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 fuel is ignited 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, so many variables appear that affect engine performance that calculating the actual cycle is practically impossible. Anyway, the theoretical cico Otto is a good approximation to the real cycle.
Otto 4-stroke Cycle
The following figure graphically represents the Otto cycle in a 4-stroke engine in both PV and TS coordinates.
The thermodynamic transformations that are verified during the Otto cycle are:
- 1-2. Adiabatic and isentrophic transformation (without heat exchange with the outside). Compression of the active fluid and corresponding to the work L 1 carried out by the piston.
- 2-3. Transformation at constant volume. Instantaneous introduction of the supplied heat Q 1 .
- 3-4. Adiabatic transformation. Constant pressure expansion and corresponding L 2 work produced by the active fluid.
- 4-1. Transformation at constant volume. Instant heat removal Q 2 .
Actually, in the 4-stroke engine, the heat subtraction is verified during the exhaust stroke 1-0, and the fluid is introduced into the engine in the intake stroke 0-1, which is represented graphically in the diagram PV 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, without gain or loss of work, which is why the aspiration and exhaust strokes 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 heat expulsion phase 4-1 reaches its end.
Otto 2-stroke Cycle
The Otto cycle changes slightly in a 2-stroke engine from the 4-stroke engine.
First Half - Compression Compression
When the reciprocating engine piston reaches the PMI (Lower Dead Center) it begins to move to the PMS (Upper Dead Center). During the stroke the piston creates a pressure difference that sucks the mixture of air and gasoline through the intake port to the pre-compression housing. The fuel enters in gaseous form.
When the piston covers the port, mix stops. During the rest of the downward stroke, the piston compresses the mixture in the lower crankcase, until the transfer port that communicates it with the compression chamber is discovered. By communicating with the compression chamber, the precompressed fresh mix helps to expel the burned gases from the exhaust.
When the piston starts to rise, the transfer port remains open for part of the stroke and the crankcase does not take in fresh air but returns part of the gases, losing pumping efficiency. At high revolutions the inertia of the mass of gases is used to minimize this effect. It is what is called renewal of cargo.
Second Time. Gas Expansion and Escape
Once the piston of the heat engine has reached the TDC and the air / gasoline mixture is compressed, it is ignited by a spark between the two spark plug electrodes. With the ignition the fuel releases energy and reaches high pressures and temperatures in the cylinder. The piston moves downward, doing work until the exhaust port is discovered. Being at high pressures, the burned gases come out of that hole.
Characteristics of the Otto 2-stroke Cycle
The performance of this engine is lower compared to the 4-stroke engine, since it has a lower volumetric performance and the exhaust of gases is less effective. 2-stroke cycles are more polluting. At the power level, the Otto 2-stroke cycle offers the highest torque in the unit of time for the same displacement. This difference in torque is due to the fact that the 2-stroke engine makes one explosion for every revolution, while the 4-stroke engine makes one explosion for every 2 revolutions, and has more moving parts.
This type of engine is used mostly in small displacement engines (mopeds, brush cutters, hedge trimmers, chainsaws, etc.), since it is cheaper and easier to build, and its high pollutant emission is very low in absolute value.
Thermal Performance of the Otto Cycle
Since the heat Q1 is introduced at constant volume, the work L 2-3 performed during that transformation is null, and the conservation equation of the energy of the fluid without flow is transformed into:
Since it is an ideal cycle and, therefore, the operating fluid is a perfect gas, the variation of the internal energy during its transformation to constant volume is worth:
Where it comes from:
Similarly, since the heat Q 2 is also subtracted at constant volume, and under such conditions that L 4-1 = 0, we can write:
and because the fluid is a perfect gas:
Therefore, the ideal thermal performance for the theoretical Otto cycle is:
h e = (heat supplied - heat subtracted) / heat supplied
For the adiabatic transformations of compression 1-2 and expansion 3-4 we obtain, respectively:
and since it is V 1 = V 4 and V 2 = V 3 , we can write:
Introducing this relationship in the expression of the performance h e (as well as the one that exists between the temperatures T 1 and T 2 of phase 1-2 of adiabatic compression), it results:
Indicating with the relationship between the respective volumes V 1 and V 2 of the beginning and end of the compression stroke - which we will call the "volumetric compression ratio" -, the final expression of the ideal thermal performance of the Otto cycle is obtained .
The thermal performance of the Otto cycle is, therefore, a function of the compression ratio and exponent k, the ratio of the specific heats of the operating fluid. Increasing , increase h e ; increasing the values of the specific heats, k decreases and, consequently, also the thermal performance h e . Therefore, the ideal cycle, for which k = 1.4, has a higher thermal performance than the air cycle, given that, for this, it has a lower average value for k, as the specific heats vary with temperature.