Definitions

# Diesel cycle

The Diesel cycle is the thermodynamic cycle which approximates the pressure and volume of the combustion chamber of the Diesel engine, invented by Rudolph Diesel in 1897. It is characterised by having constant pressure during the "combustion" phase. This is in contrast to the Otto cycle which is an idealization of the process in a petrol engine, which approximates the real behavior with constant volume during that phase.

## The Ideal Diesel Cycle

The image on the left shows a P-v diagram for the ideal diesel cycle; where P is pressure and v is specific volume. 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 (blue)
• Process 2 to 3 is reversible 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 into work.

• Work in (Win) is done by the piston compressing the working fluid
• Heat in (Qin) is done by the combustion of the fuel
• Work out (Wout) is done by the working fluid expanding on to the piston, this produces usable torque
• Heat out (Qout) 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:

$eta_\left\{th\right\}=1-frac\left\{1\right\}\left\{r^\left\{gamma-1\right\}\right\}left \left(frac\left\{alpha^\left\{gamma\right\}-1\right\}\left\{gamma\left(alpha-1\right)\right\} right \right)$

Where

$eta_\left\{th\right\}$ is thermal efficiency
$alpha$ is the cut-off ratio $frac\left\{V_3\right\}\left\{V_2\right\}$ (ratio between the end and start volume for the combustion phase)
r is the compression ratio $frac\left\{V_1\right\}\left\{V_2\right\}$
$gamma$ is ratio of specific heats (Cp/Cv)

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

$frac\left\{T_2\right\}\left\{T_1\right\} =\left\{\left(frac\left\{V_1\right\}\left\{V_2\right\}\right)^\left\{gamma-1\right\}\right\} = r^\left\{gamma-1\right\}$
$\left\{T_2\right\} =\left\{T_1\right\} r^\left\{gamma-1\right\}$
$frac\left\{V_3\right\}\left\{V_2\right\} = frac\left\{T_3\right\}\left\{T_2\right\}$
$alpha = \left(frac\left\{T_3\right\}\left\{T_1\right\}\right)\left(frac\left\{1\right\}\left\{r^\left\{gamma-1\right\}\right\}\right)$

$\left\{T_3\right\}$ can be approximated to the flame temperature of the fuel used. The flame temperature can be approximated to the adiabatic flame temperature of the fuel with corresponding air-to-fuel ratio and compression pressure, $\left\{P_3\right\}$. $\left\{T_1\right\}$ 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;

$eta_\left\{otto,th\right\}=1-frac\left\{1\right\}\left\{r^\left\{gamma-1\right\}\right\}$

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 (r), the ideal Otto cycle will be more efficient. However, a diesel engine will be more efficient overall since it will have the ability to operate at higher compression ratios. If a petrol engine was 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. In it, fuel 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 as in the Otto cycle (four-stroke/petrol) engine. Diesel engines (heat engines using the Diesel cycle) are used in automobiles, power generation, diesel-electric locomotives, and submarines.

Invented by Rudolph Diesel in 1897, it was originally intended to run on coal dust. This engine generates power (while continuously injecting fuel) to maintain the cylinder at constant pressure during its power stroke.

The Diesel cycle refers to a compression ignition engine, called the Diesel engine that can have a two or four stroke power cycle, drawing in air by its piston, or by a mechanically or exhaust driven supercharger. As air is compressed, its temperature rises from adiabatic compression until the piston reaches the top of its compression stroke. At that point fuel is injected directly into the cylinder with an atomizing fuel injector and ignites immediately; however, because diesel fuel has a higher molecular weight than gasoline, it vaporizes and burns more slowly. The piston is already moving down by the time combustion begins. Fuel injection can be limited to a short part, or continue to near the bottom of the power stroke. If combustion is incomplete when the piston reaches the bottom of its stroke, smoke is generated and fuel is wasted.

Diesel engines are nevertheless more efficient than Otto cycle engines overall, but only during partial load with fuel cut-off at part of the power stroke. Most land vehicles rarely run at the maximum rated power of an engine. Unless the vehicle is at full stroke injection, when the pedal is 'floored', it is at partial rated power. Since diesel engines use the heating effect of compressing air to ignite fuel, it can inject as little or as much fuel as the situation demands. It is important to note that Otto cycle engines can be more efficient than Diesel cycle engines, but only when the engine is running at or near maximum power.

## General information

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. In fact, two-stroke diesels with high pressure forced induction, particularly turbocharging, make up a large percentage of the very largest diesel engines.

In North America, 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 not until Nicolas Léonard Sadi Carnot that the thermodynamic value of compression was known.) An historical implication of this is that the diesel engine would eventually have been invented without the aid of electricity.