Stirling engine

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Cut away diagram of a rhombic drive beta configuration Stirling engine design.
Pink - Hot cylinder wall
Dark grey - Cold cylinder wall (with coolant inlet and outlet pipes in yellow)
Dark green - Thermal insulation separating the two cylinder ends
Light green - Displacer piston
Dark blue - Power piston
Light blue - Flywheels
Not shown: external heat-source, and external heat-sinks. In this design the displacer piston is used without a regenerator.

A Stirling engine is a closed-cycle regenerative heat engine with a gaseous working fluid. "Closed-cycle" means the working fluid is permanently contained within the engine's system, which also categorizes it as an external heat engine. "Regenerative" refers to the use of an internal heat exchanger called a 'regenerator' which increases the engine's thermal efficiency.

Noted for its high efficiency, quietness of operation and the ease with which it can utilise what would otherwise be waste heat, the Stirling engine is currently exciting much interest as the core component of domestic combined heat and power (CHP) units, the widespread adoption of which could make a significant impact on worldwide carbon dioxide emissions^[1][2].

The Stirling engine was used in small low power applications for nearly two centuries, and saw ever increasing scientific development of its technological potential. The Stirling cycle is notable for its perfect theoretical efficiency; however this ideal has proved notoriously difficult to achieve in real engines, and remains an immense engineering challenge. Nevertheless, the current technology is reasonably advanced, and the designs are useful and versatile. It continues to be used and further developed, and this device holds promise for its ability to provide mechanical or electrical power, heating or cooling in a number of applications wherever a heat source and heat sink are available.

Technically, an air-filled Stirling engine is a specific type of "hot air engine", otherwise the two categories of engines are mutually exclusive. The term "hot air engine" is used generically to include any heat engine with air working fluid. Hot air engines may use any one of several different thermodynamic cycles, including the Brayton cycle, Ericsson cycle or Stirling cycle. Air is just one of many possible gases that may be used in a modern Stirling engine.

[edit] Background

In the conversion of heat into mechanical work, the Stirling engine has the potential to achieve the highest efficiency of any real heat engine. It can perform theoretically up to the full Carnot efficiency, though in practice this is limited. The practical limitations are the non-ideal properties of the working gas, and the engine material properties such as friction, thermal conductivity, tensile strength, creep, rupture strength, and melting point. The Stirling engine can run on any heat source, including chemical, solar, geothermal and nuclear. There are many possible implementations of the Stirling engine most of which fall into the category of reciprocating piston engine.

In contrast to internal combustion engines, Stirling engines have the potential to use renewable heat sources more easily, to be quieter, and to be more reliable with lower maintenance requirements. They are preferred for certain niche applications that value these unique advantages, particularly in cases where the primary objective is not to minimize the capital cost per unit power ($/kW), but rather to minimize the cost per unit energy generated ($/kWh). On this basis, Stirling engines are cost competitive with other small generator technologies, up to about 100 kW ^[3]. 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, their maintenance requirements are typically less, so the overall energy cost is comparable. The thermal efficiency is also comparable (for small engines), ranging from 15%-30%. ^[4] For some applications, such as micro-CHP, a Stirling engine is often preferable to an internal combustion engine, however, it is generally not price-competitive as an automobile prime mover, due to high cost per unit power, low power density and higher material costs.

In recent years, the advantages of Stirling engines have become increasingly significant, given the rise in liquid fuel prices, peak oil and environmental concerns such as climate change. Stirling engines address these issues, by being very compatible with all renewable energy and fuel sources. These growing interests in Stirling technology have fostered the ongoing research and development of Stirling devices, and R&D breakthroughs have in turn increased interest in the technology. The applications include water pumping, space-based 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.

Another useful characteristic of the Stirling engine is that the cycle is reversible, meaning that if supplied with mechanical power, it can function as a heat pump for heating or cooling. Experiments have been performed using wind power driving a Stirling cycle heat pump for domestic heating and air conditioning. In the late 1930s, the Philips Corporation of the Netherlands successfully utilized the Stirling cycle in cryogenic applications.^[5]

Basic analysis is based on the closed-form Schmidt analysis.^{[6] [7]}

[edit] History

[edit] Name

Though it had been suggested as early as 1884 that all closed cycle air engine should be generically called Stirling engines after the inventor of the first practical example (see below), the idea found little favour and the various types on the market continued to be known by the name of their individual designer or manufacturer. Then, in the 1940s, the Philips company was searching for a suitable name for its version of the 'air' engine which by that time had already been tested with other gases. Rejecting many suggestions, including 'hot gas engine' ('gas engine' was already in general use for internal combustion engines running on gaseous fuels) and 'external combustion engine' (did not differentiate between open and closed cycles), Philips eventually settled on 'Stirling engine' in April 1945, though general acceptance of the term seems to have lagged a few years behind^[8].

