def gravitational_loss_in_circular_tube(temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=10, # µm
particle_density=1000, # kg/m^3
tube_diameter=0.01, # m
tube_length=0.1, # m
incline_angle=60, # degrees from horizontal (0-90)
flow_rate=3, # cc/s
mean_flow_velocity=False, # 0.1061 # m/s)
flow_type='auto',
verbose=False):
"""
Arguments
---------
temperature = 293.15, # Kelvin
pressure = 101.3, # kPa
particle_diameter = 10, # µm
particle_density = 1000, # kg/m^3
tube_diameter = 0.01, # m
tube_length = 0.1, # m
incline_angle = 60, # degrees from horizontal (0-90)
flow_rate = 3, # cc/s
mean_flow_velocity = False #0.1061 # m/s)"""
if not mean_flow_velocity:
mean_flow_velocity = _tools_sampling_efficiency.flow_rate2flow_velocity(flow_rate, tube_diameter, verbose=verbose)
if flow_type == 'auto':
flow_type = _tools_sampling_efficiency.test_flow_type_in_tube(tube_diameter, mean_flow_velocity, temperature, pressure, verbose=verbose)
if flow_type == 'laminar':
sv = _tools_sampling_efficiency.settling_velocity(temperature, particle_density, particle_diameter, pressure, verbose=verbose)
k770 = np.cos(np.pi * incline_angle / 180) * 3 * sv * tube_length / (4 * tube_diameter * mean_flow_velocity)
if np.any((k770 ** (2. / 3)) > 1):
fract = 0
else:
if np.any(k770 ** (2 / 3.) > 1):
k771 = 0
else:
k771 = np.arcsin(k770 ** (1 / 3.)) # done
fract = (1 - (2 / np.pi) * (
2 * k770 * np.sqrt(1 - k770 ** (2 / 3)) + k771 - (k770 ** (1 / 3) * np.sqrt(1 - k770 ** (2 / 3))))) # done
if np.any(fract < 0):
fract = 0
elif flow_type == 'turbulent':
raise ValueError('Sorry this loss mechanism has not been implemented for turbulent flow')
else:
raise ValueError('Unknown flow type: %s' % flow_type)
if verbose:
print('k770: %s' % k770)
print('k771: %s' % k771)
print('fraction penetrating: %s' % fract)
return fract
def loss_in_a_bent_section_of_circular_tubing(
temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=3.5, # µm
particle_density=1000, # kg/m^3
tube_air_flow_rate=3, # cc/s
tube_air_velocity=False, # m/s
tube_diameter=0.0025, # m
angle_of_bend=90, # degrees
flow_type='auto',
verbose=False):
""" (B&W 8-66 to 8-68; W&B 6-52, 6-53)
Temperature 293.15 Kelvin
Pressure 101.3 kPa
Particle Diameter 3.5 µm
Particle Density 1000 kg/m^3
Tube air velocity 6.25 m/s
Tube diameter 0.0025 m
Angle of bend 90 degrees"""
if not tube_air_velocity:
tube_air_velocity = _tools_sampling_efficiency.flow_rate2flow_velocity(
tube_air_flow_rate, tube_diameter, verbose=verbose)
if flow_type == 'auto':
flow_type = _tools_sampling_efficiency.test_flow_type_in_tube(
tube_diameter,
tube_air_velocity,
temperature,
pressure,
verbose=verbose)
velocity_ratio = 1
stnum = _tools_sampling_efficiency.stokes_number(particle_density,
particle_diameter,
pressure,
temperature,
tube_air_velocity,
velocity_ratio,
tube_diameter,
verbose=verbose)
if flow_type == 'laminar':
fract = 1 - stnum * angle_of_bend * np.pi / 180.
