condition = '${temperature}' + [] + [pressure_H2_enclosure_1] + initial_condition = '${initial_pressure_H2_enclosure_1}' + [] + [bounds_dummy_concentration_H_enclosure_1] + order = FIRST + family = LAGRANGE + [] + [bounds_dummy_concentration_H_enclosure_2] + order = FIRST + family = LAGRANGE + [] +[] + +[AuxKernels] + [pressure_H2_enclosure_1] + type = ParsedAux + variable = pressure_H2_enclosure_1 + coupled_variables = 'concentration_H_enclosure_1 temperature' + expression = '${R} * temperature * concentration_H_enclosure_1/2' + block = 1 + execute_on = 'initial timestep_end' + [] +[] + +[Materials] + [diffusivity_YHx] + type = DerivativeParsedMaterial + property_name = diffusivity_YHx + coupled_variables = 'temperature' + expression = '${diffusivity_Do} * exp(-${fparse diffusivity_Ea*N_a/R}/temperature)' + outputs = exodus + [] + [diffusivity_gas] + type = DerivativeParsedMaterial + property_name = diffusivity_gas + material_property_names = diffusivity_YHx + expression = '${diffusivity_ratio_gas_YHx}*diffusivity_YHx' + outputs = exodus + [] + [reaction_rate_surface_YHx_1] + type = ADDerivativeParsedMaterial + property_name = reaction_rate_surface_YHx + coupled_variables = 'temperature' + expression = '${reaction_rate_0} * exp(-${fparse reaction_rate_Ea/boltzmann_constant}/temperature)' # 1/s + block = '1' + [] + [reaction_rate_surface_YHx_2] + type = ADDerivativeParsedMaterial + property_name = reaction_rate_surface_YHx + coupled_variables = 'temperature' + expression = '${reaction_rate_0} * exp(-${fparse reaction_rate_Ea/boltzmann_constant}/temperature)' # 1/s + block = '2' + [] +[] + +[InterfaceKernels] + [interface_diffusion] + type = InterfaceDiffusion + variable = concentration_H_enclosure_2 + neighbor_var = concentration_H_enclosure_1 + boundary = interface_2 + D = diffusivity_YHx + D_neighbor = diffusivity_gas + [] + [interface_reaction_YHx_PCT] + type = ADMatInterfaceReactionYHxPCT_LowPressure + variable = concentration_H_enclosure_2 + neighbor_var = concentration_H_enclosure_1 + neighbor_temperature = temperature + density = ${density_Y} + boundary = interface_2 + forward_rate = 'reaction_rate_surface_YHx' + backward_rate = 'reaction_rate_surface_YHx' + [] +[] + +[Postprocessors] + [temperature] + type = ElementAverageValue + variable = temperature + block = 1 + execute_on = 'initial timestep_end' + [] + [pressure_H2_enclosure_1] + type = ElementAverageValue + variable = pressure_H2_enclosure_1 + block = 1 + execute_on = 'initial timestep_end' + [] + [concentration_H_enclosure_1_at_interface] + type = SideAverageValue + boundary = interface + variable = concentration_H_enclosure_1 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [concentration_H_enclosure_2_at_interface] + type = SideAverageValue + boundary = interface_2 + variable = concentration_H_enclosure_2 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [atomic_fraction_H_enclosure_2_at_interface] + type = ParsedPostprocessor + pp_names = 'concentration_H_enclosure_2_at_interface' + expression = 'concentration_H_enclosure_2_at_interface / ${density_Y}' + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [concentration_ratio_H2] + type = ParsedPostprocessor + expression = 'concentration_H_enclosure_1_at_interface / sqrt(concentration_H_enclosure_2_at_interface)' + pp_names = 'concentration_H_enclosure_1_at_interface concentration_H_enclosure_2_at_interface' + execute_on = 'initial timestep_end' + outputs = 'csv console' + [] + [pressure_H2_enclosure_1_at_interface] + type = SideAverageValue + boundary = interface + variable = pressure_H2_enclosure_1 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [concentration_H_encl_1_inventory] + type = ElementIntegralVariablePostprocessor + variable = concentration_H_enclosure_1 + block = 1 + execute_on = 'initial timestep_end' + [] + [concentration_H_encl_2_inventory] + type = ElementIntegralVariablePostprocessor + variable = concentration_H_enclosure_2 + block = 2 + execute_on = 'initial timestep_end' + [] + + # postprocessors for mass conservation + [mass_conservation_sum_encl1_encl2] + type = LinearCombinationPostprocessor + pp_names = 'concentration_H_encl_1_inventory concentration_H_encl_2_inventory' + pp_coefs = '1 1' + execute_on = 'initial timestep_end' + [] +[] + +[Preconditioning] + [smp] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + end_time = ${simulation_time} + dtmax = ${dt_max} + nl_max_its = 16 + l_max_its = 30 + nl_rel_tol = 1e-5 + nl_abs_tol = 4e-12 + scheme = 'bdf2' + solve_type = 'Newton' + petsc_options_iname = '-pc_type -sub_pc_type -snes_type' + petsc_options_value = 'asm lu vinewtonrsls' # This petsc option helps prevent negative concentrations with bounds' + line_search = 'none' + [TimeStepper] + type = IterationAdaptiveDT + dt = ${dt_init} + optimal_iterations = 13 + iteration_window = 1 + growth_factor = 1.2 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + [] +[] + +[Outputs] + file_base = ${output_file_base} + csv = true + exodus = true +[] diff --git a/test/tests/yttrium_hydrogen_system/comparison_YHx_PCT_LowPressure.py b/test/tests/yttrium_hydrogen_system/comparison_YHx_PCT_LowPressure.py new file mode 100644 index 000000000..799b88690 --- /dev/null +++ b/test/tests/yttrium_hydrogen_system/comparison_YHx_PCT_LowPressure.py @@ -0,0 +1,265 @@ +# Import Required Libraries +# Import the necessary libraries, including pandas. + +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +from mpl_toolkits.mplot3d import Axes3D +import os + +# Changes working directory to script directory (for consistent MooseDocs usage) +#End whitetrailingspace +script_folder = os.path.dirname(__file__) +os.chdir(script_folder) + +#============================================================================= # +# General parameters +mmHg_to_Pa = 133.322 # 1 mmHg = 133.322 Pa +C_to_K = 273.15 # 0 C = 273.15 K +temperature_list = [900, 950, 1000, 1050, 1150, 1200, 1250, 1300] # C + +temperature_list = [x + 273.15 for x in temperature_list] # K +colors = plt.cm.tab10(np.linspace(0, 1, len(temperature_list))) +# ============================================================================ # +# Extract data from experiments +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + folderPath = "../../../../../test/tests/yttrium_hydrogen_system/" +else: # if in test folder + folderPath = "" +folderNameExpData = 'PCT_data' +list_expData = [] +for temperature in temperature_list: + # Read the CSV file into a DataFrame + expData = pd.read_csv(folderPath + folderNameExpData + '/' + str(int(temperature-C_to_K)) + '.csv') + # Update units from mm HG to Pa + expData['Partial Pressure (Pa)'] = expData['Partial Pressure (mm Hg)'] * mmHg_to_Pa + # Delete column with pressure in mm Hg + expData = expData.drop(columns=['Partial Pressure (mm Hg)']) + # Add a column for temperature + expData['Temperature (K)'] = temperature + # Organize by increasing order of atom ratio + expData = expData.sort_values(by='Atom Ratio (-)') + print(expData) + list_expData.append(expData) + +# ============================================================================ # +# Identify plateau region + +# Method to calculate the numerical derivative +def calculate_derivative(expData, x_col, y_col): + x = expData.iloc[:, x_col] + y = expData.iloc[:, y_col] + dy_dx = np.gradient(y, x) + return dy_dx + +# List to store plateau positions for each temperature +plateau_positions = {} + +# Loop through each temperature and calculate the derivative +for i, temperature in enumerate(temperature_list): + x_col = 0 # atom ratio + y_col = 1 # pressure + dy_dx = calculate_derivative(list_expData[i], x_col, y_col) # derivative + dy_dx_y = dy_dx/list_expData[i].iloc[:, y_col] + + # Identify the