Table 2.4 Computed Performance Parameters for Four‐Stroke Example 2.3
| Residual Fraction |
|
0.053 |
| Net Imep (kPa) | 612.0 | |
| Ideal Thermal Efficiency |
|
0.499 |
| Net Thermal Efficiency |
|
0.461 |
| Exhaust Temperature (K) | 1309.0 | |
| Volumetric Efficiency |
|
0.91 |
Volumetric efficiency for Example 2.3.
The volumetric efficiency, Equation (2.63), the residual fraction, Equation (2.47), and the net thermal efficiency (Equation (2.67)) are plotted in Figures 2.13, and 2.14, respectively, as a function of the intake/exhaust pressure ratio.
Comment: As the pressure ratio increases, the volumetric efficiency and thermal efficiency increase, and the residual fraction decreases. The dependence of the volumetric efficiency
Net thermal efficiency for Example 2.3.
2.8 Finite Energy Release
Spark‐Ignition Energy Release
In the ideal Otto and Diesel cycles the fuel is assumed to burn at rates that result in constant volume top dead center combustion, or constant pressure combustion, respectively. Actual engine pressure and temperature profile data do not match these simple models, and more realistic modeling, such as a finite energy release model, is required. A finite energy release model is a differential equation model of an engine cycle in which the energy addition is specified as a function of the crank angle. It is also known as a
Energy release models can address questions that the simple gas cycle models cannot. If one wants to know about the effect of spark timing or heat and mass transfer on engine work and efficiency, an energy release model is required. Also, if heat transfer is included, as is done in Chapter 11, then the state changes for the compression and expansion processes are no longer isentropic, and cannot be expressed as simple algebraic equations.
A typical cumulative mass fraction burned, i.e., fraction of fuel energy released, curve for a spark‐ignition engine is shown in Figure 2.15. The figure plots the cumulative mass fraction burned
(2.69)
or an exponential relation, known as a Wiebe function, as given in Equation (2.70):
(2.70)
where
The Wiebe function is named after Ivan Wiebe (1902–1969), a Russian engineer who developed a energy release model based on analysis of combustion chain reaction events (Ghojel 2010). The Wiebe function can be used for modeling the energy release in a wide variety of combustion systems. For example, as shown in the next section, diesel engine combustion, which has a premixed phase and a diffusion phase, can be modeled using a combined double Wiebe function. The energy release curve for the diesel engine is double peaked due to the two combustion phases.
Figure 2.15 Cumulative mass fraction burned function.
Since the cumulative energy release curve asymptotically approaches a value of 1, the end of combustion needs to defined by an arbitrary limit, such as 90%, 99%, or 99.9% complete combustion; i.e.,
The values of the form factor
