How does THERMOELECTRIC work?

Strictly speaking, thermoelectric generators take a temperature difference and turn it into electrical power.  Amazingly, these materials can also be run in reverse!  If you put power into a thermoelectric generator you will create a temperature difference.  Small mini-fridges, for just a few sodas, use thermoelectric generators to efficiently cool a few drinks.

To understand how thermoelectric generates the electricity from a temperature difference we have to know a bit about how electrons move in a metal.  Metals are good conductors because electrons can move freely within them, similar to a fluid in a pipe.  Imagine you have a pipe full of water and you raise one end, what happens?  The water will flow down the pipe from the high end to the low end.  This is because when you raised the pipe you increased the potential energy and the water wants to flow downhill.  In a thermoelectric material the same thing happens to the fluid-like electrons when you heat it.

Heating one end of a thermoelectric material causes the electrons to move away from the hot end toward the cold end.  When the electrons go from the hot side to the cold side this causes an electrical current, which the PowerPot harnesses to charge USB devices.  The larger the temperature difference the more electrical current is produced and therefore more power generated.

The tricky part about thermoelectric generators is that as you heat the hot side, the cold side of the generator heats up too.  In order to generate power with the a thermoelectric generator you need both a heat source and a way of dissipating heat in order to maintain a temperature difference across the thermoelectric materials. This is done with no moving parts by heating water in the PowerPot.  Water holds several times more heat than aluminum per pound, so it makes a wonderful heatsink.  Also, water never gets hotter than 212 F (100 C) at a boil, effectively limiting the maximum temperature of the “cold” side of the thermoelectric generator.  This is why you always need to have something watery in the PowerPot or else it is possible to overheat the thermoelectric generator.

This rendering shows temperature distribution in the PowerPot during operation with some parts removed for clarity.

BACKGROUND OF THERMOELECTRICS

Thermoelectric power is the conversion of a temperature differential directly into electrical power.  Thermoelectric power results primarily from two physical effects: the Seebeck effect, and Peltier effect. 

The Seebeck effect is named after Thomas J. Seebeck, who first discovered the phenomenon in 1821.  Seebeck noticed that when a loop comprised of two dissimilar materials was heated on one side, an electromagnetic field was created.  He actually discovered the EM field directly with a compass!  He noted that the strength of the electromagnetic field, and therefore the voltage, is proportional to the temperature difference between the hot and cold sides of the material.  The magnitude of the Seebeck coefficient (S) varies with material and temperature of operation.  The Seebeck coefficient is thus defined as:

In this equation ΔV is the voltage difference between the hot and cold sides, ΔT is the temperature difference between the hot and cold sides.  The negative sign comes from the negative charge of the electron, and the conventions of current flow.  A negative Seebeck coefficient results in electrons being the dominant charge carriers (n-type), whereas holes are the dominant carrier (p-type) in materials with a positive Seebeck coefficient.  The majority charge carriers are said to move away from the heated side toward the cooler side.  Minority charge carriers move in the opposite direction, but at a slower rate due to phonon drag and charge carrier diffusion rates.  Thus, both n-type and p-type materials are required to realize current flow in a device.

Things to remember about the Seebeck effect:

• Solids have charge carriers that facilitate the flow of electrical power
• The charge carriers come in two flavors negative electrons “n-type” and positive “holes” that we use to keep track of mobile positive charge in “p-type” solids
• Heating one end of a conducting solid pushes on the charge carriers concentration and the distribution of charge creates voltage that can be measured this is called the Seebeck effect

The Peltier effect was first discovered in 1834 by Jean C.A. Peltier, for whom it was named.  Peltier discovered that whenever a circuit of two dissimilar materials passes current, heat is absorbed at one end of the junction and released at the other.  This is a linearly dependent and thermodynamically reversible process, unlike Joule heating which is irreversible and quadratic in nature mean.  This process forms the basis for thermoelectric cooling and temperature control, these are currently the widest applications of thermoelectric devices. 

However, applying a temperature differential the reverse process occurs, and current is caused to flow, thereby generating power.  The figure below shows a TEP device in both cooling and power generation configurations.

A thermoelectric cooler (left), and power generator (right).  Current flow is labeled in the direction of the electrons.

The efficiency by which a material is capable of generating power is governed by the figure of merit (Z).  As seen in the equation below, the figure of merit is most dependent on the Seebeck coefficient of the material.

In the above equation, the figure of merit is defined in terms of the Seebeck coefficient, the electrical conductivity, and the thermal conductivity.  Maximum power generation requires the minimization of the thermal conductivity, while maximizing the Seebeck coefficient and electrical conductivity. 

THE POWERPOT | THERMOELECTRIC GENERATOR

The PowerPot is a thermoelectric generator that uses heat to generate electricity.  The PowerPot has no moving parts or batteries, and since the thermoelectric technology is built into the bottom of the pot it can produce electricity from a wide variety of heat sources.  Simply add water and place the PowerPot on a fire (e.g. wood, propane, butane, alcohol, gas) and it will start generating electricity within seconds.  Just plug in the high temperature cable to the back of the pot and watch your USB devices safely charge from a fire.

