Internal Combustion Engines. Allan T. Kirkpatrick

alt="images"/> = 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 ?

      Solution

      1 From Table 2.1, the heat of combustion of octane = 44,300 kJ/kg, so the nondimensional energy addition isThe cycle average specific heats and are

      2 The thermal efficiency isand the imep/ is

      3 The maximum temperature and pressure are

Comment: The efficiency we have computed, , is about twice as large as measured for actual engines. There are a number of reasons for this. We have not accounted for internal friction, heat transfer losses, and the incomplete combustion of fuel within the engine cylinder.

2.4 Constant Pressure Energy Addition

      This cycle is often referred to as the Diesel cycle and models a gas engine cycle in which energy is added at a constant pressure. The Diesel cycle is named after Rudolph Diesel (1858–1913), who in 1897 developed an engine designed for the direct injection, mixing, and autoignition of liquid fuel into the combustion chamber. The Diesel cycle engine is also called a compression ignition engine. As we will see, actual diesel engines do not have a constant pressure combustion process.

The cycle for analysis is shown in Figure 2.3. The four basic processes are:

1 to 2	isentropic compression
2 to 3	constant pressure energy addition
3 to 4	isentropic expansion
4 to 1	constant volume energy rejection

Figure 2.3 The Diesel cycle (

,

).

Again assuming constant specific heats, the student should recognize the following equations:

       Compression stroke

      (2.21)

       Energy addition

      (2.22)

       Expansion stroke

      (2.23)

      where we have defined the parameter , a measure of the combustion duration, as

(2.24)

      In this case, the indicated efficiency is

(2.25)

      The term in brackets in Equation (2.25) is greater than one, so that for the same compression ratio, , the efficiency of the Diesel cycle is less than that of the Otto cycle. However, since Diesel cycle engines are not knock limited, they operate at about twice (20:1) the compression ratio of Otto cycle engines. For the same maximum pressure, the efficiency of the Diesel cycle is greater than that of the Otto cycle.

Diesel cycle efficiencies are shown in Figure 2.4 for a specific heat ratio of 1.30. They illustrate that high compression ratios are desirable and that the efficiency decreases as the energy input increases. As approaches one, the Diesel cycle efficiency approaches the Otto cycle efficiency.

Figure 2.4 Diesel cycle characteristics as a function of compression ratio and energy addition ().

Although Equation (2.25) is correct, its utility suffers somewhat in that is not a natural choice of independent variable. Rather, in engine operation, we think more in terms of the energy transferred in. The two are related according to Equation (2.26).

(2.26)

      The indicated mean effective pressure (imep) is represented by the same equation, Equation (2.20), as the Otto cycle:

      (2.27)

      Maximizing the mean effective pressure is important in engine design so that one can build a smaller, lighter engine to produce a given amount of work. As shown in Equation (2.20), there are evidently two ways to do this: (1) increase the compression ratio , and (2) increase the energy