Otto cycle

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Otto_cycle 

Pressure–volume diagram

Temperature-Entropy diagram
The idealized diagrams of a four-stroke Otto cycle Both diagrams: the  intake (A)  stroke is performed by an isobaric expansion, followed by an adiabatic compression (B)  stroke. Through the combustion of fuel, heat is added in a constant volume (isochoric process) process, followed by an adiabatic expansion process power (C) stroke. The cycle is closed by the  exhaust (D)  stroke, characterized by isochoric cooling and isobaric compression processes.

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, addition of heat, and removal of heat. The mass of gas that is subjected to those changes is called the system. The system, in this case, is defined to be the fluid (gas) within the cylinder. By describing the changes that take place within the system, it will also describe in inverse, the system's effect on the environment. In the case of the Otto cycle, the effect will be to produce enough net work from the system so as to propel an automobile and its occupants in the environment.

The Otto cycle is constructed from:

Top and bottom of the loop: a pair of quasi-parallel and isentropic processes (frictionless, adiabatic reversible).

Left and right sides of the loop: a pair of parallel isochoric processes (constant volume).

The isentropic process of compression or expansion implies that there will be no inefficiency (loss of mechanical energy), and there be no transfer of heat into or out of the system during that process. The cylinder and piston are assumed to be impermeable to heat during that time. Work is performed on the system during the lower isentropic compression process. Heat flows into the Otto cycle through the left pressurizing process and some of it flows back out through the right depressurizing process. The summation of the work added to the system plus the heat added minus the heat removed yields the net mechanical work generated by the system.

Processes

The processes are described by:

• Process 0–1 a mass of air is drawn into piston/cylinder arrangement at constant pressure.
• Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead center (BDC) to top dead center (TDC).
• Process 2–3 is a constant-volume heat transfer to the working gas from an external source while the piston is at top dead center. This process is intended to represent the ignition of the fuel-air mixture and the subsequent rapid burning.
• Process 3–4 is an adiabatic (isentropic) expansion (power stroke).
• Process 4–1 completes the cycle by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead center.
• Process 1–0 the mass of air is released to the atmosphere in a constant pressure process.

The Otto cycle consists of isentropic compression, heat addition at constant volume, isentropic expansion, and rejection of heat at constant volume. In the case of a four-stroke Otto cycle, technically there are two additional processes: one for the exhaust of waste heat and combustion products at constant pressure (isobaric), and one for the intake of cool oxygen-rich air also at constant pressure; however, these are often omitted in a simplified analysis. Even though those two processes are critical to the functioning of a real engine, wherein the details of heat transfer and combustion chemistry are relevant, for the simplified analysis of the thermodynamic cycle, it is more convenient to assume that all of the waste-heat is removed during a single volume change.

History

The four-stroke engine was first patented by Alphonse Beau de Rochas in 1861. Before, in about 1854–57, two Italians (Eugenio Barsanti and Felice Matteucci) invented an engine that was rumored to be very similar, but the patent was lost.

The first person to build a working four-stroke engine, a stationary engine using a coal gas-air mixture for fuel (a gas engine), was German engineer Nicolaus Otto. This is why the four-stroke principle today is commonly known as the Otto cycle and four-stroke engines using spark plugs often are called Otto engines.

Processes

The system is defined to be the mass of air that's drawn from the atmosphere into the cylinder, compressed by the piston, heated by the spark ignition of the added fuel, allowed to expand as it pushes on the piston, and finally exhausted back into the atmosphere. The mass of air is followed as its volume, pressure and temperature change during the various thermodynamic steps. As the piston is capable of moving along the cylinder, the volume of the air changes with its position in the cylinder. The compression and expansion processes induced on the gas by the movement of the piston are idealised as reversible, i.e., no useful work is lost through turbulence or friction and no heat is transferred to or from the gas during those two processes. Energy is added to the air by the combustion of fuel. Useful work is extracted by the expansion of the gas in the cylinder. After the expansion is completed in the cylinder, the remaining heat is extracted and finally the gas is exhausted to the environment. Useful mechanical work is produced during the expansion process and some of that used to compress the air mass of the next cycle. The useful mechanical work produced minus that used for the compression process is the net work gained and that can be used for propulsion or for driving other machines. Alternatively the useful work gained is the difference between the heat added and the heat removed.

