Stirling engine is a heat engine that operates by cyclic compression
and expansion of air or other gas (the working fluid) at different
temperatures, such that there is a net conversion of heat energy to
mechanical work. More specifically, the
Stirling engine is a
closed-cycle regenerative heat engine with a permanently gaseous
working fluid. Closed-cycle, in this context, means 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.
Strictly speaking, the inclusion of the regenerator is what
Stirling engine from other closed cycle hot air
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.
Stirling engines have a high efficiency compared to internal
combustion engines, being able to reach 50% efficiency. They are
also capable of quiet operation and can use almost any heat source.
The heat energy source is generated external to the Stirling engine
rather than by internal combustion as with the
Otto cycle or Diesel
cycle engines. Because the
Stirling engine is compatible with
alternative and renewable energy sources it could become increasingly
significant as the price of conventional fuels rises, and also in
light of concerns such as depletion of oil supplies and climate
change. This type of engine is currently generating 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.
However, it has a low power-to-weight ratio, rendering it more
suitable for use in static installations where space and weight are
not at a premium.
1 Name and classification
2.1 Invention and early development
2.2 Later nineteenth century
2.3 Twentieth century revival
3 Functional description
3.1 Key components
3.1.2 Heater / hot side heat exchanger
3.1.4 Cooler / cold side heat exchanger
3.2.1 Alpha configuration operation
3.2.2 Beta configuration operation
3.2.3 Gamma configuration operation
3.2.4 Other types
3.2.5 Free-piston Stirling engines
18.104.22.168 Flat Stirling engine
22.214.171.124 Thermoacoustic cycle
3.3 Other developments
4.3 Lubricants and friction
5.1 Comparison with internal combustion engines
126.96.36.199 Size and cost issues
188.8.131.52 Power and torque issues
Gas choice issues
8 See also
11 Further reading
12 External links
Name and classification
Stirling engine running.
Robert Stirling was a Scottish minister who invented the first
practical example of a closed cycle air engine in 1816, and it was
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. However, nearly thirty years later, Graham
Walker still had cause to bemoan the fact such terms as hot air engine
remained interchangeable with Stirling engine, which itself was
applied widely and indiscriminately, a situation that continues.
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 a solid boundary (heat exchanger)
thus isolating the combustion process and any contaminants it may
produce from the working parts of the engine. This contrasts with an
internal combustion engine where heat input is by combustion of a fuel
within the body of the working fluid. Most of the many possible
implementations of the
Stirling engine fall into the category of
reciprocating piston engine.
Invention and early development
Illustration from Robert Stirling's 1816 patent application of the air
engine design that later came to be known as the Stirling Engine
Stirling engine (or Stirling's air engine as it was known at the
time) was invented and patented in 1816. It followed earlier
attempts at making an air engine but was probably the first put to
practical use when, in 1818, an engine built by Stirling was employed
pumping water in a quarry. 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 in which application
it is now generally known as a "regenerator". Subsequent development
Robert Stirling and his brother James, an engineer, resulted in
patents for various improved configurations of the original engine
including pressurization, which by 1843, had sufficiently increased
power output to drive all the machinery at a
Dundee iron foundry.
Though it has been disputed, it is widely supposed that the
inventor's aims were not only to save fuel but also to create a safer
alternative to the steam engines of the time, whose boilers
frequently exploded, causing many injuries and fatalities.
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 boiler explosions). For example, the
Dundee foundry engine was replaced by a steam engine after three hot
cylinder failures in four years.
Reverend Stirling filed three patents in relation to hot air engines.
The first one in 1816,  about an "Economiser", is the predecessor
of the regenerator. In this patent (# 4081) he describes the
"economiser" technology and several applications where such technology
can be used. Out of them came a new arrangement for a hot air engine.
In 1818, one engine was built to pump water from a quarry in Ayrshire,
but due to technical issues, the engine was abandoned for a time.
