iapws.ammonia module

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

  • NH3: Multiparameter equation of state for ammonia
  • H2ONH3: Thermodynamic properties of ammonia-water mixtures
  • Ttr: Triple point of ammonia-water mixtures
class iapws.ammonia.NH3(**kwargs)[source]

Multiparameter equation of state for ammonia for internal procedures, see MEoS base class

Parameters:
  • T (float) – Temperature, [K]
  • P (float) – Pressure, [MPa]
  • rho (float) – Density, [kg/m³]
  • v (float) – Specific volume, [m³/kg]
  • h (float) – Specific enthalpy, [kJ/kg]
  • s (float) – Specific entropy, [kJ/kgK]
  • u (float) – Specific internal energy, [kJ/kg]
  • x (float) – Vapor quality, [-]
  • l (float, optional) – Wavelength of light, for refractive index, [nm]
  • rho0 (float, optional) – Initial value of density, to improve iteration, [kg/m³]
  • T0 (float, optional) – Initial value of temperature, to improve iteration, [K]
  • x0 (Initial value of vapor quality, necessary in bad input pair definition) – where there are two valid solution (T-h, T-s)

Notes

  • It needs two incoming properties of T, P, rho, h, s, u.
  • v as a alternate input parameter to rho
  • T-x, P-x, preferred input pair to specified a point in two phases region

The calculated instance has the following properties:

  • P: Pressure, [MPa]
  • T: Temperature, [K]
  • x: Vapor quality, [-]
  • g: Specific Gibbs free energy, [kJ/kg]
  • a: Specific Helmholtz free energy, [kJ/kg]
  • v: Specific volume, [m³/kg]
  • r: 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]
  • cv: Specific isochoric heat capacity, [kJ/kg·K]
  • cp_cv: Heat capacity ratio, [-]
  • Z: Compression factor, [-]
  • fi: Fugacity coefficient, [-]
  • f: Fugacity, [MPa]
  • gamma: Isoentropic exponent, [-]
  • alfav: Isobaric cubic expansion coefficient, [1/K]
  • kappa: Isothermal compressibility, [1/MPa]
  • kappas: Adiabatic compresibility, [1/MPa]
  • alfap: Relative pressure coefficient, [1/K]
  • betap: Isothermal stress coefficient, [kg/m³]
  • joule: Joule-Thomson coefficient, [K/MPa]
  • betas: Isoentropic temperature-pressure coefficient, [-]
  • Gruneisen: Gruneisen parameter, [-]
  • virialB: Second virial coefficient, [m³/kg]
  • virialC: Third virial coefficient, [m⁶/kg²]
  • dpdT_rho: Derivatives, dp/dT at constant rho, [MPa/K]
  • dpdrho_T: Derivatives, dp/drho at constant T, [MPa·m³/kg]
  • drhodT_P: Derivatives, drho/dT at constant P, [kg/m³·K]
  • drhodP_T: Derivatives, drho/dP at constant T, [kg/m³·MPa]
  • dhdT_rho: Derivatives, dh/dT at constant rho, [kJ/kg·K]
  • dhdP_T: Isothermal throttling coefficient, [kJ/kg·MPa]
  • dhdT_P: Derivatives, dh/dT at constant P, [kJ/kg·K]
  • dhdrho_T: Derivatives, dh/drho at constant T, [kJ·m³/kg²]
  • dhdrho_P: Derivatives, dh/drho at constant P, [kJ·m³/kg²]
  • dhdP_rho: Derivatives, dh/dP at constant rho, [kJ/kg·MPa]
  • kt: Isothermal Expansion Coefficient, [-]
  • ks: Adiabatic Compressibility, [1/MPa]
  • Ks: Adiabatic bulk modulus, [MPa]
  • Kt: Isothermal bulk modulus, [MPa]
  • v0: Ideal specific volume, [m³/kg]
  • rho0: Ideal gas density, [kg/m³]
  • u0: Ideal specific internal energy, [kJ/kg]
  • h0: Ideal specific enthalpy, [kJ/kg]
  • s0: Ideal specific entropy, [kJ/kg·K]
  • a0: Ideal specific Helmholtz free energy, [kJ/kg]
  • g0: Ideal specific Gibbs free energy, [kJ/kg]
  • cp0: Ideal specific isobaric heat capacity, [kJ/kg·K]
  • cv0: Ideal specific isochoric heat capacity, [kJ/kg·K]
  • w0: Ideal speed of sound, [m/s]
  • gamma0: Ideal isoentropic exponent, [-]
  • w: Speed of sound, [m/s]
  • mu: Dynamic viscosity, [Pa·s]
  • nu: Kinematic viscosity, [m²/s]
  • k: Thermal conductivity, [W/m·K]
  • alfa: Thermal diffusivity, [m²/s]
  • sigma: Surface tension, [N/m]
  • epsilon: Dielectric constant, [-]
  • n: Refractive index, [-]
  • Prandt: Prandtl number, [-]
  • Pr: Reduced Pressure, [-]
  • Tr: Reduced Temperature, [-]
  • Hvap: Vaporization heat, [kJ/kg]
  • Svap: Vaporization entropy, [kJ/kg·K]
  • Z_rho: \((Z-1)/\rho\), [m³/kg]
  • IntP: Internal pressure, [MPa]
  • invT: Negative reciprocal temperature, [1/K]
  • hInput: Specific heat input, [kJ/kg]

