The theoretical Otto cycle is the ideal cycle of the Otto engine. The Otto engine is also known as a spark ignition engine because the ignition of the fuel is done through a spark caused by a spark plug. It is also known as a gasoline engine because of the type of fuel it uses.
One way to study the performance of this engine is by analyzing its theoretical cycle. The theoretical cycle is an approximation to the real cycle with many simplifications. In practice, there are so many variables that affect the performance of the engine that calculating the actual cycle is practically impossible. Anyway, the theoretical Otto cico is a good approximation to the real cycle.
4-stroke Otto cycle
The following figure graphically represents the Otto cycle in a 4-stroke engine in both P-V coordinates and T-S coordinates.
The thermodynamic transformations that take place during the Otto cycle are:
- 1-2. Adiabatic and isentropic transformation (without heat exchange with the exterior). Compression of the active fluid and corresponding to the work L1 carried out by the piston.
- 2-3. Transformation at constant volume. Instant introduction of the supplied heat Q1.
- 3-4. Adiabatic transformation Constant pressure expansion and corresponding L2 work produced by the active fluid.
- 4-1. Transformation at constant volume. Instant subtraction of heat Q2.
Actually, in the 4-stroke engine, the subtraction of the heat is verified during the exhaust stroke 1-0, and the fluid is introduced into the engine in the suction stroke 0-1, which is graphically represented in the PV diagram by a horizontal line, while in the TS diagram it is not possible to represent it. The effects of both processes cancel each other out, with no gain or loss of work, which is why the aspiration and exhaust races are not usually considered in the ideal diagrams in PV coordinates, and the Otto cycle is represented as a closed cycle, in the which the active fluid returns to its initial state when the phase of expulsion of heat 4-1 comes to an end.
Otto 2-stroke cycle
The Otto cycle changes slightly in a 2-stroke engine compared to the 4-stroke engine.
First time - compression Amdisión
When the piston of the reciprocating engine reaches the PMI (Bottom Dead Center) it begins to move to the PMS (Top Dead Center). During the journey the piston creates a pressure difference that sucks the air and gas mixture through the intake port into the pre-compression casing. The fuel enters in gaseous form.
When the piston covers the port, mixing stops. During the rest of the downward stroke, the piston is compressed by the mixture in the lower crankcase, until the transfer port communicating with the compression chamber is discovered. When communicating with the compression chamber, the precompressed fresh mixture helps to expel the burnt gases from the exhaust.
When the piston starts to raise the transfer port a part of the stroke remains open and the crankcase does not take in fresh air but some of the gases return, losing pump efficiency. At high revolutions the inertia of the mass of the pumps is used. gases to minimize this effect. It's what's called load renewal.
Second time. Gas expansion and exhaust
Once the piston of the heat engine has reached PMS and the mixture of air and gasoline is compressed, it is ignited by a spark between the two electrodes of the spark plug. With the ignition the fuel releases energy and reaches high pressures and temperatures in the cylinder. The piston moves down, performing work until the exhaust port is discovered. When being at high pressures, the burned gases leave by that orifice.
Characteristics of the Otto 2-cycle cycle
The performance of this engine is lower compared to the 4-stroke engine, since it has a lower volumetric efficiency and gas exhaust is less efficient. The 2-cycle cycles are more polluting. At the power level, the Otto 2-stroke cycle offers a torque in the highest time unit for the same displacement. This difference in torque is due to the fact that the 2-stroke engine makes an explosion in each revolution, while the 4-stroke engine makes an explosion for every 2 revolutions, and has more moving parts.
This type of engine is mostly used in small displacement engines (mopeds, brush cutters, hedge trimmers, chainsaws, etc.), since it is cheaper and easier to build, and its emission of high pollutants is very low in absolute value.
Thermal performance of the Otto cycle
As the heat Q1 is introduced at constant volume, the L2-3 work performed during that transformation is zero, and the energy conservation equation of the fluid without flow becomes:
As it is an ideal cycle and, therefore, the operating fluid is a perfect gas, the variation of the internal energy during its transformation at constant volume is worth:
Where it turns out:
Similarly, since heat Q2 is also subtracted at constant volume, and under such conditions that L4-1 = 0, we can write:
and because the fluid is a perfect gas:
Accordingly, the ideal thermal efficiency for the theoretical Otto cycle results:
he = (supplied heat - subtracted heat) / heat supplied
For the adiabatic transformations of compression 1-2 and expansion 3-4 we obtain, respectively:
and since it is V1 = V4 and V2 = V3, we can write:
Introducing this relation in the expression of the yield he (as well as the one that exists between the temperatures T1 and T2 of phase 1-2 of adiabatic compression), results:
Indicating with the relationship between the respective volumes V1 and V2 of the beginning and end of the compression stroke - which we will call the "volumetric compression ratio" -, gives the final expression of the ideal thermal performance of the Otto cycle.
The thermal efficiency of the Otto cycle is, therefore, a function of the compression ratio and exponent k, ratio of the specific heats of operating fluid. Increasing , increase he; increasing the values of the specific heats, decreases k and, consequently, also the thermal efficiency he. Therefore, the ideal cycle, for which k = 1.4, has a thermal efficiency higher than the air cycle, given that, for this, k has a lower average value, by varying the specific heats with temperature.
Last review: April 26, 2018