Diesel cycle

# Diesel cycle

Overview
The Diesel cycle is the 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...

which approximates the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

and volume of the combustion chamber
Combustion chamber
A combustion chamber is the part of an engine in which fuel is burned.-Internal combustion engine:The hot gases produced by the combustion occupy a far greater volume than the original fuel, thus creating an increase in pressure within the limited volume of the chamber...

of the Diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...

, invented by Rudolph Diesel in 1897. It is assumed to have constant pressure during the first part of the "combustion" phase ( to in the diagram, below). This is an idealized mathematical model: real physical Diesels do have an increase in pressure during this period, but it is less pronounced than in the Otto cycle. The idealized Otto cycle
Otto cycle
An Otto cycle is an idealized thermodynamic cycle which describes the functioning of a typical reciprocating piston engine, the thermodynamic cycle most commonly found in automobile engines....

of a gasoline engine
Four-stroke cycle
A four-stroke engine, also known as four-cycle, is an internal combustion engine in which the piston completes four separate strokes—intake, compression, power, and exhaust—during two separate revolutions of the engine's crankshaft, and one single thermodynamic cycle.There are two...

approximates constant volume during that phase, generating more of a spike in a p-V diagram.
Discussion

Encyclopedia
The Diesel cycle is the 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...

which approximates the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

and volume of the combustion chamber
Combustion chamber
A combustion chamber is the part of an engine in which fuel is burned.-Internal combustion engine:The hot gases produced by the combustion occupy a far greater volume than the original fuel, thus creating an increase in pressure within the limited volume of the chamber...

of the Diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...

, invented by Rudolph Diesel in 1897. It is assumed to have constant pressure during the first part of the "combustion" phase ( to in the diagram, below). This is an idealized mathematical model: real physical Diesels do have an increase in pressure during this period, but it is less pronounced than in the Otto cycle. The idealized Otto cycle
Otto cycle
An Otto cycle is an idealized thermodynamic cycle which describes the functioning of a typical reciprocating piston engine, the thermodynamic cycle most commonly found in automobile engines....

of a gasoline engine
Four-stroke cycle
A four-stroke engine, also known as four-cycle, is an internal combustion engine in which the piston completes four separate strokes—intake, compression, power, and exhaust—during two separate revolutions of the engine's crankshaft, and one single thermodynamic cycle.There are two...

approximates constant volume during that phase, generating more of a spike in a p-V diagram.

## The Idealized Diesel Cycle

The image on the left shows a p-V diagram for the ideal Diesel cycle; where is pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

and is specific volume
Specific volume
In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density:In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass...

. The ideal Diesel cycle follows the following four distinct processes (The color references refer to the color of the line on the diagram.):
• Process 1 to 2 is isentropic compression of the fluid(blue colour)
• Process 2 to 3 is reversible
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...

constant pressure heating (red)
• Process 3 to 4 is isentropic expansion (yellow)
• Process 4 to 1 is reversible constant volume cooling (green)

The Diesel is a heat engine: it converts heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

into work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

. The isentropic processes are impermeable to heat: heat flows into the loop through the left expanding isobaric process and some of it flows back out through the right depressurizing process, and the heat that remains does the work.
• Work in () is done by the piston compressing the working fluid
• Heat in () is done by the combustion
Combustion
Combustion or burning is the sequence of exothermic chemical reactions between a fuel and an oxidant accompanied by the production of heat and conversion of chemical species. The release of heat can result in the production of light in the form of either glowing or a flame...

of the fuel
• Work out () is done by the working fluid expanding on to the piston (this produces usable torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

)
• Heat out () is done by venting the air

### Maximum thermal efficiency

The maximum thermal efficiency of a Diesel cycle is dependent on the compression ratio and the cut-off ratio. It has the following formula under cold air standard analysis:

where is 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:...

is the cut-off ratio (ratio between the end and start volume for the combustion phase)
is the compression ratio
Compression ratio
The 'compression ratio' of an internal-combustion engine or external combustion engine is a value that represents the ratio of the volume of its combustion chamber from its largest capacity to its smallest capacity...

is ratio of specific heats (Cp/Cv)

The cut-off ratio can be expressed in terms of temperature as shown below:

can be approximated to the flame temperature of the fuel used. The flame temperature can be approximated to the adiabatic flame temperature
In the study of combustion, there are two types of adiabatic flame temperature depending on how the process is completed, constant volume and constant pressure, describing the temperature the combustion products theoretically reach if no energy is lost to the outside environment.The constant volume...

of the fuel with corresponding air-to-fuel ratio and compression pressure, .
can be approximated to the inlet air temperature.

