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f421c2e | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 | # %% Package imports
import numpy as np
import openpnm as op
import matplotlib.pyplot as plt
import openpnm.models.geometry.diffusive_size_factors as gd
np.random.seed(10)
# Network
Nx = 100
shape = [Nx, Nx, 1]
spacing = 1e-2
net = op.network.Cubic(shape=shape, spacing=spacing)
# 2D square geometry (for comparison to comsol)
geo = op.geometry.GenericGeometry(network=net, pores=net.Ps, throats=net.Ts)
geo.add_model(propname='pore.diameter', model=op.models.misc.constant, value=spacing)
geo.add_model(propname='throat.length', model=op.models.misc.constant, value=1e-15)
geo.add_model(propname='throat.diameter', model=op.models.misc.constant, value=spacing)
geo["pore.cross_sectional_area"] = spacing
geo["throat.cross_sectional_area"] = spacing
geo["pore.volume"] = spacing**2
mod = gd.squares_and_rectangles
geo.add_model(propname='throat.diffusive_size_factors', model=mod)
# phase and physics
air = op.phase.Air(network=net)
phys = op.physics.GenericPhysics(network=net, phase=air, geometry=geo)
# Make diffusivity a linear function of temperature
air['pore.temperature'] = 300
air.add_model(propname='pore.diffusivity',
model=op.models.misc.linear,
m=1.860793056e-06,
b=-0.0005375624384,
prop='pore.temperature')
phys.add_model(propname='throat.diffusive_conductance',
model=op.models.physics.diffusive_conductance.generic_diffusive)
# add constant thermal conductivity
air.remove_model(propname='pore.thermal_conductivity')
air["pore.thermal_conductivity"] = 0.0262
# add thermal conducance model to physics
phys.add_model(propname='throat.thermal_conductance',
model=op.models.physics.thermal_conductance.generic_thermal)
tfd_settings = {
"conductance": "throat.diffusive_conductance",
"quantity": "pore.concentration",
}
tfc_settings = {
"conductance": "throat.thermal_conductance",
"quantity": "pore.temperature",
"pore_volume": "pore.heat_capacity",
}
pardiso = op.solvers.PardisoSpsolve()
rk45 = op.integrators.ScipyRK45(verbose=True)
# Define Algorithms
# First algorithm, transient Fourier conduction
tfc = op.algorithms.TransientReactiveTransport(network=net, phase=air)
geo['pore.heat_capacity'] = geo['pore.volume'] * 1.0035 * 1000 * 1.225
tfc.settings._update(tfc_settings)
tfc.set_value_BC(net.pores("left"), 400)
# Second algorithm, transient Fickian diffusion
tfd = op.algorithms.TransientReactiveTransport(network=net, phase=air)
tfd.settings._update(tfd_settings)
tfd.set_value_BC(net.pores("left"), 100)
# Add variable props to algs
tfd.set_variable_props('pore.temperature')
tfc.set_variable_props('pore.concentration')
# handle initial conditions
T0 = np.ones(tfc.Np) * 300
T0[net.pores('left')] = 400
c0 = np.ones(tfd.Np)*50
c0[net.pores('left')] = 100
y0 = np.hstack((T0, c0)) # ICs must include boundary condition
# Integrator parameters
t_initial = 0
t_final = 50
t_step = 5
n_steps = int((t_final - t_initial)/t_step) + 1
t = np.linspace(t_initial, t_final, n_steps)
tspan = [t_initial, t_final]
# define transient multiphysics solver
tmp = op.contrib.TransientMultiPhysics(algorithms=[tfc, tfd], network=net)
# run
sol = tmp.run(y0, tspan, saveat=t)
# plot
T = sol['pore.temperature']
C = sol['pore.concentration']
not_BC_pores = net.pores("left", mode='nor')
C_avg = C[not_BC_pores].mean(axis=0)
# Load COMSOL data from .npz file
time = np.linspace(0, 2000, 401)
data = np.load('tmp_comsol_data.npz')
C_comsol = data['a']
# Plot concentration and temperature profiles
plt.figure(1)
fig, ax = plt.subplots(ncols=2)
im_1 = ax[0].imshow(T[:, -1].reshape((Nx, Nx)))
im_2 = ax[1].imshow(C[:, -1].reshape((Nx, Nx)))
fig.colorbar(im_1, ax=ax[0], fraction=0.046, pad=0.04)
fig.colorbar(im_2, ax=ax[1], fraction=0.046, pad=0.04)
ax[0].title.set_text('Temperature (K)')
ax[1].title.set_text('Concentration (mol m-3)')
ax[0].axis('off')
ax[1].axis('off')
im_1.set_clim(300, 400)
im_2.set_clim(0, 100)
fig.suptitle('OpenPNM', y=0.85)
# Plot average concentration of COMSOL compared to OpenPNM
plt.figure(2)
fig1, ax1 = plt.subplots()
ax1.plot(t, C_avg, time, C_comsol)
ax1.legend(('OpenPNM', 'COMSOL'))
ax1.set_xlabel('Time (s)')
ax1.set_ylabel('Concentration mol/m3')
ax1.set_title('Average Concentration')
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