[edit] Early years

The Stirling engine (or Stirling's air engine as it is was known at the time) was invented by Reverend Dr. Robert Stirling and patented by him in 1816^[9]. It followed earlier attempts at making an air engine but was probably the first to be put to practical use when in 1818 an engine built by Stirling was employed pumping water in a quarry^[10]. 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^[11] 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 pressurisation which by 1843 had sufficiently increased the power output for it to drive all the machinery at a Dundee iron foundry^[12].

As well as saving fuel, the inventors were motivated to create a safer alternative to the steam engines of the time^[13], whose boilers frequently exploded causing many injuries and fatalities^[14][15]. The need for Stirling engines to run at very high temperatures to maximize power and efficiency exposed limitations in the materials of the day and the few engines that were built in those early years suffered unacceptably frequent failures (albeit with far less disastrous consequences than a boiler explosion^[16]) - for example, the Dundee foundry engine was replaced by a steam engine after three hot cylinder failures in four years^[17].

[edit] Later nineteenth century developments

Steam boilers were eventually made much safer and development increased the efficiency of the engines themselves, but, though the Stirling engine did not succeed as a competitor to the steam engine as an industrial scale prime mover, during the latter nineteenth and early twentieth centuries smaller engines of the Stirling/hot air type were produced in substantial numbers, finding application wherever a reliable source of low to medium power was required, such as raising water or providing air for church organs^[18]. These generally operated at lower temperatures so as not to tax available materials and thus tended to be rather inefficient, their major selling point being that unlike a steam engine they could be operated safely by anybody capable of managing a fire^[19]. 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^[20].

[edit] Twentieth century revival

During the early part of the twentieth century the role of the Stirling engine as a 'domestic motor'^[21] was gradually usurped by the electric motor and small internal combustion engines until by the late 1930s it was largely forgotten, only produced for toys and a few small ventilating fans^[22]. At this time Philips was seeking to expand sales of its radios into areas where mains electricity was unavailable and the supply of batteries uncertain. Philips’ management decided that offering a low-power portable generator would facilitate such sales and tasked a group of engineers at the company research lab (the Nat. Lab) in Eindhoven to evaluate the situation. After a systematic comparison of various prime movers the Stirling engine was considered to have real possibilities as it was among other things, inherently quiet (both audibly and in terms of radio interference) and capable of running from any heat source (common lamp oil was favored)^[23]. 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 felt that with the application of modern materials and know-how great improvements should be possible^[24].

Encouraged by their first experimental engine, which produced 16 watts of shaft power from a bore and stroke of 30x25mm^[25], a development program was begun. This work continued throughout World War II and by the late 1940s they had an engine – the Type 10 – which was sufficiently developed to be handed over to Philips’ subsidiary Johan de Witt in Dordrecht to be ‘productionised’ and incorporated into a generator set as originally intended. The result, rated at 200 watts electrical output from a bore and stroke of 55x27 mm, was designated MP1002CA (known as the 'Bungalow set'). Production of an initial batch of 250 began in 1951, but it became clear that they could not be made at a price that the market would support and the advent of transistor radios with their much lower power requirements meant that the original raison d'être for the set was disappearing. Only around 150 of these sets were eventually produced^[26], some of which found their way into university and college engineering departments around the world^[27] giving generations of students a valuable introduction to the Stirling engine.

Philips went on to develop experimental Stirling engines for a wide variety of applications and continued to work in the field until the late 1970s, but only achieved any commercial success with the 'reversed Stirling engine' cryocooler. They did however take out a large number of patents and amass a wealth of information relating to Stirling engine technology which was subsequently licensed to other companies forming the basis of much of the development work in the modern era^[28].

[edit] Free-piston engines

Various Free-Piston Stirling Configurations

In the early 1960s Professor W. T. Beale while at Ohio University, invented a free-piston version of the Stirling engine in order to overcome the intractable difficulty of effectively lubricating the crank mechanism of typical Stirling engines ^[29]. 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 ^{[30][31][32][33]}. G M Benson has also made important early contributions and has patented many novel free-piston configurations ^[34][35].

What appears to be the first mention of a Stirling cycle machine using freely moving components is a British patent disclosure in 1876 ^[36]. This machine was envisaged as a refrigerator (i.e., the so-called reversed Stirling cycle) and the piston was therefore driven externally. The very first consumer product to utilize a free-piston Stirling device was a portable refrigerator manufactured by Twinbird Corporation of Japan and offered in the US by Coleman in 2004.

