*4.2. Analysis of Engine Operation Stability*

For all engine operating points, the coefficient of variation of the indicative mean effective pressure CoV(IMEP) was determined according to Equation (2). The data presented (Figure 5) show that the largest values of the engine's operating irregularity are related to a large dose of fuel fed into the prechamber at λ = 1.3, independent of the fuel type in the prechamber. As mentioned earlier, the misfire of the fuel in the cylinder, shown by the large CoV(IMEP) value, also occurs at λ = 1.8 and a low fuel dose. At this point, CoV(IMEP) = 12% was obtained during propane combustion, while no combustion occurred during methane combustion (in the prechamber), which is why there is no point in Figure 5b.

**Figure 5.** Interpolated maps showing the stability of engine operation represented by the coefficient of variation CoV(IMEP): (**a**) when burning propane in the prechamber; (**b**) when burning methane in the prechamber.

As shown in Figure 5, the most stable engine operation is at λ = 1.5 over the entire range of changes in the fuel dose to the prechamber qo\_PC. The greatest unstable operation is observed with a large value of λ = 1.8 and a low dose of propane to PC (Figure 5a). A large excess air ratio and a low fuel dose do not promote the ignitability of the charge. The same is true for methane combustion—with the above conditions (λ = 1.8, qo\_PC = min) there is no ignitability of the main charge.

Therefore, the next figure shows the conditions that are the most (Figure 6a) and least favorable (Figure 6b) for ignition of the charge. The most favorable conditions for combustion (most stable engine operation) occur at the average value of the fuel dose to the PC (qo = 30 J). The value of CoV(IMEP) is below 0.8%. The least favorable conditions result in CoV(IMEP) values well above 5% and above 9%. It can be considered that at CoV(IMEP) = 9.3%, the peak pressure differences are almost 100%. At CoV(IMEP) = 5.8%, the maximum variations are 26 bar, or about 75%.

**Figure 6.** Stability of engine operation determined by maximum cylinder pressure Pmx (blue dots): (**a**) smallest CoV(IMEP) < 1% when burning methane and propane: λ = 1.5 Eqo\_PC = 30 J; (**b**) largest CoV(IMEP) > 10% when burning methane and propane: λ = 1.8 Eqo\_PC = 20 J.

A comparison of IMEP values at each point of engine operation is briefly shown in Figure 7. All curves are drawn in the same color, but those showing significant deviations are marked in blue or black. It can be seen from the data presented that the highest instability of operation occurs at λ = 1.8. Two curves significantly deviating from the stability criterion of CoV(IMEP) < 3.5% were recorded. The maximum values are 9.33% and 11.45%. Comparing the combustion of methane and propane, it was found that the combustion of methane significantly degrades the combustion process more (no combustion at qo = 10 J and λ = 1.8). At other operating points, the combustion conditions are similar (at the same fuel doses qo\_PC), i.e., combustion is deteriorated.

The engine's so-called "work maps" stability is also included in the IMEPn-IMEPn+1 coordinates (Figure 8). They indicate the variability of sequential engine cycles and illustrate in detail the changes in the cyclicality of engine operation. At the smallest value of the excess air ratio λ = 1.3, the greatest irregularity occurs at high fuel doses to the PC during the combustion of methane in the prechamber (Figure 8b—left graph). The variation averages ΔIMEP = 0.8 bar/cycle. The most stable engine operation occurs at λ = 1.5. The cyclic changes from cycle to cycle are less than ΔIMEP = 0.5 bar/cycle. The highest irregularity was observed at λ = 1.8 during propane combustion (Figure 8a). The ΔIMEP changes are almost 3 bar/cycle. During methane combustion, the ΔIMEP value is a maximum of 1.5 bar/cycle.

**Figure 7.** Instability of engine operation determined by IMEP for each value of excess air ratio: (**a**) when burning propane in the prechamber; (**b**) when burning methane in both chambers (values of the largest IMEP changes are marked in the figure).

**Figure 8.** Unevenness of engine cycles determined by IMEP maps for each value of excess air ratio and different values of fuel dose energy injected into the prechamber: (**a**) when burning propane in the prechamber; (**b**) when burning methane in both chambers.