Process 0–1 intake stroke (Blue Shade)

A mass of air (working fluid) is drawn into the cylinder, from 0 to 1, at atmospheric pressure (constant pressure) through the open intake valve, while the exhaust valve is closed during this process. The intake valve closes at point 1.

Process 1–2 compression stroke (B on diagrams)

Piston moves from crank end (BDC, bottom dead centre and maximum volume) to cylinder head end (TDC, top dead centre and minimum volume) as the working gas with initial state 1 is compressed isentropically to state point 2, through compression ratio (V₁/V₂). Mechanically this is the isentropic compression of the air/fuel mixture in the cylinder, also known as the compression stroke. This isentropic process assumes that no mechanical energy is lost due to friction and no heat is transferred to or from the gas, hence the process is reversible. The compression process requires that mechanical work be added to the working gas. Generally the compression ratio is around 9–10:1 (V₁:V₂) for a typical engine.

Process 2–3 ignition phase (C on diagrams)

The piston is momentarily at rest at TDC. During this instant, which is known as the ignition phase, the air/fuel mixture remains in a small volume at the top of the compression stroke. Heat is added to the working fluid by the combustion of the injected fuel, with the volume essentially being held constant. The pressure rises and the ratio ${\displaystyle (P_{3}/P_{2})}$ is called the "explosion ratio".

Process 3–4 expansion stroke (D on diagrams)

The increased high pressure exerts a force on the piston and pushes it towards the BDC. Expansion of working fluid takes place isentropically and work is done by the system on the piston. The volume ratio ${\displaystyle V_{4}/V_{3}}$ is called the "isentropic expansion ratio". (For the Otto cycle is the same as the compression ratio ${\displaystyle V_{1}/V_{2}}$). Mechanically this is the expansion of the hot gaseous mixture in the cylinder known as expansion (power) stroke.

Process 4–1 idealized heat rejection (A on diagrams)

The piston is momentarily at rest at BDC. The working gas pressure drops instantaneously from point 4 to point 1 during a constant volume process as heat is removed to an idealized external sink that is brought into contact with the cylinder head. In modern internal combustion engines, the heat-sink may be surrounding air (for low powered engines), or a circulating fluid, such as coolant. The gas has returned to state 1.

Process 1–0 exhaust stroke

The exhaust valve opens at point 1. As the piston moves from "BDC" (point 1) to "TDC" (point 0) with the exhaust valve opened, the gaseous mixture is vented to the atmosphere and the process starts anew.

Cycle analysis

In the process 1–2 the piston does work on the gas and in process 3–4 the gas does work on the piston during those isentropic compression and expansion processes, respectively. Processes 2–3 and 4–1 are isochoric processes; heat is transferred into the system from 2—3 and out of the system from 4—1 but no work is done on the system or extracted from the system during those processes. No work is done during an isochoric (constant volume) process because addition or removal of work from a system requires the movement of the boundaries of the system; hence, as the cylinder volume does not change, no shaft work is added to or removed from the system.

Four different equations are used to describe those four processes. A simplification is made by assuming changes of the kinetic and potential energy that take place in the system (mass of gas) can be neglected and then applying the first law of thermodynamics (energy conservation) to the mass of gas as it changes state as characterized by the gas's temperature, pressure, and volume.

During a complete cycle, the gas returns to its original state of temperature, pressure and volume, hence the net internal energy change of the system (gas) is zero. As a result, the energy (heat or work) added to the system must be offset by energy (heat or work) that leaves the system. In the analysis of thermodynamic systems, the convention is to account energy that enters the system as positive and energy that leaves the system is accounted as negative.

Equation 1a.