References

Baehr, H.D., Tillner-Roth, R.; Thermodynamic Properties of Environmentally Acceptable Refrigerants: Equations of State and Tables for Ammonia, R22, R134a, R152a, and R123. Springer-Verlag, Berlin, 1994. http://doi.org/10.1007/978-3-642-79400-1

Attributes:
CP
Gruneisen
IntP
Ks
Kt
Prandt
Z
Z_rho
a
alfa
alfap
alfav
betap
betas
calculable

Check if inputs are enough to define state

cp
cp_cv
cv
dhdP_T
dhdP_rho
dhdT_P
dhdT_rho
dhdrho_P
dhdrho_T
dpdT_rho
dpdrho_T
drhodP_T
drhodT_P
epsilon
f
fi
g
gamma
h
hInput
joule
k
kappa
ks
kt
mu
n
nu
rho
s
u
v
w

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
name = 'ammonia'
CASNumber = '7664-41-7'
formula = 'NH3'
synonym = 'R-717'
rhoc = 225.0
Tc = 405.4
Pc = 11.333
M = 17.03026
Tt = 195.495
Tb = 239.823
f_acent = 0.25601
momentoDipolar = 1.47
Fi0 = {'ao_exp': [], 'ao_hyp': [], 'ao_log': [1, -1], 'ao_pow': [-15.81502, 4.255726, 11.47434, -1.296211, 0.5706757], 'hyp': [], 'pow': [0, 1, 0.3333333333333333, -1.5, -1.75], 'titao': []}
_constants = {'R': 8.314471, 'c2': [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], 'd1': [1, 2, 1, 4, 15], 'd2': [3, 3, 1, 8, 2, 8, 1, 1, 2, 3, 2, 4, 3, 1, 2, 4], 'gamma2': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'nr1': [-1.858814, 0.04554431, 0.7238548, 0.0122947, 2.141882e-11], 'nr2': [-0.0143002, 0.3441324, -0.2873571, 2.352589e-05, -0.03497111, 0.001831117, 0.02397852, -0.04085375, 0.2379275, -0.03548972, -0.1823729, 0.02281556, -0.006663444, -0.008847486, 0.002272635, -0.0005588655], 't1': [1.5, -0.5, 0.5, 1.0, 3.0], 't2': [0, 3, 4, 4, 5, 5, 3, 6, 8, 8, 10, 10, 5, 7.5, 15, 30]}
_melting = {'Pref': 1000, 'Tmax': 700.0, 'Tmin': 195.495, 'Tref': 195.495, 'a1': [], 'a2': [], 'a3': [2533.125], 'eq': 1, 'exp1': [], 'exp2': [], 'exp3': [1]}
_surf = {'exp': [1.211, 5.585], 'sigma': [0.1028, -0.09453]}
_Pv = {'ao': [-7.0993, -2.433, 8.7591, -6.4091, -2.1185], 'eq': 5, 'exp': [1.0, 1.5, 1.7, 1.95, 4.2]}
_rhoL = {'ao': [34.488, -128.49, 173.82, -106.99, 30.339], 'eq': 1, 'exp': [0.58, 0.75, 0.9, 1.1, 1.3]}
_rhoG = {'ao': [-0.38435, -4.0846, -6.6634, -31.881, 213.06, -246.48], 'eq': 3, 'exp': [0.218, 0.55, 1.5, 3.7, 5.5, 5.8]}
_visco(rho, T, fase=None)[source]

Equation for the Viscosity

Parameters:
  • rho (float) – Density [kg/m³]
  • T (float) – Temperature [K]
Returns:

mu – Viscosity [Pa·s]

Return type:

float

References

Fenghour, A., Wakeham, W.A., Vesovic, V., Watson, J.T.R., Millat, J., and Vogel, E., The viscosity of ammonia, J. Phys. Chem. Ref. Data 24, 1649 (1995). doi:10.1063/1.555961

_thermo(rho, T, fase)[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

Tufeu, R., Ivanov, D.Y., Garrabos, Y., and Le Neindre, B., Thermal conductivity of ammonia in a large temperature and pressure range including the critical region, Ber. Bunsenges. Phys. Chem., 88:422-427, 1984. doi:10.1002/bbpc.19840880421

class iapws.ammonia.H2ONH3[source]

Ammonia-water mixtures.

