iapws.humidAir module

Module with Air-water mixture properties and related properties. The module include:

_virial(): Virial equations for humid air

_fugacity(): Fugacity equation for humid air

MEoSBlend: Special MEoS subclass to implement pseudocomponent blend with ancillary dew and bubble point

Air: Multiparameter equation of state for Air as pseudocomponent

HumidAir: Humid air mixture with complete functionality

iapws.humidAir._virial(T)[source]

Virial equations for humid air

Parameters:

T (float) – Temperature [K]

Returns:

prop –

Dictionary with critical coefficient:

Baa: Second virial coefficient of dry air, [m³/mol]

Baw: Second air-water cross virial coefficient, [m³/mol]

Bww: Second virial coefficient of water, [m³/mol]

Caaa: Third virial coefficient of dry air, [m⁶/mol]

Caaw: Third air-water cross virial coefficient, [m⁶/mol]

Caww: Third air-water cross virial coefficient, [m⁶/mol]

Cwww: Third virial coefficient of dry air, [m⁶/mol]

Bawt: dBaw/dT, [m³/molK]

Bawtt: d²Baw/dT², [m³/molK²]

Caawt: dCaaw/dT, [m⁶/molK]

Caawtt: d²Caaw/dT², [m⁶/molK²]

Cawwt: dCaww/dT, [m⁶/molK]

Cawwtt: d²Caww/dT², [m⁶/molK²]

Return type:

dict

Notes

Raise Warning if T isn’t in range of validity:

Baa: 60 ≤ T ≤ 2000

Baw: 130 ≤ T ≤ 2000

Bww: 130 ≤ T ≤ 1273

Caaa: 60 ≤ T ≤ 2000

Caaw: 193 ≤ T ≤ 493

Caww: 173 ≤ T ≤ 473

Cwww: 130 ≤ T ≤ 1273

Examples

>>> _virial(200)["Baa"]
-3.92722567e-5

References

IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air, http://www.iapws.org/relguide/VirialFugacity.html

IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 10, http://www.iapws.org/relguide/SeaAir.html

iapws.humidAir._fugacity(T, P, x)[source]

Fugacity equation for humid air

Parameters:

T (float) – Temperature, [K]
P (float) – Pressure, [MPa]
x (float) – Mole fraction of water-vapor, [-]

Returns:

fv – fugacity coefficient, [MPa]

Return type:

float

Notes

Raise NotImplementedError if input isn’t in range of validity:

193 ≤ T ≤ 473

0 ≤ P ≤ 5

0 ≤ x ≤ 1

Really the xmax is the xsaturation but isn’t implemented

Examples

>>> _fugacity(300, 1, 0.1)
0.0884061686

References

IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air, http://www.iapws.org/relguide/VirialFugacity.html

class iapws.humidAir.MEoSBlend(**kwargs)[source]

Special meos class to implement pseudocomponent blend and defining its ancillary dew and bubble point

Attributes:

Gas
Gruneisen
Hvap
IntP
Ks
Kt
Liquid
M
P
Pc
Pr
Prandt
Svap
T
Tc
Tr
Tt
Vapor
Z
Z_rho
a
a0
alfa
alfap
alfav
betap
betas
calculable: Check if inputs are enough to define state
cp
cp0
cp0_cv
cp_cv
cv
cv0
dhdP_T
dhdP_rho
dhdT_P
dhdT_rho
dhdrho_P
dhdrho_T
dpdT_rho
dpdrho_T
drhodP_T
drhodT_P
epsilon
f
fi
g
g0
gamma
gamma0
h
h0
hInput
invT
joule
k
kappa
ks
kt
mu
n
name
nu
phase
rho
rho0
rhoc
s
s0
sigma
u
u0
v
v0
virialB
virialC
w
x

Methods

`__call__`(**kwargs)	Make instance callable to can add input parameter one to one
`calculo`()	Calculate procedure
`derivative`(z, x, y, fase)	Wrapper derivative for custom derived properties where x, y, z can be: P, T, v, rho, u, h, s, g, a
`fill`(fase, estado)	Fill phase properties
`from_list`(p1name, p1val, p2name, p2val)	Speed up method using multiprocessing for multiple point calculation with a fixed input and changing other input parameter

_blend = {}

classmethod _dewP(T)[source]: Using ancillary equation return the pressure of dew point

classmethod _bubbleP(T)[source]: Using ancillary equation return the pressure of bubble point

class iapws.humidAir.Air(**kwargs)[source]

Multiparameter equation of state for Air as pseudocomponent for internal procedures, see MEoS base class

References

Lemmon, E.W., Jacobsen, R.T, Penoncello, S.G., Friend, D.G.; Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa. J. Phys. Chem. Ref. Data 29, 331 (2000). http://dx.doi.org/10.1063/1.1285884