range of derivatives that correspond to the plateau region + plateau_threshold = 1 # Define a threshold for the plateau region + plateau_edges = np.where(dy_dx_y < plateau_threshold)[0] + + # Find the start and end indices of the plateau region + if len(plateau_edges) > 0: + start_index = plateau_edges[0] + end_index = plateau_edges[-1] + else: + start_index = end_index = None + + # Store the plateau edges + plateau_positions[temperature] = { + 'start_index': int(start_index) if start_index is not None else None, + 'start': list_expData[i].iloc[start_index, [x_col, y_col]] if start_index is not None else None, + 'end_index': int(end_index) if end_index is not None else None, + 'end': list_expData[i].iloc[end_index, [x_col, y_col]] if end_index is not None else None + } + +# ============================================================================ # +# Fit the plateau pressure as a function of temperature + +# Calculate the average pressure on the plateau for each temperature +average_plateau_pressures = [ + list_expData[i].iloc[plateau_positions[temperature]['start_index']:plateau_positions[temperature]['end_index'] + 1, 1].mean() + if plateau_positions[temperature]['start_index'] is not None and plateau_positions[temperature]['end_index'] is not None + else None + for i, temperature in enumerate(temperature_list) +] + +# Define fitting function +def p0_lim_func(temperature): + return np.exp(-26.1+3.88*10**(-2)*np.array(temperature)-9.7*10**(-6)*np.square(temperature)) +p0_lim = p0_lim_func(temperature_list) + +# Plot the fit along with the data from the plateau pressure as a function of temperature +# Extract the plateau pressures for each temperature +plateau_pressures = average_plateau_pressures +# Filter out None values +filtered_temperatures = [temperature for temperature, pressure in zip(temperature_list, plateau_pressures) if pressure is not None] +filtered_pressures = [pressure for pressure in plateau_pressures if pressure is not None] + +# ============================================================================ # +# Plot the fit and the plateau pressures +fig = plt.figure(figsize=(5, 5)) +plt.plot(temperature_list, p0_lim, label='Fit', linestyle='--') +plt.scatter(filtered_temperatures, filtered_pressures, color='red', label='Plateau Pressures') +plt.xlabel('Temperature (K)') +plt.ylabel('Pressure (Pa)') +plt.yscale('log') +plt.legend() +plt.grid(True) +plt.tight_layout() +plt.savefig('YHx_PCT_plateau_pressure_fit.png', bbox_inches='tight', dpi=300) +plt.close(fig) + +# ============================================================================ # +# Fit the high pressures as a function of temperature +def atom_ratio_eq_upper_func(temperature,pressure): + return 5.0e-01-(1.0e-03+np.exp(-89.737+ 9.7537e-02*temperature + (1.1924 - 4.4125*10**(-3)*temperature)*(np.log( p0_lim_func(temperature)-pressure))))**(-1) +# Create a meshgrid for the fit surface +pressure_range = np.linspace((min(list_expData[0].iloc[:, 1])), (max(list_expData[0].iloc[:, 1])), 100) +temperature_range = np.linspace(min(temperature_list), max(temperature_list), 100) +pressure_mesh, temperature_mesh = np.meshgrid(pressure_range, temperature_range) + +atom_ratio_eq_upper = atom_ratio_eq_upper_func(temperature_range,pressure_range) + +# ============================================================================ # +# Compare simulation data against model +# Read simulation data +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = "../../../../../test/tests/yttrium_hydrogen_system/gold/" +else: # if in test folder + csv_folder = "./gold/" + +TMAP8_prediction_T1173_P2e2 = pd.read_csv(csv_folder + "YHx_PCT_T1173_P2e2_out.csv") +TMAP8_prediction_T1323_P2e2 = pd.read_csv(csv_folder + "YHx_PCT_T1323_P2e2_out.csv") +TMAP8_prediction_T1473_P1e3 = pd.read_csv(csv_folder + "YHx_PCT_T1473_P1e3_out.csv") +TMAP8_prediction_T1473_P1e4 = pd.read_csv(csv_folder + "YHx_PCT_T1473_P1e4_out.csv") + +TMAP8_prediction_T1173_P2e2_temperature = TMAP8_prediction_T1173_P2e2['temperature'].iat[-1] +TMAP8_prediction_T1173_P2e2_pressure = TMAP8_prediction_T1173_P2e2['pressure_H2_enclosure_1_at_interface'].iat[-1] +TMAP8_prediction_T1173_P2e2_atomic_fraction = TMAP8_prediction_T1173_P2e2['atomic_fraction_H_enclosure_2_at_interface'].iat[-1] +analytical_equation_T1173_P2e2_atomic_fraction = atom_ratio_eq_upper_func(TMAP8_prediction_T1173_P2e2_temperature,TMAP8_prediction_T1173_P2e2_pressure) + +TMAP8_prediction_T1323_P2e2_temperature = TMAP8_prediction_T1323_P2e2['temperature'].iat[-1] +TMAP8_prediction_T1323_P2e2_pressure = TMAP8_prediction_T1323_P2e2['pressure_H2_enclosure_1_at_interface'].iat[-1] +TMAP8_prediction_T1323_P2e2_atomic_fraction = TMAP8_prediction_T1323_P2e2['atomic_fraction_H_enclosure_2_at_interface'].iat[-1] +analytical_equation_T1323_P2e2_atomic_fraction = atom_ratio_eq_upper_func(TMAP8_prediction_T1323_P2e2_temperature,TMAP8_prediction_T1323_P2e2_pressure) + +TMAP8_prediction_T1473_P1e3_temperature = TMAP8_prediction_T1473_P1e3['temperature'].iat[-1] +TMAP8_prediction_T1473_P1e3_pressure = TMAP8_prediction_T1473_P1e3['pressure_H2_enclosure_1_at_interface'].iat[-1] +TMAP8_prediction_T1473_P1e3_atomic_fraction = TMAP8_prediction_T1473_P1e3['atomic_fraction_H_enclosure_2_at_interface'].iat[-1] +analytical_equation_T1473_P1e3_atomic_fraction = atom_ratio_eq_upper_func(TMAP8_prediction_T1473_P1e3_temperature,TMAP8_prediction_T1473_P1e3_pressure) + +TMAP8_prediction_T1473_P1e4_temperature = TMAP8_prediction_T1473_P1e4['temperature'].iat[-1] +TMAP8_prediction_T1473_P1e4_pressure = TMAP8_prediction_T1473_P1e4['pressure_H2_enclosure_1_at_interface'].iat[-1] +TMAP8_prediction_T1473_P1e4_atomic_fraction = TMAP8_prediction_T1473_P1e4['atomic_fraction_H_enclosure_2_at_interface'].iat[-1] +analytical_equation_T1473_P1e4_atomic_fraction = atom_ratio_eq_upper_func(TMAP8_prediction_T1473_P1e4_temperature,TMAP8_prediction_T1473_P1e4_pressure) + + +# ============================================================================ # +# Plot the experimental data, the fit, and the TMAP8 results +fig = plt.figure(figsize=(12, 8)) +ax = fig.add_subplot(111, projection='3d') + +# Plot all the data points +for expData in list_expData: + ax.scatter(expData['Partial Pressure (Pa)'], expData['Temperature (K)'], expData['Atom Ratio (-)'], label=f'{expData["Temperature (K)"].iloc[0]} K') + +# Initialize atom_ratio_mesh with the correct dimensions +atom_ratio_eq_upper_mesh = np.zeros_like(pressure_mesh) + +# Create a surface for the fit +for i, pressure in enumerate(pressure_range): + for j, temperature in enumerate(temperature_range): + atom_ratio_eq_upper_mesh[j, i] = atom_ratio_eq_upper_func(temperature,pressure) if pressure > p0_lim_func(temperature) else 0 + +# Plot the fit surface +ax.plot_surface(pressure_mesh, temperature_mesh, atom_ratio_eq_upper_mesh, color='blue', alpha=0.3) + +ax.set_xlabel('Partial Pressure (Pa)') +ax.set_ylabel('Temperature (K)') +ax.set_zlabel('Atom Ratio (-)') +ax.set_title('3D Plot of Partial Pressure, Temperature, and Atom Ratio with Fit Surface') +ax.set_zlim(0, 2) +ax.legend(loc='upper center', ncols=5) +plt.tight_layout() +ax.set_box_aspect(None, zoom=0.95) +plt.savefig('YHx_PCT_fit_3D_LowPressure.png', bbox_inches='tight', dpi=300) +plt.close(fig) + +# Initialize a dictionary to store RMSE values for each temperature +RMSE_values = {} + +# Plot the data points and the fit function for each temperature +fig = plt.figure(figsize=(12, 6)) + +print('temperature_list',temperature_list) + +for i, temperature in enumerate(temperature_list): + # Extract the data points for the current temperature + expData = list_expData[i] + pressures = expData['Partial Pressure (Pa)'] + atom_ratios = expData['Atom