In 1827, Stirling and his brother James patented a second engine
very similar to the Parkinson and Crossley's air engine, but
having a regenerator. In 1840, the two Stirling brothers patented a
third engine, but the changes against the 1827 patent were minor.
Nonetheless in 1842 James Stirling built in the
Dundee Foundry -
Scotland, two hot air engines.
James Stirling gave a presentation of his engine before the
Institution of Civil Engineers
Institution of Civil Engineers in 1845. The first engine of this
kind which, after various modifications, was efficiently constructed
and heated, had a cylinder of 12 inches (approx. 30 cm) in diameter,
with a length of stroke of 2 feet (approx. 61 cm), and made 40 strokes
or revolutions in a minute (40 rpm). This engine moved all the
machinery at the
Dundee Foundry Company's works for eight or ten
months, and was previously found capable of raising 700,000 lbs one
foot in a minute (approx. 21 HP).
Finding this power insufficient for their works, the
Company erected the second engine, with a cylinder of 16 inches
(approx. 40 cm) in diameter, a stroke of 4 feet (approx. 1.20 m), and
making 28 strokes in a minute. This engine has now been in continual
operation for upwards of two years, and has not only performed the
work of the foundry in the most satisfactory manner, but has been
tested (by a friction brake on a third mover) to the extent of lifting
nearly 1,500,000 lbs (approx. 45 HP).
This gives a consumption of 2.7 lbs. (approx. 1.22 kg) per horse-power
per hour; but when the engine was not fully burdened, the consumption
was considerably under 2.5 lbs. (approx. 1.13 kg) per horse-power per
hour. This performance was at the level of the best steam engines
whose efficiency was about 10%. After James Stirling, such efficiency
was possible only thanks to the use of the economiser (or
Later nineteenth century
A typical late nineteenth/early twentieth century water pumping engine
by the Rider-Ericsson Engine Company
Subsequent to the replacement 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 and steam engines more efficient, thus presenting
less of a target for rival prime movers). However, beginning about
1860, smaller engines of the Stirling/hot air type were produced in
substantial numbers for applications in which reliable sources of low
to medium power were required, such as pumping air for church organs
or raising water. These smaller engines generally operated at
lower temperatures so as not to tax available materials, and so were
relatively inefficient. Their selling point was that unlike steam
engines, they could be operated safely by anybody capable of managing
a fire. Several types remained in production beyond the end of the
century, but apart from a few minor mechanical improvements the design
Stirling engine in general stagnated during this period.
Twentieth century revival
During the early part of the twentieth century the role of the
Stirling engine as a "domestic motor" was gradually taken over by
electric motors and small internal combustion engines. By the late
1930s, it was largely forgotten, only produced for toys and a few
small ventilating fans.
Around that time,
Philips was seeking to expand sales of its radios
into parts of the world where grid electricity and batteries were not
consistently available. Philips' management decided that offering a
low-power portable generator would facilitate such sales and asked a
group of engineers at the company's research lab in
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 favored). 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
Philips MP1002CA Stirling generator of 1951
By 1951, the 180/200 W generator set designated MP1002CA (known as the
"Bungalow set") was ready for production and an initial batch of 250
was planned, but soon it became clear that they could not be made at a
competitive price. Additionally, the advent of transistor radios and
their much lower power requirements meant that the original rationale
for the set was disappearing. Approximately 150 of these sets were
eventually produced. Some found their way into university and
college engineering departments around the world giving
generations of students a valuable introduction to the Stirling
In parallel with the Bungalow set,
Philips developed 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. However, they
filed a large number of patents and amassed 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.
In 1996, the Swedish navy commissioned three Gotland-class submarines.
On the surface, these boats are propelled by marine diesel engines.
However, when submerged, they use a Stirling-driven generator
developed by Swedish shipbuilder
Kockums to recharge batteries and
provide electrical power for propulsion. A supply of liquid oxygen
is carried to support burning of diesel fuel to power the engine.
