Viscosity

pygasflow.atd.viscosity.viscosity_air_power_law(T)[source]

Compute air’s viscosity using a power law:

Parameters:

Tfloat or array_like: Temperature of the air in [K]

Returns:

mufloat or array_like: Viscosity [kg / (m * s)]

Notes

The following equation is being used:

mu(T) = 0.702e-07 * T for T <= 200
mu(T) = 0.04644e-05 * T**0.65 for T > 200

Examples

Compute air’s viscosity at T=50K:

>>> from pygasflow.atd.viscosity import viscosity_air_power_law
>>> viscosity_air_power_law(50)
np.float64(3.5100000000000003e-06)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> viscosity_air_power_law(50 * ureg.K)
<Quantity(3.51e-06, 'kilogram / meter / second')>

pygasflow.atd.viscosity.viscosity_air_southerland(T)[source]

Compute the viscosity of air with Southerland equation.

Parameters:

Tfloat or array_like: Temperature of the air in [K]

Returns:

mufloat or array_like: Viscosity [kg / (m * s)]

Examples

Compute air’s viscosity at T=50K:

>>> from pygasflow.atd.viscosity import viscosity_air_southerland
>>> viscosity_air_southerland(50)
np.float64(3.2137209693578125e-06)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> viscosity_air_southerland(50 * ureg.K)
<Quantity(3.21372097e-06, 'kilogram / meter / second')>

pygasflow.atd.viscosity.viscosity_chapman_enskog(T, gas='air', M=None, sigma=None, Sigma_mu=None)[source]

Compute the viscosity of pure motoatomic or polyatomic gases using Chapman-Enskog theory.

There are two mode of operation:

by providing the gas keyword argument, the algorithm will load pre-computed values of M, sigma and Sigma_mu. viscosity_chapman_enskog(T, gas="air" [optional])
by providing M, sigma and Sigma_mu. This is going to disregard the value of gas, and computes the viscosity of air. viscosity_chapman_enskog(T, M=M, sigma=sigma, Sigma_mu=Sigma_mu)

Parameters:

Tfloat or array_like: Temperature of the air in [K]
gasstr, optional: Possible values are: ['air', 'N2', 'O2', 'NO', 'N', 'O', 'Ar', 'He']
Mfloat or None, optional: Molecular weigth [kg / kmole]
sigmafloat or None, optional: Collision parameter (first Lennard-Jones parameter) [m]
Sigma_mufloat or None, optional: Dimensionless collision integral

Returns:

mufloat or array_like: Viscosity [kg / (m * s)]

References

“Basic of aerothermodynamics” by Ernst Heinrich, Table 13.1
“Transport Phenomena” by R. Byron Bird, Warren E. Stewart, Edwing N. Lightfoot, Table E2

Examples

Compute air’s viscosity at T=50K:

>>> from pygasflow.atd.viscosity import viscosity_chapman_enskog
>>> viscosity_chapman_enskog(50)
np.float64(3.4452054654966263e-06)

Compute the viscosity of molecular oxygen at T=300K:

>>> viscosity_chapman_enskog(300, gas="O2")
np.float64(2.069427983599303e-05)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> viscosity_chapman_enskog(50 * ureg.K)
<Quantity(3.44520547e-06, 'kilogram / meter / second')>

Comparison of the viscosity of different gases over a range of temperatures.

import numpy as np
import matplotlib.pyplot as plt
from pygasflow.atd import viscosity_chapman_enskog
T = np.linspace(200, 1000)
gases = ['air', 'N2', 'O2', 'NO', 'N', 'O', 'Ar', 'He']
fig, ax = plt.subplots()
for gas in gases:
    ax.plot(T, viscosity_chapman_enskog(T, gas=gas), label=gas)
ax.legend()
ax.set_xlabel("Temperature [K]")
ax.set_ylabel("Viscosity [kg / (m * s)]")
plt.show()

(Source code, png, hires.png, pdf)