Ratio (-)'] + index_limit = atom_ratios[atom_ratios < 0.5].index + if index_limit is not None: + # Select only the values that are above the transition region + pressures_upper = pressures.loc[index_limit] + atom_ratios_upper = atom_ratios.loc[index_limit] + + # Calculate the fit values using the function + fit_values_upper = atom_ratio_eq_upper_func(temperature, pressures_upper) + + # remove nan values from fit_values_upper and the corresponding index from atom_ratios_upper and pressures_upper + index_not_nan = ~np.isnan(fit_values_upper) + fit_values_upper = fit_values_upper[index_not_nan] + atom_ratios_upper = atom_ratios_upper[index_not_nan] + pressures_upper = pressures_upper[index_not_nan] + + # Calculate the RMSE for the current temperature + RMSE = np.sqrt(np.mean((np.array(atom_ratios_upper) - np.array(fit_values_upper))**2)) + RMSE_values[temperature] = RMSE + + # Plot the data points + #plt.scatter(pressures_upper, atom_ratios_upper, label=f'{temperature} K Data') + # Plot the data points + plt.plot(pressures_upper, atom_ratios_upper, label=f'{temperature} K Data',color=colors[i]) + + # Plot the fit function + plt.scatter(pressures_upper, fit_values_upper, label=f'{temperature} K Fit (RMSE: {RMSE:.2f})',color=colors[i]) + +# plot the TMAP8 predictions +error = abs(TMAP8_prediction_T1173_P2e2_atomic_fraction-analytical_equation_T1173_P2e2_atomic_fraction)/analytical_equation_T1173_P2e2_atomic_fraction*100 +plt.scatter(TMAP8_prediction_T1173_P2e2_pressure, TMAP8_prediction_T1173_P2e2_atomic_fraction, label =f'{TMAP8_prediction_T1173_P2e2_temperature} K and {TMAP8_prediction_T1173_P2e2_pressure:.2f} Pa prediction (error: {error:.2f} %)', marker='x', color= 'k', s=90) +error = abs(TMAP8_prediction_T1323_P2e2_atomic_fraction-analytical_equation_T1323_P2e2_atomic_fraction)/analytical_equation_T1323_P2e2_atomic_fraction*100 +plt.scatter(TMAP8_prediction_T1323_P2e2_pressure, TMAP8_prediction_T1323_P2e2_atomic_fraction, label =f'{TMAP8_prediction_T1323_P2e2_temperature} K and {TMAP8_prediction_T1323_P2e2_pressure:.2f} Pa prediction (error: {error:.2f} %)', marker='x', color= 'k', s=90) +error = abs(TMAP8_prediction_T1473_P1e3_atomic_fraction-analytical_equation_T1473_P1e3_atomic_fraction)/analytical_equation_T1473_P1e3_atomic_fraction*100 +plt.scatter(TMAP8_prediction_T1473_P1e3_pressure, TMAP8_prediction_T1473_P1e3_atomic_fraction, label =f'{TMAP8_prediction_T1473_P1e3_temperature} K and {TMAP8_prediction_T1473_P1e3_pressure:.2f} Pa prediction (error: {error:.2f} %)', marker='x', color= 'k', s=90) +error = abs(TMAP8_prediction_T1473_P1e4_atomic_fraction-analytical_equation_T1473_P1e4_atomic_fraction)/analytical_equation_T1473_P1e4_atomic_fraction*100 +plt.scatter(TMAP8_prediction_T1473_P1e4_pressure, TMAP8_prediction_T1473_P1e4_atomic_fraction, label =f'{TMAP8_prediction_T1473_P1e4_temperature} K and {TMAP8_prediction_T1473_P1e4_pressure:.2f} Pa prediction (error: {error:.2f} %)', marker='x', color= 'k', s=90) + +plt.xlabel('Partial Pressure (Pa)') +plt.ylabel('Atom Ratio (-)') +plt.xscale('log') +plt.legend(bbox_to_anchor=(1.1, 1.05)) +plt.grid(True) +plt.xlim(1e02,1e05) +plt.ylim(0,0.55) +plt.tight_layout() +plt.savefig('YHx_PCT_fit_2D_LowPressure.png', bbox_inches='tight', dpi=300) +plt.close(fig) + +# print the RMSE values for each temperature +print('temperatures (K) and RMSE values: ',RMSE_values) + +# print the average RMSE value +average_rmse = np.mean(list(RMSE_values.values())) +print(f'Average RMSE: {average_rmse:.2f}') + + diff --git a/test/tests/yttrium_hydrogen_system/gold/YHx_PCT_T1173_P2e2_out.csv b/test/tests/yttrium_hydrogen_system/gold/YHx_PCT_T1173_P2e2_out.csv new file mode 100644 index 000000000..ea296c5fc --- /dev/null +++ b/test/tests/yttrium_hydrogen_system/gold/YHx_PCT_T1173_P2e2_out.csv @@ -0,0 +1,262 @@ 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