Stirling engine

Stirling engine
Alpha type Stirling engine. There are two cylinders. The expansion cylinder (red) is maintained at a high temperature while the compression cylinder (blue) is cooled. The passage between the two cylinders contains the regenerator.
Beta Type Stirling Engine. There is only one cylinder, hot at one end and cold at the other. A loose fitting displacer shunts the air between the hot and cold ends of the cylinder. A power piston at the end of the cylinder drives the flywheel.

A Stirling engine is a heat engine operating by cyclic compression and expansion of air or other gas, the working fluid, at different temperature levels such that there is a net conversion of heat energy to mechanical work.[1][2]

Like the steam engine, the Stirling engine is traditionally classified as an external combustion engine, as all heat transfers to and from the working fluid take place through the engine wall. This contrasts with an internal combustion engine where heat input is by combustion of a fuel within the body of the working fluid. Unlike a steam engine's (or more generally a Rankine cycle engine's) usage of a working fluid in both its liquid and gaseous phases, the Stirling engine encloses a fixed quantity of permanently gaseous fluid such as air.

Typical of heat engines, the general cycle consists of compressing cool gas, heating the gas, expanding the hot gas, and finally cooling the gas before repeating the cycle. The efficiency of the process is narrowly restricted by the efficiency of the Carnot cycle, which depends on the temperature difference between the hot and cold reservoir.

Originally conceived in 1816 as an industrial prime mover to rival the steam engine, its practical use was largely confined to low-power domestic applications for over a century.[3]

The Stirling engine is noted for its high efficiency compared to steam engines,[4] quiet operation, and the ease with which it can use almost any heat source. This compatibility with alternative and renewable energy sources has become increasingly significant as the price of conventional fuels rises, and also in light of concerns such as peak oil and climate change. This engine is currently exciting interest as the core component of micro combined heat and power (CHP) units, in which it is more efficient and safer than a comparable steam engine.[5][6]

Name and definition

Robert Stirling was the Scottish inventor of the first practical example of a closed cycle air engine in 1816, and it was suggested by Fleeming Jenkin as early as 1884 that all such engines should therefore generically be called Stirling engines. This naming proposal found little favour, and the various types on the market continued to be known by the name of their individual designers or manufacturers, e.g. Rider's, Robinson's, or Heinrici's (hot) air engine. In the 1940s, the Philips company was seeking a suitable name for its own version of the 'air engine', which by that time had been tested with working fluids other than air, and decided upon 'Stirling engine' in April 1945.[7] However, nearly thirty years later Graham Walker was still bemoaning the fact such terms as 'hot air engine' continued to be used interchangeably with 'Stirling engine', which itself was applied widely and indiscriminately.[8] The situation has now improved somewhat, at least in academic literature, and it is now generally accepted 'Stirling engine' should refer exclusively to a closed-cycle regenerative heat engine with a permanently gaseous working fluid, where closed-cycle is defined as a thermodynamic system in which the working fluid is permanently contained within the system, and regenerative describes the use of a specific type of internal heat exchanger and thermal store, known as the regenerator.

It follows from the closed cycle operation the Stirling engine is an external combustion engine that isolates its working fluid from the energy input supplied by an external heat source. There are many possible implementations of the Stirling engine most of which fall into the category of reciprocating piston engine.

Functional description

The engine is designed so that the working gas is generally compressed in the colder portion of the engine and expanded in the hotter portion resulting in a net conversion of heat into work.[2] An internal Regenerative heat exchanger increases the Stirling engine's thermal efficiency compared to simpler hot air engines lacking this feature.

Key components


Cut-away diagram of a rhombic drive beta configuration Stirling engine design:

  • Pink – Hot cylinder wall
  • Dark grey – Cold cylinder wall (with coolant inlet and outlet pipes in yellow)
  • Dark green – Thermal insulation separating the two cylinder ends
  • Light green – Displacer piston
  • Dark blue – Power piston
  • Light blue – Linkage crank and flywheels
Not shown: Heat source and heat sinks. In this design the displacer piston is constructed without a purpose-built regenerator.

As a consequence of closed cycle operation, the heat driving a Stirling engine must be transmitted from a heat source to the working fluid by heat exchangers and finally to a heat sink. A Stirling engine system has at least one heat source, one heat sink and up to five heat exchangers. Some types may combine or dispense with some of these.

Heat source

Point focus parabolic mirror with Stirling engine at its center and its solar tracker at Plataforma Solar de Almería (PSA) in Spain

The heat source may be provided by the combustion of a fuel and, since the combustion products do not mix with the working fluid and hence do not come into contact with the internal parts of the engine, a Stirling engine can run on fuels that would damage other types of engines' internals, such as landfill gas which contains siloxane.

Other suitable heat sources are concentrated solar energy, geothermal energy, nuclear energy, waste heat, or even biological. If the heat source is solar power, regular solar mirrors and solar dishes may be used. Also, fresnel lenses and mirrors have been advocated to be used (for example, for planetary surface exploration).[9] Solar powered Stirling engines are becoming increasingly popular, as they are a very environmentally sound option for producing power. Also, some designs are economically attractive in development projects.[10]

Heater / hot side heat exchanger

In small, low power engines this may simply consist of the walls of the hot space(s) but where larger powers are required a greater surface area is needed in order to transfer sufficient heat. Typical implementations are internal and external fins or multiple small bore tubes

Designing Stirling engine heat exchangers is a balance between high heat transfer with low viscous pumping losses and low dead space (unswept internal volume). With engines operating at high powers and pressures, the heat exchangers on the hot side must be made of alloys retaining considerable strength at temperature that also will not corrode or creep.


