Chapter 2b - Beta Type Stirling Engines

The Beta configuration is the classic Stirling engine configuration and has enjoyed popularity from its inception until today. Stirling's original engine from his patent drawing of 1816 shows a Beta arrangement. A photograph of Robert Stirling, the original patent drawing, as well as an animated model of Stirling's engine is clearly shown in an interesting website by Robert Sier. From the figure below we see that unlike the Alpha machine, the Beta engine has a single power piston and a displacer, whose ideal purpose is to "displace" the working gas at constant volume, and shuttle it between the expansion and the compression spaces through the series arrangement cooler, regenerator, and heater. In actual engines 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. This is clearly illustrated in the adjacent animation which was produced by Richard Wheeler ( Zephyris) of Wikipedia.



A detailed description of the ideal Beta machine cycle is presented in the Engineering Thermodynamics - Chapter 3b web resource. Refer also to the animation of the Beta machine by Matt Keveney - Single Cylinder Stirling Engine, showing clearly the principle of operation.

Apart from Stirling's original engine, an important early Beta engine is Lehmann's machine on which Gustav Schmidt did the first reasonable analysis of Stirling engines in 1871. Andy Ross built a small working replica of the Lehmann machine, as well as a model air engine, both based on single cylinder Beta configurations.

Rolf Meijer of Philips, Holland, developed his famous vibrationless rhombic drive Beta engines in the early 1960s. A detailed description of this engine can be found in the Beta model Stirling engine website by Pierre Gras. In 1965 the General Motors Research Labs developed a 7.5kW rhombic drive Stirling engine/generator set GPU-3 (Ground Power Unit) for the US Army. It is described and analyzed in the book by I.Urieli & D.M.Berchowitz – Stirling Cycle Engine Analysis (Adam Hilger, 1984), pages 30 – 40, and since this book is out of print, these pages have been added here for convenience: Rhombic-GPU-3.pdf.

Free Piston Stirling Engines

Probably the most ingenious Stirling engines yet devised are the free-piston engines invented and developed by William Beale at Ohio University in the late 1960s. Legend has it that while teaching about the rhombic drive engine he suddenly realized that "this engine will still run if we simply throw away this complex drive mechanism - Eureka!". He then formed the company Sunpower, Inc., which has been the leader in the development of free-piston Stirling engines and cryocoolers to this day (refer to Sunpower's extensive Library of conference papers and other publications). Most of Sunpower's engines are Beta arrangements and employ no mechanical linkage system. The main aspect of the free piston machine is that the output power can be obtained through a linear alternator, allowing the entire system to be hermetically sealed. In fact, this is the only Stirling configuration to reach commercialization in any numbers. This is mainly because it avoids the fatal flaws of the crank, proven again and again over the years to be near-insurmountable - sealing and lubrication.

Consider for example the EG-1000 engine/generator which is gas fired and has been designed to generate electricity as well as to provide hot water for a private home. The working gas used is helium, which has the advantage of having a low molecular weight and high thermal conductivity compared to air, allowing a significant reduction in size. This engine is shown in the figure below together with a simplified schematic diagram.



The linear electrical generator (not shown in the above schematic) is comprised of powerful rare-earth magnets in the piston cutting a magnetic circuit and coils in the cylinder. This produces 240 Volts at 50 Herz - designed for operation in Europe, and is capable of producing more than one kilowatt of electrical power output at an efficiency of around 90%.

The hot water is provided by operating the cooling water at a temperature of 50°C.

The Sunpower EG-1000 free-piston Stirling engine/generator


 In this photograph we see the Sunpower EG-1000 being demonstrated using sawdust pellets as the fuel, and generating more than 1000W of electricity to a light panel. This was done at the Sustainability Fair in the Fairgrounds of Athens Ohio, 2001. A closeup photograph of the basic system is shown. Notice the closed cycle radiator and vibration pump used in the water cooling system.

Update 2013: Sunpower has made available a 1 kW Stirling Developers Kit based on the EG-1000 free piston Stirling engine fired by Propane or natural gas.

An extremely interesting free piston engine system developed by William Beale is the free-cylinder water pump. In this engine a heavy internal mass provides the reaction force driving the cylinder which is directly connected to the water pump. It has built in power adjustment and responds to load automatically. All other engines require a transmission and complicated control mechanisms to do this. Furthermore, there is no other mechanical heat engine that I know of that operates from infinite load to zero without either stalling or destroying itself.
Another attractive feature of the free cylinder system is that it can be constructed from inexpensive easy-to-obtain components. In fact, the entire pump housing can be fabricated from ordinary PVC piping and fixtures. The reliability, simplicity and low cost of this engine makes it eminently suitable for application in developing countries, and in the 1970's it was extensively tested both in the field and in the laboratory (Refer to the 1979 presentation by William Beale
A Free-Cylinder Stirling Engine for Solar Powered Water Pumps).

Two interesting free piston Stirling powered refrigeration systems have also been investigated – a duplex gas fired refrigerator having only three moving parts, one power piston and two displacer pistons (refer to the paper by L.B.Penswick & I.Urieli – Duplex Stirling Machines (I. Energy Conversion Engineering Conference, 1984), and a gas fired free piston CO2 refrigeration system (refer to the paper by D.M.Berchowitz & Yong-Rak Kwan – Hermetic Gas Fired Residential Heat Pump).

Sunpower was also involved in the manufacture of Stirling cycle cryogenic coolers for liquifying oxygen. Over the years Sunpower has transformed Athens, Ohio into a hotbed of Stirling cycle machine activity, which now includes three R&D/manufacturing companies. In 2013 Sunpower was acquired by AMETEK, Inc in Pensylvania, however continues doing Stirling cycle machine development in Athens, Ohio. Chapter 3 of the book by I.Urieli and D.M.Berchowitz – Stirling Cycle Engine Analysis (Adam Hilger 1984), is entirely about the analysis of Free-Piston machines, and since this book is out of print, this chapter has been added here in four parts for convenience: Free-Piston(1).pdf, Free-Piston(2).pdf, Free-Piston(3).pdf, Free-Piston(4).pdf. Refer also to the paper by R.W.Redlich & D.M.Berchowitz – Linear dynamics of free-piston Stirling engines (ImechE 1985), and to the Lecture Notes in Engineering by G.Walker & J.R.Senft – Free Piston Stirling Engines (Springer-Verlag 1985, currently available as an eBook).

Stirling Technology, Inc. is a spinoff of Sunpower, and was originally formed in order to continue the development and manufacture 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 the
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 are partnering with Microgen to get various systems into the market.

Global Cooling, Inc is a spinoff of Sunpower, and was formed mainly in order to develop 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). A schematic diagram followed by an animated schematic of a typical cooler (both courtesy of Global Cooling) are shown below:

At Ohio University we have a demonstration Global Cooling Stirling Cooler shown below. It will normally reach -90°C, however since the ball of ice is covering the entire regenerator section we notice that the temperature has risen to -43°C.

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.


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