Attributes:

Gas
Gruneisen
Hvap
IntP
Ks
Kt
Liquid
P
Pr
Prandt
Svap
T
Tr
Vapor
Z
Z_rho
a
a0
alfa
alfap
alfav
betap
betas
calculable: Check if inputs are enough to define state
cp
cp0
cp0_cv
cp_cv
cv
cv0
dhdP_T
dhdP_rho
dhdT_P
dhdT_rho
dhdrho_P
dhdrho_T
dpdT_rho
dpdrho_T
drhodP_T
drhodT_P
epsilon
f
fi
g
g0
gamma
gamma0
h
h0
hInput
invT
joule
k
kappa
ks
kt
mu
n
nu
phase
rho
rho0
s
s0
sigma
u
u0
v
v0
virialB
virialC
w
x

Methods

`__call__`(**kwargs)	Make instance callable to can add input parameter one to one
`calculo`()	Calculate procedure
`derivative`(z, x, y, fase)	Wrapper derivative for custom derived properties where x, y, z can be: P, T, v, rho, u, h, s, g, a
`fill`(fase, estado)	Fill phase properties
`from_list`(p1name, p1val, p2name, p2val)	Speed up method using multiprocessing for multiple point calculation with a fixed input and changing other input parameter

name = 'air'

CASNumber = '1'

formula = 'N2+Ar+O2'

synonym = 'R-729'

rhoc = 302.622436442

Tc = 132.6306

Pc = 3.786

M = 28.96546

Tt = 59.75

Tb = 78.903

f_acent = 0.0335

momentoDipolar = 0.0

Fi0 = {'ao_exp': [0.791309509, 0.212236768], 'ao_exp2': [-0.197938904], 'ao_log': [1, 2.490888032], 'ao_pow': [6.057194e-08, -2.10274769e-05, -0.000158860716, 9.7450251743948, 10.0986147428912, -0.00019536342], 'pow': [-3, -2, -1, 0, 1, 1.5], 'sum2': [0.6666666666666666], 'titao': [25.36365, 16.90741], 'titao2': [87.31279]}

_constants = {'R': 8.31451, 'Tref': 132.6312, 'c2': [1, 1, 1, 1, 2, 2, 2, 3, 3], 'd1': [1, 1, 1, 2, 3, 3, 4, 4, 4, 6], 'd2': [1, 3, 5, 6, 1, 3, 11, 1, 3], 'gamma2': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'nr1': [0.118160747229, 0.713116392079, -1.61824192067, 0.0714140178971, -0.0865421396646, 0.134211176704, 0.0112626704218, -0.0420533228842, 0.0349008431982, 0.000164957183186], 'nr2': [-0.101365037912, -0.17381369097, -0.0472103183731, -0.0122523554253, -0.146629609713, -0.0316055879821, 0.000233594806142, 0.0148287891978, -0.00938782884667], 'rhoref': 302.622436442, 't1': [0, 0.33, 1.01, 0, 0, 0.15, 0, 0.2, 0.35, 1.35], 't2': [1.6, 0.8, 0.95, 1.25, 3.6, 6, 3.25, 3.5, 15]}

_blend = {'Pj': 3.78502, 'Tj': 132.6312, 'bubble': {'i': [1, 2, 3, 4, 5, 6], 'n': [0.2260724, -7.080499, 5.700283, -12.44017, 17.81926, -10.81364]}, 'dew': {'i': [1, 2, 5, 8], 'n': [-0.1567266, -5.539635, 0.7567212, -3.514322]}}

_melting = {'Pref': 5.265, 'Tmax': 2000.0, 'Tmin': 59.75, 'Tref': 78.903, 'a1': [1, 35493.5, -35493.5], 'a2': [], 'a3': [], 'eq': 1, 'exp1': [0, 1.78963, 0], 'exp2': [], 'exp3': []}

_surf = {'exp': [1.28], 'sigma': [0.03046]}

_rhoG = {'ao': [-2.0466, -4.752, -13.259, -47.652], 'eq': 3, 'exp': [0.41, 1, 2.8, 6.5]}

_Pv = {'ao': [-0.1567266, -5.539635, 0.7567212, -3.514322], 'exp': [0.5, 1, 2.5, 4]}

classmethod _Liquid_Density(T)[source]

Auxiliary equation for the density or saturated liquid

Parameters:: T (float) – Temperature [K]
Returns:: rho – Saturated liquid density [kg/m³]
Return type:: float

static _visco(rho, T, fase=None)[source]

Equation for the Viscosity

Parameters:

rho (float) – Density, [kg/m³]
T (float) – Temperature, [K]

Returns:

μ – Viscosity, [Pa·s]