In a Stirling engine, the regenerator is an internal heat exchanger and temporary heat store placed between the hot and cold spaces such that the working fluid passes through it first in one direction then the other. Its function is to retain within the system that heat which would otherwise be exchanged with the environment at temperatures intermediate to the maximum and minimum cycle temperatures,[11] thus enabling the thermal efficiency of the cycle to approach the limiting Carnot efficiency defined by those maxima and minima.

The primary effect of regeneration in a Stirling engine is to increase the thermal efficiency by 'recycling' internal heat which would otherwise pass through the engine irreversibly. As a secondary effect, increased thermal efficiency yields a higher power output from a given set of hot and cold end heat exchangers. It is these which usually limit the engine's heat throughput. In practice this additional power may not be fully realized as the additional "dead space" (unswept volume) and pumping loss inherent in practical regenerators reduces the potential efficiency gains from regeneration.

The design challenge for a Stirling engine regenerator is to provide sufficient heat transfer capacity without introducing too much additional internal volume ('dead space') or flow resistance. These inherent design conflicts are one of many factors which limit the efficiency of practical Stirling engines. A typical design is a stack of fine metal wire meshes, with low porosity to reduce dead space, and with the wire axes perpendicular to the gas flow to reduce conduction in that direction and to maximize convective heat transfer.[12]

The regenerator is the key component invented by Robert Stirling and its presence distinguishes a true Stirling engine from any other closed cycle hot air engine. Many small 'toy' Stirling engines, particularly low-temperature difference (LTD) types, do not have a distinct regenerator component and might be considered hot air engines, however a small amount of regeneration is provided by the surface of displacer itself and the nearby cylinder wall, or similarly the passage connecting the hot and cold cylinders of an alpha configuration engine.

Cooler / cold side heat exchanger

In small, low power engines this may simply consist of the walls of the cold space(s), but where larger powers are required a cooler using a liquid like water is needed in order to transfer sufficient heat.

Heat sink

The heat sink is typically the environment at ambient temperature. In the case of medium to high power engines, a radiator is required to transfer the heat from the engine to the ambient air. Marine engines can use the ambient water. In the case of combined heat and power systems, the engine's cooling water is used directly or indirectly for heating purposes.

Alternatively, heat may be supplied at ambient temperature and the heat sink maintained at a lower temperature by such means as cryogenic fluid (see Liquid nitrogen economy) or iced water.


The displacer is a special-purpose piston, used in Beta and Gamma type Stirling engines, to move the working gas back and forth between the hot and cold heat exchangers. Depending on the type of engine design, the displacer may or may not be sealed to the cylinder, i.e. it is a loose fit within the cylinder and allows the working gas to pass around it as it moves to occupy the part of the cylinder beyond.


There are two major types of Stirling engines that are distinguished by the way they move the air between the hot and cold sides of the cylinder:

  1. The two piston alpha type design has pistons in independent cylinders, and gas is driven between the hot and cold spaces.
  2. The displacement type Stirling engines, known as beta and gamma types, use an insulated mechanical displacer to push the working gas between the hot and cold sides of the cylinder. The displacer is large enough to insulate the hot and cold sides of the cylinder thermally and to displace a large quantity of gas. It must have enough of a gap between the displacer and the cylinder wall to allow gas to flow around the displacer easily.

Alpha Stirling

An alpha Stirling contains two power pistons in separate cylinders, one hot and one cold. The hot cylinder is situated inside the high temperature heat exchanger and the cold cylinder is situated inside the low temperature heat exchanger. This type of engine has a high power-to-volume ratio but has technical problems due to the usually high temperature of the hot piston and the durability of its seals.[13] In practice, this piston usually carries a large insulating head to move the seals away from the hot zone at the expense of some additional dead space.

Action of an alpha type Stirling engine

The following diagrams do not show internal heat exchangers in the compression and expansion spaces, which are needed to produce power. A regenerator would be placed in the pipe connecting the two cylinders. The crankshaft has also been omitted.

Alpha Stirling frame 12.png
1. Most of the working gas is in contact with the hot cylinder walls, it has been heated and expansion has pushed the hot piston to the bottom of its travel in the cylinder. The expansion continues in the cold cylinder, which is 90° behind the hot piston in its cycle, extracting more work from the hot gas.
Alpha Stirling frame 16.png
2. The gas is now at its maximum volume. The hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops.
Alpha Stirling frame 4.png
3. Almost all the gas is now in the cold cylinder and cooling continues. The cold piston, powered by flywheel momentum (or other piston pairs on the same shaft) compresses the remaining part of the gas.
Alpha Stirling frame 8.png
4. The gas reaches its minimum volume, and it will now expand in the hot cylinder where it will be heated once more, driving the hot piston in its power stroke.
Alpha Stirling.gif
The complete alpha type Stirling cycle

Beta Stirling

A beta Stirling has a single power piston arranged within the same cylinder on the same shaft as a displacer piston. The displacer piston is a loose fit and does not extract any power from the expanding gas but only serves to shuttle the working gas from the hot heat exchanger to the cold heat exchanger. When the working gas is pushed to the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by a flywheel, pushes the power piston the other way to compress the gas. Unlike the alpha type, the beta type avoids the technical problems of hot moving seals.[14]

Action of a beta type Stirling engine

Again, the following diagrams do not show internal heat exchangers or a regenerator, which would be placed in the gas path around the displacer.

