diff --git a/test/tests/val-2g/comparison_val-2g.py b/test/tests/val-2g/comparison_val-2g.py new file mode 100644 index 00000000..8cfb08bf --- /dev/null +++ b/test/tests/val-2g/comparison_val-2g.py @@ -0,0 +1,111 @@ +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) + +# Read TMAP8 simulation data +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = "../../../../test/tests/val-2g/val-2g_673_out.csv" +else: # if in test folder + csv_folder = "./val-2g_673_out.csv" +simulation_673_data = pd.read_csv(csv_folder) +simulation_time_673 = simulation_673_data['time'] +simulation_flux_left_673 = simulation_673_data['scaled_flux_surface_left'] + +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = "../../../../test/tests/val-2g/val-2g_873_out.csv" +else: # if in test folder + csv_folder = "./val-2g_873_out.csv" +simulation_873_data = pd.read_csv(csv_folder) +simulation_time_873 = simulation_873_data['time'] +simulation_flux_left_873 = simulation_873_data['scaled_flux_surface_left'] + +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = "../../../../test/tests/val-2g/val-2g_973_out.csv" +else: # if in test folder + csv_folder = "./val-2g_973_out.csv" +simulation_973_data = pd.read_csv(csv_folder) +simulation_time_973 = simulation_973_data['time'] +simulation_flux_left_973 = simulation_973_data['scaled_flux_surface_left'] + +# Read TMAP4 simulation data +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = "../../../../test/tests/val-2g/tmap4_data.csv" +else: # if in test folder + csv_folder = "./tmap4_data.csv" +simulation_TMAP4_data = pd.read_csv(csv_folder) +simulation_time_TMAP4 = simulation_TMAP4_data['time'] +simulation_temperature_TMAP4 = simulation_TMAP4_data['temperature'] +simulation_flux_TMAP4_673 = simulation_TMAP4_data['TMAP - 400C'] +simulation_flux_TMAP4_873 = simulation_TMAP4_data['TMAP - 600C'] +simulation_flux_TMAP4_973 = simulation_TMAP4_data['TMAP - 700C'] + +# Read experiment data +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = "../../../../test/tests/val-2g/experimental_data.csv" +else: # if in test folder + csv_folder = "./experimental_data.csv" +experiment_data = pd.read_csv(csv_folder) +experiment_time = experiment_data['time'] +experiment_temperature = experiment_data['temperature'] +experiment_flux_673 = experiment_data['Exp - 400C'] +experiment_flux_873 = experiment_data['Exp - 600C'] +experiment_flux_973 = experiment_data['Exp - 700C'] + +# Setup mask using a random sampling method to reduce density of scatter plot points in experimental +# data (there is a lot of "noise"). +# These preserve 10% of the data points. (adjusted within the 'size' parameter). +mask = np.random.choice(len(experiment_flux_673), size=int(len(experiment_flux_673) * 0.1), replace=False) + + +file_base = 'val-2g_comparison' +############################ desorption flux atom/m$^2$/s ############################ +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +# TMAP8 +ax.semilogy(simulation_time_673-12000, simulation_flux_left_673, linestyle='-', label=r"673 K", c='blue', linewidth=3.0) +ax.semilogy(simulation_time_873-12000, simulation_flux_left_873, linestyle='-', label=r"873 K", c='red', linewidth=3.0) +ax.semilogy(simulation_time_973-12000, simulation_flux_left_973, linestyle='-', label=r"973 K", c='green', linewidth=3.0) + +# TMAP4 +ax.semilogy(simulation_time_TMAP4, simulation_flux_TMAP4_673, linestyle='--', label=r"TMAP4 - 673 K", c='blue', linewidth=3.0, alpha=0.7) +ax.semilogy(simulation_time_TMAP4, simulation_flux_TMAP4_873, linestyle='--', label=r"TMAP4 - 873 K", c='red', linewidth=3.0, alpha=0.7) +ax.semilogy(simulation_time_TMAP4, simulation_flux_TMAP4_973, linestyle='--', label=r"TMAP4 - 973 K", c='green', linewidth=3.0, alpha=0.7) + +# Experimental Data +s = (3.0)**2 +ax.scatter(experiment_time[mask], experiment_flux_673[mask], marker='o', s=s, label=r"Exp - 673 