Chapter 10

# Chapter 10 - Chapter 10 Cycles Read BS In this chapter we...

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Unformatted text preview: Chapter 10 Cycles Read BS, Chapters 11, 12 In this chapter, we will delve more deeply into some thermodynamic cycles. 10.1 Rankine Large electric power plants typically utilize a vapor power cycle. Regardless of the heat source, be it nuclear or combustion of coal, oil, natural gas, wood chips, etc., the remaining details of these plants are similar. Typically a pure working fluid, usually water, is circulated through a cycle, and that fluid trades heat and work with its surroundings. We sketch a typical power plant cycle for electricity generation in Fig. 10.1. The ideal Rankine cycle was first described in 1859 by William John Macquorn Rankine, long after the steam engine was in wide usage. The cycle has the following steps: • 1 → 2: isentropic compression in a pump, • 2 → 3: isobaric heating in a boiler, • 3 → 4: isentropic expansion in a turbine, and • 4 → 1: isobaric cooling in a condenser. Two variants of the T − s diagram are given in Fig. 10.2. The first is more efficient as it has the appearance of a Carnot cycle. However, it is impractical, as it induces liquid water in the turbine, which can damage its blades. So the second is more common. The thermal efficiency is η = ˙ W net ˙ Q H = ˙ W turbine + ˙ W pump ˙ Q boiler . (10.1) 281 282 CHAPTER 10. CYCLES 1 2 3 4 turbine boiler condenser pump fuel air work in combustion exhaust generator +- . . cooling tower cold water hot water Figure 10.1: Rankine cycle schematic. This reduces to η = ˙ m (( h 3 − h 4 ) + ( h 1 − h 2 )) ˙ m ( h 3 − h 2 ) , (10.2) = 1 − h 4 − h 1 h 3 − h 2 , (10.3) = 1 − q out,condenser q in,boiler . (10.4) Power plants are sometimes characterized by their • back work ratio : bwr , the ratio of pump work to turbine work. Here bwr = | pump work | | turbine work | = h 2 − h 1 h 3 − h 4 . (10.5) We model the pump work as an isentropic process. Recall our analysis for isentropic pumps which generated Eq. (9.46). The Gibbs equation gives Tds = dh − vdP . If ds = 0, we have dh = vdP, (10.6) Thus for the pump h 2 − h 1 = v ( P 2 − P 1 ) , (10.7) CC BY-NC-ND. 2011, J. M. Powers. 10.1. RANKINE 283 s T 1 2 3 4 s T 1 2 3 4 Figure 10.2: T − s for two Rankine cycles. since v is nearly constant, so the integration is simple. It might be tempting to make the Rankine cycle into a Carnot cycle as sketched in Fig. 10.3. However, it is practically difficult to build a pump to handle two-phase mixtures. s T 1 2 3 4 Figure 10.3: Rankine-Carnot cycle. The gas phase can seriously damage the pump. Some features which could be desirable for a Rankine cycle include • high power output: One can enhance this by raising the fluid to a high temperature during the combustion process or by pumping the fluid to a high pressure. Both CC BY-NC-ND. 2011, J. M. Powers. 284 CHAPTER 10. CYCLES strategies soon run into material limits; turbine blades melt and pipes burst. Another strategy is to lower the condenser pressure, which means that one must maintain a...
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Chapter 10 - Chapter 10 Cycles Read BS In this chapter we...

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