Beta Stirling frame 12.png
1. Power piston (dark grey) has compressed the gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger.
Beta Stirling frame 16.png
2. The heated gas increases in pressure and pushes the power piston to the farthest limit of the power stroke.
Beta Stirling frame 4.png
3. The displacer piston now moves, shunting the gas to the cold end of the cylinder.
Beta Stirling frame 8.png
4. The cooled gas is now compressed by the flywheel momentum. This takes less energy, since when it is cooled its pressure drops.
Stirling Animation.gif
The complete beta type Stirling cycle

Gamma Stirling

A gamma Stirling is simply a beta Stirling in which the power piston is mounted in a separate cylinder alongside the displacer piston cylinder, but is still connected to the same flywheel. The gas in the two cylinders can flow freely between them and remains a single body. This configuration produces a lower compression ratio but is mechanically simpler and often used in multi-cylinder Stirling engines.

Other types

Other Stirling configurations continue to interest engineers and inventors.

The hybrid between piston and rotary configuration is a double acting engine. This design rotates the displacers on either side of the power piston

Top view of two rotating displacer powering the horizontal piston. Regenerators and radiator removed for clarity

There is also the rotary Stirling engine which seeks to convert power from the Stirling cycle directly into torque, similar to the rotary combustion engine. No practical engine has yet been built but a number of concepts, models and patents have been produced for example the Quasiturbine engine.[15]

Another alternative is the Fluidyne engine (Fluidyne heat pump), which use hydraulic pistons to implement the Stirling cycle. The work produced by a Fluidyne engine goes into pumping the liquid. In its simplest form, the engine contains a working gas, a liquid and two non-return valves.

The Ringbom engine concept published in 1907 has no rotary mechanism or linkage for the displacer. This is instead driven by a small auxiliary piston, usually a thick displacer rod, with the movement limited by stops.[16]

The two-cylinder stirling with Ross yoke is a two-cylinder stirling engine (not positioned at 90°, but at 0°) connected with a special yoke. The engine configuration/yoke setup was invented by Andy Ross (engineer)[disambiguation needed ].[17]

The Franchot engine is a double acting engine invented by ‘Franchot’ in the nineteenth century. A double acting engine is one where both sides of the piston are acted upon by the pressure of the working fluid. One of the simplest forms of a double acting machine, the Franchot engine consists of two pistons and two cylinders and acts like two separate alpha machines. In the Franchot engine each piston acts in two gas phases, which makes more efficient use of the mechanical components than a single acting alpha machine. Although the downside to this machine is that one connecting rod has to have a sliding seal at the hot side of the engine, which is a difficult task when dealing with high pressures and high temperatures[citation needed].

Free piston Stirling engines

Various Free-Piston Stirling Configurations... F."free cylinder", G. Fluidyne, H. "double-acting" Stirling (typically 4 cylinders)

"Free piston" Stirling engines include those with liquid pistons and those with diaphragms as pistons. In a "free piston" device, energy may be added or removed by an electrical linear alternator, pump or other coaxial device. This sidesteps the need for a linkage, and reduces the number of moving parts. In some designs friction and wear are nearly eliminated by the use of non-contact gas bearings or very precise suspension through planar springs.

Four basic steps in the cycle of a “Free piston” Stirling engine,

  1. The power piston is pushed outwards by the expanding gas thus doing work. Gravity plays no role in the cycle.
  2. The gas volume in the engine increases and therefore the pressure reduces, which will cause a pressure difference across the displacer rod to force the displacer towards the hot end. When the displacer moves the piston is almost stationary and therefore the gas volume is almost constant. This step results in the constant volume cooling process which reduces the pressure of the gas.
  3. The reduced pressure now arrests the outward motion of the piston and it begins to accelerate towards the hot end again and by its own inertia, compresses the now cold gas which is mainly in the cold space.
  4. As the pressure increases, a point is reached where the pressure differential across the displacer rod becomes large enough to begin to push the displacer rod (and therefore also the displacer) towards the piston and thereby collapsing the cold space and transferring the cold, compressed gas towards the hot side in an almost constant volume process. As the gas arrives in the hot side the pressure increases and begins to move the piston outwards to initiate the expansion step as explained in (1).

In the early 1960s, W.T. Beale invented a free piston version of the Stirling engine in order to overcome the difficulty of lubricating the crank mechanism.[18] While the invention of the basic free piston Stirling engine is generally attributed to Beale, independent inventions of similar types of engines were made by E.H. Cooke-Yarborough and C. West at the Harwell Laboratories of the UKAERE.[19] G.M. Benson also made important early contributions and patented many novel free-piston configurations.[20]

What appears to be the first mention of a Stirling cycle machine using freely moving components is a British patent disclosure in 1876.[21] This machine was envisaged as a refrigerator (i.e., the reversed Stirling cycle). The first consumer product to utilize a free piston Stirling device was a portable refrigerator manufactured by Twinbird Corporation of Japan and offered in the US by Coleman in 2004.