The larger the temperature difference between the water in the pot and the bottom of the pot, the more electricity the PowerPot will produce.  For example, melting snow in the PowerPot is a great way to generate electricity, because snow is so much colder than a flame.  However, you don’t have to worry about overpowering your device, because the PowerPot has a built in regulator which insures that you safely charge your USB devices.  The regulator outputs 5 volts (USB standard) and up to 1000 milliAmps of current, which is the most any smartphone/MP3 player on the market can handle.  This means when you’re charging your USB device with the PowerPot, you will get the same charging time as you would from your wall outlet at home. Learn More

Glossary Of Thermoelectric Terms

ACTIVE LOAD
The amount of heat (in Watts) being generated by the device that is on top of the TE Cooler. Typically, this is the input power of this device (Voltage x current).
ALUMINA OXIDE
Ceramics made of aluminum oxide (Al2O3 ). These ceramics are used on most of our standard TECs. A positive of Al2O3 is that it is inexpensive and can be designed for snap states instead of dice, which considerably reduces production costs. Negative aspects of this material are its lower thermal conductivity and it is difficult to use in 3 to 6 stage coolers.
AIN
Aluminum NITRIDE
Al2O3 also a very popular ceramic for it’s high thermal conductivity  properties . Typically in the range of 70-200  watts/mk
AMBIENT TEMPERATURE
Temperature of the air or environment surrounding a thermoelectric cooling system; sometimes called room temperature.
ASPECT RATIO
The numerical ratio of the length (height) to cross-sectional area of a thermoelectric element. An element’s L/A aspect ratio is inversely proportional to its optimum current.
BeO2
Ceramics made of beryllium oxide thermal conductivity of 260  watts/mk. Typically used in multistage coolers due to its higher thermal conductivity. The advantages to this material are that it enhances the thermal performance of the TE Cooler as well as makes it easier to assemble because of the high heat conductance. Disadvantages are that it is more expensive and BeO22 is toxic when its dust is inhaled. The dust comes from dicing and sanding of the material, both of which are performed on a TE Cooler in its final condition. However, the risks of BeO2 sometimes prohibit it as an option
for commercial use.
BISMUTH TELLURIDE ******
A thermoelectric semiconductor Bi2Te3 material that exhibits optimum performance in a “room temperature” range. An alloy of Bismuth Telluride most often is used for thermoelectric cooling applications and also power generation. It is by far the most efficient thermoelectric material presently used for power generation in the 250°C hot side temperature range.
LEAD TELLURIDE ******
A Thermo electric material used for high temperature (hot side 500°C Thermal Electric power generation). This material although is well known for it’s power generation ability is very difficult to find as a module. Sources of this material can only be found in completed thermoelectric power generation appliances.
BISMUTH-ANTIMONY
A thermoelectric semiconductor material that exhibits optimum performance characteristics at relatively low temperatures.
BTU (British Thermal Unit)
The amount of thermal energy required to raise one pound of water by one° Celsius at a standard temperature of 15¼C.
Bonded Heat Sink
A heat sink which has Fins which have been bonded to the base plate.  Heat sinks constructed in this manner typically have much greater heat dissipation characteristics and their much lower thermal resistance is far superior to that of an extruded heat sink.
BURN-IN TEST
A power cycling test performed by repeatedly powering on and off the TE Cooler for short intervals of time. The test is designed to detect latent manufacturing or material defects that would cause premature failure of the TE Cooler.
CASCADE MODULE (MULTISTAGE MODULE)
A thermoelectric cooler configuration whereby one cooler is stacked on top of another so as to be thermally in series. This arrangement makes it possible to reach lower temperatures than can be achieved with a single-stage cooler.

