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)

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, [μm]
• 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:

Gas

Gruneisen

Hvap

IntP

Ks

Kt

Liquid

P

Pr

Prandt

Svap

T

Tr

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

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)

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)

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

Ammonia-water mixtures.

_prop(rho, T, x)

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

static _phi0(rho, T, x)

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)

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

static _Dphir(tau, delta, x)

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)

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