Boundary treatment 3d - adjusting resistance ratio
A boundary treatment based on the work of Inglis et. al. (2020). Here, we introduce a parameter $\phi$ defined as the ratio of lateral resistance to axial resistance of unit cell close to accumulation sidewall on $N^{th}$ row, set to 1 by default in the package. We modify this param in the following to show the effects.
from mnflow.mfda.cad.dld.theme.block import DLD
for phi in [0.5, 1, 3]:
dld = DLD(
Np=10,
Nw=8,
gap_w=1.,
boundary_treatment='3d',
phi=phi,
num_unit=2,
rot_last=90,
# constraints OFF
turn_off_constraints=True,
# image
fname_cad=f'phi_{phi}.gds',
img_core_fname=f'phi_{phi}',
opt_save_image=True,
img_dpu=40,
)
----------------------------------------
core.DLD___Np:10_Nw:8_gap_w:1.000_pitch_w:2.000_gap_a:1.000_pitch_a:2.000_height:4.000_boundary_treatment:3d
block.DLD___num_unit:2_opt_mirror:False_array_counts:[1, 1]_opt_mirror_before_array:[False, False]
----------------------------------------
{'Np': 10,
'Nw': 8,
'area': 853.3199999999999,
'bb': [(-39.0, -5.208), (1.0, 16.125)],
'count of 1D arrays of core.DLD': 1,
'd_c': 0.4635835700756275,
'lx': 40.0,
'ly': 21.333,
'performance': {'Flow rate @ 1 bar/area (micro-liter/min/mm-sq)': 669.9722330922818,
'die area (mm-sq)': 0.0008533199999999999,
'gap over crit. dia.': 2.157108371715726,
'volumetric flow rate at 1 bar (micro-liter/min)': 0.5717007059423058},
'resistance (Pa.sec/m^3)': 1.0495001908578192e+16,
'volumetric flow rate at 1 bar (m^3/sec)': 9.528345099038431e-12,
'volumetric flow rate at 1 bar (milli-liter/hr)': 0.03430204235653835}
/usr/bin/xdg-open: 882: www-browser: not found
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/usr/bin/xdg-open: 882: w3m: not found
xdg-open: no method available for opening '/tmp/tmphz66_4dk.PNG'
----------------------------------------
core.DLD___Np:10_Nw:8_gap_w:1.000_pitch_w:2.000_gap_a:1.000_pitch_a:2.000_height:4.000_boundary_treatment:3d
block.DLD___num_unit:2_opt_mirror:False_array_counts:[1, 1]_opt_mirror_before_array:[False, False]
----------------------------------------
{'Np': 10,
'Nw': 8,
'area': 858.4800000000001,
'bb': [(-39.0, -5.208), (1.0, 16.254)],
'count of 1D arrays of core.DLD': 1,
'd_c': 0.4635835700756275,
'lx': 40.0,
'ly': 21.462000000000003,
'performance': {'Flow rate @ 1 bar/area (micro-liter/min/mm-sq)': 665.945282292314,
'die area (mm-sq)': 0.0008584800000000001,
'gap over crit. dia.': 2.157108371715726,
'volumetric flow rate at 1 bar (micro-liter/min)': 0.5717007059423058},
'resistance (Pa.sec/m^3)': 1.0495001908578192e+16,
'volumetric flow rate at 1 bar (m^3/sec)': 9.528345099038431e-12,
'volumetric flow rate at 1 bar (milli-liter/hr)': 0.03430204235653835}
/usr/bin/xdg-open: 882: www-browser: not found
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/usr/bin/xdg-open: 882: w3m: not found
xdg-open: no method available for opening '/tmp/tmpk7r6um4j.PNG'
----------------------------------------
core.DLD___Np:10_Nw:8_gap_w:1.000_pitch_w:2.000_gap_a:1.000_pitch_a:2.000_height:4.000_boundary_treatment:3d
block.DLD___num_unit:2_opt_mirror:False_array_counts:[1, 1]_opt_mirror_before_array:[False, False]
----------------------------------------
{'Np': 10,
'Nw': 8,
'area': 873.6000000000001,
'bb': [(-39.0, -5.208), (1.0, 16.632)],
'count of 1D arrays of core.DLD': 1,
'd_c': 0.4635835700756275,
'lx': 40.0,
'ly': 21.840000000000003,
'performance': {'Flow rate @ 1 bar/area (micro-liter/min/mm-sq)': 654.4193062526393,
'die area (mm-sq)': 0.0008736000000000002,
'gap over crit. dia.': 2.157108371715726,
'volumetric flow rate at 1 bar (micro-liter/min)': 0.5717007059423058},
'resistance (Pa.sec/m^3)': 1.0495001908578192e+16,
'volumetric flow rate at 1 bar (m^3/sec)': 9.528345099038431e-12,
'volumetric flow rate at 1 bar (milli-liter/hr)': 0.03430204235653835}
It can be perceived that as $\phi$ increases, the axial and lateral gaps of unit cell on $N^{th}$ row of acc. sidewall increases and decreases, respectively, to allow for the ratio of lateral to axial resistance to increase.
Output layout; $\phi=0.5$:
Output layout; $\phi=1.0$:
Output layout; $\phi=3.0$:
