Wet steam is characterized by the vapor quality, ranging from zero to unity – open interval (0,1). When the vapor quality is equal to 0, it is the saturated liquid state (single-phase). On the other hand, when the vapor quality is equal to 1, it is referred to as the saturated vapor state or dry steam (single-phase). Between these two states, we talk about vapor-liquid mixture or wet steam (two-phase mixture). At constant pressure, the addition of energy does not change the mixture’s temperature, but the vapor quality and specific volume change. In the case of dry steam (100% quality), it contains 100% of the latent heat available at that pressure. Saturated liquid water, with no latent heat and therefore 0% quality, will only contain sensible heat.
Typically most nuclear power plants operate multi-stage condensing steam turbines. In these turbines, the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhausts it to a moisture separator-reheater (point D). The steam must be reheated to avoid damages that could be caused to the steam turbine blades by low-quality steam. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam is well below atmospheric pressure and is in a partially condensed state (point F), typically of a quality near 90%.
Specific Enthalpy of Wet Steam
The specific enthalpy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual enthalpy can be calculated with the vapor quality, x, and the specific enthalpies of saturated liquid water and dry steam:
hwet = hs x + (1 – x ) hl
hwet = enthalpy of wet steam (J/kg)
hs = enthalpy of “dry” steam (J/kg)
hl = enthalpy of saturated liquid water (J/kg)
As can be seen, wet steam will always have lower enthalpy than dry steam.
Specific Entropy of Wet Steam
Similarly, the specific entropy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual entropy can be calculated with the vapor quality, x, and the specific entropies of saturated liquid water and dry steam:
swet = ss x + (1 – x ) sl
swet = entropy of wet steam (J/kg K)
ss = entropy of “dry” steam (J/kg K)
sl = entropy of saturated liquid water (J/kg K)
Specific Volume of Wet Steam
Similarly, the specific volume of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual specific volume can be calculated with the vapor quality, x, and the specific volumes of saturated liquid water and dry steam:
vwet = vs x + (1 – x ) vl
vwet = specific volume of wet steam (m3/kg)
vs = specific volume of “dry” steam (m3/kg)
vl = specific volume of saturated liquid water (m3/kg)
A high-pressure steam turbine stage operates at a steady state with inlet conditions of 6 MPa, t = 275.6°C, x = 1 (point C). Steam leaves this turbine stage at a pressure of 1.15 MPa, 186°C, and x = 0.87 (point D). Calculate the enthalpy difference between these two states.
The enthalpy for the state C can be picked directly from steam tables, whereas the enthalpy for the state D must be calculated using vapor quality:
h1, wet = 2785 kJ/kg
h2, wet = h2,s x + (1 – x ) h2,l = 2782 . 0.87 + (1 – 0.87) . 790 = 2420 + 103 = 2523 kJ/kg
Δh = 262 kJ/kg
Vapor Quality – Dryness Fraction
As seen from the phase diagram of water, in the two-phase regions (e.g.,, on the border of vapor/liquid phases), specifying temperature alone will set the pressure, and specifying pressure will set the temperature. But these parameters will not define the volume and enthalpy because we will need to know the relative proportion of the two phases present.
The mass fraction of the vapor in a two-phase liquid-vapor region is called the vapor quality (or dryness fraction), x, and it is given by the following formula:
The value of the quality ranges from zero to unity. Although defined as a ratio, the quality is frequently given as a percentage. From this point of view, we distinguish between three basic types of steam. It must be added, at x=0, we are talking about the saturated liquid state (single-phase).
This classification of steam has its limitation. Consider the system’s behavior, which is heated at a pressure that is higher than the critical pressure. In this case, there would be no change in phase from liquid to steam. In all states, there would be only one phase. Vaporization and condensation can occur only when the pressure is less than the critical pressure. The terms liquid and vapor tend to lose their significance.
See also: Saturation.
See also: Throttling of Steam
Properties of Steam – Steam Tables
Water and steam are common fluids used for heat exchange in the primary circuit (from the surface of fuel rods to the coolant flow) and in the secondary circuit. It is used due to its availability and high heat capacity, both for cooling and heating. It is especially effective to transport heat through vaporization and condensation of water because of its very large latent heat of vaporization.
A disadvantage is that water-moderated reactors have to use the high-pressure primary circuit to keep water in the liquid state and achieve sufficient thermodynamic efficiency. Water and steam also react with metals commonly found in industries such as steel and copper, oxidized faster by untreated water and steam. In almost all thermal power stations (coal, gas, nuclear), water is used as the working fluid (used in a closed-loop between boiler, steam turbine, and condenser), and the coolant (used to exchange the waste heat to a water body or carry it away by evaporation in a cooling tower).
Water and steam are common medium because their properties are very well known. Their properties are tabulated in so-called “Steam Tables”. In these tables, the basic and key properties, such as pressure, temperature, enthalpy, density, and specific heat, are tabulated along the vapor-liquid saturation curve as a function of both temperature and pressure. The properties are also tabulated for single-phase states (compressed water or superheated steam) on a grid of temperatures and pressures extending to 2000 ºC and 1000 MPa.
Further comprehensive, authoritative data can be found at the NIST Webbook page on thermophysical properties of fluids.
See also: Steam Tables.
Special Reference: Allan H. Harvey. Thermodynamic Properties of Water, NISTIR 5078. Retrieved from https://www.nist.gov/sites/default/files/documents/srd/NISTIR5078.htm