Allan T. Kirkpatrick - Internal Combustion Engines

The reader should be able to show that the following thermodynamic relations for the Otto cycle processes are valid:

Compression stroke

(2.11)

Constant volume energy addition

(2.12)

(2.13)

(2.14)

Expansion stroke

(2.15)

Energy rejection

(2.16)

where

The thermal efficiency n tis given by the usual definition:

(2.17)

where . If we introduce the previously cited relations for , Equation ( 2.12) and , Equation ( 2.16), we get

(2.18)

This cycle analysis indicates that the thermal efficiency of the Otto cycle depends only on the specific heat ratio and the compression ratio. Figure 2.2plots the thermal efficiency versus compression ratio for a range of specific heat ratios from 1.2 to 1.4. Compression ratios found in actual spark‐ignition engines typically range from 6 to 11. The compression ratio is limited by two practical considerations: material strength and engine knock. The maximum pressure, , of the cycle scales with compression ratio as . Engine heads and blocks have a design maximum stress, which should not be exceeded, thus limiting the compression ratio. In addition, the maximum temperature also scales with the compression ratio as . If exceeds the autoignition temperature of the fuel–air mixture, combustion will occur ahead of the flame, a condition termed . The pressure waves that are produced are damaging to the engine, and they reduce the combustion efficiency. The knock phenomena is discussed further in Chapter 7.

The indicated mean effective pressure (imep) is

(2.19)

and if we nondimensionalize by the initial pressure , then

(2.20)

The nondimensional indicated mean effective pressure is plotted versus compression ratio and energy addition in Figure 2.2. As shown by Equation ( 2.20), the imep increases linearly with energy addition and to a lesser degree with compression ratio.

Figure 2.2Otto cycle thermal efficiency and imep as a function of compression ratio and energy addition ( ).

The operation of a single‐cylinder engine with a compression ratio = 8 is to be modeled using an Otto cycle. The engine is fueled with octane and operates at a lean air–fuel ratio of 17:1. At the beginning of compression at bottom dead center, the cylinder pressure = 100 kPa and temperature = 320 K. Assume the cycle average = 0.29 kJ/kg‐K and = 1.26. (a) What is the nondimensional energy addition and the cycle average specific heats and , (b) What is the thermal efficiency and imep/ , and (c) What is the maximum temperature and pressure ?