The analysis of inter-chamber tides is shown in Figure 9. The pressure difference between chambers was chosen as the parameter representing mass transfer intensity. The combustion of fuels at λ = 1.3 (Figure 9a) shows the smallest pressure difference between volumes when various fuels are combusted. A higher value was recorded during the combustion of propane in the prechamber, the pressure difference between the main and prechamber being about 0.9 bar. An earlier ignition of methane than propane is observed to achieve CoC = 8 deg aTDC. This means that propane combustion occurs faster, especially in the range of the first phase of combustion. This phase lasts from the beginning of combustion until 50% of the heat is released. When burning fuels at λ = 1.5, the start of combustion in the PC is slightly later for both fuels (Figure 9b). The pressure differences in the prechamber are already greater at about 1.4 bar. The combustion pressure in the PC during propane fueling is higher, and again the maximum falls slightly later than during methane combustion. The largest differences were observed when sparging the fuels at λ = 1.8 (Figure 9c). Differences in the onset of combustion in the PC are large at about 4 deg. Pressure differences in PC are about 2.1 bar.

**Figure 9.** Inter-chamber flows (Delta\_P) and pressure in the prechamber and main chamber during combustion of methane (blue line) and propane (red line): (**a**) during combustion of fuels with excess air λ = 1.3; (**b**) during combustion of fuels with excess air λ = 1.5; (**c**) during combustion of fuels with excess air λ = 1.8.

At all points, the maximum pressure in the MC is several bars higher than in the PC. This is mainly due to the throttling effect of the flow orifices produced in the prechamber.

The specific changes in the pressure values in the two chambers are shown in Figure 10. It shows the high intensity of the processes in the prechamber under the conditions of the mean energy supplied to this chamber. On this basis, it is possible to conclude the optimal amount of fuel delivered to the prechamber. As can be seen from the data presented, the best value is the energy in the range of 20–30 J delivered to the PC. Too small as well as too large a dose of fuel to the PC results in a non-intensive combustion in the prechamber. Regardless of the dose, higher pressure values were always recorded in the MC than in the PC.

Based on the above considerations of engine stability, the average values of IMEP in both combustion chambers were determined (Figure 11). It was found that the IMEP in MC has about 0.2 bar higher values than in PC. As the dose to the PC increases, the value decreases almost linearly. The change in IMEP is about 0.2 bar per 50 J of energy delivered to the PC. This decrease may be due mainly to the lower energy of the fuel contained in the main chamber. This means that the minimum dose delivered to the PC is sufficient to initiate the combustion process and maximize IMEP. The figures also show the effect of the loss of stability of engine operation, which is a very large drop in IMEP at λ = 1.8 and low energy fed to the PC. With such conditions of high excess air, the minimum dose given to the PC is too low to achieve proper combustion.

λ

**Figure 10.** Conditions of pressure change in the cylinder during the combustion of propane (PC) and methane (MC), as well as combinations of methane (PC) and methane (MC) at different values of energy injected into the prechamber at λ = 1.5 (the most favorable combustion conditions regardless of the fuel initial dose).

**Figure 11.** Variation in IMEP with respect to energy delivered to the prechamber at different values of excess air ratio λ: (**a**) variation in IMEP in the main chamber; (**b**) variation in IMEP in the prechamber.

O O O The combustion of methane and propane at λ = 1.8 is not beneficial. In both cases, an unsatisfactory combustion was obtained at small values of qo\_PC. At larger values of qo\_PC, the smallest IMEP values were observed, indicating that the excess air ratio limit was exceeded with the combustion system used.

Based on the pressure curve in the cylinder and Equation (3), the rate of heat release was determined. Integrating these values, the total amount of heat released was obtained. The analysis of this quantity in Figure 12 confirms the above information about the minimization of the dose delivered to the PC.

**Figure 12.** The heat release path in the cylinder (in the main chamber) with the determination of the minimum dose of fuel injected into the prechamber for both types of fuels: (**a**) at λ = 1.3; (**b**) at λ = 1.5; (**c**) at λ = 1.8.

The combustion of propane and methane in the PC results in the maximum heat release values being obtained with the minimum fuel dose. The combustion of very lean mixtures (λ = 1.8—Figure 12c) results in a different process when methane or propane is injected into the PC. When burning propane, the minimum dose is too low to achieve proper combustion, and the amount of heat released is the smallest. In this case, very large spreads in the path of heat release were obtained, depending on the amount of energy delivered to the PC. The combustion of methane (Figure 12c) also results in a maximum of heat released at qo → min, i.e., 10 J of energy delivered to the PC. However, the amount of heat released is at the same time the smallest (compared to other values λ).