During a complete cycle, the net change of energy of the system is zero:

${\displaystyle \Delta E=E_{\text{in}}-E_{\text{out}}=0}$

The above states that the system (the mass of gas) returns to the original thermodynamic state it was in at the start of the cycle.

Where ${\displaystyle E_{\text{in}}}$is energy added to the system from 1–2–3 and ${\displaystyle E_{\text{out}}}$ is energy removed from the system from 3–4–1. In terms of work and heat added to the system

Equation 1b:

${\displaystyle W_{1-2}+Q_{2-3}+W_{3-4}+Q_{4-1}=0}$

Each term of the equation can be expressed in terms of the internal energy of the gas at each point in the process:

${\displaystyle W_{1-2}=U_{2}-U_{1}}$

${\displaystyle Q_{2-3}=U_{3}-U_{2}}$

${\displaystyle W_{3-4}=U_{4}-U_{3}}$

${\displaystyle Q_{4-1}=U_{1}-U_{4}}$

The energy balance Equation 1b becomes

${\displaystyle W_{1-2}+Q_{2-3}+W_{3-4}+Q_{4-1}=\left(U_{2}-U_{1}\right)+\left(U_{3}-U_{2}\right)+\left(U_{4}-U_{3}\right)+\left(U_{1}-U_{4}\right)=0}$

To illustrate the example we choose some values to the points in the illustration:

${\displaystyle U_{1}=1}$

${\displaystyle U_{2}=5}$

${\displaystyle U_{3}=9}$

${\displaystyle U_{4}=4}$

These values are arbitrarily but rationally selected. The work and heat terms can then be calculated.

The energy added to the system as work during the compression from 1 to 2 is

${\displaystyle \left(U_{2}-U_{1}\right)=\left(5-1\right)=4}$

The energy added to the system as heat from point 2 to 3 is

${\displaystyle \left({U_{3}-U_{2}}\right)=\left(9-5\right)=4}$

The energy removed from the system as work during the expansion from 3 to 4 is

${\displaystyle \left(U_{4}-U_{3}\right)=\left(4-9\right)=-5}$

The energy removed from the system as heat from point 4 to 1 is

${\displaystyle \left(U_{1}-U_{4}\right)=\left(1-4\right)=-3}$

The energy balance is

${\displaystyle \Delta E=+4+4-5-3=0}$

Note that energy added to the system is counted as positive and energy leaving the system is counted as negative and the summation is zero as expected for a complete cycle that returns the system to its original state.

From the energy balance the work out of the system is:

${\displaystyle \sum {\text{Work}}=W_{1-2}+W_{3-4}=\left(U_{2}-U_{1}\right)+\left(U_{4}-U_{3}\right)=4-5=-1}$

The net energy out of the system as work is -1, meaning the system has produced one net unit of energy that leaves the system in the form of work.

The net heat out of the system is:

${\displaystyle \sum {\text{Heat}}=Q_{2-3}+Q_{4-1}=\left(U_{3}-U_{2}\right)+\left(U_{1}-U_{4}\right)=4-3=1}$

As energy added to the system as heat is positive. From the above it appears as if the system gained one unit of heat. This matches the energy produced by the system as work out of the system.

Thermal efficiency is the quotient of the net work from the system, to the heat added to system. Equation 2:

${\displaystyle \eta ={\frac {W_{1-2}+W_{3-4}}{Q_{2-3}}}={\frac {\left(U_{2}-U_{1}\right)+\left(U_{4}-U_{3}\right)}{\left(U_{3}-U_{2}\right)}}}$

${\displaystyle \eta =1+{\frac {U_{1}-U_{4}}{\left(U_{3}-U_{2}\right)}}=1+{\frac {(1-4)}{(9-5)}}=0.25}$

Alternatively, thermal efficiency can be derived by strictly heat added and heat rejected.