Cascade Seebeck Module A Cascade Seebeck module takes advantage of large temperature gradients, by exploiting each temperature zone with a material that peck efficiency equals that zones temperature. Typically, up to 2 different materials are thermally stacked (Hot Side to Cold side). The Seebeck effect module is constructed using material that is most efficient in that temperature range. Semi-conductors are most efficient when they are exposed to specific temperatures that exploit their targeted peak efficiency.
CERAMIC
A patterned substrate, the finished part which goes into a TE Cooler. This material conducts heat and insulates electric current. Typically comprised of Al2O3 , BeO2 or AIN. At least one side of the ceramic has a metal pattern required for the operation of the TE Cooler. Al2O3 , AIN, BeO2 Thermal Conductivity (W/in C) .051 4.0 6.5 CTE (10-6/C) 7.0 4.0 9.0
CFM (Cubic Feet per Minute)
The volumetric flow rate of a gas, typically air, expressed in the English system of units. For thermoelectric applications, this generally refers to the amount of air passing through the fins of a forced convection heat sink.
CLOSED-LOOP TEMPERATURE CONTROLLER
A temperature controlling device having some type of temperature sensor (thermocouple, thermistor, RTD, etc.) that will transmit or “feed back” temperature data to the controller. Based on the returned information, the controller will automatically adjust its output to maintain the desired temperature.
COEFFICIENT OF PERFORMANCE (COP)
A measures of the efficiency of a thermoelectric cooler, device or system. Mathematically, COP is the total heat transferred through the thermo electric device divided by the electric input power (COP=Qc/W). COP sometimes is stated as COPR (Coefficient of Performance as a Refrigerator) or as COPH (Coefficient of Performance as a Heater).
COLD SIDE OF A THERMOELECTRIC MODULE
The side of a cooler that normally is placed in contact with the object being cooled. When the positive and negative cooler leads are connected to the respective positive and negative terminals of a DC power source, the cooler’s cold side will absorb heat. Typically, the leads of a TE cooler are attached to the hot side.
CONDUCTION (THERMAL)
The transfer of heat within a material caused by a temperature difference through the material. The actual material may be a solid, liquid or gas (or a combination) where heat will flow by means of direct contact from a high temperature region to a lower temperature region.
CONVECTION (THERMAL)
The transfer of heat by air (gas) movement over a surface. Convection actually is a combined heat transfer process that involves elements of conduction, mixing action, and energy storage.
COUPLE
A pair of thermoelectric elements consisting of one N-type and one P-type connected electrically in series and thermally in parallel. Because the input voltage to a single couple is quite low, a number of couples normally are joined together to form a “cooler.”
DC
Direct Current is the electricity that comes from a battery or electronics power supply. DC powers TEC but can be stress tested using AC.
DELTA-T
The temperature difference between the cold and hot sides of a thermoelectric power  generation module. Delta T may also be expressed as “DT” or “DT.” The larger the differential there is the higher output of power achieved !
DELTA-T Test For cooling application
Test performed in which the TE Cooler is placed on a temperature controlled base plate (typically 27°C) and powered at Imax. A thermocouple is pressed onto the top ceramic using a spring plunger and the cold side temperature as well as voltage is measured.
DENSITY
The mass of a material per unit volume, often expressed as pounds per cubic foot or grams per cubic centimeter.
DICE
A general term for blocks of the thermoelectric semiconductor material or “elements” prepared for use in a thermoelectric cooler.
EFFICIENCY
For thermoelectric coolers, mathematical efficiency is the heat pumped by a cooler divided by the electrical input power; for thermoelectric generators, efficiency is the electrical output power from the cooler divided by the heat input (Qc/ Qh). To convert to percent, multiply by 100. See definition of Coefficient of Performance.
ELEMENT
An individual block of thermo electric semiconductor material. Slicing an ingot of TE material into wafers, then dicing these wafers into very tiny, very precise, and accurately sized blocks, which are placed inside a TE Cooler, makes elements. Each TE Cooler has P elements and N elements. Elements are sometimes referred to as columns or TE material. See definition of DIE.
FIGURE-OF-MERIT (Z factor)
A measure of the overall performance of a thermo electric device or material. Material having the highest figure-of-merit also has the highest thermoelectric performance. A good thermoelectric material will have a high Z, high Seebeck coefficient and low thermal conductivity and resistively. Unfortunately the testing of figure of merit is not standardized
so many claims of High-Z cannot be  validated.
FORCED CONVECTION HEAT SINK
A heat sink that incorporates a fan or blower to actively move air over the heat sink’s fins. Greatly improved cooling performance may be realized with a forced convection system when compared to a natural convection heat sink.
HEAT LOAD
The quantity of heat presented to a thermoelectric device that must be absorbed by the device’s cold side. The term heat load, when used by itself, tends to be somewhat ambiguous and it is preferable to be more specific. Terms such as active heat load, passive heat load or total heat load are more descriptive and less uncertain as to meaning.
HEAT PUMP
A general term describing a thermoelectric cooling device, often being used as a synonym for a thermoelectric cooler. In somewhat less common usage, the term heat pump has been applied to a thermoelectric device operating in the heating mode.
HEAT PUMPING CAPACITY
The amount of heat that a thermoelectric device is capable of pumping at a given set of operating parameters. Frequently, this term will be used interchangeably with the expression maximum heat pumping capacity. The two terms are not strictly synonymous, however, because maximum heat pumping capacity specifically defines the maximum amount of heat that a cooler will pump at the maximum rated input current and at a zero temperature differential.
HEAT SINK
A body that is in contact with a hotter object and that expedites the removal of heat from the object. Heat sinks typically are intermediate stages in the heat removal process whereby heat flows into a heat sink and then is transferred to an external medium. Common heat sinks include natural (free) convection, forced convection and fluid cooled.
HEAT SINK RESISTANCE
Also referred to as HSR. The thermal path from the hot side of the TE cooler to the ambient, including mounting interfaces, fans, etc., is measure of the effectiveness of a heat sink. In other words, how well does the heat sink remove the heat from the TE cooler? Its units are °C/W and is used to determine the number of degrees the hot side will rise in temperature for a given amount of heat that is dumped into it. For example, a heat sink resistance of 0.1°C/W will result in a hot side temperature rise of 1°C when 10 Watts is applied. The effectiveness of the heat sink greatly affects the performance of the TE cooler. Therefore, the better the heat sink (better is a lower °C/W) results in less input power to the TE cooler or a colder cold side temperature.
HEAT TRANSFER COEFFICIENT
A numerical value that describes the degree of coupling that exists between an object and a cooling or heating fluid. The heat transfer coefficient actually is an extremely complex value that encompasses many physical factors.
HOT SIDE OF A THERMOELECTRIC MODULE
