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_at_an_abrupt_contraction_in_circular_tubing(
temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=1, # µm
particle_density=1000, # kg/m^3
tube_air_velocity=False, # m/s
flow_rate_in_inlet=3, # cc/s
tube_diameter=0.0025, # m
contraction_diameter=0.00125, # m
contraction_angle=90, # degrees
verbose=False,
):
"""
(B&W 8-69 to 8-71; W&B 6-54, 17-25)
Temperature 293.15 Kelvin
Pressure 101.3 kPa
Particle diameter 1 µm
Particle density 1000 kg/m^3
Tube air velocity 10 m/s
Tube diameter 0.0025 m
Contraction diameter 0.00125 m
Contraction angle 90 degrees
"""
if not tube_air_velocity:
tube_air_velocity = _tools_sampling_efficiency.flow_rate2flow_velocity(
flow_rate_in_inlet, tube_diameter, verbose=verbose)
st_num = _tools_sampling_efficiency.stokes_number(particle_density,
particle_diameter,
pressure,
temperature,
tube_air_velocity,
1,
contraction_diameter,
verbose=verbose)
# st_num = (particle_density * particle_diameter * particle_diameter * 0.000000000001 * slip_correction_factor * B906 / (18*B912*B908))
frac = 1 - (1 / (1 +
((2 * st_num *
(1 - (contraction_diameter / tube_diameter)**2)) /
(3.14 * np.exp(-0.0185 * contraction_angle)))**-1.24))
return frac
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_at_an_abrupt_contraction_in_circular_tubing(temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=1, # µm
particle_density=1000, # kg/m^3
tube_air_velocity=False, # m/s
flow_rate_in_inlet=3, # cc/s
tube_diameter=0.0025, # m
contraction_diameter=0.00125, # m
contraction_angle=90, # degrees
verbose=False,
):
"""
(B&W 8-69 to 8-71; W&B 6-54, 17-25)
Temperature 293.15 Kelvin
Pressure 101.3 kPa
Particle diameter 1 µm
Particle density 1000 kg/m^3
Tube air velocity 10 m/s
Tube diameter 0.0025 m
Contraction diameter 0.00125 m
Contraction angle 90 degrees
"""
if not tube_air_velocity:
tube_air_velocity = _tools_sampling_efficiency.flow_rate2flow_velocity(flow_rate_in_inlet, tube_diameter, verbose=verbose)
st_num = _tools_sampling_efficiency.stokes_number(particle_density, particle_diameter, pressure, temperature, tube_air_velocity, 1,
contraction_diameter, verbose=verbose)
# st_num = (particle_density * particle_diameter * particle_diameter * 0.000000000001 * slip_correction_factor * B906 / (18*B912*B908))
frac = 1 - (1 / (1 + ((2 * st_num * (1 - (contraction_diameter / tube_diameter) ** 2)) / (
3.14 * np.exp(-0.0185 * contraction_angle))) ** -1.24))
return frac
def inlet_efficiency_isoaxial_horizontal_sharp_edged(
temperature=293.15, # Kelvin
pressure=101.3, # kPa
particle_diameter=15, # µm
particle_density=1000, # kg/m^3
inlet_diameter=0.0127, # m
inlet_length=0.1, # m
sampling_flow_rate=3, # cc/s
air_velocity_inlet=False, # m/s
ambient_air_speed=25.5, # m/s
velocity_ratio=False, # R is 1 for isokinetic, > 1 for subisokinetic
verbose=False):
"""
Inlet efficiency for an isoaxial horizontal sharp-edged inlet: aspiration + transmission (B&W 8-8, 8-14, 8-16, 8-18; W&B 6-8, 6-14, 6-16, 6-18, Hinds 10-7)
Temperature 293.15 Kelvin
Pressure 101.3 kPa
Particle diameter 15 µm
Particle density 1000 kg/m^3
Inlet diameter 0.0127 m
Inlet length 0.1 m
Air velocity in inlet (Vi) 0.05 m/s
Velocity ratio (Vw/Vi) 15
Parameters
----------
temperature
pressure
particle_diameter
particle_density
inlet_diameter
inlet_length
air_velocity_inlet
velocity_ratio
verbose
Returns
-------
"""
if not air_velocity_inlet:
air_velocity_inlet = _tools_sampling_efficiency.flow_rate2flow_velocity(
sampling_flow_rate, inlet_diameter, verbose=verbose)
if not velocity_ratio:
velocity_ratio = ambient_air_speed / air_velocity_inlet
st_no = _tools_sampling_efficiency.stokes_number(particle_density,
