The entire chapter is required reading, however we will defer our discussion on Heat (Section 3.6) until after we have introduced the First Law in Chapter 4.
We recommend that you attempt as many of the following 15 Supplementary Problems as possible during this week:
All answers to the Supplementary Problems are given at the end of the chapter
This chapter covers the concept of energy transfer across the boundary of a system in terms of work and heat. At this stage we mainly deal with so-called 'boundary' work associated with the compression or expansion of a fluid in piston/cylinder devices. We will cover some of the examples presented by Potter and Somerton in detail in class, however we would like to introduce some more meaningful examples below, associated with the work processes of the ideal Stirling Cycle engine (in place of Example 3.3) and the air standard ideal Diesel cycle engine (in place of Supplemental Problems 3.15 and 3.19). Once we introduce the First Law in Chapter 4 we will complete these examples by considering the heat transfer and thermal efficiencies of these heat engines.
Conceptually the Stirling engine is the simplest of all heat engines. It has no valves, and includes an externally heated space and an externally cooled space. It was invented by Robert Stirling, and an interesting website by Bob Sier includes a photograph of Robert Stirling, his original patent drawing of 1816, and an animated model of Stirling's engine.
In its original single cylinder form the working gas (typically air or helium) is sealed within its cylinders by the piston and shuttled between the hot and cold spaces by a displacer. The linkage driving the piston and displacer will move them such that the gas will compress while it is mainly in the cool compression space and expand while in the hot expansion space, as illustrated in an excellent animation produced by Matt Keveney in his Stirling engine website, showing clearly the principle of operation. Since the gas is at a higher temperature, and therefore pressure, during its expansion than during its compression, more power is produced during expansion than is reabsorbed during compression, and this net excess power is the useful output of the engine. Note that there are no valves or intermittent combustion, which is the major source of noise in an internal combustion engine. The same working gas is used over and over again, making the Stirling engine a sealed, closed cycle system. All that is added to the system is steady high temperature heat, and all that is removed from the system is low temperature (waste) heat and mechanical power.
Athens, Ohio, is a hotbed of Stirling cycle machine activity, both engines and coolers, and includes R&D and manufacturing companies as well as internationally recognized consultants in the area of Stirling cycle computer analysis. The parent company of this activity is Sunpower, Inc. It was formed by William Beale more than thirty years ago, mainly based on his invention of the free-piston Stirling engine which we describe below and we will demonstrate a working model in class.
The free-piston Stirling engine is unique in that there is no mechanical connection between the piston and the displacer, thus the correct phasing between them occurs by use of gas pressure and spring forces. Electrical power is removed from the engine by permanent magnets attached to the piston driving a linear alternator. Basically the ideal Stirling engine undergoes 4 distinct processes, each one of which can be separately analysed, as shown in the P-V diagram below.
The net work Wnet done over the cycle is given by: Wnet = (W3-4 + W1-2), where the compression work W1-2 is negative (work done on the system).
Some examples of single cylinder Stirling engines: Stirling Technology Inc. is a spinoff of Sunpower, and was formed in order to continue the development and manufacture of the 5 kW ST-5 Air engine. This large single cylinder engine burns biomass fuel (such as sawdust pellets or rice husks) and can function as a cogeneration unit in rural areas. It is not a free-piston engine, and uses a bell crank mechanism to obtain the correct displacer phasing. Another important early Stirling engine is Lehmann's machine on which Gusav Schmidt did the first reasonable analysis of Stirling engines in 1871. Andy Ross of Columbus, Ohio has recently built a small working replica of the Lehmann machine, as well as a model air engine.
The Air Standard Diesel cycle is the ideal cycle for Compression-Ignition (CI) reciprocating Engines, first proposed by Rudolph Diesel over 100 years ago. The following links present an animated basic description of a four-stroke diesel cycle (usually used on motor vehicle systems), and a basic description of a two-stroke diesel cycle (usually used on larger marine systems). The actual CI cycle is extremely complex, thus in initial analysis we use an ideal "air-standard" assumption. Thus the working fluid is a fixed mass of air undergoing the complete cycle which is treated throughout as an ideal gas, all processes are ideal, combustion is replaced by heat addition to the air, and exhaust is replaced by a heat rejection process which restores the air to the initial state. In this example we consider only the work processes during expansion and compression, while in Chapter 4 we will extend the analysis to include the heat absorbtion and rejection processes, as well as evaluate the thermal efficiency of the cycle. This example is an extension and modification of the Potter Supplementary Problems 3.15 and 3.19.
The ideal air-standard Diesel engine undergoes 4 distinct processes, each one of which can be separately analysed, as shown in the P-V diagram below.
The net work Wnet done over the cycle is given by: Wnet = (Wexp + W1-2), where as before the compression work W1-2 is negative (work done on the system).
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