_prop(rho, T, x)[source]

Thermodynamic properties of ammonia-water mixtures

Parameters:
  • T (float) – Temperature [K]
  • rho (float) – Density [kg/m³]
  • x (float) – Mole fraction of ammonia in mixture [mol/mol]
Returns:

prop

Dictionary with thermodynamic properties of ammonia-water mixtures:

  • M: Mixture molecular mass, [g/mol]
  • P: Pressure, [MPa]
  • u: Specific internal energy, [kJ/kg]
  • s: Specific entropy, [kJ/kgK]
  • h: Specific enthalpy, [kJ/kg]
  • a: Specific Helmholtz energy, [kJ/kg]
  • g: Specific gibbs energy, [kJ/kg]
  • cv: Specific isochoric heat capacity, [kJ/kgK]
  • cp: Specific isobaric heat capacity, [kJ/kgK]
  • w: Speed of sound, [m/s]
  • fugH2O: Fugacity of water, [-]
  • fugNH3: Fugacity of ammonia, [-]

Return type:

dict

References

IAPWS, Guideline on the IAPWS Formulation 2001 for the Thermodynamic Properties of Ammonia-Water Mixtures, http://www.iapws.org/relguide/nh3h2o.pdf, Table 4

_phi0(rho, T, x)[source]

Ideal gas Helmholtz energy of binary mixtures and derivatives

Parameters:
  • rho (float) – Density, [kg/m³]
  • T (float) – Temperature, [K]
  • x (float) – Mole fraction of ammonia in mixture, [mol/mol]
Returns:

prop – Dictionary with ideal adimensional helmholtz energy and derivatives:

  • tau: the adimensional temperature variable, [-]
  • delta: the adimensional density variable, [-]
  • fio,[-]
  • fiot: [∂fio/∂τ]δ [-]
  • fiod: [∂fio/∂δ]τ [-]
  • fiott: [∂²fio/∂τ²]δ [-]
  • fiodt: [∂²fio/∂τ∂δ] [-]
  • fiodd: [∂²fio/∂δ²]τ [-]

Return type:

dict

References

IAPWS, Guideline on the IAPWS Formulation 2001 for the Thermodynamic Properties of Ammonia-Water Mixtures, http://www.iapws.org/relguide/nh3h2o.pdf, Eq 2

_phir(rho, T, x)[source]

Residual contribution to the free Helmholtz energy

Parameters:
  • rho (float) – Density, [kg/m³]
  • T (float) – Temperature, [K]
  • x (float) – Mole fraction of ammonia in mixture, [mol/mol]
Returns:

prop – dictionary with residual adimensional helmholtz energy and derivatives:

  • tau: the adimensional temperature variable, [-]
  • delta: the adimensional density variable, [-]
  • fir, [-]
  • firt: [∂fir/∂τ]δ,x [-]
  • fird: [∂fir/∂δ]τ,x [-]
  • firtt: [∂²fir/∂τ²]δ,x [-]
  • firdt: [∂²fir/∂τ∂δ]x [-]
  • firdd: [∂²fir/∂δ²]τ,x [-]
  • firx: [∂fir/∂x]τ,δ [-]
  • F: Function for fugacity calculation, [-]

Return type:

dict

References

IAPWS, Guideline on the IAPWS Formulation 2001 for the Thermodynamic Properties of Ammonia-Water Mixtures, http://www.iapws.org/relguide/nh3h2o.pdf, Eq 3

_Dphir(tau, delta, x)[source]

Departure function to the residual contribution to the free Helmholtz energy

Parameters:
  • tau (float) – Adimensional temperature, [-]
  • delta (float) – Adimensional density, [-]
  • x (float) – Mole fraction of ammonia in mixture, [mol/mol]
Returns:

prop – Dictionary with departure contribution to the residual adimensional helmholtz energy and derivatives:

  • fir [-]
  • firt: [∂Δfir/∂τ]δ,x [-]
  • fird: [∂Δfir/∂δ]τ,x [-]
  • firtt: [∂²Δfir/∂τ²]δ,x [-]
  • firdt: [∂²Δfir/∂τ∂δ]x [-]
  • firdd: [∂²Δfir/∂δ²]τ,x [-]
  • firx: [∂Δfir/∂x]τ,δ [-]

Return type:

dict

References

IAPWS, Guideline on the IAPWS Formulation 2001 for the Thermodynamic Properties of Ammonia-Water Mixtures, http://www.iapws.org/relguide/nh3h2o.pdf, Eq 8

iapws.ammonia.Ttr(x)[source]

Equation for the triple point of ammonia-water mixture

Parameters:x (float) – Mole fraction of ammonia in mixture, [mol/mol]
Returns:Ttr – Triple point temperature, [K]
Return type:float

Notes

Raise NotImplementedError if input isn’t in limit:

  • 0 ≤ x ≤ 1

References

IAPWS, Guideline on the IAPWS Formulation 2001 for the Thermodynamic Properties of Ammonia-Water Mixtures, http://www.iapws.org/relguide/nh3h2o.pdf, Eq 9