displacement volume is used to increase the imep.
Figure 2.9 Ratio of Miller to Otto cycle imep with same compression ratio,
A related cycle, the Atkinson cycle, is one in which the expansion stroke continues until the cylinder pressure at point 4 decreases to atmospheric pressure. This cycle is named after James Atkinson (1846–1914), an English engineer, who invented and built an engine he named the
Example 2.2 Miller Cycle Analysis
Derive the equations for the Miller cycle efficiency, Equation (2.36), and the Miller cycle imep, Equation (2.37).
Solution
We need to write
1 Miller cycle efficiency derivation:Solving for efficiency:
2 Miller cycle imep derivation:
2.7 Ideal Four‐Stroke Process and Residual Fraction
The simple gas cycle models assume that the heat rejection process occurs at constant volume, and neglect the gas flow that occurs when the intake and exhaust valves are opened and closed. In this section, we use the energy equation to model the exhaust and intake strokes, and determine the residual fraction of gas remaining in the cylinder.
At this level of modeling, we need to make some assumptions about the operation of the intake and exhaust valves. During the exhaust stroke, the exhaust valve is assumed to open instantaneously at bottom dead center and close instantaneously at top dead center. Similarly, during the intake stroke, the intake valve is assumed to open at top dead center and remain open until bottom dead center. The intake and exhaust valve overlap, that is, the time during which they are open simultaneously, is therefore assumed to be zero.
The intake and exhaust strokes are also assumed to occur adiabatically and at constant pressure. Constant pressure intake and exhaust processes occur only at low engine speeds. More realistic computations model the instantaneous pressure drop across the valves and furthermore would account for the heat transfer, which is especially significant during the exhaust. Such considerations are deferred to Chapters 5 and 9.
Referring to Figure 2.10, the ideal intake and exhaust processes are as follows:
| 4 to 5a | Constant cylinder volume blowdown |
| 5a to 6 | Constant pressure exhaustion |
| 6 to 7 | Constant cylinder volume reversion |
| 7 to 1 | Constant pressure induction |
Figure 2.10 Four‐stroke inlet and exhaust flow.
Exhaust Stroke
The exhaust stroke has two processes: gas blowdown and gas displacement. At the end of the expansion stroke 3 to 4, the pressure in the cylinder is greater than the exhaust pressure. Hence, when the exhaust valve opens, gas will flow out of the cylinder even if the piston does not move. Typically the pressure ratio,
Therefore, the temperature and pressure of the exhaust gases remaining in the cylinder are
(2.38)
(2.39)
As the piston moves upward from bottom dead center, it pushes the remaining cylinder gases out of the cylinder. The cylinder pressure is assumed to remain constant at
The state of the gas remaining in the cylinder during the exhaust stroke can be found by applying the closed‐system first law to the cylinder gas from state 5 to state 6 as shown in Figure 2.11. The closed‐system control volume will change in shape as the cylinder gases flow out the exhaust port across the exhaust valve. Note that while the blowdown is assumed to occur at constant cylinder