[edit] Functional description

[edit] Engine operation

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

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

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

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

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

Very low-power engines have been built which will run on a temperature difference of as little as 7 °C, for example between the palm of a hand and the surrounding air, or between room temperature and melting water ice.^[37][38][39]

[edit] Pressurization

In most high power Stirling engines, both the minimum pressure and mean pressure of the working fluid are above atmospheric pressure. This initial engine pressurization can be realized by a pump, or by filling the engine from a compressed gas tank, or even just by sealing the engine when the mean temperature is lower than the mean operating temperature. All of these methods increase the mass of working fluid in the thermodynamic cycle. All of the heat exchangers must be sized appropriately to supply the necessary heat transfer rates. If the heat exchangers are well designed and can supply the heat flux needed for convective heat transfer, then the engine will produce power in proportion to the mean pressure, as predicted by the West number, and Beale number.^{[40] [41]} 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. ^[42]

[edit] Lubricants and Friction

At high temperatures and pressures, the oxygen in air-pressurized crankcases, or in the working gas of hot air engines, tends to combine with any lubricating oil that may exist in the engine, resulting in a very serious explosion hazard. (At least one person has been killed this way.)^[43]

Lubricants also cause problems with clogging the heat exchangers, especially the regenerator. For these reasons, to minimize mechanical power losses and wear on sliding surfaces, preferred designs use non-lubricated, low-coefficient of friction materials (such as Rulon (plastic) or graphite), with low normal-forces on the moving parts, especially for sliding seals. Alternatively, sliding surfaces can be avoided altogether by using diaphragms for sealed pistons. These are some of the factors that allow Stirling engines to often have lower maintenance requirements and longer life than internal-combustion engines.

A Stirling engine and generator set with 55 kW electrical output, for combined heat and power applications. Click image for detailed description.

[edit] The Stirling cycle

For a detailed description see the Stirling cycle thermodynamics section below

The idealized or "text book" Stirling cycle is a thermodynamic cycle with two isochores (constant volume) and two isotherms (constant temperature). It is the most efficient thermodynamic cycle capable of practical implementation in an engine - its theoretical efficiency equaling that of the hypothetical Carnot cycle. However real-world issues reduce the efficiency of actual engines, due to limits of convective heat transfer, and viscous flow (friction). There are also practical mechanical considerations, for instance a simple kinematic linkage may be favored over a more complex mechanism needed to replicate the idealized cycle. See also Stirling cycle

[edit] The regenerator

Main article: Regenerative heat exchanger

In a Stirling engine, the regenerator is an internal heat exchanger and temporary store placed between the hot and cold spaces such that the working fluid passes through it first in one direction then the other. Its function is to retain within the system that heat which would otherwise be exchanged with the environment at temperatures intermediate to the maximum and minimum cycle temperatures,^[44] thus enabling the thermal efficiency of the cycle to approach the limiting Carnot efficiency defined by those maxima and minima.

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

A regenerator is challenging to design. The ideal regenerator would be: a perfect insulator in one direction, a perfect conductor in another, have no internal volume yet infinite flow area and infinite surface area. As with the hot and cold exchangers, achieving a successful regenerator is a delicate balancing act between high heat transfer with low viscous pumping losses and low dead space. These inherent design conflicts are one of many factors which limit the efficiency of practical Stirling engines. A typical embodiment might consist of a stack of fine metal wire meshes, with low porosity to reduce dead space, and with the wire axes perpendicular to the gas flow to reduce conduction in that direction and to maximize convective heat transfer.

The regenerator is the key component invented by Robert Stirling and its presence distinguishes a true Stirling engine from any other closed cycle hot air engine. However, many engines with no apparent regenerator may still be correctly described as Stirling engines as, in the simple beta and gamma configurations with a 'loose fitting' displacer, the surfaces of the displacer and its cylinder will cyclically exchange heat with the working fluid providing a significant regenerative effect particularly in small, low-pressure engines.

Also see: Economiser

[edit] Engine configurations

Engineers classify Stirling engines into three distinct types. The Alpha type engine relies on interconnecting the power pistons of multiple cylinders to move the working gas, with the cylinders held at different temperatures. The Beta and Gamma type Stirling engines use a displacer piston to move the working gas back and forth between hot and cold heat exchangers in the same cylinder.

[edit] Alpha Stirling

• An alpha Stirling contains two separate power pistons in separate cylinders, one "hot" piston and one "cold" piston. The hot piston cylinder is situated inside the higher temperature heat exchanger and the cold piston cylinder is situated inside the low temperature heat exchanger. This type of engine has a very high power-to-volume ratio but has technical problems due to the usually high temperature of the "hot" piston and the durability of its seals. (See animation here^[45])

[edit] Action of an alpha type Stirling engine

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

1. Most of the working gas is in contact with the hot cylinder walls, it has been heated and expansion has pushed the hot piston to the bottom of its travel in the cylinder. The expansion continues in the cold cylinder, which is 90o behind the hot piston in its cycle, extracting more work from the hot gas.