${\displaystyle \eta ={\frac {Q_{2-3}+Q_{4-1}}{Q_{2-3}}}=1+{\frac {\left(U_{1}-U_{4}\right)}{\left(U_{3}-U_{2}\right)}}}$

Supplying the fictitious values

${\displaystyle \eta =1+{\frac {1-4}{9-5}}=1+{\frac {-3}{4}}=0.25}$

In the Otto cycle, there is no heat transfer during the process 1–2 and 3–4 as they are isentropic processes. Heat is supplied only during the constant volume processes 2–3 and heat is rejected only during the constant volume processes 4–1.

The above values are absolute values that might, for instance, have units of joules (assuming the MKS system of units are to be used) and would be of use for a particular engine with particular dimensions. In the study of thermodynamic systems the extensive quantities such as energy, volume, or entropy (versus intensive quantities of temperature and pressure) are placed on a unit mass basis, and so too are the calculations, making those more general and therefore of more general use. Hence, each term involving an extensive quantity could be divided by the mass, giving the terms units of joules/kg (specific energy), meters³/kg (specific volume), or joules/(kelvin·kg) (specific entropy, heat capacity) etc. and would be represented using lower case letters, u, v, s, etc.

Equation 1 can now be related to the specific heat equation for constant volume. The specific heats are particularly useful for thermodynamic calculations involving the ideal gas model.

${\displaystyle C_{\text{v}}=\left({\frac {\delta u}{\delta T}}\right)_{\text{v}}}$

Rearranging yields:

${\displaystyle \delta u=(C_{\text{v}})(\delta T)}$

Inserting the specific heat equation into the thermal efficiency equation (Equation 2) yields.

${\displaystyle \eta =1-\left({\frac {C_{\text{v}}(T_{4}-T_{1})}{C_{\text{v}}(T_{3}-T_{2})}}\right)}$

Upon rearrangement:

${\displaystyle \eta =1-\left({\frac {T_{1}}{T_{2}}}\right)\left({\frac {T_{4}/T_{1}-1}{T_{3}/T_{2}-1}}\right)}$

Next, noting from the diagrams ${\displaystyle T_{4}/T_{1}=T_{3}/T_{2}}$, thus both of these can be omitted. The equation then reduces to:

Equation 2:

${\displaystyle \eta =1-\left({\frac {T_{1}}{T_{2}}}\right)}$

Since the Otto cycle uses isentropic processes during the compression (process 1 to 2) and expansion (process 3 to 4) the isentropic equations of ideal gases and the constant pressure/volume relations can be used to yield Equations 3 & 4.

Equation 3:

${\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)=\left({\frac {p_{2}}{p_{1}}}\right)^{(\gamma -1)/{\gamma }}}$

Equation 4:

${\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)=\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}}$

where

${\displaystyle {\gamma }=\left({\frac {C_{\text{p}}}{C_{\text{v}}}}\right)}$

${\displaystyle {\gamma }}$ is the specific heat ratio

The derivation of the previous equations are found by solving these four equations respectively (where ${\displaystyle R}$ is the specific gas constant):

${\displaystyle C_{\text{p}}\ln \left({\frac {V_{1}}{V_{2}}}\right)-R\ln \left({\frac {p_{2}}{p_{1}}}\right)=0}$

${\displaystyle C_{\text{v}}\ln \left({\frac {T_{2}}{T_{1}}}\right)-R\ln \left({\frac {V_{2}}{V_{1}}}\right)=0}$

${\displaystyle C_{\text{p}}=\left({\frac {\gamma R}{\gamma -1}}\right)}$

${\displaystyle C_{\text{v}}=\left({\frac {R}{\gamma -1}}\right)}$

Further simplifying Equation 4, where ${\displaystyle r}$ is the compression ratio ${\displaystyle (V_{1}/V_{2})}$:

Equation 5:

${\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)=\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}=r^{(\gamma -1)}}$

From inverting Equation 4 and inserting it into Equation 2 the final thermal efficiency can be expressed as:

Equation 6:

