The **Air
Standard Otto cycle** is the ideal cycle
for **Spark-Ignition** (SI) internal combustion engines, first proposed by
Nikolaus Otto over 130 years ago, and which is currently used
most motor vehicles. The following link by the **Kruse
Technology Partnership** presents a description of the **four-stroke
Otto cycle** operation including a short history of Nikolaus
Otto. Once again we have excellent animations produced by **Matt Keveney** presenting
both the **four-stroke**
and the **two-stroke**
spark-ignition internal combustion engine engine operation

The analysis of the Otto cycle is very similar
to that of the Diesel cycle which we analysed in the **previous
section**. We will use the ideal "air-standard"
assumption in our analysis. Thus the working fluid is a fixed
mass of air undergoing the complete cycle which is treated throughout
as an ideal gas. All processes are ideal, combustion is replaced
by heat addition to the air, and exhaust is replaced by a heat
rejection process which restores the air to the initial state.

The most significant difference between the ideal Otto cycle and the ideal Diesel cycle is the method of igniting the fuel-air mixture. Recall that in the ideal Diesel cycle the extremely high compression ratio (around 18:1) allows the air to reach the ignition temperature of the fuel. The fuel is then injected such that the ignition process occurs at a constant pressure. In the ideal Otto cycle the fuel-air mixture is introduced during the induction stroke and compressed to a much lower compression ratio (around 8:1) and is then ignited by a spark. The combustion results in a sudden jump in pressure while the volume remains essentially constant. The continuation of the cycle including the expansion and exhaust processes are essentially identical to that of the ideal Diesel cycle. We find it convenient to develop the analysis approach of the ideal Otto cycle through the following solved problem:

**Solved Problem 3.7
- **An ideal air-standard Otto cycle
engine has a compression ratio of 8. At the beginning of the compression
process, the working fluid is at 100 kPa, 27°C (300 K), and
800 kJ/kg heat is supplied during the constant volume heat addition
process. Neatly sketch the pressure-volume [*P-v*] diagram
for this cycle, and using the specific heat values for air at
a typical average cycle temperaure of 900K determine:

- a) the temperature and pressure of the air at the end of each process
- b) the net work output/cycle [kj/kg], and
- c) the thermal efficiency [η
_{th}] of this engine cycle.

**Solution Approach:**

The first step is to draw the *P-v* diagram
of the complete cycle, including all the relevant information.
We notice that neither volume nor mass have been provided, hence
the diagram and solution will be in terms of specific quantities.

We assume that the fuel-air mixture is represented by pure air. The relevant equations of state, internal energy and adiabatic process for air follow:

We recall from the previous section that the
nominal specific heat capacity values used for air at 300K are
C_{v} = 0.717 kJ/kg.K,, and k = 1.4. However they are
all functions of temperature, and with the extremely high temperature
range experienced in internal combustion engines one can obtain
significant errors. In this problem we use a typical average cycle
temperature of 900K taken from the table of **Specific
Heat Capacities of Air**.

We now go through all four processes in order to determine the temperature and pressure at the end of each process, as well as the work done and heat transferred during each process.

Note that the pressure P_{4} (as well
as P_{2} above) could also be evaluated from the adiabatic
process equation. We do so below as a vailidity check, however
we find it more convenient to use the ideal gas equation of state
wherever possible. Either method is satisfactory.

We continue with the final process to determine the heat rejected:

Notice that we have applied the energy equation to all four processes allowing us two alternative means of evaluating the "net work output per cycle" and the thermal efficiency, as follows:

Note that using constant specific heat values over the cycle we can determine the thermal efficiency directly from the ratio of specific heat capacities k with the following formula:

where r is the compression ratio

**Quick Quiz:** Using
the heat and work energy equations derived above, derive this
relation

**Problem 3.8 - **This is an extension of Solved Problem 3.7, in which
we wish to use throughout all four processes the nominal standard
specific heat capacity values for air at 300K. Using the values
C_{v} = 0.717 kJ/kg.K, and k = 1.4, determine:

- a) the temperature and pressure of the air
at the end of each process [P
_{2}= 1838 kPa, T_{2}= 689K, T_{3}= 1805K, P_{3}= 4815 kPa, P_{4}= 262 kPa, T_{4}= 786K] - b) the net work output/cycle [451.5 kJ/kg], and
- c) the thermal efficiency of this engine
cycle. [η
_{th}= 56%]

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Engineering Thermodynamics by Israel Urieli is licensed under a
Creative Commons Attribution-Noncommercial-Share
Alike 3.0 United States License