2. The gas is now at its maximum volume. The hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops.

3. Almost all the gas is now in the cold cylinder and cooling continues. The cold piston, powered by flywheel momentum (or other piston pairs on the same shaft) compresses the remaining part of the gas.

4. The gas reaches its minimum volume, and it will now expand in the hot cylinder where it will be heated once more, driving the hot piston in its power stroke.

Alpha type Stirling. Animated version.

[edit] Beta Stirling

• A beta Stirling has a single power piston arranged within the same cylinder on the same shaft as a displacer piston. The displacer piston is a loose fit and does not extract any power from the expanding gas but only serves to shuttle the working gas from the hot heat exchanger to the cold heat exchanger. When the working gas is pushed to the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by a flywheel, pushes the power piston the other way to compress the gas. Unlike the alpha type, the beta type avoids the technical problems of hot moving seals. (See animation here^[46])

[edit] Action of a beta type Stirling engine

A beta Stirling has two pistons within the same cylinder both connected to the same crankshaft. One of these is the tightly fitted power piston and the other a loosely fitted displacement piston.

1. Power piston (dark grey) has compressed the gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger.	2. The heated gas increases in pressure and pushes the power piston to the farthest limit of the power stroke.
3. The displacer piston now moves, shunting the gas to the cold end of the cylinder.	4. The cooled gas is now compressed by the flywheel momentum. This takes less energy, since when it is cooled its pressure dropped.

[edit] Gamma Stirling

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

[edit] Other types

Changes to the configuration of mechanical Stirling engines continue to interest engineers and inventors. Notably, some are in pursuit of the rotary Stirling engine; the goal here is to convert power from the Stirling cycle directly into torque, a similar goal to that which led to the design of the rotary combustion engine. No practical engine has yet been built but a number of concepts, models and patents have been produced.^[47][48]

An alternative to the mechanical Stirling device is the Fluidyne engine or heat pump, which use hydraulic piston(s) 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.

There is also a field of "free piston" Stirling cycles engines, including those with liquid pistons and those with diaphragms as pistons. In a "free-piston" device, electrical energy may be added or removed by a linear alternator. This sidesteps the need for a linkage, and reduces the number of moving parts, friction and wear.

[edit] Thermoacoustic cycle

Thermoacoustic devices are very different from Stirling devices, although the individual path traveled 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 traveling 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.

[edit] Heat sources

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

Virtually any temperature difference will power a Stirling engine. The heat source may be derived from fuel combustion, hence the term "external combustion engine", although the heat source may also be solar, geothermal, waste heat, nuclear or even biological. Likewise a "cold sink" can be used in lieu of a heat source, if it is below the ambient temperature (see also: liquid nitrogen economy). A cold source may be the result of a cryogenic fluid or ice water. In the case where a small temperature differential is used to generate a significant amount of power, large mass flows of heating and cooling fluids must be pumped through the external heat exchangers, thus causing parasitic losses that tend to reduce the efficiency of the cycle.

In all external heat engines, a heat exchanger separates the working gas from the heat source, so a wide range of heat sources can be used, including any fuel or waste heat from some other process. Since the combustion products do not contact the internal moving parts of the engine, a Stirling engine can run on landfill gas containing siloxanes without the accumulation of silica that damages internal combustion engines running on this fuel.

The U.S. Department of Energy in Washington, NASA Glenn Research Center in Cleveland, and Infinia Corporation of Kennewick, Wash., are developing a free-piston Stirling converter for a Stirling Radioisotope Generator. This device would use a plutonium source to supply heat.

[edit] Recent commercial development

[edit] Acoustic Stirling Heat Engine

Los Alamos National Laboratory has developed an "Acoustic Stirling Heat Engine"^[49] with no moving parts. It converts heat into intense acoustic power which (quoted from given source) "can be used directly in acoustic refrigerators or pulse-tube refrigerators to provide heat-driven refrigeration with no moving parts, or ... to generate electricity via a linear alternator or other electroacoustic power transducer".

[edit] MicroCHP

WhisperGen, a New Zealand-based company has developed stirling engines that can be powered by natural gas or diesel. Recently an agreement has been signed with Mondragon Corporación Cooperativa, a Spanish firm, to produce WhisperGen's microCHP and make them available for the domestic market in Europe. Some time ago E.ON UK announced a similar initiative for the UK. Stirling engines would supply the client with hot water, space heating and a surplus electric power that could be fed back into the electric grid.