${\displaystyle \eta =1-\left({\frac {1}{r^{(\gamma -1)}}}\right)}$

From analyzing equation 6 it is evident that the Otto cycle efficiency depends directly upon the compression ratio ${\displaystyle r}$. Since the ${\displaystyle \gamma }$ for air is 1.4, an increase in ${\displaystyle r}$ will produce an increase in ${\displaystyle \eta }$. However, the ${\displaystyle \gamma }$ for combustion products of the fuel/air mixture is often taken at approximately 1.3. The foregoing discussion implies that it is more efficient to have a high compression ratio. The standard ratio is approximately 10:1 for typical automobiles. Usually this does not increase much because of the possibility of autoignition, or "knock", which places an upper limit on the compression ratio. During the compression process 1–2 the temperature rises, therefore an increase in the compression ratio causes an increase in temperature. Autoignition occurs when the temperature of the fuel/air mixture becomes too high before it is ignited by the flame front. The compression stroke is intended to compress the products before the flame ignites the mixture. If the compression ratio is increased, the mixture may auto-ignite before the compression stroke is complete, leading to "engine knocking". This can damage engine components and will decrease the brake horsepower of the engine.

Power

The power produced by the Otto cycle is an energy developed per unit of time. The Otto engines are called four-stroke engines. The intake stroke and compression stroke require one rotation of the engine crankshaft. The power stroke and exhaust stroke require another rotation. For two rotations there is one work generating stroke..

From the above cycle analysis the net work produced by the system :

${\displaystyle \sum {\text{ Work}}=W_{1-2}+W_{3-4}=\left(U_{2}-U_{1}\right)+\left(U_{4}-U_{3}\right)=+4-5=-1}$

(again, using the sign convention, the minus sign implies energy is leaving the system as work)

If the units used were MKS the cycle would have produced one joule of energy in the form of work. For an engine of a particular displacement, such as one liter, the mass of gas of the system can be calculated assuming the engine is operating at standard temperature (20 °C) and pressure (1 atm). Using the Universal Gas Law the mass of one liter of gas is at room temperature and sea level pressure:

${\displaystyle M={\frac {PV}{RT}}}$

V=0.001 m³, R=0.286 kJ/(kg·K), T=293 K, P=101.3 kN/m²

M=0.00121 kg

At an engine speed of 3000 RPM there are 1500 work-strokes/minute or 25 work-strokes/second.

${\displaystyle \sum {\text{ Work}}=1\,{\text{J}}/({\text{kg}}\cdot {\text{stroke}})\times 0.00121\,{\text{kg}}=0.00121\,{\text{J}}/{\text{stroke}}}$

Power is 25 times that since there are 25 work-strokes/second

${\displaystyle P=25\times 0.00121=0.0303\,{\text{J}}/{\text{s}}\;{\text{or}}\;{\text{W}}}$

If the engine is multi-cylinder, the result would be multiplied by that factor. If each cylinder is of a different liter displacement, the results would also be multiplied by that factor. These results are the product of the values of the internal energy that were assumed for the four states of the system at the end each of the four strokes (two rotations). They were selected only for the sake of illustration, and are obviously of low value. Substitution of actual values from an actual engine would produce results closer to that of the engine. Whose results would be higher than the actual engine as there are many simplifying assumptions made in the analysis that overlook inefficiencies. Such results would overestimate the power output.

Increasing power and efficiency

The difference between the exhaust and intake pressures and temperatures means that some increase in efficiency can be gained by use of a turbocharger, removing from the exhaust flow some part of the remaining energy and transferring that to the intake flow to increase the intake pressure. A gas turbine can extract useful work energy from the exhaust stream and that can then be used to pressurize the intake air. The pressure and temperature of the exhausting gases would be reduced as they expand through the gas turbine and that work is then applied to the intake gas stream, increasing its pressure and temperature. The transfer of energy amounts to an efficiency improvement and the resulting power density of the engine is also improved. The intake air is typically cooled so as to reduce its volume as the work produced per stroke is a direct function of the amount of mass taken into the cylinder; denser air will produce more work per cycle. Practically speaking the intake air mass temperature must also be reduced to prevent premature ignition in a petrol fueled engine; hence, an intercooler is used to remove some energy as heat and so reduce the intake temperature. Such a scheme both increases the engine's efficiency and power.

