4.2.1. Four-Cylinder Averaged Pressure Signals

According to definition of the basic and advanced Seiliger process presented in Section 3, the combustion fitting results of these two Seiliger process types are compared and analyzed in terms of the four-cylinder averaged pressure signals at engine nominal operating point. Table 4 shows the Seiliger parameters and engine performance parameters chosen in the system of equations as variables and equivalence criteria for basic and advanced Seiliger process models, which actually are the same as each other, although the engine performance parameter *qin* includes a different heat input definition as explained in Section 3.

**Table 4.** Variables and equivalence criteria in combustion fit functions.


Before combustion fitting numerical calculation, the Seiliger parameters *ncomp*, *rc* and Δ*EO*, which are not taken into account as the variables in the fitting process, have to be set as constants. Considering the engine operating conditions in reality, the *ncomp* is set to be 1.36 to indicate proper heat loss during engine compression process; the *rc* 13.107 means constant volumetric process occurring at top dead centre and Δ*EO* is 0 without regarding the effect of exhaust valve open. Then based on Equations (12)–(15), the system of equations of combustion fitting is set up. During the system of equations root finding procedure, the mathematic setting should be thought over, including initial values, iterations, termination criteria, etc.

The termination criteria for the iteration in this paper, which affect the accuracy and the calculation speed, in both basic and advanced Seiliger process models fitting is set as follows:

$$\begin{aligned} \lfloor p\_3 - p\_{\text{max}} \rfloor &\le 1 \text{ bar}, \\\\ \lfloor T\_4 - T\_{\text{max}} \rfloor &\le 1 \text{ K}, \\\\ \lfloor q\_{\text{in,Selling}} - q\_{\text{in,measured}} \rfloor &\le 10 \text{ J/kg}, \\\\ \lfloor w\_{i,\text{Selling}} - w\_{i,\text{measured}} \rfloor &\le 10 \text{ J/kg}. \end{aligned}$$

The combustion fitting results of both basic and advanced Seiliger process models are shown in Table 5, in which the Seiliger parameters values and heat input during the Seiliger parameters effect stages are compared. The values of *a* and *b* are the same of these two types, the latter's small difference is caused by the numerical calculation errors. The value of *c* is quite different between these two Seiliger process models, together with heat input ratio in Seiliger stage 4–5 (isothermal process) large differences. In the basic Seiliger process, besides in stage 1–2 (isochoric process), the heat input occurs in isothermal process and the ratio is 36.02%, but in the advanced Seiliger process model it is only 16.53% with the others at 19.51% in stage 5–6 (expansion process), which means there is a very late combustion during operation of the engine.

**Table 5.** Results of combustion fit of basic and advanced Seiliger process models.


Figure 10 illustrates the basic and advanced Seiliger process models of combustion fitting results compared with the measurements in diversified diagrams. Figure 10a,b presents the comparison between pressure signals, due to relatively small scale, the difference among the three curves are not distinct. However, in the in-cylinder temperature diagram shown in Figure 10c, it is more likely to observe the trend and comparison of these curves, in which the basic and advanced Seiliger process before peak temperature completely coincide with each other and the duration of the isothermal process are different, and have a longer crank angle time with a larger *c* value in the basic Seiliger process model. The temperature at Exhaust Open (EO) in the basic Seiliger process is lower than that in the advanced Seiliger process model (around 150 K), which is caused by the late combustion occurring during expansion process in advanced Seiliger process model.

**Figure 10.** Comparison of basic and advanced Seiliger process models: (**a**) *p*-*ϕ* diagram; (**b**) *p*-*V* diagram; (**c**) *T*-*ϕ* diagram; (**d**) *T*-*s* diagram.

Figure 10d shows the fitting results compared with measurement in temperature-entropy diagram, which is even more clear to reveal the differences between the two Seiliger process models. The same trend as the in-cylinder temperature in Figure 10c before peak temperature and the two fitting curves are slightly different from the measurement. Nevertheless, the discrepancy among them in the expansion process is especially evident. The vertical curve in the *T*-*S* diagram means adiabatic expansion and the negative slope indicated heat input to the work medium and vice versa. As a result, the advanced Seiliger process model fitted the same case as the measurement with heat input in the expansion process and in the basic Seiliger process model, the result is totally different, i.e., heat loss during expansion.

Based on the fitting definition, when the basic Seiliger process model is used, the basic Seiliger process fitting shares the same equivalence criteria as the advanced Seiliger process model, but some of the heat enters the in-cylinder work medium in the isothermal process instead of the expansion process of advanced Seiliger process. From the fitting diagram, the advanced Seiliger process model fitting seems closer to the measurements, and when the ancient engine is operating with very late combustion, which is not expected, the advanced Seiliger process model is closer to the reality to describe the detailed phenomena of engine combustion. If the Seiliger process model fitting is used

in the modern engine without late combustion, the basic process model fitting is preferred to avoid making errors in the heat input analysis with relatively simple modelling.