[edit] Chip cooling

MSI (Taiwan) recently developed a miniature Stirling engine cooling system for personal computer chips that use the waste heat from the chip to drive a fan. ^[50]

[edit] Other

Think Nordic, an electric car company in Norway, is working with inventor Dean Kamen on plans to install Stirling engines in the Think City, an otherwise all-electric vehicle announced in 2007.

Figure #1 from US patent 7,340,879 showing Stirling generator 10 coupled to water still 12

Dean Kamen has also developed a water distillation, cogeneration system optionally based on a Stirling engine electric generator for both electrical and heat input. The unit is patented U.S. Patent 7,340,879  with other patents pending. ^{[51] [52]}

Since 1988,^[53] Kockums shipyards have equipped submarines with Stirling engines. They are currently used on submarines of the Gotland and Södermanland classes. These engines use diesel fuel and liquid oxygen and are called Stirling AIP for air-independent propulsion.

[edit] Stirling cycle thermodynamics

A pressure/volume graph of the idealized Stirling cycle. In applications of the Stirling cycles (ie. Stirling engines) this cycle is quasi-elliptical, or at the very least, curved at the sharp corners.

The idealized Stirling cycle consists of four thermodynamic processes acting on the working fluid ( See diagram to right):

• Points 1 to 2, Isothermal Expansion. The expansion-space is heated externally, and the gas undergoes near-isothermal expansion.
• Points 2 to 3, Constant-Volume (known as isometric or isochoric) heat-removal. The gas is passed through the regenerator, thus cooling the gas, and transferring heat to the regenerator for use in the next cycle.
• Points 3 to 4, Isothermal Compression. The compression space is intercooled, so the gas undergoes near-isothermal compression.
• Points 4 to 1, Constant-Volume (known as isometric or isochoric) heat-addition. The compressed air flows back through the regenerator and picks-up heat on the way to the heated expansion space.

This idealized Stirling cycle is commonly known as a "squared-cycle"^{[citation needed]}, because when graphed on a Pressure-Volume plot, the rapid transitions between the processes produce a shape with corners. In a real Stirling engine, physical design constraints limit the net force on each engine component, and thus limit the maximum acceleration (or rate-of-change of velocity). Thus a real Stirling cycle in a Stirling engine requires relatively smooth motion, which is commonly sinusoidal or quasi-sinusoidal. In this case the shape of the PV-plot is quasi-elliptical. Also in a real engine cycle, the heat transfer performance of the heat exchangers ranges from 100% effectiveness in an isothermal process, to 0% effectiveness in an adiabatic process (no heat transfer). The compression and expansion processes can be modeled as a polytropic processes^[54]

where k is constant, and n is bounded by:

.

where c_V is the specific heat capacity at constant volume (J/kgK) and c_p is the specific heat capacity at constant pressure (J/kgK)

Compared to the idealized cycle, the efficiency of a real engine is reduced by irreversibilities, friction, and the loss of short-circuit conducted heat, so that the overall efficiency is often only about half of the ideal (Carnot) efficiency.^[55]

1. The working gas is heated at a constant volume to a higher temperature. This increases its pressure. (points 4 to 1 on the graph)	2. The working gas expands at a constant temperature to a larger volume. This decreases its pressure. The gas does work to move the piston up. (points 1 to 2 on the graph)	2a. The gas is now fully transferred to the cool cylinder. (Point 2 on the graph)
3. The working gas is cooled at constant volume to a lower temperature. This decreases its pressure. (Points 2 to 3 on the graph)	4. The working gas contracts at a constant temperature to a smaller volume. This increases its pressure. (Points 3 to 4 on the graph)The Piston does work to compress the gas as it moves down. But this is less than that delivered to the piston on cycle 2	4a. The gas is now fully transferred to the hot cylinder. (Point 4 on the graph)

[edit] Advantages of Stirling engines

• They 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 most types of emissions can be reduced.
• Most types of Stirling engines have the bearing and seals on the cool side of the engine, and they require less lubricant and last longer than other reciprocating engine types.
• The engine mechanisms are in some ways simpler than other reciprocating engine types. No valves are needed, and the burner system can be relatively simple.
• A Stirling engine uses a single-phase working fluid which maintains an internal pressure close to the design pressure, and thus for a properly designed system the risk of explosion is low. In comparison, a steam engine uses a two-phase gas/liquid working fluid, so a faulty 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 warm-up) and run more efficiently in cold weather, in contrast to the internal combustion which starts quickly in warm weather, but not in cold weather.
• A Stirling engine used for pumping water can be configured so that the water cools the compression space. This is most effective when pumping cold water.
• They are extremely flexible. They can be used as CHP (combined heat and power) in the winter and as coolers in summers.
• Waste heat is relatively easily harvested (compared to waste heat from an internal combustion engine) making Stirling engines useful for dual-output heat and power systems.