The application of a supercharger driven by the crankshaft does increase the power output (power density) but does not increase efficiency as it uses some of the net work produced by the engine to pressurize the intake air and fails to extract otherwise wasted energy associated with the flow of exhaust at high temperature and a pressure to the ambient.

 

Reciprocating engine

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Reciprocating_engine 

 

Internal combustion piston engine Components of a typical, four-stroke cycle, internal combustion piston engine.

1. C. Crankshaft
2. E. Exhaust camshaft
3. I. Intake camshaft
4. P. Piston
5. R. Connecting rod
6. S. Spark plug
7. W. Water jacket for coolant flow
8. V. Valves

A reciprocating engine, also often known as a piston engine, is typically a heat engine (although there are also pneumatic and hydraulic reciprocating engines) that uses one or more reciprocating pistons to convert pressure into a rotating motion. This article describes the common features of all types. The main types are: the internal combustion engine, used extensively in motor vehicles; the steam engine, the mainstay of the Industrial Revolution; and the Stirling engine for niche applications. Internal combustion engines are further classified in two ways: either a spark-ignition (SI) engine, where the spark plug initiates the combustion; or a compression-ignition (CI) engine, where the air within the cylinder is compressed, thus heating it, so that the heated air ignites fuel that is injected then or earlier.

Common features in all types

Ray-traced image of a piston engine

There may be one or more pistons. Each piston is inside a cylinder, into which a gas is introduced, either already under pressure (e.g. steam engine), or heated inside the cylinder either by ignition of a fuel air mixture (internal combustion engine) or by contact with a hot heat exchanger in the cylinder (Stirling engine). The hot gases expand, pushing the piston to the bottom of the cylinder. This position is also known as the Bottom Dead Center (BDC), or where the piston forms the largest volume in the cylinder. The piston is returned to the cylinder top (Top Dead Centre) (TDC) by a flywheel, the power from other pistons connected to the same shaft or (in a double acting cylinder) by the same process acting on the other side of the piston. This is where the piston forms the smallest volume in the cylinder. In most types the expanded or "exhausted" gases are removed from the cylinder by this stroke. The exception is the Stirling engine, which repeatedly heats and cools the same sealed quantity of gas. The stroke is simply the distance between the TDC and the BDC, or the greatest distance that the piston can travel in one direction.

In some designs the piston may be powered in both directions in the cylinder, in which case it is said to be double-acting.

Steam piston engine
A labeled schematic diagram of a typical single-cylinder, simple expansion, double-acting high pressure steam engine. Power takeoff from the engine is by way of a belt.

1. Piston
2. Piston rod
3. Crosshead bearing
4. Connecting rod
5. Crank
6. Eccentric valve motion
7. Flywheel
8. Sliding valve
9. Centrifugal governor

In most types, the linear movement of the piston is converted to a rotating movement via a connecting rod and a crankshaft or by a swashplate or other suitable mechanism. A flywheel is often used to ensure smooth rotation or to store energy to carry the engine through an un-powered part of the cycle. The more cylinders a reciprocating engine has, generally, the more vibration-free (smoothly) it can operate. The power of a reciprocating engine is proportional to the volume of the combined pistons' displacement.

A seal must be made between the sliding piston and the walls of the cylinder so that the high pressure gas above the piston does not leak past it and reduce the efficiency of the engine. This seal is usually provided by one or more piston rings. These are rings made of a hard metal, and are sprung into a circular groove in the piston head. The rings fit closely in the groove and press lightly against the cylinder wall to form a seal, and more heavily when higher combustion pressure moves around to their inner surfaces.

