Allan T. Kirkpatrick - Internal Combustion Engines

(2.1)

where is the mass of the fuel–air mixture in the cylinder. If the fuel mass in the cylinder is known, can be computed from the heat of combustion, (kJ/ ), of a fuel:

(2.2)

Finally, the energy addition can be found by analysis of the fuel–air mixture in the cylinder at bottom dead center (bdc). The mass of fuel and air in the cylinder is

(2.3)

and the air–fuel ratio is

(2.4)

Solving for ,

(2.5)

The mass of the fuel–air mixture can be determined from the ideal gas law,

(2.6)

where is the air–fuel mixture gas constant.

(2.7)

Upon substitution of Equations ( 2.5) and ( 2.6), the energy addition can be expressed as

(2.8)

and in nondimensional form,

(2.9)

Values of the heat of combustion, (MJ/ ) and the stoichiometric air–fuel ratio are given in Table 2.1for some representative fuels that are widely used in internal combustion engines. The effect of the residual fraction on the determination of the energy addition is included in the the analysis of intake and exhaust strokes later in this chapter.

Table 2.1Fuel Properties

Formula	Name
		(MJ/kg)
CH 4(g)	Methane	50.01	17.12
C 8H 18(l)	Octane	44.30	15.03
C 14.4H 24.9(l)	Diesel	42.94	14.30
C 2H 6O (l)	Ethanol	26.82	8.94

This cycle is often referred to as the Otto cycle and considers the idealized case of an internal combustion engine whose combustion is so rapid that the piston does not move during the combustion process, and thus combustion is assumed to take place at constant volume. The Otto cycle is named after Nikolaus Otto (1832–1891) who developed a four‐stroke engine in 1876. Otto is considered the inventor of the modern internal combustion engine and founder of the internal combustion engine industry.

The Otto cycle engine is also called a spark‐ignition engine since a spark is needed to initiate the combustion process. As we shall see, the combustion in a spark‐ignition engine is not necessarily at constant volume. The working fluid in the Otto cycle is assumed to be an ideal gas. The Otto cycle example plotted in Figure 2.1has a dimensionless energy addition = 20, a compression ratio = 8, and a specific heat ratio = 1.4.

The state processes for the Otto cycle are plotted in Figure 2.1. The four basic processes are:

Figure 2.1The Otto cycle ( , ).

The compression ratio of an engine is

(2.10)