[edit] Disadvantages of Stirling engines

[edit] Size and cost issues

• Stirling engine designs require heat exchangers for heat input and for heat output, and these must contain the pressure of the working fluid, where the pressure is proportional to the engine power output. In addition, the expansion-side heat exchanger is often at very high temperature, so the materials must resist the corrosive effects of the heat source, and have low creep (deformation). Typically these material requirements substantially increase the cost of the engine. The materials and assembly costs for a high temperature heat exchanger typically accounts for 40% of the total engine cost.^[43]

• 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 a Otto engine or Diesel engine, where the expansion temperature can far exceed the metallurgical limit of the engine materials, because the input heat-source is not conducted through the engine, so engine materials operate closer to the average temperature of the working gas.

• Dissipation of waste heat is especially complicated because the coolant temperature is kept as low as possible to maximize thermal efficiency. This increases the size of the radiators, which can make packaging difficult. Along with materials cost, this has been one of the factors limiting the adoption of Stirling engines as automotive prime movers. For other applications high power density is not required, such as Ship propulsion, and stationary microgeneration systems using combined heat and power (CHP).^[56]

[edit] Power and torque issues

• Stirling engines, especially those that run on small temperature differentials, are quite large for the amount of power that they produce (i.e. they have low specific power). This is primarily due to the heat transfer coefficient of gaseous convection which limits the heat flux that can be attained in a typical cold heat exchanger to about 500 W/(m·K), and in a hot heat exchanger to about 500-5000 W/(m·K).^[57] Compared to internal combustion engines, this makes it more challenging for the engine designer to transfer heat into and out of the working gas. 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 shorter for Stirling's than for others of this type such as steam engines. Stirling engines are best used as constant speed engines.

• Power output of a Stirling tends to be constant and to adjust it can sometimes require careful design and additional mechanisms. Typically, changes in output are achieved by varying the displacement of the engine (often through use of a swashplate crankshaft arrangement), or by changing the quantity of working fluid, or by altering the piston/displacer phase angle, or in some cases simply by altering the engine load. This property is less of a drawback in hybrid electric propulsion or "base load" utility generation where constant power output is actually desirable.

[edit] Gas choice issues

The use of working fluids other than air was pioneered by Phillips following a fatal accident involving a lubricating oil explosion in a highly pressurized air engine^[43] see Pressurization

• Hydrogen's low viscosity and high thermal conductivity make it the most powerful working gas, primarily because the engine can run faster than with other gases. However, due to hydrogen bonding, and given the high diffusion rate associated with this low molecular weight gas, particularly at high temperatures, H₂ will leak through solid metal of the heater. Diffusion though carbon steel is too high to be practical, but may be acceptably low for metals such as aluminium, 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 HTD engines, auxiliary systems may need to be added to maintain high pressure working fluid. These systems can be a gas storage bottle or a gas generator. Hydrogen can be generated by electrolysis of water, the action of steam on red hot carbon-based fuel, by gasification of hydrocarbon fuel, or by the reaction of acid on metal. Hydrogen can also cause the embrittlement of metals. Hydrogen is a flammable gas, which is a safety concern, although the quantity used is very small, and it is arguably safer than other commonly used flammable gases.
• Most technically advanced Stirling engines, like those developed for United States government labs, use helium as the working gas, because it functions close to the efficiency and power density of hydrogen with fewer of the material containment issues. Helium is inert, which removes all risk of flammability, both real and perceived. Helium is relatively expensive, and must be supplied by bottled gas. One test showed hydrogen to be 5 percentage points absolutely (24% relatively) more efficient than helium in the GPU-3 Stirling engine.^[58] The researcher Allan Organ demonstrated that a well designed air engine is theoretically just as efficient as a helium or hydrogen engine. However, helium or 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.

[edit] Applications

A desktop alpha Stirling engine. The working fluid in this engine is air. The hot heat exchange is the glass cylinder on the right, and the cold heat exchanger is the finned cylinder on the top. This engine uses a small alcohol burner (bottom right) as a heat source.

[edit] Combined heat and power applications

Power plants on the electric grid use fuel to produce electricity, however there are large quantities of waste-heat produced which often go unused. In other situations, high-grade fuel is burned at high-temperature for a low-temperature application. According to the second law of thermodynamics, a heat engine can generate power from this temperature difference. In a CHP system, the high-temperature primary heat enters the Stirling engine heater, then some of the energy is converted to mechanical power in the engine, and the rest passes through to the cooler, where it exits at a low temperature. The "waste" heat actually comes from engine's main cooler, and possibly from other sources such as the exhaust of the burner, if there is one.