Thermoacoustic cycle

Thermoacoustic devices are very different from Stirling devices, although the individual path travelled by each working gas molecule does follow a real Stirling cycle. These devices include the thermoacoustic engine and thermoacoustic refrigerator. High-amplitude acoustic standing waves cause compression and expansion analogous to a Stirling power piston, while out-of-phase acoustic travelling waves cause displacement along a temperature gradient, analogous to a Stirling displacer piston. Thus a thermoacoustic device typically does not have a displacer, as found in a beta or gamma Stirling.


Illustration to Robert Stirling's 1816 patent application of the air engine design which later came to be known as the Stirling Engine

The Stirling engine (or Stirling's air engine as it was known at the time) was invented and patented by Robert Stirling in 1816.[22] It followed earlier attempts at making an air engine but was probably the first to be put to practical use when in 1818 an engine built by Stirling was employed pumping water in a quarry.[23] The main subject of Stirling's original patent was a heat exchanger which he called an "economiser" for its enhancement of fuel economy in a variety of applications. The patent also described in detail the employment of one form of the economiser in his unique closed-cycle air engine design[24] in which application it is now generally known as a 'regenerator'. Subsequent development by Robert Stirling and his brother James, an engineer, resulted in patents for various improved configurations of the original engine including pressurization which had by 1843 sufficiently increased power output to drive all the machinery at a Dundee iron foundry.[25]

Though it has been disputed[26] it is widely supposed that as well as saving fuel the inventors were motivated to create a safer alternative to the steam engines of the time,[27] whose boilers frequently exploded causing many injuries and fatalities.[28][29] The need for Stirling engines to run at very high temperatures to maximize power and efficiency exposed limitations in the materials of the day and the few engines that were built in those early years suffered unacceptably frequent failures (albeit with far less disastrous consequences than a boiler explosion[30]) — for example, the Dundee foundry engine was replaced by a steam engine after three hot cylinder failures in four years.[31]

Later nineteenth century

A typical late nineteenth/early twentieth century water pumping engine by the Rider-Ericsson Engine Company

Subsequent to the failure of the Dundee foundry engine there is no record of the Stirling brothers having any further involvement with air engine development and the Stirling engine never again competed with steam as an industrial scale power source (steam boilers were becoming safer[32] and steam engines more efficient, thus presenting less of a target to rival prime movers). However, from about 1860 smaller engines of the Stirling/hot air type were produced in substantial numbers finding applications wherever a reliable source of low to medium power was required, such as raising water or providing air for church organs.[33] These generally operated at lower temperatures so as not to tax available materials, so were relatively inefficient. But their selling point was that, unlike a steam engine, they could be operated safely by anybody capable of managing a fire.[34] Several types remained in production beyond the end of the century, but apart from a few minor mechanical improvements the design of the Stirling engine in general stagnated during this period.[35]

Twentieth century revival

During the early part of the twentieth century the role of the Stirling engine as a "domestic motor"[36] was gradually taken over by the electric motor and small internal combustion engines. By the late 1930s it was largely forgotten, only produced for toys and a few small ventilating fans.[37]

At this time Philips was seeking to expand sales of its radios into parts of the world where mains electricity was unavailable and the supply of batteries uncertain. Philips' management decided that offering a low-power portable generator would facilitate such sales and tasked a group of engineers at the company's research lab in Eindhoven to evaluate alternative ways of achieving this aim. After a systematic comparison of various prime movers, the team decided to go forward with the Stirling engine, citing its quiet operation (both audibly and in terms of radio interference) and ability to run on a variety of heat sources (common lamp oil – "cheap and available everywhere" – was favoured).[38] They were also aware that, unlike steam and internal combustion engines, virtually no serious development work had been carried out on the Stirling engine for many years and asserted that modern materials and know-how should enable great improvements.[39]

Philips MP1002CA Stirling generator of 1951

Encouraged by their first experimental engine, which produced 16 W of shaft power from a bore and stroke of 30mm × 25mm,[40] various development models were produced in a program which continued throughout World War II. By the late 1940s the 'Type 10' was ready to be handed over to Philips' subsidiary Johan de Witt in Dordrecht to be productionised and incorporated into a generator set as originally planned. The result, rated at 180/200 W electrical output from a bore and stroke of 55 mm x 27 mm, was designated MP1002CA (known as the "Bungalow set"). Production of an initial batch of 250 began in 1951, but it became clear that they could not be made at a competitive price besides which the advent of transistor radios with their much lower power requirements meant that the original rationale for the set was disappearing. Approximately 150 of these sets were eventually produced.[41] Some found their way into university and college engineering departments around the world[42] giving generations of students a valuable introduction to the Stirling engine.

