iapws (version 1.1)

iapws95: IAPWS-95 Formulation in Single Phase Regions

Description

Compute thermodynamic and transport properties of water and steam using the IAPWS formulation 1995.

Usage

iapws95(what, p, t, rho, h, state = NULL)

Value

A numeric matrix of dimension c(n, length(what)) with n

the maximum length of either rho, p, t, h

or state.

Arguments

what

a character vector listing the output properties. See Details for available properties.

p

a numeric vector giving the pressure values in MPa.

t

a numeric vector giving the temperature values in K.

rho

a numeric vector giving the density values in kg/m\(^3\).

h

a numeric vector giving the specific enthalpy values in kJ/kg.

state

NULL or a character vector giving the physical state. One of "liquid", "gas" or "supercritical". In case of NULL, the state is determined by the function iapws95_state().

Author

Jonathan Debove

Details

The available properties for what are:

• "f": the specific free energy in kJ/kg.

• "g": the specific Gibbs enthalpy in kJ/kg.

• "u": the specific internal energy in kJ/kg.

• "h": the specific enthalpy in kJ/kg.

• "s": the specific entropy in kJ/K/kg.

• "t": the temperature in K.

• "p": the pressure in MPa.

• "v": the specific volume in m\(^3\)/kg.

• "rho": the mass density in kg/m\(^3\).

• "cv": the specific isochoric heat capacity in kJ/K/kg.

• "cp": the specific isobaric heat capacity in kJ/K/kg.

• "alpha": the expansion coefficient in 1/K

• "beta": the pressure coefficient in MPa/K.

• "kappat": the isothermal compressibility in 1/MPa.

• "w": the speed of sound in m/s.

• "eta": the dynamic viscosity in \(\mu\)Pa.s.

• "lambda": the thermal conductivity in mW/K/m.

A valid pair of p, rho, t and h is needed: either (p, t), (rho, t) or (p, h).

References

International Association for the Properties of Water and Steam, IAPWS R6-95(2018), Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use.

International Association for the Properties of Water and Steam, IAPWS R12-08(2008), Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance.

International Association for the Properties of Water and Steam, IAPWS R15-11(2011), Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance.

Examples

# IAPWS-95 Tab. 7
tab <- iapws95(c("p", "cv", "w", "s"),
               t = c(300, 300, 300,
                     500, 500, 500, 500,
                     647,
                     900, 900, 900),
               rho = c(0.9965560e3, 0.1005308e4, 0.1188202e4,
                       0.4350000e0, 0.4532000e1, 0.8380250e3, 0.1084564e4,
                       0.3580000e3,
                       0.2410000e0, 0.5261500e2, 0.8707690e3))
format(tab, scientific = TRUE, digits = 9)
# \dontshow{
stopifnot(all.equal(tab[, "p", drop = FALSE],
          matrix(c(0.992418352e-1, 0.200022515e2, 0.700004704e3,
                   0.999679423e-1, 0.999938125e0, 0.100003858e2,
                   0.700000405e3, 0.220384756e2,
                   0.100062559e0, 0.200000690e2, 0.700000006e3),
                 11, 1, dimnames = list(NULL, c("p"))), tolerance = 1e-9))
# }

# Viscosity Tab. 4
tab <- iapws95("eta",
               t = c(298.15, 298.15, 373.15,
                     433.15, 433.15,
                     873.15, 873.15, 873.15,
                     1173.15, 1173.15, 1173.15),
               rho = c(998, 1200, 1000,
                       1, 1000,
                       1, 100, 600,
                       1, 100, 400))
format(tab, digits = 8)
# \dontshow{
stopifnot(all.equal(tab[, "eta", drop = FALSE],
          matrix(c(889.735100, 1437.649467, 307.883622,
                   14.538324, 217.685358,
                   32.619287, 35.802262, 77.430195,
                   44.217245, 47.640433, 64.154608),
                 11, 1, dimnames = list(NULL, c("eta"))), tolerance = 1e-8))
# }

# Viscosity Tab. 5
tab <- iapws95("eta", t = 647.35, rho = c(122, 222, 272, 322, 372, 422))
format(tab, digits = 8)
# \dontshow{
stopifnot(all.equal(tab[, "eta", drop = FALSE],
          matrix(c(25.520677, 31.337589, 36.228143,
                   42.961579, 45.688204, 49.436256),
                 6, 1, dimnames = list(NULL, c("eta"))), tolerance = 1e-8))
# }

# Thermal conductivity Tab. 4
tab <- iapws95("lambda", t = c(298.15, 298.15, 298.15, 873.15),
               rho = c(0, 998, 1200, 0))
format(tab, digits = 9)
# \dontshow{
stopifnot(all.equal(tab[, "lambda", drop = FALSE],
          matrix(c(18.4341883, 607.712868, 799.038144, 79.1034659),
                 4, 1, dimnames = list(NULL, c("lambda"))), tolerance = 1e-9))
# }

# Thermal conductivity Tab. 5
tab <- iapws95("lambda", t = 647.35,
               rho = c(1, 122, 222, 272, 322, 372, 422, 750))
format(tab, digits = 9)
# \dontshow{
stopifnot(all.equal(tab[, "lambda", drop = FALSE],
          matrix(c(51.9298924, 130.922885, 367.787459, 757.959776,
                   1443.75556, 650.319402, 448.883487, 600.961346),
                 8, 1, dimnames = list(NULL, c("lambda"))), tolerance = 1e-9))
# }