Allan T. Kirkpatrick - Internal Combustion Engines

(2.28)

Why then do we build engines that resemble constant pressure energy addition when we recognize that constant volume energy addition would be better? To illustrate how difficult that question is let us ask the following: Suppose that the maximum pressure in the cycle must be less than some value . How should the energy be added to produce the required work? The answer is now

(2.29)

This can be demonstrated with the aid of a temperature‐entropy diagram. If the Otto cycle and the Diesel cycle are drawn on such a diagram so that the work done in each cycle is the same, it can then be shown that the Diesel cycle is rejecting less energy and must therefore be the most efficient.

Modern compression ignition engines resemble neither the constant‐volume nor the constant‐pressure cycle, but rather a cycle in which some of the energy is added at constant volume and then the remaining energy is added at constant pressure. This limited pressure or 'dual' cycle is a gas cycle model that can be used to model combustion processes that are slower than constant volume, but more rapid than constant pressure. The limited pressure cycle also can provide algebraic equations for performance parameters such as the thermal efficiency and imep. The distribution of energy added in the two processes is something an engine designer can specify approximately by choice of fuel, the fuel injection system, and the engine geometry to limit the peak pressure in the cycle.

The cycle notation is illustrated in Figure 2.5. In this case we have the following Equation ( 2.30) for :

Energy addition

(2.30)

Figure 2.5The limited pressure cycle ( , ).

The expansion stroke is still described by Equation ( 2.24), provided we write . If we let , a pressure rise parameter, it can be shown that

(2.31)

The constant‐volume and constant‐pressure cycles can be considered as special cases of the limited‐pressure cycle in which and , respectively. The use of the limited‐pressure cycle model requires information about either the fractions of constant volume and constant pressure energy addition or the maximum pressure, . A common assumption is to equally split the energy addition. Results for the case of / = 50 and are shown in Figure 2.6, showing efficiencies and imep that are between the Otto and Diesel limits. For the same compression ratio, the Otto cycle has the largest net work, followed by the limited pressure, and the Diesel. Transformation of and to more useful variables yields

(2.32)

(2.33)

Figure 2.6Comparison of limited pressure cycle with Otto and Diesel cycles ( ).

The efficiency of an internal combustion engine will increase if the expansion ratio is larger than the compression ratio. There have been many mechanisms of varying degrees of complexity designed to produce different compression and expansion ratios, and thus greater efficiency. The Miller cycle was patented by R. H. Miller (1890–1967), an American inventor, in 1957. It is a cycle that uses early or late inlet valve closing to decrease the effective compression ratio, and allowing a higher geometric compression ratio (Miller 1947).

This cycle has been is used in ship diesel engines since the 1960s, and has been adopted by a number of automotive manufacturers for use in vehicles. A 2.3 L supercharged V‐6 Miller cycle engine was used as the replacement for a 3.3 L naturally aspirated V‐6 engine in the 1995 Mazda Millennia. This engine used late inlet valve closing at 30 after the start of the compression stroke. The 2017 3.0 L turbocharged Audi V‐6 uses early inlet valve closing, which also effectively creates a smaller compression ratio.

The Miller gas cycle is shown in Figure 2.7. In this cycle as the piston moves downward on the intake stroke, the cylinder pressure follows the constant pressure line from point 6 to point 1. For early inlet valve closing, the inlet valve is closed at point 1 and the cylinder pressure decreases during the expansion to point 7. As the piston moves upward on the compression stroke, the cylinder pressure retraces the path from point 7 through point 1 to point 2. The net work done along the two paths 1‐7 and 7‐1 cancel, so that the effective compression ratio = / is therefore less than the expansion ratio = / .