Philips went on to develop experimental Stirling engines for a wide variety of applications and continued to work in the field until the late 1970s, but only achieved commercial success with the 'reversed Stirling engine' cryocooler. They did however take out a large number of patents and amass a wealth of information which they licensed to other companies and which formed the basis of much of the development work in the modern era.[43]

Starting in 1986, Infinia Corporation began developing both highly reliable pulsed free-piston Stirling engines, and thermoacoustic coolers using related technology. The published design uses flexural bearings and hermetically sealed Helium gas cycles, to achieve tested reliabilities exceeding 20 years. As of 2010, the corporation had amassed more than 30 patents, and developed a number of commercial products for both combined heat and power, and solar power.[44]


A pressure/volume graph of the idealized Stirling cycle

The idealised Stirling cycle consists of four thermodynamic processes acting on the working fluid:

  1. Isothermal Expansion. The expansion-space and associated heat exchanger are maintained at a constant high temperature, and the gas undergoes near-isothermal expansion absorbing heat from the hot source.
  2. Constant-Volume (known as isovolumetric or isochoric) heat-removal. The gas is passed through the regenerator, where it cools transferring heat to the regenerator for use in the next cycle.
  3. Isothermal Compression. The compression space and associated heat exchanger are maintained at a constant low temperature so the gas undergoes near-isothermal compression rejecting heat to the cold sink
  4. Constant-Volume (known as isovolumetric or isochoric) heat-addition. The gas passes back through the regenerator where it recovers much of the heat transferred in 2, heating up on its way to the expansion space.

Theoretical thermal efficiency equals that of the hypothetical Carnot cycle - i.e. the highest efficiency attainable by any heat engine. However, though it is useful for illustrating general principles, the text book cycle is a long way from representing what is actually going on inside a practical Stirling engine and should only be regarded as a starting point for analysis. In fact it has been argued that its indiscriminate use in many standard books on engineering thermodynamics has done a disservice to the study of Stirling engines in general.[45][46]

Other real-world issues reduce the efficiency of actual engines, due to limits of convective heat transfer, and viscous flow (friction). There are also practical mechanical considerations, for instance a simple kinematic linkage may be favoured over a more complex mechanism needed to replicate the idealized cycle, and limitations imposed by available materials such as non-ideal properties of the working gas, thermal conductivity, tensile strength, creep, rupture strength, and melting point. A question that often arises is whether the ideal cycle with isothermal expansion and compression is in fact the correct ideal cycle to apply to the Stirling engine. Professor C. J. Rallis has pointed out that it is very difficult to imagine any condition where the expansion and compression spaces may approach isothermal behavior and it is far more realistic to imagine these spaces as adiabatic.[47] An ideal analysis where the expansion and compression spaces are taken to be adiabatic with isothermal heat exchangers and perfect regeneration was analyzed Rallis and presented as a better ideal yardstick for Stirling machinery. He called this cycle the 'pseudo-Stirling cycle' or 'ideal adiabatic Stirling cycle'. An important consequence of this ideal cycle is that is does not predict Carnot efficiency. A further conclusion of this ideal cycle is that maximum efficiencies are found at lower compression ratios, a characteristic observed in real machines. In an independent work, T. Finkelstein also assumed adiabatic expansion and compression spaces in his analysis of Stirling machinery [48]


Since the Stirling engine is a closed cycle, it contains a fixed mass of gas called the "working fluid", most commonly air, hydrogen or helium. In normal operation, the engine is sealed and no gas enters or leaves the engine. No valves are required, unlike other types of piston engines. The Stirling engine, like most heat engines, cycles through four main processes: cooling, compression, heating and expansion. This is accomplished by moving the gas back and forth between hot and cold heat exchangers, often with a regenerator between the heater and cooler. The hot heat exchanger is in thermal contact with an external heat source, such as a fuel burner, and the cold heat exchanger being in thermal contact with an external heat sink, such as air fins. A change in gas temperature will cause a corresponding change in gas pressure, while the motion of the piston causes the gas to be alternately expanded and compressed.

The gas follows the behaviour described by the gas laws which describe how a gas' pressure, temperature and volume are related. When the gas is heated, because it is in a sealed chamber, the pressure rises and this then acts on the power piston to produce a power stroke. When the gas is cooled the pressure drops and this means that less work needs to be done by the piston to compress the gas on the return stroke, thus yielding a net power output.

When one side of the piston is open to the atmosphere, the operation is slightly different. As the sealed volume of working gas comes in contact with the hot side, it expands, doing work on both the piston and on the atmosphere. When the working gas contacts the cold side, its pressure drops below atmospheric pressure and the atmosphere pushes on the piston and does work on the gas.

To summarize, the Stirling engine uses the temperature difference between its hot end and cold end to establish a cycle of a fixed mass of gas, heated and expanded, and cooled and compressed, thus converting thermal energy into mechanical energy. The greater the temperature difference between the hot and cold sources, the greater the thermal efficiency. The maximum theoretical efficiency is equivalent to the Carnot cycle, however the efficiency of real engines is less than this value due to friction and other losses.

Video showing the compressor and displacer of a very small Stirling Engine in action

Very low-power engines have been built which will run on a temperature difference of as little as 0.5 K.[49]

In a displacer type stirling engine you have one piston and one displacer. A temperature difference is required between the top and bottom of the large cylinder in order to run the engine. In the case of the low-temperature difference (LTD) stirling engine, temperature difference between your hand and the surrounding air can be enough to run the engine. The power piston in the displacer type stirling engine, is tightly sealed and is controlled to move up and down as the gas inside expands. The displacer on the other hand is very loosely fitted so that air can move freely between the hot and cold sections of the engine as the piston moves up and down. The dispacer moves up and down to control the heating and cooling of the gas in the engine.
There are two positions,

1) When the displacer is near the top of the large cylinder.
• Inside the engine most of the gas has been heated by the heat source and it expands. This causes the pressure to increase which forces the piston up.