The face of a thermoelectric cooler that usually is placed in contact with the heat sink. When the positive and negative cooler leads are connected to the respective positive and negative terminals of a DC power source, the cooler’s hot side will reject heat. Normally, the wire leads are attached to the hot side ceramic substrate.
Imax
Current which, the maximum delta T is produced. Generally, it is not a good to operate a TE cooler at Imax because the amount of input power increases significantly without a significant change in delta T. 70 – 80 % of Imax is usually an optimal operating condition.
INGOT
A cast alloy of thermoelectric material. The ingot is sawed into wafers that are then diced into elements.
INTERSTAGE TEMPERATURE
The temperature between specific stages or levels of a multistage or cascade cooler.
JOULE HEATING
The passage of an electrical current through a conductor or material due to the internal resistance, resulting in Heat
LEAD TELLURIDE
A thermoelectric semiconductor that exhibits its optimum performance within a temperature range of 250-450°C. Lead Telluride is used most often for thermoelectric power generation applications.
LIQUID COOLING
A heat sink method involving the use of water or other fluids to carry away unwanted heat. When comparing alternative heat-sinking methods, liquid cooled heat sinks normally provide the highest thermal performance per unit volume.
MAXIMUM HEAT PUMPING CAPACITY (MAXIMUM Qc)
The maximum quantity of heat that can be absorbed at the cold face of a thermoelectric cooler when the temperature differential between the cold and hot cooler faces is zero and when the cooler is being operated at its rated optimum current. Qmax is one of the significant thermoelectric cooler/device specifications.
MAXIMUM TEMPERATURE DIFFERENTIAL (MAXIMUM Delta T)
The largest difference that can be obtained between the hot and cold faces of a thermoelectric cooler when heat applied to the cold face is effectively zero. DTmax or Dmax is one of the significant thermoelectric cooler/device specifications.
METALLIZATION
The conductive copper pattern printed on the ceramics.
MODULE
A thermoelectric cooling component or device fabricated with multiple thermoelectric couples that are connected thermally in parallel and electrically in series.
MULTISTAGE MODULE (CASCADE MODULE)
A thermoelectric configuration whereby one TEC is mechanically stacked on top of another in series. This arrangement makes it possible to reach lower temperatures than can be achieved with a single-stage cooler.
NATURAL CONVECTION HEAT SINK
A heat sink from which heat is transferred to the surrounding air by means of natural air currents within the environment. No external fan, blower or other appliance is used to facilitate air movement around the heat sink.
N-TYPE MATERIAL
The doping of semiconductor material creating an excess of electrons.
OPTIMUM CURRENT
The specific level of electrical current that will produce the greatest heat absorption by the cold side of a thermal electric cooler. At the optimum current, a thermoelectric cooler will be capable of pumping the maximum quantity of heat; maximum temperature differential (Delta Tmax) typically occurs at a somewhat lower current level.
PASSIVE LOADS
The amount of non-active heat (in Watts) being applied on the TE cooler. This includes conductance through wires that extend from the cold side of the TE cooler to the ambient, the convective loads from the surrounding atmosphere (note: Convective loads are present in Nitrogen, Argon, and Xenon, but are not present in a vacuum).
PELTIER EFFECT
The phenomenon whereby the passage of an electrical current through a junction consisting of two dissimilar metals results in a cooling effect; when the direction of current flow is reversed heating will occur.
P-TYPE MATERIAL
Semiconductor material that is doped so as to have a deficiency of electrons.
Qmax
The maximum amount of heat (in Watts) that a TE cooler can pump. This occurs when the delta T is zero. Only for multistage coolers operating near a Delta Tmax condition.
RESISTIVELY (ELECTRICAL)
Resistively is a bulk or inherent property of a material that is unrelated to the physical dimensions of the material. Electrical resistance, on the other hand, is an absolute value dependent upon the cross-sectional area (A) and Length (L) of the material.
SEEBECK EFFECT or SEEBECK Coefficient
The phenomenon whereby an electrical current will flow in a closed circuit made up of two dissimilar metals when the junctions of the metals are maintained at two different temperatures. A common thermocouple used for temperature measurement utilizes this principle.
SILICON-GERMANIUM
A high temperature thermoelectric semiconductor material that exhibits its optimum performance within a temperature range of 500-1000°C. Silicon-Germanium material most often is used for special thermoelectric power generation applications that utilize a radioisotope/nuclear heat source.
SINGLE-STAGE MODULE
The most common type of thermoelectric cooling module using a single layer of thermoelectric couples connected electrically in series and thermally in parallel. Single-stage coolers will produce a maximum temperature differential of approximately 70°C under a no-load condition.
SLICING
The process of cutting the ingots into wafers.
SOLDER
Metals or alloys that melt below 425°C. Common solders used are: 118°C 52 In/48 Sn (mounting); 138°C 42Sn/58 Bi (TEC assembly); 183°C 63 Sn/37 Pd (TEC assembly); 232°C 95 Sn/5 Sb (TEC assembly).
THERMAL COEFFICIENT OF EXPANSION
A measure of the dimensional change of a material due to a change in temperature. Common measurement units include centimeter per centimeter per degree Celsius and inch per inch per degree Fahrenheit.
THERMAL CONDUCTANCE
The amount of heat a given object will transmit per unit of temperature. Thermal conductance is independent of the physical dimensions, i.e., cross-sectional area and length of the object. Typical units include watts per degree Celsius and BTU per hour per degree Fahrenheit.
THERMAL CONDUCTIVITY
The amount of heat a material will transmit per unit of temperature based on the material’s cross-sectional area and thickness.
THERMAL GREASE
A grease-like material used to enhance heat transfer between two surfaces by filling in the microscopic voids caused by surface roughness. Most thermal greases, also known as Transistor Heat Sink Compound or Thermal Joint Compound, are made from silicone grease loaded with zinc oxide. Non-silicone based compounds are also available which in most cases are superior but more expensive than silicone-based alternatives.
THERMAL RESISTANCE (HEAT SINK)
A measure of a heat sink’s performance based on the temperature rise per unit of applied heat. The best heat sinks have the lowest thermal resistance.
THERMAL SHOCK
Thermal Shock also is referred to as temperature cycling in some MIL specs. In a thermal shock test, the TE cooler (not powered throughout test) is placed in a hot chamber (for example, 85°C) for a set time (for example, 30 minutes). The part is then transferred to the cold chamber (for example, -40°C) for the same time. This cycle is repeated several times depending on the requirement.
THERMOELECTRIC
A term used to denote not only the products produced but also the basic scientific principle upon which products are designed.
THERMOELECTRIC GENERATOR
A device that directly converts energy into electrical energy based on the Seebeck Effect. Bismuth telluride-based thermoelectric generators have very low efficiencies (generally not exceeding two or three percent) but may provide useful electrical power in certain applications.
THERMOELECTRIC MATERIAL
An alloy of materials that produce thermoelectric properties.
TINNING
Applying solder paste over the copper or tabbed pattern. The bottom ceramic can also be tinned enabling the ability to mount the TEC on a header or heat sink.
Vmax
The optimum voltage the maximum delta T is produced for a thermal electric cooling module.