K", c='blue') +ax.scatter(experiment_time[mask], experiment_flux_873[mask], marker='o', s=s, label=r"Exp - 873 K", c='red') +ax.scatter(experiment_time[mask], experiment_flux_973[mask], marker='o', s=s, label=r"Exp - 973 K", c='green') + + +# Font sizes for labels and axes +SMALL_SIZE = 10 +MEDIUM_SIZE = 14 +BIGGER_SIZE = 16 + +ax.set_xlabel(u'Time (s)', weight='bold', fontsize=BIGGER_SIZE) +ax.set_ylabel(u"Desorption flux (H$_2$/m$^2$/s)", weight='bold', fontsize=BIGGER_SIZE) +ax.legend(loc="upper left", fontsize=SMALL_SIZE) +ax.set_ylim(bottom=6e15, top=4.0e18) +ax.set_xlim(left=0,right=7200) +ax.xaxis.set_ticks(np.arange(0, 7205, 1800)) +plt.grid(visible=True, which='major', color='0.65', linestyle='--', alpha=0.3) +# tmap_flux_for_rmspe = numerical_solution_on_experiment_input(experiment_time, simulation_time_TMAP7, simulation_flux_left_TMAP7/2 + flux_environment) +# RMSE = np.sqrt(np.mean((tmap_flux_for_rmspe-experiment_flux)**2) ) +# RMSPE = RMSE*100/np.mean(experiment_flux) +# ax.text(6000.0,0.85e18, 'RMSPE = %.2f '%RMSPE+'%',fontweight='bold') +ax.tick_params(axis='both', which='both', direction='out', bottom=True, top=True, left=True, + right=True, labelsize=MEDIUM_SIZE) +ax.grid(True, which='minor', color='0.9', linestyle='--') +ax.set_axisbelow(True) # Ensures that grid is drawn behind data. Without this, sometimes the grid is seen atop marker points. +plt.savefig(f'{file_base}.png', bbox_inches='tight', dpi=300) +plt.close(fig) diff --git a/test/tests/val-2g/experimental_data.csv b/test/tests/val-2g/experimental_data.csv new file mode 100644 index 00000000..fe6283ca --- /dev/null +++ b/test/tests/val-2g/experimental_data.csv @@ -0,0 +1,3490 @@ +time,temperature,Exp - 400C,Exp - 600C,Exp - 700C +0.00E+00,2.95E+02,1.25E+15,8.36E+14,5.22E+15 +2.06E+00,2.95E+02,3.29E+15,2.35E+15,2.56E+15 +4.13E+00,2.95E+02,1.57E+15,1.36E+15,5.74E+15 +6.19E+00,2.95E+02,8.46E+04,4.70E+14,2.09E+15 +8.26E+00,2.95E+02,8.46E+04,8.46E+04,5.07E+15 +1.03E+01,2.95E+02,5.22E+13,8.46E+04,3.34E+15 +1.24E+01,2.95E+02,8.46E+04,8.46E+04,5.22E+15 +1.45E+01,2.95E+02,8.46E+04,8.46E+04,2.87E+15 +1.65E+01,2.95E+02,8.46E+04,8.46E+04,3.34E+15 +1.86E+01,2.95E+02,8.46E+04,7.83E+14,4.65E+15 +2.06E+01,2.95E+02,8.46E+04,0.00E+00,6.95E+15 +2.27E+01,2.95E+02,8.46E+04,8.46E+04,2.56E+15 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PhysicalConstants.h - https://physics.nist.gov/cgi-bin/cuu/Value?r) + +# Model parameters +TPE_hold_time = '${units 7200 s}' +TDS_initial_time = '${units 12000 s}' +TDS_ramp_end = '${units 17238 s}' +simulation_time = '${units 19200 s}' +outputs_initial_time = '${units 12000 s}' +step_interval_max = 15 # (-) +step_interval_min = 6 # (-) +bound_value_min = '${units 1e-10 at/mum^3}' + +# Diffusion parameters +flux_high = '${units 7.1e21 at/m^2/s -> at/mum^2/s}' +flux_low = '${units 0 at/mum^2/s}' +reflection_coefficient = 0.90 # (-) +transmission_coefficient = '${fparse 1 - ${reflection_coefficient}}' # (-) +diffusivity_coefficient = '${fparse ${units 4.1e-7 m^2/s -> mum^2/s} / sqrt(2)}' +E_D = '${units 0.39 eV -> J}' +initial_concentration = '${units 0.0 at/m^3 -> at/mum^3}' +width_source = '${units 3.58e-9 m -> mum}' +depth_source = '${units 2.64e-9 m -> mum}' + +# Traps parameters +N = '${units 6.323e28 at/m^3 -> at/mum^3}' +trapping_energy = '${fparse ${units 0.39 eV -> J} / ${kB}}' +binding_energy = '${fparse ${units 1.41 eV -> J} / ${kB}}' +detrapping_energy_1 = '${fparse ${trapping_energy} + ${binding_energy}}' # (K) +W_lattice_constant = '${units 3.16e-10 m -> mum}' +trapping_site_fraction_1 = 0.002 # (-) +trapping_rate_prefactor = '${fparse ${diffusivity_coefficient} / ${W_lattice_constant}^2}' # (1/s) +release_rate_prefactor = '${units 1e13 1/s}' +trap_per_free_1 = 1e6 # (-) + + +# Thermal parameters +temperature_exposure = '${units 673 K}' +time_constant = '${units 1200 s}' +temperature_TDS = '${units 1173 K}' +temperature_rate = '${fparse ${units 10 K} / ${units 60 