2) When the displacer is near the bottom of the large cylinder.
• Most of the gas in the engine has now cooled and contracts causing the pressure to decrease, which in turn allows the piston to move down and compress the gas.


In most high power Stirling engines, both the minimum pressure and mean pressure of the working fluid are above atmospheric pressure. This initial engine pressurization can be realized by a pump, or by filling the engine from a compressed gas tank, or even just by sealing the engine when the mean temperature is lower than the mean operating temperature. All of these methods increase the mass of working fluid in the thermodynamic cycle. All of the heat exchangers must be sized appropriately to supply the necessary heat transfer rates. If the heat exchangers are well designed and can supply the heat flux needed for convective heat transfer, then the engine will in a first approximation produce power in proportion to the mean pressure, as predicted by the West number, and Beale number. In practice, the maximum pressure is also limited to the safe pressure of the pressure vessel. Like most aspects of Stirling engine design, optimization is multivariate, and often has conflicting requirements.[50] A difficulty of pressurization is that while it improves the power, the heat required increases proportionately to the increased power. This heat transfer is made increasingly difficult with pressurization since increased pressure also demands increased thicknesses of the walls of the engine which, in turn, increase the resistance to heat transfer.

Lubricants and friction

A modern Stirling engine and generator set with 55 kW electrical output, for combined heat and power applications

At high temperatures and pressures, the oxygen in air-pressurized crankcases, or in the working gas of hot air engines, can combine with the engine's lubricating oil and explode. At least one person has died in such an explosion.[51]

Lubricants can also clog heat exchangers, especially the regenerator. For these reasons, designers prefer non-lubricated, low-coefficient of friction materials (such as rulon or graphite), with low normal forces on the moving parts, especially for sliding seals. Some designs avoid sliding surfaces altogether by using diaphragms for sealed pistons. These are some of the factors that allow Stirling engines to have lower maintenance requirements and longer life than internal-combustion engines.


Comparison with internal combustion engines

In contrast to internal combustion engines, Stirling engines have the potential to use renewable heat sources more easily, to be quieter, and to be more reliable with lower maintenance. They are preferred for applications that value these unique advantages, particularly if the cost per unit energy generated ($/kWh) is more important than the capital cost per unit power ($/kW). On this basis, Stirling engines are cost competitive up to about 100 kW.[52]

Compared to an internal combustion engine of the same power rating, Stirling engines currently have a higher capital cost and are usually larger and heavier. However, they are more efficient than most internal combustion engines.[53] Their lower maintenance requirements make the overall energy cost comparable. The thermal efficiency is also comparable (for small engines), ranging from 15% to 30%.[52] For applications such as micro-CHP, a Stirling engine is often preferable to an internal combustion engine. Other applications include water pumping, astronautics, and electrical generation from plentiful energy sources that are incompatible with the internal combustion engine, such as solar energy, and biomass such as agricultural waste and other waste such as domestic refuse. Stirlings have also been used as a marine engine in Swedish Gotland-class submarines.[54] However, Stirling engines are generally not price-competitive as an automobile engine, due to high cost per unit power, low power density and high material costs.

Basic analysis is based on the closed-form Schmidt analysis.[55][56]


  • Stirling engines can run directly on any available heat source, not just one produced by combustion, so they can run on heat from solar, geothermal, biological, nuclear sources or waste heat from industrial processes.
  • A continuous combustion process can be used to supply heat, so those emissions associated with the intermittent combustion processes of a reciprocating internal combustion engine can be reduced.
  • Most types of Stirling engines have the bearing and seals on the cool side of the engine, and they require less lubricant and last longer than other reciprocating engine types.
  • The engine mechanisms are in some ways simpler than other reciprocating engine types. No valves are needed, and the burner system can be relatively simple. Crude Stirling engines can be made using common household materials.[57]
  • A Stirling engine uses a single-phase working fluid which maintains an internal pressure close to the design pressure, and thus for a properly designed system the risk of explosion is low. In comparison, a steam engine uses a two-phase gas/liquid working fluid, so a faulty release valve can cause an explosion.
  • In some cases, low operating pressure allows the use of lightweight cylinders.
  • They can be built to run quietly and without an air supply, for air-independent propulsion use in submarines.
  • They start easily (albeit slowly, after warmup) and run more efficiently in cold weather, in contrast to the internal combustion which starts quickly in warm weather, but not in cold weather.
  • A Stirling engine used for pumping water can be configured so that the water cools the compression space. This is most effective when pumping cold water.
  • They are extremely flexible. They can be used as CHP (combined heat and power) in the winter and as coolers in summer.
  • Waste heat is easily harvested (compared to waste heat from an internal combustion engine) making Stirling engines useful for dual-output heat and power systems.


