## Info

#2, p. 149; #1, Chap. 4

Brayton(gas)

2 isentropic; 2 isobaric

1 - (plw-i)/'

#2, p. 201

Otto (gas)

2 isentropic, 2 isochoric

1 - (Vl/VH)y-1

#3, p. 38

Stirling

2 isochoric; 2 isothermal

1 - Tl/Th

#2, p. 199

Ericsson

2 isobaric, 2 isothermal

1 - Tl/Th

#2, p. 199

The Rankine and Brayton cycles differ in the nature of the circulating fluid. The Rankine cycle (Fig. 4.3) is close to the Carnot cycle because water is used as the working medium, so the isobaric steps involve condensation or vaporization of water also occur isothermally. Cycles that include a pair of isothermal steps (Stirling and Ericsson) have the same theoretical efficiency as the Carnot cycle. The Otto cycle utilizes a gas as a working fluid, and is the basis of the internal combustion engine. The Stirling and Ericsson cycles also normally use gases, but Problem 4.3 analyzes an Ericsson cycle using water/steam as the working fluid

Equation (4.9) is the starting point for the following analyses of power cycles, starting with the steam power plant in Fig. 4.3. The units of V2 are m2/s2. Because a Joule is one kg-m2/s2, the units of all terms in Eq (4.9) are J/kg.

4.5.1 The Rankine cycle - a steam power plant

This cycle consists of four components:

1. a means of producing heat, typically a hydrocarbon-burning furnace or a nuclear reactor. The actual device that receives this energy and transmits it to the circulating fluid is a boiler or a steam-generator, respectively

2. an apparatus that converts the energy in the flowing steam to shaft work. This is invariably a turbine (Fig. 4.10)

3. A condenser that converts the exhaust steam from the turbine to subcooled liquid.

4. A pump that pressurizes the water to the value at which the boiler and turbine operate

The Rankine cycle is best understood by example. The four components are shown in the flow chart in Fig. 4.11 along with the quantities that need to be specified to undertake the analysis. Figure 4.12 is the T - v projection of the equation of state of water (see Fig. 2.6) upon which is drawn process diagram of the cycle. The high and low temperatures of the cycle are labeled TH ahnd TL, respectively, in order to compare the efficiency to that of a hypothetical Carnot engine operating between these temperatures.

High-pressure steam (state 1) The enthalpy and entropy of the superheated steam entering the turbine are obtained Table A.3 and the pressure and temperature at this location.

Turbine exhaust (state 2) Here water is a two-phase mixture with the enthalpy and entropy of the saturated liquid and the saturated vapor determined by the specified pressure and Table A.2. The given steam quality provides the mixture enthalpy via Eq (2.22) and the analogous equation for the mixture entropy.

Condensed water (state 3) The pressure and temperature determine the remaining properties of the condensed liquid from the single-phase steam table A.4.

Compressed water (state 4) the enthalpy at the exit of the condenser is obtained from extrapolation of the data in steam table A.4 to low pressure.

With the above information in hand, the heat and work associated with each component can be determined by application of the First law in the form of Eq (4.9). In all cases, the kinetic energy terms are neglected because V2 is small compared to the enthalpy terms. The results are summarized in Table 4.2.

Table 4.2 First Law/EOS analysis of a Rankine cycle turbine

condenser ^

pump

boiler

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