There are many equations that describe the thermodynamic state and properties of steam. While some of these equations are accurate in generating property tables, they are not suitable for fast CFD computations. Therefore, Ansys Fluent uses simpler forms of the thermodynamic state equations for efficient CFD calculations that are accurate over a wide range of temperatures and pressures. Two alternative formulations for the equation of state that are used in the solver are taken from [58] and [726], and they are described below along with the equations of steam properties.
There are two available formulations for the equation of state for steam and they are described in the following sections:
The equations of state developed for steam in literature often refer to equilibrium states (dry steam region). To calculate properties of supercooled vapor, it is necessary to extrapolate these equations into the meta-stable region which may be beyond their range of validity. The problem was investigated in [57]and it was found that the virial equation developed by Vukalovich [682] could be extrapolated into these states with negligible error. It has therefore been adopted in the solver as the default option and the equation reads as:
 | (14–549) |
In this equation, B, C and D are the second, third, and fourth virial coefficients, respectively. They are given by the following empirical functions:
 | (14–550) |
 | (14–551) |
 | (14–552) |
The units for the variables in Equation 14–549 are 
for the static pressure 
, 
for the static temperature 
, and 
for the vapor density 
. Virial coefficients (Equation 14–550) are given in
the units 
, 
, and 
for B, C, and D, respectively. The specific gas constant of water vapor 
is equal to 461.52 
.
The vapor specific enthalpy 
is given in 
by:
 | (14–553) |
The vapor specific entropy 
is given in 
by:
 | (14–554) |
The vapor isobaric and isochoric specific heat capacities, 
and 
, are given in 
by:
 | (14–555) |
The empirical functions that define the virial coefficients and the
thermodynamic properties cover the temperature range 273-973 
and the pressure range 
.
The vapor dynamic viscosity 
and thermal conductivity 
are functions of temperature only and were obtained from [725].
An alternative equation of state used in the solver, which relates the pressure to the vapor density and the temperature, is given by Young [726]:
 | (14–556) |
where 
, and 
are the second and the third virial coefficients given by the following
empirical functions:
 | (14–557) |
where 
is given in m3/kg, 
= 
with 
given in Kelvin, 
= 10000.0, 
= 0.0015, 
= -0.000942, and 
= -0.0004882.
 | (14–558) |
where 
is given in m6/kg2,
= 
with 
given in Kelvin, 
= 0.8978, 
=11.16, 
= 1.772, and 
= 1.5E-06.
The two empirical functions that define the virial coefficients
and 
cover the temperature range from 273 K to 1073 K.
The vapor isobaric specific heat capacity 
is given by:
 | (14–559) |
The vapor specific enthalpy, 
is given by:
 | (14–560) |
The vapor specific entropy, 
is given by:
 | (14–561) |
The isobaric specific heat at zero pressure is defined by the following empirical equation:
 | (14–562) |
where 
is in KJ/kg K, 
= 46.0, 
= 1.47276, 
= 8.38930E-04, 
= -2.19989E-07, 
= 2.46619E-10, and 
= -9.70466E-14.
Both 
and 
are functions of temperature and they are defined by:
 | (14–563) |
 | (14–564) |
where 
and 
are arbitrary constants.
The vapor dynamic viscosity 
and thermal conductivity 
are also functions of temperature and were obtained from [725].
The saturation pressure equation as a function of temperature was obtained from [551]. The example provided in UDWSPF Example in the User's Guide contains a function called
wetst_satP() that represents the formulation for the saturation
pressure.
At the saturated liquid-line, the liquid density, surface tension,
specific heat 
, dynamic viscosity, and thermal
conductivity must be defined. The equation for liquid density, 
,
was obtained from [551]. The liquid surface
tension equation was obtained from [725]. While
the values of 
, 
and 
were curve fit using published data from [157] and then written in polynomial forms. The
example provided in UDWSPF Example in the User's Guide contains
functions called wetst_cpl(), wetst_mul(), and wetst_ktl() that represent formulations for 
, 
and 
.