Size and cost issues
  • Stirling engine designs require heat exchangers for heat input and for heat output, and these must contain the pressure of the working fluid, where the pressure is proportional to the engine power output. In addition, the expansion-side heat exchanger is often at very high temperature, so the materials must resist the corrosive effects of the heat source, and have low creep (deformation). Typically these material requirements substantially increase the cost of the engine. The materials and assembly costs for a high temperature heat exchanger typically accounts for 40% of the total engine cost.[51]
  • All thermodynamic cycles require large temperature differentials for efficient operation. In an external combustion engine, the heater temperature always equals or exceeds the expansion temperature. This means that the metallurgical requirements for the heater material are very demanding. This is similar to a Gas turbine, but is in contrast to an Otto engine or Diesel engine, where the expansion temperature can far exceed the metallurgical limit of the engine materials, because the input heat source is not conducted through the engine, so engine materials operate closer to the average temperature of the working gas.
  • Dissipation of waste heat is especially complicated because the coolant temperature is kept as low as possible to maximize thermal efficiency. This increases the size of the radiators, which can make packaging difficult. Along with materials cost, this has been one of the factors limiting the adoption of Stirling engines as automotive prime movers. For other applications such as ship propulsion and stationary microgeneration systems using combined heat and power (CHP) high power density is not required.[58]
Power and torque issues
  • Stirling engines, especially those that run on small temperature differentials, are quite large for the amount of power that they produce (i.e., they have low specific power). This is primarily due to the heat transfer coefficient of gaseous convection which limits the heat flux that can be attained in a typical cold heat exchanger to about 500 W/(m2·K), and in a hot heat exchanger to about 500–5000 W/(m2·K).[50] Compared with internal combustion engines, this makes it more challenging for the engine designer to transfer heat into and out of the working gas. Because of the Thermal efficiency the required heat transfer grows with lower temperature difference, and the heat exchanger surface (and cost) for 1 kW output grows with second power of 1/deltaT. Therefore the specific cost of very low temperature difference engines is very high. Increasing the temperature differential and/or pressure allows Stirling engines to produce more power, assuming the heat exchangers are designed for the increased heat load, and can deliver the convected heat flux necessary.
  • A Stirling engine cannot start instantly; it literally needs to "warm up". This is true of all external combustion engines, but the warm up time may be longer for Stirlings than for others of this type such as steam engines. Stirling engines are best used as constant speed engines.
  • Power output of a Stirling tends to be constant and to adjust it can sometimes require careful design and additional mechanisms. Typically, changes in output are achieved by varying the displacement of the engine (often through use of a swashplate crankshaft arrangement), or by changing the quantity of working fluid, or by altering the piston/displacer phase angle, or in some cases simply by altering the engine load. This property is less of a drawback in hybrid electric propulsion or "base load" utility generation where constant power output is actually desirable.
Gas choice issues

The used gas should have a low heat capacity, so that a given amount of transferred heat leads to a large increase in pressure. Considering this issue, helium would be the best gas because of its very low heat capacity. Air is a viable working fluid,[59] but the oxygen in a highly pressurized air engine can cause fatal accidents caused by lubricating oil explosions.[51] Following one such accident Philips pioneered the use of other gases to avoid such risk of explosions.

  • Hydrogen's low viscosity and high thermal conductivity make it the most powerful working gas, primarily because the engine can run faster than with other gases. However, due to hydrogen absorption, and given the high diffusion rate associated with this low molecular weight gas, particularly at high temperatures, H2 will leak through the solid metal of the heater. Diffusion through carbon steel is too high to be practical, but may be acceptably low for metals such as aluminum, or even stainless steel. Certain ceramics also greatly reduce diffusion. Hermetic pressure vessel seals are necessary to maintain pressure inside the engine without replacement of lost gas. For high temperature differential (HTD) engines, auxiliary systems may need to be added to maintain high pressure working fluid. These systems can be a gas storage bottle or a gas generator. Hydrogen can be generated by electrolysis of water, the action of steam on red hot carbon-based fuel, by gasification of hydrocarbon fuel, or by the reaction of acid on metal. Hydrogen can also cause the embrittlement of metals. Hydrogen is a flammable gas, which is a safety concern if released from the engine.
  • Most technically advanced Stirling engines, like those developed for United States government labs, use helium as the working gas, because it functions close to the efficiency and power density of hydrogen with fewer of the material containment issues. Helium is inert, which removes all risk of flammability, both real and perceived. Helium is relatively expensive, and must be supplied as bottled gas. One test showed hydrogen to be 5% (absolute) more efficient than helium (24% relatively) in the GPU-3 Stirling engine.[60] The researcher Allan Organ demonstrated that a well-designed air engine is theoretically just as efficient as a helium or hydrogen engine, but helium and hydrogen engines are several times more powerful per unit volume.
  • Some engines use air or nitrogen as the working fluid. These gases have much lower power density (which increases engine costs), but they are more convenient to use and they minimize the problems of gas containment and supply (which decreases costs). The use of compressed air in contact with flammable materials or substances such as lubricating oil, introduces an explosion hazard, because compressed air contains a high partial pressure of oxygen. However, oxygen can be removed from air through an oxidation reaction or bottled nitrogen can be used, which is nearly inert and very safe.
  • Other possible lighter-than-air gases include: methane, and ammonia.


Applications of the Stirling engine range from heating and cooling to underwater power systems. A Stirling engine can function in reverse as a heat pump for heating or cooling. Other uses include: combined heat and power, solar power generation, Stirling cryocoolers, heat pump, marine engines, and low temperature difference engines


Alternative thermal energy harvesting devices include the Thermogenerator. Thermogenerators allow less efficient conversion (5-10%) but may be useful in situations where the end product needs to be electricity and where a small conversion device is a critical factor.

