Chapter 1 – Background and Introduction

The essential background requirements for this resource is a knowledge of thermodynamics, forced convection heat transfer and flow friction, and MATLAB computer programing. The ubiquitous Wikipedia - Stirling engine website presents an overview and introduction to the Stirling engine which includes some excellent animations giving a clear insight as to the operating principles of these machines.

History

We are currently celebrating the 200th anniversary of Robert Stirling's original patent and many books and articles have been written about the history and development (or reasons for the lack of development) of hot air engines. The most recommended is the book by Theodore Finkelstein and Allan J. Organ: 'Air Engines: The History, Science, and Reality of the Perfect Engine' (ASME Press, 2001). Also recommended are the two books by Robert Sier: 'Rev Robert Stirling D.D. - Inventor of the Heat Economiser & Stirling Cycle Engine' ( L A Mair, 1995 – Unfortunately out of print), and 'HOT AIR CALORIC and STIRLING ENGINES, Volume One: A History' (L A Mair, 2000). Refer also to Robert Sier's web-page of Robert Stirling, which includes an animation of Stirling's original machine.
Another interesting web-page of Stirling engine history is that of the National Museums of Scotland.

Robert Stirling published his famous patent in 1816, and Sadi Carnot published his treatise 'Reflections on the Motive Power of Fire' in 1824. In this treatise Carnot stated that a heat engine can only attain the ideal maximum efficiency if the heat is transferred isothermally with the source and sink, and proposed the Carnot cycle as an example of the ideal heat engine cycle. The ingenious aspect of Stirling's patent is the regenerator, which allows the non isothermal heat transfer to be done internally, enabling the ideal Stirling engine cycle to attain the ideal maximum efficiency (refer to the fictitious discussion: A Meeting between Robert Stirling and Sadi Carnot in 1824). Probably one of the main reasons for the lack of development of Stirling engines was that the importance of the regenerator was not understood for about 100 years after Stirling's original patent. The initial attempt at an analysis of the Stirling engine was published in 1871 by Gustav Schmidt. The Lehmann machine on which Schmidt based his analysis was not fitted with a regenerator (Refer: C. Lyle Cummins Jr. (1976). Internal Fire, Carnot Press/Graphics Arts Center, Portland, Oregon. Chapter 2 - Air Engines, page 23) and it is conceivable that Schmidt did not appreciate its importance. He refers to the textbook by Zeuner as containing a "complete, simple and clear theory" of air engines, but in the same textbook Zeuner decries the use of regenerators for air engines (Refer: Finkelstein, T., 1959, Air Engines in The Engineer part 1, 27 March).

From the 1950's through the 1980's there was an ambitious effort to develop automobile Stirling engines in the USA and Europe (refer to NASA publications on the Ford Motor Company program and the Mechanical Technology Inc. (MTI) program.) There are a number of reasons why this program was ultimately unsuccessful: A significantly high pressure of Hydrogen gas is required in order to obtain an acceptable specific power output. This lead ultimately to sealing problems for the output crankshaft, hydrogen embrittlement of the casing, and a complex valve system to increase or decrease pressure for acceleration.

The current focus is on fully sealed Stirling cycle machines for electrical power production or refrigeration using Helium or Nitrogen gas. Since the Stirling engine is the only conceivable heat engine that can operate on a low temperature difference, this enables CHP (combined heat and power), low temperature (flat plate) solar, or waste heat recovery systems. Stirling cycle refrigerator systems using Helium gas have higher COP (coefficient of performance) values than regular vapor-compression refrigerators, and can operate at cryogenic temperature levels.

Athens, Ohio

Since the 1970's, Athens, Ohio has been a hotbed of Stirling cycle machine activity, both engines and coolers, and includes three R&D and manufacturing companies:

Sunpower was formed by William Beale in 1974, mainly based on his invention of the free-piston Stirling engine in 1964. Sunpower was mainly an R&D company, licensing its technology globally, and also manufactured Stirling cycle cryogenic coolers for liquifying oxygen. Sunpower developed a 1kW free-piston engine/generator in 1983, and since 1995 this technology was used by British Gas to develop CHP (Combined Heat and Power) units – the 1kW engine/generator is currently manufactured by Microgen Engine Corporation (refer to their History and Engine web pages).
An interesting paper describing the chronology of the development of Free Piston Stirling engine technology was presented by David Berchowitz at the 2018 International Stirling Engine Conference (Refer: A Personal History in the Development of the Modern Stirling Engine).
In 2013 Sunpower was acquired by AMETEK, Inc in Pensylvania, however continues doing Stirling cycle machine development in Athens, Ohio.

