iapws (version 1.1)

if97: IAPWS-IF97 Equations for Regions 1, 2, 3 and 5

Description

Compute thermodynamic and transport properties of water and steam using the IAPWS industrial formulation 1997.

Usage

if97(what, p, t, h, state = NULL)

Value

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

the maximum length of either 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.

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 if97_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, t and h is needed: either (p, t) or (p, h).

References

International Association for the Properties of Water and Steam, IAPWS R7-97(2012), Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam.

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

what <- c("v", "h", "u", "s", "cp", "w")

# Region 1 Tab. 5
tab5 <- if97(what, t = c(300, 300, 500), p = c(3, 80, 3))
format(tab5, scientific = TRUE, digits = 9)

# Region 2 Tab. 15
tab15 <- if97(what, t = c(300, 700, 700), p = c(3.5e-3, 3.5e-3, 30))
format(tab15, scientific = TRUE, digits = 9)

# Region 2 metastable Tab. 18
tab18 <- if97(what, t = c(450, 440, 450), p = c(1, 1, 1.5), state = "gas")
format(tab18, scientific = TRUE, digits = 9)

# Region 3 Tab. 33
tab33 <- if97(what, t = c(650, 650, 750),
              p = c(0.255837018e2, 0.222930643e2, 0.783095639e2))
format(tab33, scientific = TRUE, digits = 9)

# Region 5 Tab. 42
tab42 <- if97(what, t = c(1500, 1500, 2000), p = c(0.5, 30, 30))
format(tab42, scientific = TRUE, digits = 9)

# \dontshow{
stopifnot(all.equal(tab5[, "v", drop = FALSE],
          matrix(c(0.100215168e-2, 0.971180894e-3, 0.120241800e-2),
                 3, 1, dimnames = list(NULL, "v")),
          tolerance = 2e-9),
          all.equal(tab15[, "v", drop = FALSE],
          matrix(c(0.394913866e2, 0.923015898e2, 0.542946619e-2),
                 3, 1, dimnames = list(NULL, "v")),
          tolerance = 2e-9),
          all.equal(tab18[, "v", drop = FALSE],
          matrix(c(0.192516540, 0.186212297, 0.121685206),
                 3, 1, dimnames = list(NULL, "v")),
          tolerance = 2e-9),
          all.equal(tab33[, "v", drop = FALSE],
          matrix(1 / c(500, 200, 500),
                 3, 1, dimnames = list(NULL, "v")),
          tolerance = 2e-8),
          all.equal(tab42[, "v", drop = FALSE],
          matrix(c(0.138455090e1, 0.230761299e-1, 0.311385219e-1),
                 3, 1, dimnames = list(NULL, "v")),
          tolerance = 2e-9))
# }

# Viscosity and thermal conductivity
what <- c("lambda", "eta")

# Region 1 Tab. 7
tab7 <- if97(what, p = c(20, 50), t = c(620, 620))
format(tab7, scientific = TRUE, digits = 9)

# Region 2 Tab. 8
tab8 <- if97(what, p = c(0.3, 50), t = c(650, 800))
format(tab8, scientific = TRUE, digits = 9)

## Region 3 Tab. 9
#tab9 <- if97_rhot(c("lambda", "rho", "cp", "cv", "eta"),
#      rho = c(0.3, 50), t = c(222, 322)),
#format(tab9, scientific = TRUE, digits = 9)

# \dontshow{
stopifnot(all.equal(tab7[, "lambda", drop = FALSE],
          matrix(c(0.481485195e3, 0.545038940e3),
                 2, 1, dimnames = list(NULL, "lambda")),
          tolerance = 2e-9),
          all.equal(tab8[, "lambda", drop = FALSE],
          matrix(c(0.522311024e2, 0.177709914e3),
                 2, 1, dimnames = list(NULL, "lambda")),
          tolerance = 3e-9))
# }