s}}' +temperature_ambient = '${units 293 K}' +temperature_min = '${units 300 K}' + +[Mesh] + [cmg] + nx_scale = 2 + type = CartesianMeshGenerator + dim = 1 + dx = '${fparse 15 * ${units 1.79e-9 m -> mum}} + ${units 1e-9 m -> mum} ${units 1e-8 m -> mum} ${units 1e-7 m -> mum} ${units 1e-6 m -> mum} ${units 3.8711e-6 m -> mum} ${units 5e-6 m -> mum} ${fparse 9 * ${units 1e-5 m -> mum}} ${fparse 4 * ${units 1e-4 m -> mum}}' + ix = '${fparse 10 * ${nx_scale}} + ${fparse 1 * ${nx_scale}} ${fparse 1 * ${nx_scale}} ${fparse 1 * ${nx_scale}} ${fparse 1 * ${nx_scale}} ${fparse 1 * ${nx_scale}} ${fparse 50 * ${nx_scale}} ${fparse 50 * ${nx_scale}} ${fparse 50 * ${nx_scale}}' + subdomain_id = '0 0 0 0 0 0 0 0 0' + [] +[] + +[Problem] + type = ReferenceResidualProblem + extra_tag_vectors = 'ref' + reference_vector = 'ref' +[] + +[Bounds] + [concentration_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = concentration + bound_type = lower + bound_value = ${bound_value_min} + [] + [trapped_1_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = trapped_1 + bound_type = lower + bound_value = ${bound_value_min} + [] +[] + +[Variables] + [concentration] + order = FIRST + family = LAGRANGE + initial_condition = ${initial_concentration} + [] + [trapped_1] + order = FIRST + family = LAGRANGE + outputs = none + [] +[] + +[AuxVariables] + [temperature] + [] + [source] + [] + [bounds_dummy] + order = FIRST + family = LAGRANGE + [] +[] + +[AuxKernels] + [temperature_aux] + type = FunctionAux + variable = temperature + function = temperature_function + execute_on = 'initial timestep_end linear' + [] + [source_aux] + type = FunctionAux + variable = source + function = concentration_source_normal_function + execute_on = 'initial timestep_end linear' + [] +[] + +[Kernels] + [time_diffusion_implantation] + type = ADTimeDerivative + variable = concentration + extra_vector_tags = ref + [] + [diffusion_implantation] + type = ADMatDiffusion + variable = concentration + diffusivity = diffusivity + extra_vector_tags = ref + [] + [source] + type = ADBodyForce + variable = concentration + function = concentration_source_normal_function + [] + + # Trapping kernel + [coupled_time_trap_1] + type = ADCoefCoupledTimeDerivative + variable = concentration + v = trapped_1 + coef = ${trap_per_free_1} + extra_vector_tags = ref + [] +[] + +[NodalKernels] + # First traps + [time_1] + type = TimeDerivativeNodalKernel + variable = trapped_1 + [] + [trapping_1] + type = TrappingNodalKernel + variable = trapped_1 + mobile_concentration = concentration + alpha_t = '${trapping_rate_prefactor}' + trapping_energy = '${trapping_energy}' + N = '${N}' + Ct0 = '${trapping_site_fraction_1}' + temperature = 'temperature' + trap_per_free = ${trap_per_free_1} + extra_vector_tags = ref + [] + [release_1] + type = ReleasingNodalKernel + variable = trapped_1 + alpha_r = '${release_rate_prefactor}' + detrapping_energy = '${detrapping_energy_1}' + temperature = 'temperature' + [] +[] + +[BCs] + [left] + type = ADDirichletBC + variable = concentration + boundary = left + value = 0 + [] + [right] + type = ADDirichletBC + variable = concentration + boundary = right + value = 0 + [] +[] + +[Materials] + [diffusivity_tungsten] + type = ADDerivativeParsedMaterial + property_name = 'diffusivity' + functor_names = 'temperature_function' + functor_symbols = 'temperature_function' + expression = '${diffusivity_coefficient} * exp(- ${E_D} / ${kB} / temperature_function)' + output_properties = 'diffusivity' + [] + [converter_to_regular] + type = MaterialADConverter + ad_props_in = 'diffusivity' + reg_props_out = 'diffusivity_nonAD' + outputs = none + [] +[] + +[Functions] + [temperature_function] + type = ParsedFunction + expression = 'if(t<${TPE_hold_time}, ${temperature_exposure}, + if(t<${TDS_initial_time}, ${temperature_ambient} + + (${temperature_exposure} - ${temperature_ambient}) * + exp(-1.0 * (t - ${TPE_hold_time}) / ${time_constant}), + if(t<${TDS_ramp_end}, ${temperature_rate} * (t - ${TDS_initial_time}) + + ${temperature_min}, + ${temperature_TDS})))' + [] + + [surface_flux_function] + type = ParsedFunction + expression = 'if(t<${TPE_hold_time}, ${flux_high}, ${flux_low})' + [] + + [source_distribution_function] + type = ParsedFunction + expression = '1 / ( ${width_source} * sqrt(2 * pi) ) * exp(-0.5 * ((x - ${depth_source}) / ${width_source} ) ^ 2)' + [] + + [concentration_source_normal_function] + type = ParsedFunction + symbol_names = 'source_distribution_function surface_flux_function transmission_coefficient' + symbol_values = 'source_distribution_function surface_flux_function ${transmission_coefficient}' + expression = 'source_distribution_function * surface_flux_function * transmission_coefficient' + [] + + [max_dt_size_function] + type = ParsedFunction + expression = 'if(t<${TDS_initial_time}, ${step_interval_max}, ${step_interval_min})' + [] +[] + +[Postprocessors] + [flux_surface_left] + type = SideDiffusiveFluxIntegral + variable = concentration + diffusivity = 'diffusivity_nonAD' + boundary = 'left' + outputs = none + [] + [scaled_flux_surface_left] + type = ScalePostprocessor + scaling_factor = '${units 1 m^2 -> mum^2}' + value = flux_surface_left + execute_on = 'initial nonlinear linear timestep_end' + outputs = 'console csv exodus' + [] + [flux_surface_right] + type = SideDiffusiveFluxIntegral + variable = concentration + diffusivity = 'diffusivity_nonAD' + boundary = 'right' + outputs = none + [] + [scaled_flux_surface_right] + type = ScalePostprocessor + scaling_factor = '${units 1 m^2 -> mum^2}' + value = flux_surface_right + execute_on = 'initial nonlinear linear timestep_end' + outputs = none + [] + [max_time_step_size] + type = FunctionValuePostprocessor + function = max_dt_size_function + execute_on = 'initial nonlinear linear timestep_end' + outputs = none + [] +[] + +[Preconditioning] + [SMP] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + scheme = bdf2 + solve_type = NEWTON + petsc_options_iname = '-pc_type -snes_type' + petsc_options_value = 'lu vinewtonrsls' + + end_time = ${simulation_time} + line_search = 'none' + automatic_scaling = true + nl_abs_tol = 1e-10 + [TimeStepper] + type = IterationAdaptiveDT + dt = 1.0 + iteration_window = 5 + optimal_iterations = 26 + growth_factor = 1.1 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + timestep_limiting_postprocessor = max_time_step_size + [] +[] + +[Outputs] + file_base = 'val-2g_${temperature_exposure}_out' + [csv] + type = CSV + start_time = ${outputs_initial_time} + [] + [exodus] + type = Exodus + start_time = ${outputs_initial_time} + output_material_properties = true + time_step_interval = 20 + [] +[] diff --git a/test/tests/val-2g/val-2g_temperature.py b/test/tests/val-2g/val-2g_temperature.py new file mode 100644 index 00000000..413e36d5 --- /dev/null +++ b/test/tests/val-2g/val-2g_temperature.py @@ -0,0 +1,113 @@ +import matplotlib.pyplot as plt +import numpy as np +from matplotlib import gridspec +import os +import math + +# This file recreates Figure 3 from M. Shimada, et al., Fus. Eng. Des., 136, 1161 (2018) +# Caption: +# "Temperature profiles used in the modeling for 673, 873, and 973 K. The time constant of 1200 s +# was used to simulate the cool-down process after the TPE plasma exposure. Thermal desorption +# was simulated with the ramp rate (10 K/min) from 293 K to 1173 K and the temperature hold at +# 1173 K for 0.5 h from t = 12000 s to 19190 s." +# Deviations, adjustments, and definitions: +# - Explicit hold times were not given in the figure, or the body text. Only, "slightly different +# plasma exposure time was used to obtain the similar D ion fluence of 5.0 \times 10^25 m^{-2} +# with the different ion flux densities in W53A, W55A, and W26A." So, assuming a constant TPE +# exposure flux, the exposure time was determined by taking