It is common to classify such engines by the number and alignment of cylinders and total volume of displacement of gas by the pistons moving in the cylinders usually measured in cubic centimetres (cm³ or cc) or litres (l) or (L) (US: liter). For example, for internal combustion engines, single and two-cylinder designs are common in smaller vehicles such as motorcycles, while automobiles typically have between four and eight, and locomotives, and ships may have a dozen cylinders or more. Cylinder capacities may range from 10 cm³ or less in model engines up to thousands of liters in ships' engines.

The compression ratio affects the performance in most types of reciprocating engine. It is the ratio between the volume of the cylinder, when the piston is at the bottom of its stroke, and the volume when the piston is at the top of its stroke.

The bore/stroke ratio is the ratio of the diameter of the piston, or "bore", to the length of travel within the cylinder, or "stroke". If this is around 1 the engine is said to be "square", if it is greater than 1, i.e. the bore is larger than the stroke, it is "oversquare". If it is less than 1, i.e. the stroke is larger than the bore, it is "undersquare".

Cylinders may be aligned in line, in a V configuration, horizontally opposite each other, or radially around the crankshaft. Opposed-piston engines put two pistons working at opposite ends of the same cylinder and this has been extended into triangular arrangements such as the Napier Deltic. Some designs have set the cylinders in motion around the shaft, such as the Rotary engine.

Stirling piston engine Rhombic Drive – Beta Stirling Engine Design, showing the second displacer piston (green) within the cylinder, which shunts the working gas between the hot and cold ends, but produces no power itself.

1.   Hot cylinder wall
2.   Cold cylinder wall

5.   Displacer piston
6.   Power piston
7.   Flywheels

In steam engines and internal combustion engines, valves are required to allow the entry and exit of gases at the correct times in the piston's cycle. These are worked by cams, eccentrics or cranks driven by the shaft of the engine. Early designs used the D slide valve but this has been largely superseded by Piston valve or Poppet valve designs. In steam engines the point in the piston cycle at which the steam inlet valve closes is called the cutoff and this can often be controlled to adjust the torque supplied by the engine and improve efficiency. In some steam engines, the action of the valves can be replaced by an oscillating cylinder.

Internal combustion engines operate through a sequence of strokes that admit and remove gases to and from the cylinder. These operations are repeated cyclically and an engine is said to be 2-stroke, 4-stroke or 6-stroke depending on the number of strokes it takes to complete a cycle.

In some steam engines, the cylinders may be of varying size with the smallest bore cylinder working the highest pressure steam. This is then fed through one or more, increasingly larger bore cylinders successively, to extract power from the steam at increasingly lower pressures. These engines are called Compound engines.

Aside from looking at the power that the engine can produce, the Mean Effective Pressure (MEP), can also be used in comparing the power output and performance of reciprocating engines of the same size. The mean effective pressure is the fictitious pressure which would produce the same amount of net work that was produced during the power stroke cycle. This is shown by:

${\displaystyle W_{net}={\text{MEP}}\cdot A_{p}S={\text{MEP}}\cdot V_{d}}$

where ${\displaystyle A_{p}}$ is the total piston area of the engine, ${\displaystyle S}$ is the stroke length of the pistons, and ${\displaystyle V_{d}}$ is the total displacement volume of the engine. Therefore:

${\displaystyle {\text{MEP}}={\frac {W_{net}}{V_{d}}}}$

Whichever engine with the larger value of MEP produces more net work per cycle and performs more efficiently.

History

Further information: History of the steam engine and History of the internal combustion engine

An early known example of rotary to reciprocating motion is the crank mechanism. The earliest hand-operated cranks appeared in China during the Han Dynasty (202 BC–220 AD). The Chinese used the crank-and-connecting rod for operating querns as far back as the Western Han dynasty (202 BC - 9 AD). Eventually crank-and-connecting rods were used in the inter-conversion of rotary and reciprocating motion for other applications such as flour-sifting, silk-reeling machines, treadle spinning wheels, and furnace bellows driven either by horses or waterwheels.  Several saw mills in Roman Asia and Byzantine Syria during the 3rd–6th centuries AD had a crank and connecting rod mechanism which converted the rotary motion of a water wheel into the linear movement of saw blades. In 1206, Arab engineer Al-Jazari invented a crankshaft.

