Referring to Figure 8.5, we define notation to be used in what follows. The states and denote the conditions at which all the fluid is in the liquid state and the gaseous state respectively.
The specific volumes corresponding to these states are
For conditions corresponding to specific volumes between these two values, i.e., for state , the system would exist with part of the mass in a liquid state and part of the mass in a gaseous (vapor) state. The average specific volume for this condition is
We can relate the average specific volume to the specific volumes for liquid and vapor and the mass that exists in the two phases as follows. The total mass of the system is given by
The volume of the system is
The average specific volume, , is the ratio of the total volume to the total mass of the system
The fraction of the total mass in the vapor phase is called quality , and denoted by :
In terms of the quality and specific volumes, the average specific volume can be expressed as
8.1 Behavior of Two-Phase Systems
Quality, x, is the mass fraction of vapor in a liquid/vapor mixture. In thermal equilibrium, the quality of a two-phase mixture is directly related to heat input and is sometimes called the thermodynamic quality. For example, if an amount Q of heat is applied to a mass of liquid M at saturation temperature, then the mass of vapor generated is MG = Q/ΔhLG where ΔhLG is the latent heat of vaporization. Hence the quality of the two-phase mixture created is given by
If a liquid is flowing in a pipe of diameter D with mass velocity m as shown in Figure 1 and a uniform heat flux q is applied to the walls, then measuring distance L from the point A, where the liquid reaches saturation temperature Tsat,
However, in most practical situations thermal equilibrium does not apply and the true quality is often different from the equilibrium quality calculated from a simple heat balance of the type described above. For example, at the lower quality end of the boiling process (A) part of the heat input may be used in superheating the liquid and the amount of vapor generated correspondingly reduced. Similarly at the higher quality end (B) the vapor may be superheated while droplets of liquid remain in suspension so that the true quality is less than that calculated on the basis of thermal equilibrium (see Boiling). Equilibrium quality is sometimes denoted by xe and actual quality by xa.
Figure 1. Quality, x, in thermal equilibrium.
QUALITY Quality, x, is the mass fraction of vapor in a liquid/vapor mixture. In thermal equilibrium, the quality of a two-phase mixture is directly related to heat input and is sometimes called