the fluence and dividing by the flux +# from Table 1 in the article. This gave a very reasonable approximation to the Figure 3 data. +# - Cool-down period in article figure seems to end at around 300 K, not 293 K. There is a visible dip +# from the cool-down period into the ramp-up. Assuming 293 K is the ambient room temperature +# for the purposes of Newton's law of cooling, and the cool-down period was really stopped at +# around 300 K (as it seems to do), then we'll set the ramp up period to start at 300 K in order +# to keep the function relatively smooth at the end of the cool-down period into the ramp up. +# - Given the 10 K/min ramp rate and the time alloted above for the ramp up, the ramp up temperature +# actually overshoots 1173 K (this is regardless of the starting temperature adjustment above). +# In order to keep the temperature hold period consistent at 0.5 h in the model, the ramp end +# time was set to 17238 s and the final end time set to 19038 s. + +# Changes working directory to script directory (for consistent MooseDocs usage) +script_folder = os.path.dirname(__file__) +os.chdir(script_folder) + +# Necessary parameters +initial_temperature = [673, 873, 973] # K +hold_time = [7183, 6341, 5952] # s +cooling_time_constant = 1200 # s +temperature_room = 293 # K +temperature_min = 300 # K +TDS_start = 12000 # s +TDS_ramp_end = 17238 # s +TDS_end = 19038 # s +final_temperature = 1173 # K +temperature_ramp_rate = 10/60 # K/s + +file_base = 'val-2g_temperature' + +def newton_cool_down(initial_temperature, time_constant, environment_temperature, current_time, start_time=0.0): + """Calculate current temperature of a pre-heated sample over time using Newton's law of cooling + + Args: + initial_temperature (float): starting temperature of the sample (K) + time_constant (float): time constant of heat transfer (s) + environment_temperature (float): temperature of the environment, suitably far from the surface (K) + start_time (float): time when source heating the sample is removed and cooling begins, defaulted to zero (s) + current_time (float): current time (s) + + Returns: + float: current temperature of the sample (K) + """ + return environment_temperature + (initial_temperature - environment_temperature) \ + * math.exp(-(current_time - start_time) / time_constant) + +time_series = [] +cooling_data = [] +for i in range(len(initial_temperature)): + # Build complete time series for all phases + time_series = list(range(0, TDS_end, 1)) + + # Calculate temperature at each point in time + temp = [] + for t in time_series: + if t < hold_time[i]: + # Constant heat source phase + temp.append(initial_temperature[i]) + elif t < TDS_start: + # Cooldown phase + temp.append(newton_cool_down(initial_temperature[i], cooling_time_constant, + temperature_room, t, hold_time[i])) + elif t < TDS_ramp_end: + # Ramp phase + temp.append(temperature_ramp_rate * (t - TDS_start) + temperature_min) + else: + # Final hold phase + temp.append(final_temperature) + + cooling_data.append(temp) + +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +for i in range(len(cooling_data)): + label = "TMAP8 - " + str(initial_temperature[i]) + " K" + ax.plot(time_series, cooling_data[i], linestyle='-', linewidth=4.0, label=label) + +# Font sizes for labels and axes +SMALL_SIZE = 12 +MEDIUM_SIZE = 14 +BIGGER_SIZE = 16 + +ax.set_xlabel(u'Time [s]', weight='bold', fontsize=BIGGER_SIZE) +ax.set_ylabel(u'Temperature [K]', weight='bold', fontsize=BIGGER_SIZE) +ax.legend(loc="best", fontsize=SMALL_SIZE) +ax.set_xlim(left=0, right=20001) +start, end = ax.get_xlim() +ax.xaxis.set_ticks(np.arange(start, end, 5000)) +ax.set_ylim(bottom=290, top=1200) +ax.minorticks_on() +ax.tick_params(axis='both', which='both', direction='out', bottom=True, top=True, left=True, + right=True, labelsize=MEDIUM_SIZE) +plt.savefig(f'{file_base}.png', bbox_inches='tight', dpi=300) +plt.close(fig) +