Stirling cycle - AbsoluteAstronomy.com

This article is about the "adiabatic" Stirling cycle. For the "idealized" Stirling cycle , see the Stirling engine article.

The Stirling cycle is a thermodynamic cycle

Thermodynamic cycle

A thermodynamic cycle consists of a series of thermodynamic processes transferring heat and work, while varying pressure, temperature, and other state variables, eventually returning a system to its initial state...

that describes the general class of Stirling devices. This includes the original Stirling engine

Stirling engine

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

that was invented, developed and patented in 1816 by Reverend Dr. Robert Stirling

Robert Stirling

The Reverend Dr Robert Stirling was a Scottish clergyman, and inventor of the stirling engine.- Biography :Stirling was born at Cloag Farm near Methven, Perthshire, the third of eight children...

with help from his brother, an engineer.

The cycle is reversible, meaning that if supplied with mechanical power, it can function as a heat pump

Heat pump

A heat pump is a machine or device that effectively "moves" thermal energy from one location called the "source," which is at a lower temperature, to another location called the "sink" or "heat sink", which is at a higher temperature. An air conditioner is a particular type of heat pump, but the...

for heating or refrigeration

Refrigeration

Refrigeration is a process in which work is done to move heat from one location to another. This work is traditionally done by mechanical work, but can also be done by magnetism, laser or other means...

cooling, and even for cryogenic cooling. The cycle is defined as a closed-cycle regenerative cycle with a gas

Gas

Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

eous working fluid. "Closed-cycle" means the working fluid is permanently contained within the thermodynamic system

Thermodynamic system

A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....

. This also categorizes the engine device as an external heat engine

External combustion engine

An external combustion engine is a heat engine where an working fluid is heated by combustion in an external source, through the engine wall or a heat exchanger. The fluid then, by expanding and acting on the mechanism of the engine, produces motion and usable work...

. "Regenerative" refers to the use of an internal heat exchanger called a regenerator which increases the device's thermal efficiency

Thermal efficiency

In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a boiler, a furnace, or a refrigerator for example.-Overview:...

.

The cycle is the same as most other heat cycles in that there are four main processes: 1.Compression, 2. heat-addition, 3. expansion and 4. heat removal. However, these processes are not discrete, but rather the transitions overlap.

Idealized Stirling cycle thermodynamics

The idealized Stirling cycle consists of four thermodynamic processes

Thermodynamic processes

A thermodynamic process may be defined as the energetic development of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant...

acting on the working fluid ( See diagram to right):

Isothermal Expansion
Thermal expansion
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...

. The expansion-space is heated externally, and the gas undergoes near-isothermal expansion.
Constant-Volume (known as isovolumetric or isochoric
Isochoric
Isochoric may refer to:*cell-transitive, in geometry*isochoric process, in chemistry or thermodynamics...

) 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.
Isothermal Compression. The compression space is intercooled
Intercooler
An intercooler , or charge air cooler, is an air-to-air or air-to-liquid heat exchange device used on turbocharged and supercharged internal combustion engines to improve their volumetric efficiency by increasing intake air charge density through nearly isobaric cooling, which removes...

, so the gas undergoes near-isothermal compression.
Constant-Volume (known as isovolumetric or isochoric
Isochoric
Isochoric may refer to:*cell-transitive, in geometry*isochoric process, in chemistry or thermodynamics...

) heat-addition. The compressed air flows back through the regenerator and picks-up heat on the way to the heated expansion space.

Technical complexity of topic

The Stirling cycle is a highly advanced subject that has defied analysis by many experts for over 190 years. Highly advanced thermodynamics are required to describe the cycle. Professor Israel Urieli writes: "...the various 'ideal' cycles (such as the Schmidt cycle) are neither physically realizable nor representative of the Stirling cycle"

The analytical problem of the regenerator (the central heat exchanger in the Stirling cycle) is judged by Jakob to rank 'among the most difficult and involved that are encountered in engineering '.

Piston motion variations

Most thermodynamic textbooks use a highly-simplified form of a Stirling cycle consisting of 4-processes. This is known as an "ideal Stirling cycle", because it is an "idealized" model, and not necessarily an optimized cycle. Theoretically, the "ideal cycle" does have high net work output per cycle. However, it is rarely used for practical reasons, in part because other cycles are simpler or reduce peak stresses on bearings and/or other components. For convenience, the designer may elect to use piston motions dictated by system dynamics, such as the mechanical linkage mechanisms. At any rate, the efficiency and cycle power are nearly as good as an actual implementation of the idealized case. A typical piston-crank or linkage in a so named "kinematic" design, often results in a near-sinusoidal piston motion. Some designs will cause the piston to "dwell" at either extreme of travel.

Many kinematic linkages, such as the well known "Ross yoke", will exhibit near-sinusoidal motion. However, other linkages, such as the "rhombic drive", will exhibit more non-sinusoidal motion. To a lesser extent, the ideal cycle introduces complications, since to implement the cycle in a real engine would require somewhat higher accelerations of the pistons and higher viscous pumping-losses of the working fluid, although the material stresses and pumping-losses in an optimized engine, would only be intolerable when approaching the "ideal cycle" and/or at high cycle rates. Other issues include the time required for heat transfer, particularly for the isothermal process

Isothermal process

An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir , and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir...

es. In an engine with a cycle approaching the "ideal cycle", the cycle rate might have to be slowed down to address these issues.