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See also


  1. ^ "Stirling Engines", G. Walker (1980), Clarenden Press, Oxford, page 1: "A Stirling engine is a mechanical device which operates on a *closed* regenerative thermodynamic cycle, with cyclic compression and expansion of the working fluid at different temperature levels."
  2. ^ a b W.R. Martini (1983), p.6
  3. ^ T. Finkelstein; A.J. Organ (2001), Chapters 2&3
  4. ^ Sirling engines capable of reaching 40% efficiency
  5. ^ Sleeve notes from A.J. Organ (2007)
  6. ^ F. Starr (2001)
  7. ^ C.M. Hargreaves (1991), Chapter 2.5
  8. ^ Graham Walker (1971) Lecture notes for Stirling engine symposium at Bath University. Page 1.1 "Nomenclture"
  9. ^ W.H. Brandhorst; J.A. Rodiek (2005)
  10. ^ B. Kongtragool; S. Wongwises (2003)
  11. ^ A.J. Organ (1992), p.58
  12. ^ K. Hirata (1998)
  13. ^ M.Keveney (2000a)
  14. ^ M. Keveney (2000b)
  15. ^ Quasiturbine Agence (a)
  16. ^ "Ringbom Stirling Engines", James R. Senft, 1993, Oxford University Press
  17. ^ Two-cylinder stirling with Ross yoke
  18. ^ "Free-Piston Stirling Engines", G. Walker et al.,Springer 1985, reprinted by Stirling Machine World, West Richland WA
  19. ^ "The Thermo-mechanical Generator...", E.H. Cooke-Yarborough, (1967) Harwell Memorandum No. 1881 and (1974) Proc. I.E.E., Vol. 7, pp. 749-751
  20. ^ G.M. Benson (1973 and 1977)
  21. ^ D. Postle (1873)
  22. ^ R. Sier (1999)
  23. ^ T. Finkelsteinl; A.J. Organ (2001), Chapter 2.2
  24. ^ English patent 4081 of 1816 Improvements for diminishing the consumption of fuel and in particular an engine capable of being applied to the moving (of)machinery on a principle entirely new. as reproduced in part in C.M. Hargreaves (1991), Appendix B, with full transcription of text in R. Sier (1995), p.??
  25. ^ R. Sier (1995), p. 93
  26. ^ A.J. Organ (2008a)
  27. ^ Excerpt from a paper presented by James Stirling in June 1845 to the Institute of Civil Engineers. As reproduced in R. Sier (1995), p.92.
  28. ^ A. Nesmith (1985)
  29. ^ R. Chuse; B. Carson (1992), Chapter 1
  30. ^ R. Sier (1995), p.94
  31. ^ T. Finkelstein; A.J. Organ (2001), p.30
  32. ^ Hartford Steam Boiler (a)
  33. ^ T. Finkelstein; A.J. Organ (2001), Chapter 2.4
  34. ^ The 1906 Rider-Ericsson Engine Co. catalog claimed that "any gardener or ordinary domestic can operate these engines and no licensed or experienced engineer is required".
  35. ^ T. Finkelstein; A.J. Organ (2001), p.64
  36. ^ T. Finkelstein; A.J. Organ (2001), p.34
  37. ^ T. Finkelstein; A.J. Organ (2001), p.55
  38. ^ C.M. Hargreaves (1991), pp.28–30
  39. ^ Philips Technical Review Vol.9 No.4 page 97 (1947)
  40. ^ C.M. Hargreaves (1991), Fig. 3
  41. ^ C.M. Hargreaves (1991), p.61
  42. ^ Letter dated March 1961 from Research and Control Instruments Ltd. London WC1 to North Devon Technical College, offering "remaining stocks...... to institutions such as yourselves..... at a special price of £75 nett"
  43. ^ C.M. Hargreaves (1991), p.77
  44. ^ Infinia web site, accessed 2010-12-29
  45. ^ T. Finkelstein; A.J. Organ (2001), Page 66 & 229
  46. ^ A.J. Organ (1992), Chapter 3.1 - 3.2
  47. ^ Rallis C. J., Urieli I. and Berchowitz D.M. A New Ported Constant Volume External Heat Supply Regenerative Cycle, 12th IECEC, Washington DC, 1977, pp 1534-1537.
  48. ^ Finkelstein, T. Generalized Thermodynamic Analysis of Stirling Engines. Paper 118B, Society of Automotive Engineers, 1960.
  49. ^ "An Introduction to Low Temperature Differential Stirling Engines", James R. Senft, 1996, Moriya Press
  50. ^ a b A.J. Organ (1997), p.??
  51. ^ a b c C.M. Hargreaves (1991), p.??
  52. ^ a b WADE (a)
  53. ^ Krupp and Horn. Earth: The Sequel. p. 57
  54. ^ Kockums (a)
  55. ^ Z. Herzog (2008)
  56. ^ K. Hirata (1997)
  57. ^ MAKE: Magazine (2006)
  58. ^ BBC News (2003), "The boiler is based on the Stirling engine, dreamed up by the Scottish inventor Robert Stirling in 1816. [...] The technical name given to this particular use is Micro Combined Heat and Power or Micro CHP."
  59. ^ A.J. Organ (2008b)
  60. ^ L.G. Thieme (1981)


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