Stirling engine

From Wikipedia, the free encyclopedia

For the adiabatic Stirling cycle, see Stirling cycle.

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 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.^[1][2] More specifically, the Stirling engine is a closed-cycle regenerative heat engine with a permanently gaseousworking 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 differentiates a Stirling engine from other closed cycle hot air engines.

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]

Stirling engines have a high efficiency compared to internal combustion engines,^[4] 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.^[5][6] However, it has a low power-to-weight ratio,^[4] rendering it more suitable for use in static installations where space and weight are not at a premium.

Contents

  [hide] 

• 1Name and classification
• 2History
  • 2.1Invention and early development
  • 2.2Later nineteenth century
  • 2.3Twentieth century revival
• 3Functional description
  • 3.1Key components
  • 3.2Configurations
  • 3.3Other developments
• 4Theory
  • 4.1Operation
  • 4.2Pressurization
  • 4.3Lubricants and friction
• 5Analysis
  • 5.1Comparison with internal combustion engines
• 6Applications
• 7Alternatives
• 8See also
• 9References
• 10Bibliography
• 11Further reading
• 12External links

Name and classification[edit]

Stirling engine running.

Robert Stirlingwas a Scottish minister who invented 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 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,^[8] a situation that continues.^[9]

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 enginewhere 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.

History[edit]

Invention and early development[edit]

Illustration from Robert Stirling’s 1816 patent application of the air engine design that 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 in 1816.^[10] 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.^[11] 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^[12] 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 by 1843, had sufficiently increased power output to drive all the machinery at a Dundee iron foundry.^[13]

Though it has been disputed,^[14] it is widely supposed that the inventors aims were not only to save fuel but also to create a safer alternative to the steam enginesof the time,^[15] whose boilers frequently exploded, causing many injuries and fatalities.^[16][17]

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).^[18]For example, the Dundee foundry engine was replaced by a steam engine after three hot cylinder failures in four years.^[19]

Reverend Stirling filed three patents in relation to hot air engines. The first one in 1816, ^[20] 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^[21] very similar to the Parkinson and Crossley’s air engine,^[22] 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 in 1845.^[23] 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 Dundee Foundry 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 regenerator).

Later nineteenth century[edit]

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^[24] 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.^[25] 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.^[26] 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.^[27]

Twentieth century revival[edit]

During the early part of the twentieth century the role of the Stirling engine as a “domestic motor”^[28] 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.^[29]

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 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 favored).^[30] 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.^[31]

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.^[32] Some found their way into university and college engineering departments around the world^[33]giving generations of students a valuable introduction to the Stirling engine.

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.^[34]

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.^[35] 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, license-built by 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 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 electricity.^[36]

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 homes.^[37]

Functional description[edit]

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.^[2] An internal regenerative heat exchanger increases the Stirling engine’s thermal efficiency compared to simpler hot air engines lacking this feature.

Key components[edit]

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.

Heat source[edit]

Point focus parabolic mirror with Stirling engine at its centre and its solar tracker at 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 engines.^[38]

Other suitable heat sources include concentrated solar energy, geothermal energy, nuclear energy, waste heatand 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.^[39] 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.^[40]

Heater / hot side heat exchanger[edit]

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 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). 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.

Regenerator[edit]

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.^[41] 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,^[42] thus enabling the thermal efficiency of the cycle (though not of any practical engine^[43]) to approach the limiting Carnotefficiency.

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.^[44]

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[edit]

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.

Heat sink[edit]

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 efficiency.

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.

Displacer[edit]

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.

Configurations[edit]

There are three major types of Stirling engines, that are distinguished by the way they move the air between the hot and cold areas:

1. 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.
2. 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 crankshaft.
3. 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[edit]

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.^[45] 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 regeneratorwould be placed in the pipe connecting the two cylinders.

Beta configuration operation[edit]

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.^[46]

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 mesh.

Gamma configuration operation[edit]

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 ratiobecause of the volume of the connection between the two but is mechanically simpler and often used in multi-cylinder Stirling engines.

Other types[edit]

Other Stirling configurations continue to interest engineers and inventors.

The rotary 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 engine.^[47]

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 displacer 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 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.^[48][49]

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.^[50]

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 needed]}.

Free-piston Stirling engines[edit]

Various free-piston Stirling configurations… F. “free cylinder”, G. Fluidyne, H. “double-acting” Stirling (typically 4 cylinders)

Free-piston Stirlingengines 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:

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 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.
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 to overcome the difficulty of lubricating the crank mechanism.^[51] 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.^[52] G.M. Benson also made important early contributions and patented many novel free-piston configurations.^[53]

The first known mention of a Stirling cycle machine using freely moving components is a British patent disclosure in 1876.^[54] 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 Colemanin 2004.

Flat Stirling engine[edit]

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. ^[55]

Thermoacoustic cycle[edit]

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.

Other developments[edit]

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.^[56] More recently, NASA has considered nuclear-decay heated Stirling Engines for extended missions to the outer solar system.^[57] 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 Stirling engine.^[58][59]

Theory[edit]

Main article: Stirling cycle

A pressure/volume graph of the idealized Stirling cycle

The idealised Stirling cycle consists of four thermodynamic processesacting 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 process 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 ideal cycle deviates substantially from practical Stirling engines.^[60]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.^[61][62]

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.^[63]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 machinery ^[64]

Operation[edit]

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 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.

The ideal Stirling cycle is unattainable in the real world (as with any heat engine); efficiencies of 50% have been reached,^[4] similar to the maximum figure for Diesel cycle engines.^[65] 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.^[66] A displacer type stirling enginehas 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):

1. 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 displacer down.
2. 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.

Pressurization[edit]

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 aspects of Stirling engine design, optimization is multivariate, and often has conflicting requirements.^[67] 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[edit]

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.^[68]

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.

