Page 64 - Entrophy Analysis in Thermal Engineering Systems

56 Entropy Analysis in Thermal Engineering Systems

It is natural to be also curious about the design of an ideal engine when all
engines are constrained to undergo an identical degree of volume change. In
the following sections, we will derive and compare expressions for the effi-
ciency of common thermodynamic power cycles. The efficiency compari-
son will be made under the assumption that the largest and smallest volumes
experienced by the working medium are the same (i.e., design constraint) in
all engines.

5.2 Thermodynamic power cycles
A list of common power cycles is provided in Table 5.1 along with the
inventor, year, and place of invention for each design. Evident from
Table 5.1 is that all these engines (except the Miller cycle) were invented
throughout the 19th century. There are other engine designs such as Ran-
kine cycle, Lenoir cycle, Dual cycle, and Stoddard engine as well as modern
designs such as Allam and Kalina power cycles [3, 4], but they will not be
discussed in this chapter.
In the following sections, an expression will be derived for the thermal
efficiency of the cycles given in Table 5.1. It will be assumed that the work-
ing fluid is an ideal gas with a constant specific heat throughout the cycle.
The idea is to describe the engine efficiency in terms of the compression
ratio (CR) and pressure ratio (PR).

η ¼ fCR, PRÞ (5.1)
ð
where
(5.2)
CR ¼ V max =V min

Table 5.1 A list of common gas power cycles.
Cycle Inventor Year of invention Place of invention
Stirling Robert Stirling 1816 United Kingdom
Carnot Nicolas L eonard Sadi Carnot 1824 France
Ericsson John Ericsson 1853 United States
Brayton George Bailey Brayton 1872 United States
Otto Nikolaus August Otto 1876 Germany
Atkinson James Atkinson 1882 United Kingdom
Diesel Rudolf Christian Karl Diesel 1893 Germany
Miller Ralph Miller 1957 United States