In a combined heat and power (CHP) system, mechanical or electrical power is generated in the usual way, however, the waste heat given off by the engine is used to supply a secondary heating application. This can be virtually anything that uses low-temperature heat. It is often a pre-existing energy use, such as commercial space heating, residential water heating, or an industrial process.

The power produced by the engine can be used to run an industrial or agricultural process, which in turn creates biomass waste refuse that can be used as free fuel for the engine, thus reducing waste removal costs. The overall process can be efficient and cost-effective.

WhisperGen, a New Zealand firm with offices in Christchurch, has developed an "AC Micro Combined Heat and Power" Stirling cycle engine. These microCHP units are gas-fired central heating boilers which sell unused power back into the electricity grid. WhisperGen announced in 2004 that they were producing 80,000 units for the residential market in the United Kingdom. A 20 unit trial in Germany started in 2006.

[edit] Solar power generation

Placed at the focus of a parabolic mirror a Stirling engine can convert solar energy to electricity with an efficiency better than non-concentrated photovoltaic cells, and comparable to Concentrated Photo Voltaics. On August 11, 2005, Southern California Edison announced^[59] an agreement to purchase solar powered Stirling engines from Stirling Energy Systems^[60] over a twenty year period and in quantity (20,000 units) sufficient to generate 500 megawatts of electricity. These systems, on a 4,500 acre (19 km²) solar farm, will use mirrors to direct and concentrate sunlight onto the engines which will in turn drive generators.

[edit] Stirling cryocoolers

Any Stirling engine will also work in reverse as a heat pump: i.e. when a motion is applied to the shaft, a temperature difference appears between the reservoirs. The essential mechanical components of a Stirling cryocooler are identical to a Stirling engine. In both the engine and the heat pump, heat flows from the expansion space to the compression space; however, input work is required in order for heat to flow against a thermal gradient, specifically when the compression space is hotter than the expansion space. The external side of the expansion-space heat-exchanger may be placed inside a thermally insulated compartment such as a vacuum flask. Heat is in effect pumped out of this compartment, through the working gas of the cryocooler and into the compression space. The compression space will be above ambient temperature, and so heat will flow out into the environment.

One of their modern uses is in cryogenics, and to a lesser extent, refrigeration. At typical refrigeration temperatures, Stirling coolers are generally not economically competitive with the less expensive mainstream Rankine cooling systems, even though they are typically 20% more energy efficient. However, below about -40 to -30 deg.C, Rankine is not effective because there are no suitable refrigerants with boiling points this low. Stirling cryocoolers are able to "lift" heat down to -200 deg.C (73 K), which is sufficient to liquefy air (oxygen, nitrogen and argon). They can go as low as 60K - 40K, depending on the particular design. Cryocoolers for this purpose are more-or-less competitive with other cryocooler technologies. The coefficient of performance at cryogenic temperatures is typically 4-5%.[2] Empirically, the devices show a linear trend, where typically the COP = 0.0015 × Tc - 0.065 , where Tc is the cryogenic temperature. At these temperatures, solid materials have lower values for specific heat, so the regenerator must be made out of unexpected materials, such as cotton.

The first Stirling-cycle cryocooler was developed at Philips in the 1950s and commercialized in such places as liquid air production plants. The Philips Cryogenics business evolved until it was split off in 1990 to form the Stirling Cryogenics & Refrigeration BV,^[61] The Netherlands. This company is still active in the development and manufacturing of Stirling cryocoolers and cryogenic cooling systems.

A wide variety of smaller size Stirling cryocoolers are commercially available for tasks such as the cooling of electronic sensors and sometimes microprocessors. For this application, Stirling cryocoolers are the highest performance technology available, due to their ability to lift heat efficiently at very low temperatures. They are silent, vibration-free, and can be scaled down to small sizes, and have very high reliability and low maintenance. As of 2008, cryocoolers are considered to be the only commercially successful Stirling devices.

[edit] Heat pump

A Stirling heat pump is very similar to a Stirling cryocooler, the main difference being that it usually operates at room-temperature and its principal application to date is to pump heat from the outside of a building to the inside, thus cheaply heating it.

As with any other Stirling device, heat flows from the expansion space to the compression space; however, in contrast to the Stirling engine, the expansion space is at a lower temperature than the compression space, so instead of producing work, an input of mechanical work is required by the system (in order to satisfy the second law of thermodynamics). When the mechanical work for the heat-pump is provided by a second Stirling engine, then the overall system is called a "heat-driven, heat-pump".

The expansion-side of the heat-pump is thermally coupled to the heat-source, which is often the external environment. The compression side of the Stirling device is placed in the environment to be heated, for example a building, and heat is "pumped" into it. Typically there will be thermal insulation between the two sides so there will be a temperature rise inside the insulated space.

