def test_cones_and_cylinders(self):
L_actual = mods.cones_and_cylinders(self.geo)
L_desired = np.array([[0.25, 0.3, 0.45], [0.45, 0.2, 0.35]])
assert_allclose(L_actual, L_desired)
# Overlapping pores
self.geo["pore.diameter"][0] = 1.2
L_actual = mods.cones_and_cylinders(self.geo)
L_desired = np.array([[5.7875e-01, 1.0000e-15, 4.2125e-01],
[4.5000e-01, 2.0000e-01, 3.5000e-01]])
assert_allclose(L_actual, L_desired)
self.geo["pore.diameter"][0] = 0.5
def cones_and_cylinders(
target,
pore_diameter='pore.diameter',
throat_diameter='throat.diameter'
):
r"""
Finds throat length assuming pores are cones and throats are
cylinders.
Parameters
----------
target : GenericGeometry
Geometry object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_diameter : str
Dictionary key of the pore diameter values.
throat_diameter : str
Dictionary key of the throat diameter values.
Returns
-------
ndarray
Array containing throat length values.
"""
from openpnm.models.geometry import conduit_lengths
out = conduit_lengths.cones_and_cylinders(
target, pore_diameter=pore_diameter, throat_diameter=throat_diameter
)
return out[:, 1]
def trapezoids_and_rectangles(
target,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes hydraulic size factors for conduits assuming pores are
trapezoids and throats are rectangles.
Parameters
----------
target : GenericGeometry
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_diameter : str
Dictionary key of the pore diameter values.
throat_diameter : str
Dictionary key of the throat diameter values.
Returns
-------
dict
Dictionary containing conduit size factors. Size factors are
accessible via the keys: 'pore1', 'throat', and 'pore2'.
Notes
-----
The hydraulic size factor is the geometrical part of the pre-factor in
Stoke's flow:
.. math::
Q = \frac{A^2}{8 \pi \mu L} \Delta P
= \frac{S_{hydraulic}}{\mu} \Delta P
Thus :math:`S_{hydraulic}` represents the combined effect of the area
and length of the *conduit*, which consists of a throat and 1/2 of the
pores on each end.
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = _get_conduit_diameters(target, pore_diameter, throat_diameter)
L1, Lt, L2 = _conduit_lengths.cones_and_cylinders(
target, pore_diameter=pore_diameter, throat_diameter=throat_diameter).T
# Fi is the integral of (1/A^3) dx, x = [0, Li]
F1 = L1 / 2 * (D1 + Dt) / (D1 * Dt)**2
F2 = L2 / 2 * (D2 + Dt) / (D2 * Dt)**2
Ft = Lt / Dt**3
# S is 1 / (12 * F)
S1, St, S2 = [1 / (Fi * 12) for Fi in [F1, Ft, F2]]
return {"pore1": S1, "throat": St, "pore2": S2}
def cones_and_cylinders(
target,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes diffusive shape coefficient assuming pores are truncated cones
and throats are cylinders.
Parameters
----------
target : GenericGeometry
Geometry object which this model is associated with. This controls
the length of the calculated array, and also provides access to
other necessary properties.
pore_diameter : str
Dictionary key of the pore diameter values.
throat_diameter : str
Dictionary key of the throat diameter values.
Returns
-------
A dictionary containing the diffusive_shape_coefficient, which can be
accessed via the dict keys 'pore1', 'pore2', and 'throat'.
Notes
-----
The diffusive size factor is the geometrical part of the pre-factor in
Fick's law:
.. math::
n_A = \frac{A}{L} \Delta C_A
= S_{diffusive} D_{AB} \Delta C_A
Thus :math:`S_{diffusive}` represents the combined effect of the area and
length of the *conduit*, which consists of a throat and 1/2 of the pore
on each end.
"""
D1, Dt, D2 = _get_conduit_diameters(target, pore_diameter, throat_diameter)
L1, Lt, L2 = _conduit_lengths.cones_and_cylinders(
target, pore_diameter=pore_diameter, throat_diameter=throat_diameter).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = 4 * L1 / (D1 * Dt * _np.pi)
F2 = 4 * L2 / (D2 * Dt * _np.pi)
Ft = Lt / (_np.pi * Dt**2 / 4)
return {"pore1": 1 / F1, "throat": 1 / Ft, "pore2": 1 / F2}
def cones_and_cylinders(
target,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes hydraulic size factors for conduits assuming pores are
truncated cones and throats are cylinders.
Parameters
----------
target : GenericGeometry
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_diameter : str
Dictionary key of the pore diameter values.
throat_diameter : str
Dictionary key of the throat diameter values.
Returns
-------
dict
Dictionary containing conduit size factors. Size factors are
accessible via the keys: 'pore1', 'throat', and 'pore2'.
Notes
-----
The hydraulic size factor is the geometrical part of the pre-factor in
Stoke's flow:
.. math::
Q = \frac{A^2}{8 \pi \mu L} \Delta P
= \frac{S_{hydraulic}}{\mu} \Delta P
Thus :math:`S_{hydraulic}` represents the combined effect of the area
and length of the *conduit*, which consists of a throat and 1/2 of the
pores on each end.
"""
D1, Dt, D2 = _get_conduit_diameters(target, pore_diameter, throat_diameter)
L1, Lt, L2 = _conduit_lengths.cones_and_cylinders(
target, pore_diameter=pore_diameter, throat_diameter=throat_diameter).T
# Fi is the integral of (1/A^2) dx, x = [0, Li]
F1 = 16 / 3 * (L1 * (D1**2 + D1 * Dt + Dt**2) /
(D1**3 * Dt**3 * _np.pi**2))
F2 = 16 / 3 * (L2 * (D2**2 + D2 * Dt + Dt**2) /
(D2**3 * Dt**3 * _np.pi**2))
Ft = Lt / (_np.pi * Dt**2 / 4)**2
# I is the integral of (y^2 + z^2) dA, divided by A^2
I1 = I2 = It = 1 / (2 * _np.pi)
# S is 1 / (16 * pi^2 * I * F)
S1 = 1 / (16 * _np.pi**2 * I1 * F1)
St = 1 / (16 * _np.pi**2 * It * Ft)
S2 = 1 / (16 * _np.pi**2 * I2 * F2)
return {"pore1": S1, "throat": St, "pore2": S2}