Stirling engines are also fitted to the Swedish Södermanland-class
submarines, the Archer-class submarines in service in Singapore and,
Kawasaki Heavy Industries
Kawasaki Heavy Industries for the Japanese
Sōryū-class submarines. In a submarine application, the Stirling
engine offers the advantage of being exceptionally quiet when running.
Stirling engines are frequently used in the dish version of
Concentrated Solar Power
Concentrated Solar Power systems. A mirrored dish similar to a very
large satellite dish directs and concentrates sunlight onto a thermal
receiver, which absorbs and collects the heat and using a fluid
transfers it into the Stirling engine. The resulting mechanical power
is then used to run a generator or alternator to produce
Stirling engines are forming the core component of micro combined heat
and power (CHP) units, as they are more efficient and safer than a
comparable steam engine. CHP units are being installed in people's
The engine is designed so 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. An internal
regenerative heat exchanger increases the Stirling engine's thermal
efficiency compared to simpler hot air engines lacking this feature.
Cut-away diagram of a rhombic drive beta configuration Stirling engine
Hot cylinder wall
Cold cylinder wall
Coolant inlet and outlet pipes
Thermal insulation separating the two cylinder ends
Linkage crank and flywheels
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[clarification needed] heat exchangers. Some types may combine or
dispense with some of these.
Point focus parabolic mirror with
Stirling engine at its centre and
its solar tracker at
Plataforma Solar de Almería
Plataforma Solar de Almería (PSA) in Spain
Dish Stirling from SES
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 engines
types' internals, such as landfill gas, which may contain siloxane
that could deposit abrasive silicon dioxide in conventional
Other suitable heat sources include concentrated solar energy,
geothermal energy, nuclear energy, waste heat and bioenergy. If solar
power is used as a heat source, regular solar mirrors and solar dishes
may be utilised. The use of Fresnel lenses and mirrors has also been
advocated, for example in planetary surface exploration. Solar
powered Stirling engines are increasingly popular as they offer an
environmentally sound option for producing power while some designs
are economically attractive in development projects.
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 to transfer sufficient heat. Typical
implementations are internal and external fins or multiple small bore
Stirling engine heat exchangers is a balance between high
heat transfer with low viscous pumping losses, and low dead space
(unswept internal volume). Engines that operate at high powers and
pressures require that heat exchangers on the hot side be made of
alloys that retain considerable strength at high temperatures and that
don't corrode or creep.
Main article: Regenerative heat exchanger
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, taking heat from the fluid in one direction, and returning
it in the other. It can be as simple as metal mesh or foam, and
benefits from high surface area, high heat capacity, low conductivity
and low flow friction. Its function is to retain within the system
that heat that would otherwise be exchanged with the environment at
temperatures intermediate to the maximum and minimum cycle
temperatures, thus enabling the thermal efficiency of the cycle
(though not of any practical engine) to approach the limiting
The primary effect of regeneration in a
Stirling engine is to increase
the thermal efficiency by 'recycling' internal heat that 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. These 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 that 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.
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 the 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 to transfer sufficient heat.
The larger the temperature difference between the hot and cold
sections of a Stirling engine, the greater the engine's efficiency.
The heat sink is typically the environment the engine operates in, 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 have the advantage of using cool ambient
sea, lake, or river water, which is typically cooler than ambient air.
In the case of combined heat and power systems, the engine's cooling
water is used directly or indirectly for heating purposes, raising
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 may be
a loose fit within the cylinder, allowing the working gas to pass
around it as it moves to occupy the part of the cylinder beyond.
There are three major types of Stirling engines, that are
distinguished by the way they move the air between the hot and cold
The alpha configuration has two power pistons, one in a hot cylinder,
one in a cold cylinder, and the gas is driven between the two by the
pistons; it is typically in a V-formation with the pistons joined at
the same point on a crankshaft.
The beta configuration has a single cylinder with a hot end and a cold
end, containing a power piston and a 'displacer' that drives the gas
between the hot and cold ends. It is typically used with a rhombic
drive to achieve the phase difference between the displacer and power
pistons, but they can be joined 90 degrees out of phase on a
The gamma configuration has two cylinders: one containing a displacer,
with a hot and a cold end, and one for the power piston; they are
joined to form a single space with the same pressure in both
cylinders; the pistons are typically in parallel and joined 90 degrees
out of phase on a crankshaft.