Heat-pumps are by far the most energy-efficient types of heating systems. Stirling heat-pumps also often have a higher coefficient of performance than conventional heat-pumps. To date, these systems have seen limited commercial use; however, use is expected to increase along with market demand for energy conservation, and adoption will likely be accelerated by technological refinements.

[edit] Marine engines

Kockums,^[62] the Swedish shipbuilder, had built at least 8 commercially successful Stirling powered submarines during the 1980s. As of 2005 they have started to carry compressed oxygen with them (see Gotland class submarine).^[clarify]

[edit] Nuclear power

There is a potential for nuclear-powered Stirling engines in electric power generation plants. Replacing the steam turbines of nuclear power plants with Stirling engines might simplify the plant, yield greater efficiency, and reduce the radioactive by-products. A number of breeder reactor designs use liquid sodium as coolant. If the heat is to be employed in a steam plant, a water/sodium heat exchanger is required, which raises some concern as sodium reacts violently with water. A Stirling engine eliminates the need for water anywhere in the cycle.

United States government labs have developed a modern Stirling engine design known as the Stirling Radioisotope Generator for use in space exploration. It is designed to generate electricity for deep space probes on missions lasting decades. The engine uses a single displacer to reduce moving parts and uses high energy acoustics to transfer energy. The heat source is a dry solid nuclear fuel slug and the heat sink is space itself.

[edit] Automotive engines

It is often claimed that the Stirling engine has too low a power/weight ratio, too high a cost, and too long a starting time for automotive applications. They also have complex and expensive heat-exchangers. A Stirling cooler must reject twice as much heat as an Otto or Diesel engine radiator. The heater must be made of stainless steel, exotic alloy or ceramic in order to support high heater temperatures needed for high power density, and to contain hydrogen gas that is often used in automotive Stirlings to maximize power. The main difficulties involved in using the Stirling engine in an automotive application are start-up time, acceleration response, shut-down time, and weight, not all of which have ready-made solutions.

There have been at least two automobiles exclusively powered by Stirling engines that were developed by NASA, as well as earlier projects by the Ford Motor Company and the American Motor Company. The NASA vehicles were designed by contractors and designated MOD I and MOD II. The MOD II replaced the normal spark-ignition engine in a 1985 4-door Chevrolet Celebrity Notchback. In the 1986 MOD II Design Report (Appendix A) the results show that the highway gas mileage was increased from 40 to 58 mpg and the urban mileage from 26 to 33 mpg with no change in gross weight of the vehicle. Start-up time in the NASA vehicle maxed out at 30 seconds^{[citation needed]}, while Ford's research vehicle used an internal electric heater to jump-start the vehicle started in only a few seconds.

Many people believe that Stirling engines as part of a hybrid electric drive system can bypass all of the perceived design challenges or disadvantages of a non-hybrid Stirling automobile. In November 2007, a prototype hybrid car using solid biofuel and a Stirling engine was announced by the Precer project in Sweden. ^[63]

[edit] Aircraft engines

Stirling engines may hold theoretical promise as aircraft engines, if high power density and low cost can be achieved. They are quieter, less polluting, gain efficiency with altitude^{[citation needed]}, are more reliable due to fewer parts and the absence of an ignition system, produce much less vibration (airframes last longer) and safer, less explosive fuels may be used. However, the Stirling engine often has low power density compared to the commonly used Otto engine and Brayton cycle gas turbine. This issue has been a point of contention in automobiles, and this performance characteristic is even more critical in aircraft engines. (see below "Argument on why the Stirling engine can be applied in aviation" or "Why Aviation Needs the Stirling Engine" by Darryl Phillips, a 4-part series in the March 1993 to March 1994 issues of Stirling Machine World)

[edit] Low temperature difference engines

A low temperature difference Stirling Engine by American Stirling Company shown here running on the heat from a warm hand

A low temperature difference (Low Delta T, or LTD) Stirling engine will run on any low temperature differential, for example the difference between the palm of a hand and room-temperature or room temperature and an ice cube. Usually they are designed in a gamma configuration, for simplicity, and without a regenerator. They are typically unpressurized, running at near-atmospheric pressure. The power produced is less than one watt, and they are intended for demonstration purposes only. They are sold as toys and educational models.

[edit] See also

• Thermomechanical generator
• Beale Number
• West Number
• Schmidt number
• Fluidyne
• Stirling Radioisotope Generator
• Distributed Energy Resources

[edit] Notes

[edit] References

The references in this article would be clearer with a different or consistent style of citation, footnoting, or external linking.

[edit] External links

Wikimedia Commons has media related to:

Stirling engine

• Stirling Engines at the Open Directory Project