This formula only gives the ideal thermal efficiency. The actual thermal efficiency will be significantly lower due to heat and friction losses. The formula is more complex than the Otto cycle (petrol/gasoline engine) relation that has the following formula;

The additional complexity for the Diesel formula comes around since the heat addition is at constant pressure and the heat rejection is at constant volume. The Otto cycle by comparison has both the heat addition and rejection at constant volume.

Comparing the two formulae it can be seen that for a given compression ratio , the ideal Otto cycle will be more efficient. However, a Diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...

will be more efficient overall since it will have the ability to operate at higher compression ratios. If a petrol engine were to have the same compression ratio, then knocking (self-ignition) would occur and this would severely reduce the efficiency, whereas in a Diesel engine, the self ignition is the desired behavior. Additionally, both of these cycles are only idealizations, and the actual behavior does not divide as clearly or sharply. And the ideal Otto cycle formula stated above does not include throttling losses, which do not apply to Diesel engines.

The Diesel cycle is a combustion process of a reciprocating internal combustion engine
Internal combustion engine
The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber. In an internal combustion engine, the expansion of the high-temperature and high -pressure gases produced by combustion apply direct force to some component of the engine...

. In it, fuel
Fuel
Fuel is any material that stores energy that can later be extracted to perform mechanical work in a controlled manner. Most fuels used by humans undergo combustion, a redox reaction in which a combustible substance releases energy after it ignites and reacts with the oxygen in the air...

is ignited by heat generated by compressing air in the combustion chamber, into which fuel is injected. This is in contrast to igniting it with a spark plug
Spark plug
A spark plug is an electrical device that fits into the cylinder head of some internal combustion engines and ignites compressed fuels such as aerosol, gasoline, ethanol, and liquefied petroleum gas by means of an electric spark.Spark plugs have an insulated central electrode which is connected by...

as in the Otto cycle
Otto cycle
An Otto cycle is an idealized thermodynamic cycle which describes the functioning of a typical reciprocating piston engine, the thermodynamic cycle most commonly found in automobile engines....

(four-stroke/petrol) engine. Diesel engines (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...

s using the Diesel cycle) are used in automobile
Automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...

s, power generation, Diesel-electric locomotive
Locomotive
A locomotive is a railway vehicle that provides the motive power for a train. The word originates from the Latin loco – "from a place", ablative of locus, "place" + Medieval Latin motivus, "causing motion", and is a shortened form of the term locomotive engine, first used in the early 19th...

s, and submarines.

### Diesel engines

The Diesel engine has the lowest specific fuel consumption of any large internal combustion engine, 0.26 lb/hp.h (0.16 kg/kWh) for very large marine engines. Two-stroke Diesels with high pressure forced induction, particularly turbocharging, make up a large percentage of the very largest Diesel engines.

In North America
North America
North America is a continent wholly within the Northern Hemisphere and almost wholly within the Western Hemisphere. It is also considered a northern subcontinent of the Americas...

, Diesel engines are primarily used in large trucks, where the low-stress, high-efficiency cycle leads to much longer engine life and lower operational costs. These advantages also make the Diesel engine ideal for use in the heavy-haul railroad environment.

### Other internal combustion engines without spark plugs

Many model airplanes use very simple "glow" and "Diesel" engines. Glow engines use glow plugs. "Diesel" model airplane engines have variable compression ratios. Both types depend on special fuels (easily obtainable in such limited quantities) for their ignition timing.

Some 19th century or earlier experimental engines used external flames, exposed by valves, for ignition, but this becomes less attractive with increasing compression. (It was the research of Nicolas Léonard Sadi Carnot
Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...

that established the thermodynamic value of compression.) A historical implication of this is that the Diesel engine would eventually have been invented without the aid of electricity.

See the development of the hot bulb engine
Hot bulb engine
The hot bulb engine, or hotbulb or heavy oil engine is a type of internal combustion engine. It is an engine in which fuel is ignited by being brought into contact with a red-hot metal surface inside a bulb....

and indirect injection
Indirect injection
In an internal combustion engine, the term indirect injection refers to a fuel injection where fuel is not directly injected into the combustion chamber...

for historical significance.