Return type:

float

References

Lemmon, E.W., Jacobsen, R.T. Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air. Int. J. Thermophys. 25 (1) (2004) 21-69. http://dx.doi.org/10.1023/B:IJOT.0000022327.04529.f3

_thermo(rho, T, fase=None)[source]

Equation for the thermal conductivity

Parameters:

rho (float) – Density, [kg/m³]
T (float) – Temperature, [K]
fase (dict) – phase properties

Returns:

k – Thermal conductivity, [W/mK]

Return type:

float

References

Lemmon, E.W., Jacobsen, R.T. Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air. Int. J. Thermophys. 25 (1) (2004) 21-69. http://dx.doi.org/10.1023/B:IJOT.0000022327.04529.f3

class iapws.humidAir.HumidAir(**kwargs)[source]

Humid air class with complete functionality

Parameters:

T (float) – Temperature, [K]
P (float) – Pressure, [MPa]
rho (float) – Density, [kg/m³]
v (float) – Specific volume, [m³/kg]
A (float) – Mass fraction of dry air in humid air, [kg/kg]
xa (float) – Mole fraction of dry air in humid air, [-]
W (float) – Mass fraction of water in humid air, [kg/kg]
xw (float) – Mole fraction of water in humid air, [-]
HR (float) – Humidity ratio, Mass fraction of water in dry air, [kg/kg]

Notes

It needs two incoming properties of T, P, rho.
v as a alternate input parameter to rho
For composition need one of A, xa, W, xw, HR.

The calculated instance has the following properties:

P: Pressure, [MPa]

T: Temperature, [K]

g: Specific Gibbs free energy, [kJ/kg]

a: Specific Helmholtz free energy, [kJ/kg]

v: Specific volume, [m³/kg]

rho: Density, [kg/m³]

h: Specific enthalpy, [kJ/kg]

u: Specific internal energy, [kJ/kg]

s: Specific entropy, [kJ/kg·K]

cp: Specific isobaric heat capacity, [kJ/kg·K]

w: Speed of sound, [m/s]

alfav: Isobaric cubic expansion coefficient, [1/K]

betas: Isoentropic temperature-pressure coefficient, [-]

xkappa: Isothermal Expansion Coefficient, [-]

ks: Adiabatic Compressibility, [1/MPa]

A: Mass fraction of dry air in humid air, [kg/kg]

W: Mass fraction of water in humid air, [kg/kg]

xa: Mole fraction of dry air, [-]

xw: Mole fraction of water, [-]

Pv: Partial pressure of water, [MPa]

xa_sat: Mole fraction of dry air at saturation state, [-]

mu: Relative chemical potential, [kJ/kg]

muw: Chemical potential of water, [kJ/kg]

M: Molar mass of humid air, [g/mol]

HR: Humidity ratio, Mass fraction of water in dry air, [kg/kg]

RH: Relative humidity, [-]

Attributes:

A
HR
M
P
Pv
RH
T
W
alfav
betas
calculable: Check if inputs are enough to define state
cp
g
h
ks
mu
muw
rho
s
u
v
w
xa
xa_sat
xkappa
xw

Methods

`__call__`(**kwargs)	Make instance callable to can add input parameter one to one
`calculo`()	Calculate procedure
`derivative`(z, x, y)	Wrapper derivative for custom derived properties where x, y, z can be: P, T, v, rho, u, h, s, g, a

status = 0

msg = 'Undefined'

_mode = None

_composition = None

T = None

rho = None

v = None

P = None

s = None

cp = None

h = None

g = None

u = None

alfav = None

betas = None

xkappa = None

ks = None

w = None

A = None

W = None

mu = None

muw = None

M = None

HR = None

xa = None

xw = None

Pv = None

xa_sat = None

RH = None

kwargs = {'A': None, 'HR': None, 'P': 0.0, 'T': 0.0, 'W': None, 'rho': 0.0, 'v': 0.0, 'xa': None, 'xw': None}

property calculable: Check if inputs are enough to define state

calculo()[source]: Calculate procedure

derivative(z, x, y)[source]: Wrapper derivative for custom derived properties where x, y, z can be: P, T, v, rho, u, h, s, g, a

_eq(T, P)[source]

Procedure for calculate the composition in saturation state

Parameters:

T (float) – Temperature [K]
P (float) – Pressure [MPa]

Returns:

Asat – Saturation mass fraction of dry air in humid air [kg/kg]

Return type:

float

static _prop(T, rho, fav)[source]

Thermodynamic properties of humid air

Parameters:

T (float) – Temperature, [K]
rho (float) – Density, [kg/m³]
fav (dict) – dictionary with helmholtz energy and derivatives

Returns:

prop –

Dictionary with thermodynamic properties of humid air:

