Internal Combustion Engines. Allan T. Kirkpatrick

an expansion temperature of 2250 K the equilibrium combustion product mixture has = 1.19 and = 0.30 kJ/kg‐K.

The scientific theory of heat engine cycles was first developed by Sadi Carnot (1796–1832), a French engineer, in 1824. His theory has two main axioms. The first axiom is that in order to to use a flow of energy to generate power, there needs to be two bodies at different temperatures, a hot body and a cold body. Work is extracted from the flow of energy from the hot to the cold body or reservoir. The second axiom is that there must be at no point a useless flow of energy, so heat transfer at a constant temperature is needed. Carnot developed an ideal heat engine cycle, which is reversible, i.e., if the balance of pressures is altered, the cycle of operation is reversed. The efficiency of this cycle, known as the Carnot cycle, is a function only of the reservoir temperatures, and the efficiency is increased as the temperature of the high temperature reservoir is increased. The Carnot cycle, since it is reversible, is the most efficient possible, and it is the standard to which all real engines are compared.

2.2 Gas Cycle Energy Addition

      In performing an ideal gas cycle computation, the energy addition (kJ) is required. There are a number of methods used to determine , depending on what initial information is available. If , the energy addition per unit mass of fuel–air mixture (kJ/) is known, then

      (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 2.1 for 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 2.1 Fuel Properties

Formula	Name
		(MJ/kg)
CH4 (g)	Methane	50.01	17.12
C8H18 (l)	Octane	44.30	15.03
C14.4H24.9 (l)	Diesel	42.94	14.30
C2H6O (l)	Ethanol	26.82	8.94

2.3 Constant Volume Energy Addition

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