elif flow_type == 'turbulent':
fract = np.exp(-2.823 * stnum * angle_of_bend * np.pi / 180)
else:
raise ValueError('Unknown flow type: %s' % flow_type)
return fract
def loss_in_a_bent_section_of_circular_tubing(temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=3.5, # µm
particle_density=1000, # kg/m^3
tube_air_flow_rate=3, # cc/s
tube_air_velocity=False, # m/s
tube_diameter=0.0025, # m
angle_of_bend=90, # degrees
flow_type='auto',
verbose=False
):
""" (B&W 8-66 to 8-68; W&B 6-52, 6-53)
Temperature 293.15 Kelvin
Pressure 101.3 kPa
Particle Diameter 3.5 µm
Particle Density 1000 kg/m^3
Tube air velocity 6.25 m/s
Tube diameter 0.0025 m
Angle of bend 90 degrees"""
if not tube_air_velocity:
tube_air_velocity = _tools_sampling_efficiency.flow_rate2flow_velocity(tube_air_flow_rate, tube_diameter, verbose=verbose)
if flow_type == 'auto':
flow_type = _tools_sampling_efficiency.test_flow_type_in_tube(tube_diameter, tube_air_velocity, temperature, pressure, verbose=verbose)
velocity_ratio = 1
stnum = _tools_sampling_efficiency.stokes_number(particle_density, particle_diameter, pressure, temperature, tube_air_velocity,
velocity_ratio, tube_diameter, verbose=verbose)
if flow_type == 'laminar':
fract = 1 - stnum * angle_of_bend * np.pi / 180.
elif flow_type == 'turbulent':
fract = np.exp(-2.823 * stnum * angle_of_bend * np.pi / 180)
else:
raise ValueError('Unknown flow type: %s' % flow_type)
return fract
def gravitational_loss_in_circular_tube(
temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=10, # µm
particle_density=1000, # kg/m^3
tube_diameter=0.01, # m
tube_length=0.1, # m
incline_angle=60, # degrees from horizontal (0-90)
flow_rate=3, # cc/s
mean_flow_velocity=False, # 0.1061 # m/s)
flow_type='auto',
verbose=False):
"""
Arguments
---------
temperature = 293.15, # Kelvin
pressure = 101.3, # kPa
particle_diameter = 10, # µm
particle_density = 1000, # kg/m^3
tube_diameter = 0.01, # m
tube_length = 0.1, # m
incline_angle = 60, # degrees from horizontal (0-90)
flow_rate = 3, # cc/s
mean_flow_velocity = False #0.1061 # m/s)"""
if not mean_flow_velocity:
mean_flow_velocity = _tools_sampling_efficiency.flow_rate2flow_velocity(
flow_rate, tube_diameter, verbose=verbose)
if flow_type == 'auto':
flow_type = _tools_sampling_efficiency.test_flow_type_in_tube(
tube_diameter,
mean_flow_velocity,
temperature,
pressure,
verbose=verbose)
if flow_type == 'laminar':
sv = _tools_sampling_efficiency.settling_velocity(temperature,
particle_density,
particle_diameter,
pressure,
verbose=verbose)
k770 = np.cos(np.pi * incline_angle / 180) * 3 * sv * tube_length / (
4 * tube_diameter * mean_flow_velocity)
if np.any((k770**(2. / 3)) > 1):
fract = 0
else:
if np.any(k770**(2 / 3.) > 1):
k771 = 0
else:
k771 = np.arcsin(k770**(1 / 3.)) # done
fract = (1 - (2 / np.pi) *
(2 * k770 * np.sqrt(1 - k770**(2 / 3)) + k771 -
(k770**(1 / 3) * np.sqrt(1 - k770**(2 / 3))))) # done
if np.any(fract < 0):
fract = 0
elif flow_type == 'turbulent':
raise ValueError(
'Sorry this loss mechanism has not been implemented for turbulent flow'
)
else:
raise ValueError('Unknown flow type: %s' % flow_type)
if verbose:
print('k770: %s' % k770)
print('k771: %s' % k771)
print('fraction penetrating: %s' % fract)
return fract