P: Pressure, [MPa]

s: Specific entropy, [kJ/kgK]

cp: Specific isobaric heat capacity, [kJ/kgK]

h: Specific enthalpy, [kJ/kg]

g: Specific gibbs energy, [kJ/kg]

alfav: Thermal expansion coefficient, [1/K]

betas: Isentropic T-P coefficient, [K/MPa]

xkappa: Isothermal compressibility, [1/MPa]

ks: Isentropic compressibility, [1/MPa]

w: Speed of sound, [m/s]

Return type:

dict

References

IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 5, http://www.iapws.org/relguide/SeaAir.html

static _coligative(rho, A, fav)[source]

Miscelaneous properties of humid air

Parameters:

rho (float) – Density, [kg/m³]
A (float) – Mass fraction of dry air in humid air, [kg/kg]
fav (dict) – dictionary with helmholtz energy and derivatives

Returns:

prop –

Dictionary with calculated properties:

mu: Relative chemical potential, [kJ/kg]

muw: Chemical potential of water, [kJ/kg]

M: Molar mass of humid air, [g/mol]

HR: Humidity ratio, [-]

xa: Mole fraction of dry air, [-]

xw: Mole fraction of water, [-]

Return type:

dict

References

IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 12, http://www.iapws.org/relguide/SeaAir.html

_fav(T, rho, A)[source]

Specific Helmholtz energy of humid air and derivatives

Parameters:

T (float) – Temperature, [K]
rho (float) – Density, [kg/m³]
A (float) – Mass fraction of dry air in humid air, [kg/kg]

Returns:

prop –

Dictionary with helmholtz energy and derivatives:

fir, [kJ/kg]

fira: \(\left.\frac{\partial f_{av}}{\partial A}\right|_{T,\rho}\), [kJ/kg]

firt: \(\left.\frac{\partial f_{av}}{\partial T}\right|_{A,\rho}\), [kJ/kgK]

fird: \(\left.\frac{\partial f_{av}}{\partial \rho}\right|_{A,T}\), [kJ/m³kg²]

firaa: \(\left.\frac{\partial^2 f_{av}}{\partial A^2}\right|_{T, \rho}\), [kJ/kg]

firat: \(\left.\frac{\partial^2 f_{av}}{\partial A \partial T}\right|_{\rho}\), [kJ/kgK]

firad: \(\left.\frac{\partial^2 f_{av}}{\partial A \partial \rho}\right|_T\), [kJ/m³kg²]

firtt: \(\left.\frac{\partial^2 f_{av}}{\partial T^2}\right|_{A, \rho}\), [kJ/kgK²]

firdt: \(\left.\frac{\partial^2 f_{av}}{\partial \rho \partial T}\right|_A\), [kJ/m³kg²K]

firdd: \(\left.\frac{\partial^2 f_{av}}{\partial \rho^2}\right|_{A, T}\), [kJ/m⁶kg³]

Return type:

dict

References

IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 6, http://www.iapws.org/relguide/SeaAir.html

static _fmix(T, rho, A)[source]

Specific Helmholtz energy of air-water interaction

Parameters:

T (float) – Temperature, [K]
rho (float) – Density, [kg/m³]
A (float) – Mass fraction of dry air in humid air, [kg/kg]

Returns:

prop –

Dictionary with helmholtz energy and derivatives:

fir, [kJ/kg]

fira: \(\left.\frac{\partial f_{mix}}{\partial A}\right|_{T,\rho}\), [kJ/kg]

firt: \(\left.\frac{\partial f_{mix}}{\partial T}\right|_{A,\rho}\), [kJ/kgK]

fird: \(\left.\frac{\partial f_{mix}}{\partial \rho}\right|_{A,T}\), [kJ/m³kg²]

firaa: \(\left.\frac{\partial^2 f_{mix}}{\partial A^2}\right|_{T, \rho}\), [kJ/kg]

firat: \(\left.\frac{\partial^2 f_{mix}}{\partial A \partial T}\right|_{\rho}\), [kJ/kgK]

firad: \(\left.\frac{\partial^2 f_{mix}}{\partial A \partial \rho}\right|_T\), [kJ/m³kg²]

firtt: \(\left.\frac{\partial^2 f_{mix}}{\partial T^2}\right|_{A, \rho}\), [kJ/kgK²]

firdt: \(\left.\frac{\partial^2 f_{mix}}{\partial \rho \partial T}\right|_A\), [kJ/m³kg²K]

firdd: \(\left.\frac{\partial^2 f_{mix}}{\partial \rho^2}\right|_{A, T}\), [kJ/m⁶kg³]

Return type:

dict

References

IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 10, http://www.iapws.org/relguide/SeaAir.html