Alpha configuration operation
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 because of the
usually high temperature of the hot piston and the durability of its
seals. 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. The crank angle has a major effect on
efficiency and the best angle frequently must be found experimentally.
An angle of 90° frequently locks.
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.
1. Most of the working gas is in the hot cylinder and has more contact
with the hot cylinder's walls. This results in overall heating of the
gas. Its pressure increases and the gas expands. Because the hot
cylinder is at its maximum volume and the cold cylinder is at the top
of its stroke (minimum volume), the volume of the system is increased
by expansion into the cold cylinder.
2. The system is at its maximum volume and the gas has more contact
with the cold cylinder. This cools the gas, lowering its pressure.
Because of flywheel momentum or other piston pairs on the same shaft,
the hot cylinder begins an upstroke reducing the volume of the system.
3. Almost all the gas is now in the cold cylinder and cooling
continues. This continues to reduce the pressure of the gas and cause
contraction. Because the hot cylinder is at minimum volume and the
cold cylinder is at its maximum volume, the volume of the system is
further reduced by compression of the cold cylinder inwards.
4. The system is at its minimum volume and the gas has greater contact
with the hot cylinder. The volume of the system increases by expansion
of the hot cylinder.
The complete alpha type Stirling cycle. Note that if the application
of heat and cold is reversed, the engine runs in the opposite
direction without any other changes.
Beta configuration operation
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 between the hot and cold
heat exchangers. 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, as the power piston
is not in contact with the hot gas.
Again, the following diagrams do not show any internal heat exchangers
or a regenerator, which would be placed in the gas path around the
displacer. If a regenerator is used in a beta engine, it is usually in
the position of the displacer and moving, often as a volume of wire
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.
2. The heated gas increases in pressure and pushes the power piston to
the farthest limit of the power stroke.
3. The displacer piston now moves, shunting the gas to the cold end of
4. The cooled gas is now compressed by the flywheel momentum. This
takes less energy, since its pressure drops when it is cooled.
The complete beta type Stirling cycle
Gamma configuration operation
A gamma Stirling is simply a beta Stirling with the power piston
mounted in a separate cylinder alongside the displacer piston
cylinder, but 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 because of the volume
of the connection between the two but is mechanically simpler and
often used in multi-cylinder Stirling engines.
Other Stirling configurations continue to interest engineers and
Stirling engine 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, such as the Quasiturbine
A hybrid between piston and rotary configuration is a double acting
engine. This design rotates the displacers on either side of the power
piston. In addition to giving great design variability in the heat
transfer area, this layout eliminates all but one external seal on the
output shaft and one internal seal on the piston. Also, both sides can
be highly pressurized as they balance against each other.
Top view of two rotating displacers powering the horizontal piston.
Regenerators and radiator removed for clarity
Another alternative is the
Fluidyne engine (Fluidyne heat pump), which
uses 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
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.
The two-cylinder Stirling with Ross yoke is a two-cylinder stirling
engine (positioned at 0°, not 90°) connected using a special yoke.
The engine configuration/yoke setup was invented by Andy Ross.
The Franchot engine is a double acting engine invented by
Charles-Louis-Félix Franchot (de) in the nineteenth century. In
a double acting engine, the pressure of the working fluid acts on both
sides of the piston. 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.
However, a disadvantage of this machine is that one connecting rod
must have a sliding seal at the hot side of the engine, which is
difficult when dealing with high pressures and temperatures[citation
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 avoids 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 are:
The power piston is pushed outwards by the expanding gas thus doing
work. Gravity plays no role in the cycle.
The gas volume in the engine increases and therefore the pressure
reduces, which causes 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.