The reciprocating engine developed in Europe during the 18th century, first as the atmospheric engine then later as the steam engine. These were followed by the Stirling engine and internal combustion engine in the 19th century. Today the most common form of reciprocating engine is the internal combustion engine running on the combustion of petrol, diesel, Liquefied petroleum gas (LPG) or compressed natural gas (CNG) and used to power motor vehicles and engine power plants.

One notable reciprocating engine from the World War II Era was the 28-cylinder, 3,500 hp (2,600 kW) Pratt & Whitney R-4360 Wasp Major radial engine. It powered the last generation of large piston-engined planes before jet engines and turboprops took over from 1944 onward. It had a total engine capacity of 71.5 L (4,360 cu in), and a high power-to-weight ratio.

The largest reciprocating engine in production at present, but not the largest ever built, is the Wärtsilä-Sulzer RTA96-C turbocharged two-stroke diesel engine of 2006 built by Wärtsilä. It is used to power the largest modern container ships such as the Emma Mærsk. It is five stories high (13.5 m or 44 ft), 27 m (89 ft) long, and weighs over 2,300 metric tons (2,500 short tons) in its largest 14 cylinders version producing more than 84.42 MW (114,800 bhp). Each cylinder has a capacity of 1,820 L (64 cu ft), making a total capacity of 25,480 L (900 cu ft) for the largest versions.

Engine capacity

For piston engines, an engine's capacity is the engine displacement, in other words the volume swept by all the pistons of an engine in a single movement. It is generally measured in litres (l) or cubic inches (c.i.d., cu in, or in³) for larger engines, and cubic centimetres (abbreviated cc) for smaller engines. All else being equal, engines with greater capacities are more powerful and consumption of fuel increases accordingly (although this is not true of every Reciprocating engine), although power and fuel consumption are affected by many factors outside of engine displacement.

Power

Reciprocating engines can be characterized by their specific power, which is typically given in kilowatts per litre of engine displacement (in the U.S. also horsepower per cubic inch). The result offers an approximation of the peak power output of an engine. This is not to be confused with fuel efficiency, since high efficiency often requires a lean fuel-air ratio, and thus lower power density. A modern high-performance car engine makes in excess of 75 kW/L (1.65 hp/in³).

Other modern non-internal combustion types

Reciprocating engines that are powered by compressed air, steam or other hot gases are still used in some applications such as to drive many modern torpedoes or as pollution-free motive power. Most steam-driven applications use steam turbines, which are more efficient than piston engines.

The French-designed FlowAIR vehicles use compressed air stored in a cylinder to drive a reciprocating engine in a local-pollution-free urban vehicle.

Torpedoes may use a working gas produced by high test peroxide or Otto fuel II, which pressurize without combustion. The 230 kg (510 lb) Mark 46 torpedo, for example, can travel 11 km (6.8 mi) underwater at 74 km/h (46 mph) fuelled by Otto fuel without oxidant.

Reciprocating quantum heat engine

Quantum heat engines are devices that generate power from heat that flows from a hot to a cold reservoir. The mechanism of operation of the engine can be described by the laws of quantum mechanics. Quantum refrigerators are devices that consume power with the purpose to pump heat from a cold to a hot reservoir.

In a reciprocating quantum heat engine, the working medium is a quantum system such as spin systems or a harmonic oscillator. The Carnot cycle and Otto cycle are the ones most studied. The quantum versions obey the laws of thermodynamics. In addition, these models can justify the assumptions of endoreversible thermodynamics. A theoretical study has shown that it is possible and practical to build a reciprocating engine that is composed of a single oscillating atom. This is an area for future research and could have applications in nanotechnology.

Miscellaneous engines

There are a large number of unusual varieties of piston engines that have various claimed advantages, many of which see little if any current use:

• Free-piston engine
• Opposed-piston engine
• Swing-piston engine
• IRIS engine
• Bourke engine
• Thermo-magnetic motor