Boundary treatment pow - adjusting power value

A boundary treatment based on the work of Ebadi et. al. (2020). Here, we adjust the power value of flow rate-gap dependency, i.e., $b$ in the original work, to show the effects.

from mnflow.mfda.cad.dld.theme.block import DLD

for pow_val in [2.0, 2.5, 3.0]:
    dld = DLD(
        Np=10,
        Nw=8,
        gap_w=1.,
        boundary_treatment='pow',
        pow_val=pow_val,
        num_unit=2,
        rot_last=90,
        # constraints OFF
        turn_off_constraints=True,
        # image
        fname_cad=f'pow_{pow_val}.gds',
        img_core_fname=f'pow_{pow_val}',
        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:pow
block.DLD___num_unit:2_opt_mirror:False_array_counts:[1, 1]_opt_mirror_before_array:[False, False]
----------------------------------------
{'Np': 10,
 'Nw': 8,
 'area': 844.64,
 'bb': [(-39.0, -5.116), (1.0, 16.0)],
 'count of 1D arrays of core.DLD': 1,
 'd_c': 0.4635835700756275,
 'lx': 40.0,
 'ly': 21.116,
 'performance': {'Flow rate @ 1 bar/area (micro-liter/min/mm-sq)': 676.8572479900381,
                 'die area (mm-sq)': 0.00084464,
                 '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}

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----------------------------------------
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:pow
block.DLD___num_unit:2_opt_mirror:False_array_counts:[1, 1]_opt_mirror_before_array:[False, False]
----------------------------------------
{'Np': 10,
 'Nw': 8,
 'area': 847.9200000000001,
 'bb': [(-39.0, -5.198), (1.0, 16.0)],
 'count of 1D arrays of core.DLD': 1,
 'd_c': 0.4635835700756275,
 'lx': 40.0,
 'ly': 21.198,
 'performance': {'Flow rate @ 1 bar/area (micro-liter/min/mm-sq)': 674.2389682308541,
                 'die area (mm-sq)': 0.00084792,
                 '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}

----------------------------------------
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:pow
block.DLD___num_unit:2_opt_mirror:False_array_counts:[1, 1]_opt_mirror_before_array:[False, False]
----------------------------------------
{'Np': 10,
 'Nw': 8,
 'area': 850.56,
 'bb': [(-39.0, -5.264), (1.0, 16.0)],
 'count of 1D arrays of core.DLD': 1,
 'd_c': 0.4635835700756275,
 'lx': 40.0,
 'ly': 21.264,
 'performance': {'Flow rate @ 1 bar/area (micro-liter/min/mm-sq)': 672.1462400563228,
                 'die area (mm-sq)': 0.0008505599999999999,
                 '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}

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It can be perceived that as $b$ increases, the maximum gap decreases. The maximum gap is about $38%$, $30%$, and $24%$ larger than that in the bulk of domain for $b=2,~2.5$ and $3.0$, respectively.

Output layout; $b=2.0$:

Layout

Output layout; $b=2.5$:

Layout

Output layout; $b=3.0$:

Layout