Week 14 - Basic Otto Cycle

Example - Maximum Cycle Pressure and Temperature

Consider an Otto cycle that receives a heat input of 1000 kJ/kg of air from combustion. The cycle has a compression ratio of 9 and a pressure and temperature at the beginning of the compression process of 100 kPa and 27oC. Assuming variable specific heats, find the maximum cycle pressure and temperature.

Solution:

Take state 1 to be the state at the beginning of the compression, state 2 at the end of the compression, state 3 at the end of the combustion, and state 4 at the end of the expansion.

Given: T1 = 27oC; p1 = 100 kPa; Q23 = 1000 kJ/kg; r = 9

First find the state at the end of the compression process, which is the beginning of the combustion process. The peak pressure and temperature will be at the state at the end of the combustion process. We will use the air tables, as the specific heats are variable, and the expansion and compression processes are isentropic. So, using the vr column, we find that at state 1, vr1 = 621.2. The compression ratio is equal to

r = v1/v2=vr1 / vr2

So, vr2 = 69.01. This corresponds to a temperature of T2 = 702.8 K. The relative pressure at state 1 is 1.3860, and the relative pressure at state 2 is 29.24. Considering the relation

p2/p1 = pr2 / pr1

we can find p2 = 2110 kPa. This gives us the state at the beginning of the combustion process. For the combustion process, we know that with no work, and no changes in kinetic and potential energy for this closed system, we will have

Q23/m = u3 - u2

We can find the value for u2 in the tables. This is u2 = 514.5 kJ/kg. Solving, we find u3 = 1514.5 kJ/kg. Then, on the air tables, we find that this corresponds to a temperature after the combustion of T3 = 1828.6 K. We can not use the air tables to find the pressure at this state, as the combustion process is not isentropic. Rather, we will treat air as an ideal gas, and the combustion process to have a constant volume and mass. This results is the relation

T3/T2 = p3/p2

Using this, we find that p3 = 5490 kPa.

So, the peak pressure and temperature in this Otto cycle are T3 = 1830 K, and p3 = 5490 kPa.

Return to ME 301 Introduction