In the most basic model of a free piston device, the kinematics will result in simple harmonic motion

Simple harmonic motion

Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Additionally, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum and molecular vibration....

Volume variations

In beta and gamma engines, generally the phase angle difference between the piston motions is not the same as the phase angle of the volume variations. However, in the alpha Stirling, they are the same. The rest of the article assumes sinusoidal volume variations, as in an alpha Stirling with co-linear pistons, so named an "opposed piston" alpha device.

Pressure-versus-volume graph

This type of plot is used to characterize almost all thermodynamic cycles. The result of sinusoidal volume variations is the quasi-elliptical shaped cycle shown in Figure 1. Compared to the idealized cycle, this cycle is a more realistic representation of most real Stirling engines. The four points in the graph, label the crank-angle in degree

Degree (angle)

A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

s.

The adiabatic Stirling cycle is similar to the idealized Stirling cycle; however, the four thermodynamic processes are slightly different (see graph above):

180° to 270°, pseudo-Isothermal Expansion
Thermal expansion
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...

. The expansion-space is heated externally, and the gas undergoes near-isothermal expansion.
270° to 0°, near-constant-Volume (or near-isometric or isochoric
Isochoric
Isochoric may refer to:*cell-transitive, in geometry*isochoric process, in chemistry or thermodynamics...

) 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.
0° to 90°, pseudo-Isothermal Compression. The compression space is intercooled
Intercooler
An intercooler , or charge air cooler, is an air-to-air or air-to-liquid heat exchange device used on turbocharged and supercharged internal combustion engines to improve their volumetric efficiency by increasing intake air charge density through nearly isobaric cooling, which removes...

, so the gas undergoes near-isothermal compression.
90° to 180°, near-constant-Volume (near-isometric or isochoric
Isochoric
Isochoric may refer to:*cell-transitive, in geometry*isochoric process, in chemistry or thermodynamics...

) heat-addition. The compressed air flows back through the regenerator and picks-up heat on the way to the heated expansion space.

With the exception of a Stirling thermoacoustic engine, none of the gas particles actually flows through the complete cycle. So this approach is not amenable to further analysis of the cycle. However, it provides an overview and indicates the cycle work.

Particle/mass motion

Figure 2, shows the streaklines which indicate how gas flows through a real Stirling engine. The vertical colored lines, delineate the volume spaces of the engine. From left-to-right they are: the volume swept by the expansion (power) piston, the clearance volume (which prevents the piston from contacting the hot heat-exchanger), the heater, the regenerator, the cooler, the cooler clearance volume, and the compression volume swept by the compression piston.

Heat-exchanger pressure-drop

Also referred to as "pumping losses", the pressure drops shown in Figure 3, are caused by viscous flow through the heat exchangers. The red line represents the heater, green is the regenerator, and blue is the cooler. To properly design the heat exchangers, multivariate optimization is required to obtain sufficient heat transfer with acceptable flow losses. The flow losses shown here are relatively low, and they are barely visible in the following image, which will show the overall pressure variations in the cycle.

Pressure versus crank-angle

Figure 4 shows results from an "adiabatic simulation" with non-ideal heat exchangers. Note that the pressure-drop across the regenerator is very low compared to the overall pressure variation in the cycle.

Temperature versus crank-angle

Figure 5 illustrates the adiabatic properties of a real heat exchanger. The straight lines represent the temperatures of the solid portion of the heat exchanger, and the curves are the gas temperatures of the respective spaces. The gas temperature fluctuations are caused by the effects of compression and expansion in the engine, together with non-ideal heat exchangers which have a limited rate of heat transfer

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

. When the gas temperature deviates above and below the heat exchanger temperature, it causes thermodynamic losses known as "heat transfer losses" or "hysteresis losses". However, the heat exchangers still work well enough to allow the real cycle to be effective, even if the actual thermal efficiency of the overall system is only about half of the theoretical limit

Second law of thermodynamics

The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

Cumulative heat and work energy

Figure 6 shows a graph of the alpha-type Stirling engine data, where 'Q' denotes heat energy, and 'W' denotes work energy. The blue dotted-line shows the work output

Work output

In physics, work output is the work done by a simple machine, compound machine, or any type of engine model. In common terms, it is the energy output, which for simple machines is always less than the energy input, even though the forces may be drastically different.In thermodynamics, work output...

of the compression space. As the trace dips down, and work is done on the gas as it is compressed. During the expansion process of the cycle, some work is actually done on the compression piston, as reflected by the upward movement of the trace. At the end of the cycle, this value is negative, indicating that compression piston requires a net input of work. The blue solid line shows the heat flowing out of the cooler heat-exchanger. Notice that the heat from the cooler, and the work from the compression piston both have the same cycle energy! This is consistent with the zero-net heat transfer of the regenerator (solid green line). As would be expected, the heater and the expansion space both have positive energy flow. The black dotted-line shows the net-work output of the cycle. On this trace, the cycle ends higher that it started, indicating that the heat engine

Heat engine

In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...

converts energy from heat into work.