Analysis[edit]

Comparison with internal combustion engines[edit]

In contrast to internal combustion engines, Stirling engines have the potential to use renewable heatsources 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.^[69]

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.^[70] Their lower maintenance requirements make the overall energy cost comparable. The thermal efficiency is also comparable (for small engines), ranging from 15% to 30%.^[69] 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.^[71][72]

Advantages[edit]

• 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.
• 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.^[73]
• A 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 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 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.
• In 1986 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.^[74] A catalytic converter, muffler and frequent oil changes are not required.^[74]

Disadvantages[edit]

Size and cost issues[edit]

• 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.^[68]
• 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 engineor 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.^[37]

Power and torque issues[edit]

• 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).^[67] 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 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 swashplatecrankshaft 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[edit]

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 capacity. Air is a viable working fluid,^[75] but the oxygen in a highly pressurized air engine can cause fatal accidents caused by lubricating oil explosions.^[68]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 on metal. Hydrogen can also cause the embrittlementof 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.^[76] The researcher Allan Organ demonstrated that a well-designed air engine is theoretically just as efficientas 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[edit]

Main article: 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,^[77] and low temperature difference engines.

Alternatives[edit]

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.

See also[edit]

• Beale number
• Bore
• Cogeneration
• Distributed generation
• Fluidyne engine
• Quasiturbine
• Relative cost of electricity generated by different sources
• Schmidt number
• Stirling radioisotope generator
• Stroke
• Thermomechanical generator
• West Number

References[edit]

1. Jump up^ “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.”
   1. ^ Jump up to:^a b W.R. Martini (1983), p.6
   1. Jump up^ T. Finkelstein; A.J. Organ (2001), Chapters 2&3
   1. ^ Jump up to:^a b c “The Stirling Engine”. mpoweruk.com.
   1. Jump up^ Sleeve notes from A.J. Organ (2007)
   1. Jump up^ F. Starr (2001)
   1. Jump up^ C.M. Hargreaves (1991), Chapter 2.5
   1. Jump up^ Graham Walker (1971) Lecture notes for Stirling engine symposium at Bath University. Page 1.1 “Nomenclature”
   1. Jump up^ “Previous Survey Results – StirlingBuilder.com”. stirlingbuilder.com. Archived from the original on 26 May 2014.
   1. Jump up^ R. Sier (1999)
   1. Jump up^ T. Finkelsteinl; A.J. Organ (2001), Chapter 2.2
   1. Jump up^ 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.??
   1. Jump up^ R. Sier (1995), p. 93
   1. Jump up^ A.J. Organ (2008a)
   1. Jump up^ Excerpt from a paper presented by James Stirling in June 1845 to the Institution of Civil Engineers. As reproduced in R. Sier (1995), p.92.
   1. Jump up^ A. Nesmith (1985)
   1. Jump up^ R. Chuse; B. Carson (1992), Chapter 1
   1. Jump up^ R. Sier (1995), p.94
   1. Jump up^ T. Finkelstein; A.J. Organ (2001), p.30
   1. Jump up^ “Stirling patent of 1816”. hotairengines.org.
   1. Jump up^ “The Stirling Engine of 1827”. hotairengines.org.
   1. Jump up^ “The Parkinson and Crossley’s Hot Air Engine of 1827”. hotairengines.org.
   1. Jump up^ “The 1842 Stirling Engine presented by James Stirling”. hotairengines.org.
   1. Jump up^ Hartford Steam Boiler (a)
   1. Jump up^ T. Finkelstein; A.J. Organ (2001), Chapter 2.4
   1. Jump up^ 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”.
