Modern Engineering Thermodynamics

488 CHAPTER 13: Vapor and Gas Power Cycles
CRITICAL THINKING
When we say that an engine or compressor is isentropic, we mean that the entropy at the exit is the same as the entropy at
the inlet. But this condition alone is not enough to fix the exit state, since we must specify two independent thermodynamic
properties to fix a state. We could choose the actual exit pressure or the actual exit temperature as the second independent
property at the exit. However, in practice, we always choose the actual exit pressure as the second independent
property. Why do we do this?
The answer is simply that the exit pressure is more often known or easily specified than the exit temperature. For example,
when an engine exhausts into the atmosphere, the exhaust pressure is always atmospheric pressure, independent of
the inlet pressure and the processes that occur inside the engine. But the exhaust temperature always depends on the inlet
temperature and the complex processes that occur between the inlet and the exit inside the engine.
Therefore, the isentropic pressure is always taken to be equal to the actual pressure at the exit of an isentropic process, and the isentropic
pressure ratio is always the same as the actual pressure ratio for these systems.
The equation for the thermal efficiency of the Carnot cold ASC can now be written as
ðη T Þ Carnot
= 1 − T L /T H = 1 − PR ð1−kÞ/k = 1 − CR 1−k (13.18)
cold ASC
Most vapor power cycles fall at least partially under the vapor dome and can therefore be modeled with a single
practical thermodynamic cycle, the Rankine cycle. Unfortunately, outside the vapor dome, no one thermodynamic
cycle models all possible practical gas power cycles. In the next sections, we discuss a few commercially
valuable gas power cycles and evaluate their ASC thermal efficiencies. While these cycles do not cover all possible
cycles, they are the ones that have had significant economic success over the years. We discuss them in the
chronological order in which they were developed.
13.13 STIRLING CYCLE
Many early steam boilers exploded because of weak materials, faulty design, and poor construction. The resulting
loss in human life and property inspired many people to attempt to develop engines that did not need a
high-pressure boiler. In 1816, the Scottish clergyman Robert Stirling (1790–1878) patented a remarkable closed
loop external combustion engine in which a fixed mass of air passed through a thermodynamic cycle composed
of two isothermal processes and two isochoric (constant volume) processes. Figure 13.38 shows the T–s and
p − V diagrams for this cycle, along with an equipment schematic.
Stirling’s engine was remarkable, not only in its mechanical and thermodynamic complexity, but also because he
originated a thermal regeneration process in which the heat released during the isochoric expansion process
from state 1 to state 2 is stored within the system (in the regenerator) and reintroduced into the working fluid
(air) during the isochoric compression process from state 3 to state 4. This was the first use of thermal regeneration
in a power cycle and predates its use in steam engines by many years. 8 The complexity of construction and
high cost limited production of Stirling’s engine to small units (0.5 to 10 hp). Generally known as hot air
engines, they found extensive use on small farms between 1820 and 1920 for pumping water and other light
duties.
The thermal efficiency of the Stirling cycle is given by
ðη T Þ Stirling = ð _W out Þ net Q
= _ H − j _Q L j
_Q H
_Q H
where (see Figure 13.38a) for a reversible ASC engine, we can write
and
_Q H = _mT H ðs 1 − s 4 Þ
j _Q L j = _mT L ðs 2 − s 3 Þ
= 1 − j _Q L j
_Q H
8 Note that this is a completely different type of “regeneration” than that used with the Rankine vapor cycle.