Stirling Technology (note recent company name change: Combined Energy Technology) is a spinoff of Sunpower, and was originally formed in order to continue the development of the 3.5 kW ST-5 Air engine. This large Beta type engine uses a bell crank mechanism to obtain the correct displacer phasing, burns biomass fuel (such as sawdust pellets or rice husks), and can function as a cogeneration unit in rural areas.
Currently Stirling Technology is working with Microgen Engine Corporation, an international company which produces the MEC 1kW free-piston engine/generator. Stirling Technology has developed a multifuel burner for the engine and is partnering with Microgen to get various systems into the market.

Global Cooling (currently ) was a spinoff from Sunpower, and was formed in 1995 by David Berchowitz mainly in order to develop and commercialize free-piston Stirling cycle coolers for home refrigerator applications. These systems, apart from being significantly more efficient than regular vapor-compression refrigerators, have the added advantage of being compact, portable units using helium as the working fluid (and not the HFC refrigerants such as R134a, having a Global Warming Potential of 1,300). More recently Global Cooling decided to concentrate their development efforts on systems in which there are virtually no competitive systems - cooling between -40°C and -80°C, and they established a new company name: Stirling Ultracold.
Update - January 2021: Stirling Ultracold's Ultra-Low Temperature (ULT) freezers meets today's unprecedented COVID-19 deployment challenges.

Sage Software for engineering modeling and optimization of Stirling cycle machines, developed and maintained by David Gedeon.

Solar Heat and Power Cogeneration and Waste Heat Recovery

With the current energy and global warming crises, there is renewed interest in renewable energy systems, such as wind and solar energy, distributed heat and power cogeneration systems and waste heat recovery sysrems..

Cool Energy, Inc of Boulder, Colorado, developed a complete solar heat and power cogeneration system for home usage incorporating Stirling engine technology for electricity generation. This unique application included evacuated tube solar thermal collectors (slide courtesy of rusticresource.com ), thermal storage, hot water and space heaters, and a Stirling engine/generator using nitrogen gas. Currently they are concentrating on low temperature (150°C - 400°C) waste heat recovery systems (Refer: Cool Energy ThermoHeart 25kW Engine Overview).

Various Links

Since 2005 Siegfried "Zig" Herzog from Pennsylvania State University (currently retired) has developed a web resource: Stirling Cycle Analysis that essentially parallels this web resource, the major difference being that he provides an on-line simulation program, whereas I provide the MATLAB source files which can be modified by the user as required.

Andy Ross of Columbus, Ohio has been developing small air engines with extremely innovative Alpha designs, including the classical Ross-Yoke drive and more recently a balanced "Rocker-V" mechanism. Refer to his book: Making Stirling Engines (Ross Experimental, 1993). Matt Keveney has done an animation showing clearly the principles of operation of the Ross yoke linkage mechanism. Andy Ross wrote an article on the model Climax locomotive that he built using a small Rocker-V engine: 'A Class A Climax Locomotive'. We will be using both of Andy Ross' engines as examples in our simulation programs.

Analysis of Stirling Cycle Machines

The ideal Stirling cycle machine is easily analyzed using basic thermodynamics, however the analysis of actual Stirling cycle machines is extremely complex, mainly because of heat transfer between the external heat source/sink and the working gas, the regenerator, and the nonsteady reversing flow of the working gas, requiring sophisticated computer analysis. This learning resource is an attempt to develop this process in stages, from the Ideal Isothermal model followed by the Ideal Adiabatic model (including sections in which there is no heat transfer) through to the complexity of actual heat transfer processes, allowing more practical predictions of actual machine performance, as well as enabling parametric analysis. This does not include dynamic analysis, thus the operating frequency is specified as an independent variable.
Update 2016: A unique alternative approach was presented by David Berchowitz at the 2016 International Stirling Engine Conference (Refer: A Phasor Description of the Stirling Cycle). The phasor description includes both thermodynamic processes and mechanical dynamics, resulting in a useful guide to the understanding of these machines.

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Stirling Cycle Machine Analysis by Israel Urieli is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License