   1. Jump up^ T. Finkelstein; A.J. Organ (2001), p.64
   1. Jump up^ T. Finkelstein; A. J. Organ (2001), p. 34
   1. Jump up^ T. Finkelstein; A. J. Organ (2001), p. 55
   1. Jump up^ C. M. Hargreaves (1991), p. 28–30
   1. Jump up^ Philips Technical Review (1947), Vol. 9, No. 4, p. 97.
   1. Jump up^ C. M. Hargreaves (1991), p. 61
   1. Jump up^ 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”
   1. Jump up^ C. M. Hargreaves (1991), p. 77
   1. Jump up^ Kockums (a)
   1. Jump up^ “Learning about renewable energy”. NREL – National Renewable Energy Laboratory. Archivedfrom the original on 2 May 2016. Retrieved 25 April2016.
   1. ^ Jump up to:^a b 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.”
   1. Jump up^ Dudek, Jerzy; Klimek, Piotr; Kołodziejak, Grzegorz; Niemczewska, Joanna; Zaleska-Bartosz, Joanna (2010). “Landfill Gas Energy Technologies” (PDF). Global Methane Initiative. Instytut Nafty i Gazu / US Environmental Protection Agency. Archived (PDF)from the original on 25 July 2015. Retrieved 24 July2015.
   1. Jump up^ W.H. Brandhorst; J.A. Rodiek (2005)
   1. Jump up^ B. Kongtragool; S. Wongwises (2003)
   1. Jump up^ “Archived copy” (PDF). Archived (PDF) from the original on 26 May 2014. Retrieved 25 May 2014.
   1. Jump up^ A.J. Organ (1992), p.58
   1. Jump up^ Stirling Cycle Engines, A J Organ (2014), p.4
   1. Jump up^ K. Hirata (1998)
   1. Jump up^ M.Keveney (2000a)
   1. Jump up^ M. Keveney (2000b)
   1. Jump up^ Quasiturbine Agence (a)
   1. Jump up^ “Ringbom Stirling Engines”, James R. Senft, 1993, Oxford University Press
   1. Jump up^ Ossian Ringbom (of Borgå, Finland) “Hot-air engine” Archived 17 October 2015 at the Wayback Machine. U.S. Patent no. 856,102 (filed: 17 July 1905; issued: 4 June 1907).
   1. Jump up^ “Animated Engines”. animatedengines.com. Archived from the original on 11 November 2011.
   1. Jump up^ “Free-Piston Stirling Engines”, G. Walker et al., Springer 1985, reprinted by Stirling Machine World, West Richland WA
   1. Jump up^ “The Thermo-mechanical Generator…”, E.H. Cooke-Yarborough, (1967) Harwell Memorandum No. 1881 and (1974) Proc. I.E.E., Vol. 7, pp. 749-751
   1. Jump up^ G.M. Benson (1973 and 1977)
   1. Jump up^ D. Postle (1873)
   1. Jump up^ “DOUBLE ACTING DISPLACER WITH SEPARATE HOT AND COLD SPACE AND THE HEAT ENGINE WITH A DOUBLE ACTING DISPLACE Archived14 January 2015 at the Wayback Machine.” WO/2012/062231 PCT/CZ2011/000108
   1. Jump up^ Infinia web site Archived 10 January 2013 at the Wayback Machine., accessed 2010-12-29
   1. Jump up^ Schimdt, George. Radio Isotope Power Systems for the New Frontier. Presentation to New Frontiers Program Pre-proposal Conference. 13 November 2003. (Accessed 2012-Feb-3)
   1. Jump up^ Mari Silbey. “New alliance could make cable a catalyst for cleaner power”. ZDNet.
   1. Jump up^ “Archived copy”. Archived from the original on 25 November 2012. Retrieved 28 November 2012.
   1. Jump up^ A. Romanelli Alternative thermodynamic cycle for the Stirling machine, American Journal of Physics 85, 926 (2017)
   1. Jump up^ T. Finkelstein; A.J. Organ (2001), Page 66 & 229
   1. Jump up^ A.J. Organ (1992), Chapter 3.1 – 3.2
   1. Jump up^ 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.
   1. Jump up^ Finkelstein, T. Generalized Thermodynamic Analysis of Stirling Engines. Paper 118B, Society of Automotive Engineers, 1960.
   1. Jump up^ http://www.mpoweruk.com/piston_engines.htmSection heading “Energy Conversion Efficiency”
   1. Jump up^ “An Introduction to Low Temperature Differential Stirling Engines”, James R. Senft, 1996, Moriya Press
   1. ^ Jump up to:^a b A.J. Organ (1997), p.??
   1. ^ Jump up to:^a b c C.M. Hargreaves (1991), p.??
   1. ^ Jump up to:^a b WADE (a)
   1. Jump up^ Krupp and Horn. Earth: The Sequel. p. 57
   1. Jump up^ Z. Herzog (2008)
   1. Jump up^ K. Hirata (1997)
   1. Jump up^ MAKE: Magazine (2006)
   1. ^ Jump up to:^a b Nightingale, Noel P. (October 1986). “Automotive Stirling Engine: Mod II Design Report” (PDF). NASA. Archived (PDF) from the original on 29 April 2017.
   1. Jump up^ A.J. Organ (2008b)
   1. Jump up^ L.G. Thieme (1981)
   1. Jump up^ Mcconaghy, Robert (1986). “Design of a Stirling Engine for Model Aircraft”. IECEC: 490–493.

