08_part2b - 2.B Power Cycles with Two-Phase Media (Vapor...

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2B-1 2.B Power Cycles with Two-Phase Media (Vapor Power Cycles) [SB&VW – Chapter 3, Chapter 11, Sections 11.1 to 11.7] In this section, we examine cycles that use two-phase media as the working fluid. These can be combined with gas turbine cycles to provide combined cycles which have higher efficiency than either alone. They can also be used by themselves to provide power sources for both terrestrial and space applications. The topics to be covered are: i) Behavior of two-phase systems: equilibrium, pressure temperature relations ii) Carnot cycles with two-phase media iii) Rankine cycles iv) Combined cycles 2.B.1 Behavior of Two-Phase Systems The definition of a phase, as given by SB&VW, is “a quantity of matter that is homogeneous throughout”. Common examples of systems that contain more than one phase are a liquid and its vapor and a glass of ice water. A system which has three phases is a container with ice, water, and water vapor. We wish to find the relations between phases and the relations that describe the change of phase (from solid to liquid, or from liquid to vapor) of a pure substance, including the work done and the heat transfer. To start we consider a system consisting of a liquid and its vapor in equilibrium, which are enclosed in a container under a moveable piston, as shown in Figure 2B-1. The system is maintained at constant temperature through contact with a heat reservoir at temperature T, so there can be heat transfer to or from the system. (a) Liquid water Liquid water Water vapor Water vapor (b) (c) Figure 2B-1: Two-phase system in contact with constant temperature heat reservoir For a pure substance, as shown at the right, there is a one-to-one correspondence between the temperature at which vaporization occurs and the pressure. These values are called the saturation pressure and saturation temperature (see Ch. 3 in SB&VW). P-T relation for liquid-vapor system
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2B-2 This means there is an additional constraint for a liquid-vapor mixture, in addition to the equation of state. The consequence is that we only need to specify one variable to determine the state of the system. For example, if we specify T then P is set. In summary, for two phases in equilibrium, PP T = () . If both phases are present, any quasi-static process at constant T is also at constant P . Let us examine the pressure-volume behavior of a liquid-vapor system at constant temperature. For a single-phase perfect gas we know that the curve would be Pv = constant. For the two-phase system the curve looks quite different, as indicated in Figure 2B-2. Volume, V Pressure, P Liquid phase Mixture of liquid and vapor Liquid saturation curve Vapor saturation curve Critical point V apor phase Gas phase Critical isotherm D B A C Figure 2B-2 – P-v diagram for two-phase system showing isotherms Several features of the figure should be noted. First, there is a region in which liquid and vapor can coexist. This is roughly dome-shaped and is thus often referred to as the “vapor dome”.
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This note was uploaded on 01/28/2012 for the course AERO 16.050 taught by Professor Zoltanspakovszky during the Fall '02 term at MIT.

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08_part2b - 2.B Power Cycles with Two-Phase Media (Vapor...

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