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
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 to overcome the difficulty of lubricating the crank
mechanism. 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. G.M. Benson also
made important early contributions and patented many novel free-piston
The first known mention of a
Stirling cycle machine using freely
moving components is a British patent disclosure in 1876. 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.
Flat Stirling engine
Cutaway of the flat Stirling engine: 10 - Hot cylinder. 11 - A volume
of hot cylinder. 12 - B volume of hot cylinder. 17 - Warm piston
diaphragm. 18 - Heating medium. 19 -
Piston rod. 20 - Cold cylinder.
21 - A
Volume of cold cylinder. 22 - B
Volume of cold cylinder. 27 -
Cold piston diaphragm. 28 - Coolant medium. 30 - Working cylinder. 31
- A volume of working cylinder. 32 - B volume of working cylinder. 37
- Working piston diaphragm. 41 - Regenerator mass of A volume. 42 -
Regenerator mass of B volume. 48 -
Heat accumulator. 50 - Thermal
insulation. 60 - Generator. 63 - Magnetic circuit. 64 - Electrical
winding. 70 - Channel connecting warm and working cylinders.
Design of the flat double-acting
Stirling engine solves the drive of a
displacer with the help of the fact that areas of the hot and cold
pistons of the displacer are different. The drive does so without any
mechanical transmission. Using diaphragms eliminates friction and need
for lubricants. When the displacer is in motion, the generator holds
the working piston in the limit position, which brings the engine
working cycle close to an ideal Stirling cycle. The ratio of the area
of the heat exchangers to the volume of the machine increases by the
implementation of a flat design. Flat design of the working cylinder
approximates thermal process of the expansion and compression closer
to the isothermal one. The disadvantage is a large area of the thermal
insulation between the hot and cold space. 
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.
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. More
NASA has considered nuclear-decay heated Stirling Engines
for extended missions to the outer solar system. At the 2012
Cable-Tec Expo put on by the Society of Cable Telecommunications
Engineers, Dean Kamen took the stage with Time Warner Cable Chief
Technology Officer Mike LaJoie to announce a new initiative between
his company Deka Research and the SCTE. Kamen refers to it as a
Main article: Stirling cycle
A pressure/volume graph of the idealized Stirling cycle
Stirling cycle consists of four thermodynamic processes
acting on the working fluid:
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
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.
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
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 process 2, heating up on its way to the
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
ideal cycle deviates substantially from practical Stirling
engines. 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.
Other real-world issues reduce the efficiency of actual engines,
because of 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. An ideal analysis
where the expansion and compression spaces are taken to be adiabatic
with isothermal heat exchangers and perfect regeneration was analyzed
by 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 it 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
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 is in thermal contact with an external heat sink, such as
air fins. A change in gas temperature causes a corresponding change in
gas pressure, while the motion of the piston makes the gas alternately
expand and compress.
The gas follows the behaviour described by the gas laws, which
describe how a gas's pressure, temperature and volume are related.
When the gas is heated the pressure rises (because it is in a sealed
chamber) and this pressure then acts on the power piston to produce a
power stroke. When the gas is cooled the pressure drops and this drop
means that the piston needs to do less work to compress the gas on the
return stroke. The difference in work between the strokes yields a net
positive power output.
Stirling cycle is unattainable in the real world (as with
any heat engine); efficiencies of 50% have been reached, similar to
the maximum figure for
Diesel cycle engines. The efficiency of
Stirling machines is also linked to the environmental temperature;
higher efficiency is obtained when the weather is cooler, thus making
this type of engine less interesting in places with warmer climates.
As with other external combustion engines, Stirling engines can use
heat sources other than from combustion of fuels.