Bibliography[edit]

• S. Backhaus; G. Swift (2003). “Acoustic Stirling Heat Engine: More Efficient than Other No-Moving-Parts Heat Engines”. Los Alamos National Laboratory. Archived from the original on 2008-08-01. Retrieved 2009-01-19.
• BBC News (2003-10-31). “Power from the people”. Retrieved 2009-01-19.
• W.T. Beale (1971). “Stirling Cycle Type Thermal Device”, US patent 3552120. Granted to Research Corp, 5 January 1971.
• G.M. Benson (1977). “Thermal Oscillators”, US patent 4044558. Granted to New Process Ind, 30 August 1977 .
• G.M. Benson (1973). “Thermal Oscillators”. Proceedings of the 8th IECEC. Philadelphia: American Society of Mechanical Engineers. pp. 182–189.
• H.W. Brandhorst; J.A. Rodiek (2005). “A 25 kW Solar Stirling Concept for Lunar Surface Exploration” (PDF). In International Astronautics Federation. Proceedings of the 56th International Astronautical Congress. IAC-05-C3.P.05. Retrieved 2012-03-18.
• Carbon Trust (2007). “Micro-CHP Accelerator — Interim Report — Executive summary”. Retrieved March 19,2012.
• E.H. Cooke-Yarborough; E. Franklin; J. Geisow; R. Howlett; C.D. West (1974). “Harwell Thermo-Mechanical Generator”. Proceedings of the 9th IECEC. San Francisco: American Society of Mechanical Engineers. pp. 1132–1136. Bibcode:1974iece.conf.1132C.
• E.H. Cooke-Yarborough (1970). “Heat Engines”, US patent 3548589. Granted to Atomic Energy Authority UK, 22 December 1970.
• E.H. Cooke-Yarborough (1967). “A Proposal for a Heat-Powered Nonrotating Electrical Alternator”, Harwell Memorandum AERE-M881.
• R. Chuse; B. Carson (1992). Pressure Vessels, The ASME Code Simplified. McGraw–Hill. ISBN 0-07-010939-7.
• T. Finkelstein; A.J. Organ (2001). Air Engines. Professional Engineering Publishing. ISBN 1-86058-338-5.
• C.M. Hargreaves (1991). The Philips Stirling Engine. Elsevier Science. ISBN 0-444-88463-7.
• J. Harrison (2008). “What is micro generation?”. Claverton Energy Research Group. Retrieved 2009-01-19.
• Hartford Steam Boiler. “Hartford Steam Boiler: Steam Power and the Industrial Revolution”. Retrieved 2009-01-18.
• J. Hasci (2008). “Modified Stirling Engine With Greater Power Density”. Create the Future Design Contest. NASA & SolidWorks. Archived from the original on 6 January 2009. Retrieved 19 January 2009.
• Z. Herzog (2008). “Schmidt Analysis”. Retrieved 2009-01-18.
• K. Hirata (1998). “Design and manufacturing of a prototype engine”. National Maritime Research Institute. Retrieved 2009-01-18.
• K. Hirata (1997). “Schmidt Theory For Stirling Engines”. Retrieved 2009-01-18.
• K. Hirata. “Palm Top Stirling Engine”. Retrieved 2009-01-18.
• M. Keveney (2000a). “Two Cylinder Stirling Engine”. animatedengines.com. Retrieved 2009-01-18.
• M. Keveney (2000b). “Single Cylinder Stirling Engine”. animatedengines.com. Retrieved 2009-01-18.
• Kockums. “The Stirling Engine: An Engine for the Future”. Retrieved 2009-01-18.
• B. Kongtragool; S. Wongwises (2003). “A review of solar-powered Stirling engines and low temperature differential Stirling engines”. Renewable and Sustainable Energy Reviews. 7 (2): 131–154. doi:10.1016/S1364-0321(02)00053-9.
• D. Liao. “The Working Principles”. Retrieved 2009-01-18.
• W.R. Martini (1983). “Stirling Engine Design Manual (2nd ed)” (17.9 MB PDF). NASA. Retrieved 2009-01-19.
• Micro-Star International (2008). “World’s First Powerless Air Cooler on a Mainboard!”. Archived from the original on 13 September 2008. Retrieved 2009-01-19.
• A. Nesmith (1985). “A Long, Arduous March Toward Standardization”. Smithsonian Magazine. Retrieved 2009-01-18.
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• A.J. Organ (2008b). “Why Air?”. Communicable Insight. Retrieved 2009-01-18.
• A.J. Organ (2007). The Air Engine: Stirling Cycle Power for a Sustainable Future. Woodhead Publishing. ISBN 1-84569-231-4.
• A.J. Organ (1997). The Regenerator and the Stirling Engine. Wiley. ISBN 1-86058-010-6.
• A.J. Organ (1992). Thermodynamics and Gas Dynamics of the Stirling Cycle Machine. Cambridge University Press. ISBN 0-521-41363-X.
• PASCO Scientific (1995). “Instruction Manual and Experiment Guide for the PASCO scientific Model SE-8575” (PDF). Retrieved 2009-01-18.
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• Precer Group. “Solid Biofuel-Powered Vehicle Technology” (PDF). Retrieved 2009-01-19.
• Quasiturbine Agence. “Quasiturbine Stirling – Hot Air Engine”. Retrieved 2009-01-18.
• R. Sier (1999). Hot Air Caloric and Stirling Engines: A History. 1 (1st (Revised) ed.). L.A. Mair. ISBN 0-9526417-0-4.
• R. Sier (1995). Reverend Robert Stirling D.D: A Biography of the Inventor of the Heat Economiser and Stirling Cycle Engine. L.A Mair. ISBN 0-9526417-0-4.
• F. Starr (2001). “Power for the People: Stirling Engines for Domestic CHP” (PDF). Ingenia (8): 27–32. Retrieved 2009-01-18.
• WADE. “Stirling Engines”. Retrieved 2009-01-18.
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• Y. Timoumi; I. Tlili; S.B. Nasrallah (2008). “Performance Optimization of Stirling Engines”. Renewable Energy. 33(9): 2134–2144. doi:10.1016/j.renene.2007.12.012.
• G. Walker (1971). “Lecture notes for Stirling engine seminar”, University of Bath. Reprinted in 1978.
• C.D. West (1970). “Hydraulic Heat Engines”, Harwell Momorandum AERE-R6522.
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• MAKE: Magazine (2006). “Two Can Stirling Engine”(PDF). Retrieved 2012-03-18.

Further reading[edit]

• R.C. Belaire (1977). “Device for decreasing the start-up time for stirling engines”, US patent 4057962. Granted to Ford Motor Company, 15 November 1977.
• P.H. Ceperley (1979). “A pistonless Stirling engine—The traveling wave heat engine”. Journal of the Acoustical Society of America. 66 (5): 1508–1513. Bibcode:1979ASAJ…66.1508C. doi:10.1121/1.383505.
• P. Fette. “About the Efficiency of the Regenerator in the Stirling Engine and the Function of the Volume Ratio V_max/V_min“. Retrieved 2009-01-19.
• P. Fette. “A Twice Double Acting α-Type Stirling Engine Able to Work with Compound Fluids Using Heat Energy of Low to Medium Temperatures”. Retrieved 2009-01-19.
• D. Haywood. “An Introduction to Stirling-Cycle Machine” (PDF). Retrieved 2013-12-20.
• Z. Herzog (2006). “Stirling Engines”. Mont Alto: Pennsylvania State University. Archived from the original on 2007-04-03. Retrieved 2009-01-19.
• F. Kyei-Manu; A. Obodoako (2005). “Solar Stirling-Engine Water Pump Proposal Draft” (PDF). Retrieved 2009-01-19.
• Lund University, Department of Energy Science: Division of Combustion Engines. “Stirling Engine Research”. Archived from the original on 19 April 2008. Retrieved 2009-01-19.
• D. Phillips (1994). “Why Aviation Needs the Stirling Engine”. Archived from the original on 19 January 2009. Retrieved 19 January 2009.

External links[edit]

• NASA Stirling Engine Based Nuclear Power Plant For Lunar Use on YouTube
• 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 Fabrication
• Simple Performance Prediction Method for Stirling Engine
• Shockwave3D models: Beta Stirling and LTD
• Inquiry into the Hot Air Engines of the 19th Century

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• Cooling technology

• Heat pumps
• Stirling engines
• Hot air engines
• Piston engines
• Scottish inventions
• External combustion engines

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