During the intake process, the gas within the control volume does work since the piston is expanding the cylinder volume. During exhaust, work is done on the gas. The net effect during the intake and exhaust strokes is
(2.64)
The negative of that work is called pumping work since it is a loss of useful work for the throttled engine. The pumping mean effective pressure is defined as the pumping work per unit displacement volume:
(2.65)
The indicated mean effective pressure (imep) is defined as the work per unit displacement volume done by the gas during the compression and expansion stroke. The work per unit displacement volume required to pump the working fluid into and out of the engine during the intake and exhaust strokes is termed the pumping mean effective pressure (pmep). It is the sum of the pressure drops across flow restrictions during the intake and exhaust strokes, including intake system, valves, and the exhaust system.
The following relations should be clear:
(2.66)
(2.67)
Four‐Stroke Otto Gas Cycle Analysis
When we include the exhaust and intake strokes, we have two additional equations for the gas cycle analysis, the exhaust energy equation and the intake energy equation. The two unknown parameters in these equations are the residual gas fraction,
(2.68)
where
The cycle input parameters in this four‐stroke gas cycle analysis are summarized in Table 2.2. Since it is difficult to solve these two equations algebraically, the solution is found by iteration, as shown in this section. Since
Table 2.2 Input Parameters for Four‐Stroke Gas Cycle
| Parameter | Description |
|
|
inlet air or mixture temperature |
|
|
compression ratio |
|
|
exhaust pressure |
|
|
inlet pressure |
|
|
ideal gas specific heat ratio |
|
|
energy addition per unit mass of gas induced |
6, i ‐1: Intake stroke
1‐2: Isentropic compression stroke
2‐3: Constant volume heat addition
3‐4: Isentropic expansion stroke
4‐5: Isentropic blowdown
5‐6: Constant pressure adiabatic exhaust stroke
Appendix F contains a listing of the program FourStrokeOtto.m, which iterates through the above four‐stroke Otto gas cycle equations to determine the cycle pressures, temperatures, and the overall thermal parameters.
Example 2.3 Four‐Stroke Otto Cycle
Compute the volumetric efficiency, net thermal efficiency, residual fraction, intake stroke temperature