particle_diameter,
pressure,
temperature,
air_velocity_inlet,
velocity_ratio,
inlet_diameter,
verbose=verbose)
asp_eff = 1 + (velocity_ratio -
1) * (1 - (1 / (1 + (2 +
(0.617 / velocity_ratio)) * st_no)))
set_vel = _tools_sampling_efficiency.settling_velocity(temperature,
particle_density,
particle_diameter,
pressure,
verbose=verbose)
grav_param = (inlet_length / air_velocity_inlet) / (inlet_diameter /
set_vel)
flow_reyno = _tools_sampling_efficiency.flow_reynolds_number(
inlet_diameter,
air_velocity_inlet,
temperature,
pressure,
verbose=verbose)
grav_eff = np.exp(
-4.7 * (np.sqrt(grav_param * st_no / np.sqrt(flow_reyno)))**0.75)
if velocity_ratio > 1:
init_trans_eff = (1 + (velocity_ratio - 1) /
(1 + 2.66 / st_no**
(2 / 3))) / (1 + (velocity_ratio - 1) /
(1 + 0.418 / st_no))
else:
init_trans_eff = 1
def vena_contracta_efficiency():
if velocity_ratio < 1:
eff = np.exp(
-75 *
(0.09 *
(st_no *
(air_velocity_inlet - air_velocity_inlet * velocity_ratio) /
(air_velocity_inlet * velocity_ratio))**0.3)**2)
else:
eff = 1
return eff
vena_cont_eff = vena_contracta_efficiency()
efficiency = asp_eff * grav_eff * init_trans_eff * vena_cont_eff
return efficiency
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 inlet_efficiency_isoaxial_horizontal_sharp_edged(temperature = 293.15, # Kelvin
pressure = 101.3, # kPa
particle_diameter = 15, # µm
particle_density = 1000, # kg/m^3
inlet_diameter = 0.0127, # m
inlet_length = 0.1, # m
sampling_flow_rate = 3, # cc/s
air_velocity_inlet = False,# m/s
ambient_air_speed = 25.5, # m/s
velocity_ratio = False, # R is 1 for isokinetic, > 1 for subisokinetic
verbose = False
):
"""
Inlet efficiency for an isoaxial horizontal sharp-edged inlet: aspiration + transmission (B&W 8-8, 8-14, 8-16, 8-18; W&B 6-8, 6-14, 6-16, 6-18, Hinds 10-7)
Temperature 293.15 Kelvin
Pressure 101.3 kPa
Particle diameter 15 µm
Particle density 1000 kg/m^3
Inlet diameter 0.0127 m
Inlet length 0.1 m
Air velocity in inlet (Vi) 0.05 m/s
Velocity ratio (Vw/Vi) 15
Parameters
----------
temperature
pressure
particle_diameter
particle_density
inlet_diameter
inlet_length
air_velocity_inlet
velocity_ratio
verbose
Returns
-------
"""
if not air_velocity_inlet:
air_velocity_inlet = _tools_sampling_efficiency.flow_rate2flow_velocity(sampling_flow_rate, inlet_diameter, verbose=verbose)
if not velocity_ratio:
velocity_ratio = ambient_air_speed/air_velocity_inlet
st_no = _tools_sampling_efficiency.stokes_number(particle_density, particle_diameter, pressure, temperature, air_velocity_inlet, velocity_ratio, inlet_diameter, verbose=verbose)
asp_eff = 1 + (velocity_ratio - 1) * (1 - (1 / (1 + (2 + (0.617 / velocity_ratio)) * st_no)))
set_vel = _tools_sampling_efficiency.settling_velocity(temperature, particle_density, particle_diameter, pressure, verbose=verbose)
grav_param =(inlet_length / air_velocity_inlet) / (inlet_diameter / set_vel)
flow_reyno = _tools_sampling_efficiency.flow_reynolds_number(inlet_diameter, air_velocity_inlet, temperature, pressure, verbose=verbose)
grav_eff = np.exp(-4.7 * (np.sqrt(grav_param * st_no / np.sqrt(flow_reyno)))**0.75)
if velocity_ratio > 1:
init_trans_eff = (1 + (velocity_ratio - 1) / (1 + 2.66 / st_no**(2/3))) / (1 + (velocity_ratio - 1) / (1 + 0.418 / st_no))
else:
init_trans_eff = 1
def vena_contracta_efficiency():
if velocity_ratio < 1:
eff = np.exp(-75 * (0.09 * (st_no * (air_velocity_inlet - air_velocity_inlet * velocity_ratio) / (air_velocity_inlet * velocity_ratio))**0.3)**2)
else:
eff = 1
return eff
vena_cont_eff = vena_contracta_efficiency()
efficiency = asp_eff * grav_eff * init_trans_eff * vena_cont_eff
return efficiency
