The theoretical diesel cycle is the theoretical cycle of a diesel engine, also known as a compression ignition engine.

The theoretical cycle of a thermal engine is a theoretical approximation of its operation to calculate its performance.

The cycle of an internal combustion engine is constituted by the physical and chemical transformations suffered by the fuel during its passage inside the engine.

The study of a real cycle taking into account all the numerous variables, represents a very complex problem. For this reason, it is usually simplified by resorting to theoretical approximations, based on different simplified assumptions.

The fundamental difference between the Otto cycle and the diesel cycle is in the heat introduction phase. In the Otto cycle, the heat is introduced at constant volume, while in the diesel cycle it is carried out at constant pressure. Another difference between both cycles lies in the values of the compression ratio, which varies from 12 to 22 for the diesel engine, while it oscillates only between 6 and 10 for the Otto engine or gasoline engines.

## Diagram of the theoretical diesel cycle

As seen in the figure, the ideal diesel cycle consists of four thermal lines that represent:

- Adiabatic compression. Without heat exchange. (1-2);
- Introduction of heat at constant pressure (2-3);
- Adiabatic expansion. Without heat exchange (3-4);
- Expulsion of heat at constant volume (4-1).

### Ideal thermal performance of the theoretical diesel cycle

During the transformation 2-3 of introduction of heat Q1 at constant pressure, the piston comes into operation, and therefore, the fluid produces the work:

Consequently, the energy equation without flow becomes

and the enthalpy h of the fluid is given by the expression

The equation transforms into

Because the fluid is a perfect gas, we can use, for its enthalpy variation at constant pressure, the expression

Next, the heat introduced will have the following value:

It should be noted that in a transformation with introduction of heat at constant pressure the value of the enthalpy of the active fluid varies, while in the case of the transformation at constant volume, the change in the internal energy of the fluid varies. As the subtraction of the heat Q2 is carried out as in the Otto cycle, we can write:

Q2 = U4-U1

and as the fluid is a perfect gas and the cycle is ideal:

Q2 = Cv (T4-T1).

Therefore, the ideal thermal performance of the theoretical diesel cycle is valid:

he = (supplied heat - subtracted heat) / heat supplied

expression fully analogous to that found for the ideal performance of the Otto theoretical cycle.

For the transformation 2-3 of combustion at constant pressure we have:

For the adiabatic transformations 1-2 of compression and 3-4 of expansion we have, respectively:

from where:

and since they are V4 = V1 and T3 / T2 = V3 / V2, you can write:

Substituting this expression in the ideal thermal performance, it results:

indicating with t & rsquo; the relation between the volumes V3 and V2 at the end and at the beginning, respectively, of the phase of combustion at constant pressure, to which we will give the name of "combustion relation at constant pressure", and remembering that

Finally, we obtain the expression of the ideal thermal performance of the theoretical diesel cycle:

In this expression we see that it is, for the diesel cycle, function of the compression ratio, of the combustion relation at constant pressure and the relation k between the specific heats.

Expressions of the thermal performances of the Otto and diesel cycles differ only by the term in parentheses, which is always greater than 1, and, therefore, it appears clear that the same compression ratio is greater for the Otto cycle than for the other cycle. for the diesel cycle. Reducing t & rsquo; that is, the heat introduced at constant pressure, the yield of the diesel cycle is close to that of the Otto cycle, with which it matches for t & rsquo; = 1.