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 that of the Carnot cycle, but the efficiency of real
engines is less than this value because of 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 that run on a temperature
difference of as little as 0.5 K. A displacer type stirling engine
has one piston and one displacer. A temperature difference is required
between the top and bottom of the large cylinder to run the engine. In
the case of the low-temperature difference (LTD) stirling engine, the
temperature difference between one's 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
displacer moves up and down to cause most of the gas in the displacer
cylinder to be either heated, or cooled. Note that in the following
description of the cycle the heat source at the bottom (the engine
would run equally well with the heat source at the top):
When the displacer is near the top of the large cylinder; most of the
gas is in the lower section and will be heated by the heat source and
it expands. This increases the pressure, which forces the piston up,
powering the flywheel. The turning of the flywheel then moves the
When the displacer is near the bottom of the large cylinder; most of
the gas is in the upper section and will cooled and contract causing
the pressure to decrease, which in turn moves the piston down,
imparting more energy to the flywheel.
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, in a first approximation,
produces 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
Stirling engine design, optimization is multivariate, and
often has conflicting requirements. 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
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.
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
Comparison with internal combustion engines
In contrast to internal combustion engines, Stirling engines have the
potential to use renewable heat sources more easily, and to be quieter
and more reliable with lower maintenance. They are preferred for
applications that value these unique advantages, particularly if the
cost per unit energy generated is more important than the capital cost
per unit power. On this basis, Stirling engines are cost competitive
up to about 100 kW.
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. Their lower maintenance requirements
make the overall energy cost comparable. The thermal efficiency is
also comparable (for small engines), ranging from 15% to 30%. 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. However, Stirling engines are generally
not price-competitive as an automobile engine, because of high cost
per unit power, low power density, and high material costs.
Basic analysis is based on the closed-form Schmidt analysis.
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
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.
Some types of Stirling engines have the bearings and seals on the cool
side of the engine, where they require less lubricant and last longer
than equivalents on 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.
Stirling engine uses a single-phase working fluid that 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
overpressure relief valve can cause an explosion.
In some cases, low operating pressure allows the use of lightweight
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.
Stirling engine used for pumping water can be configured so that the
water cools the compression space. This increases efficiency 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.
NASA built a Stirling automotive engine and installed it in a
Chevrolet Celebrity. Fuel economy was improved 45% and emissions were
greatly reduced. Acceleration (power response) was equivalent to the
standard internal combustion engine. This engine, designated the Mod
II, also nullifies arguments that Stirling engines are heavy,
expensive, unreliable, and demonstrate poor performance. A
catalytic converter, muffler and frequent oil changes are not
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. 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.
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
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. The
Stirling cycle is not actually achievable, the real
cycle in Stirling machines is less efficient than the theoretical
Stirling cycle, also the efficiency of the
Stirling cycle is lower
where the ambient temperatures are mild, while it would give its best
results in a cool environment, such as northern countries' winters.
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.
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). 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 (1/ΔT)2. 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
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
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 gas used 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
Air is a viable working fluid, but the oxygen in a
highly pressurized air engine can cause fatal accidents caused by
lubricating oil explosions. 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, because of hydrogen absorption, and
given the high diffusion rate associated with this low molecular
weight gas, particularly at high temperatures, H2 leaks 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
required 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
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, and
hence not flammable.
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. 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.
Main article: Applications of the Stirling engine
Applications of the Stirling engine
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, low power aviation engines, and low temperature
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 must be
electricity, and where a small conversion device is a critical factor.
Relative cost of electricity generated by different sources
Stirling radioisotope generator
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Wikimedia Commons has media related to Stirling engines.
Stirling engine in Wiktionary, the free dictionary.
NASA Stirling Engine Based Nuclear Power Plant For Lunar Use on
Stirling engine at Curlie (based on DMOZ)
I. Urieli (2008). Stirling Cycle Machine Analysis 2008 Winter Syllabus
How to build your
Stirling engine (2017). Stirling Engines: Design and
Simple Performance Prediction Method for Stirling Engine
Shockwave3D models: Beta Stirling and LTD
Inquiry into the Hot
Air Engines of the 19th Century
Without phase change
(hot air engines)
Brayton / Joule
Stirling (pseudo / adiabatic)
With phase change
Rankine (Organic Rankine)
Brayton / Joule
Homogeneous charge compression ignition
Mixed / Dual
Timeline of heat engine technology
BNF: cb12378418h (d