**3. Results**

### *3.1. Range of the Implemented Research*

Pressure measurements in the fired cylinder and additional expansion cylinder were carried out for the selected points of the engine operating map. The maximum boost pressure (pbst) was limited in the study to 0.9 bar. Figure 8 shows the operating map of the engine with the additional expansion of exhaust gas, with the highlighted points in which the in-cylinder pressure waveforms were recorded.

**Figure 8.** Measuring points for indicating measurements of the engine; Brake Torque (T).

As shown in Figure 8, the in-cylinder pressure of the tested engine were measured at various values of the engine brake torque in the rotational speed (n) range from 2000 to 3600 rpm. During these tests, the engine throttle was fully open (WOT), and the wastegate valve of the exhaust gases remained closed. In addition, measurements of pressure in the cylinders at partial load for rotational speeds of 2000, 2200, and 3000 rpm were carried out. For the rotational speed of 3000 rpm of the engine, a minimum brake specific fuel consumption was achieved. During the course of the tests, a stoichiometric composition of the air-fuel mixture was maintained—relative air-to-fuel ratio was equal to 1 (rel. AFR). The engine was fueled with gasoline during the tests.

### *3.2. Measurements of the In-Cylinder Pressure of the Tested Engine*

After testing the engine the results saved to the files were calculated in a popular spreadsheet software, but using a specialized template in order to shorten the calculation time. This allowed us to obtain the average waveforms of pressure in the fired cylinder and in the cylinders of additional expansion as a function of the crank angle (CA). Furthermore, after introducing the geometrical data of the engine into the calculation program, p-V diagrams were developed for the fired cylinders, as well as for the cylinders of the additional expansion. Development of the p-V indicator diagrams allowed the calculation of the indicated mean effective pressure and the indicated power for fired cylinders and additional expansion cylinders for each of the measurement points.

The following are examples of the work carried out on the recorded waveforms of in-cylinder pressure for the fired and additional expansion cylinders.

In Figure 9 the p-CA diagram of the engine with the additional-expansion registered for a full load 123 Nm at 3000 rpm rotational speed is presented. A turbocharger wastegate valve remained closed, and the boost pressure was 0.5 bar. The exhaust gas temperature measured at the outlet of the turbine had a value of 437 ◦C.

**Figure 9.** Chart in a p-CA for the fired cylinder and additional expansion cylinder recorded at 3000 rpm and a torque equal to 123 Nm.

The peak pressure in the fired cylinder reached 7 MPa for the case above, for the position of the crankshaft at 380 CAD ATDC (Crank Angle Degrees) (After Top Dead Center). The difference in pressure peaks recorded in the cylinders of additional expansion in the case of filling by exhaust cylinder No. 3 from fired cylinder No. 4 and No. 1 (through cylinder No. 2 and the passage) was approximately 0.06 MPa.

The aforementioned difference in the value of the maximum pressure in the additional expansion cylinder for the crank angle of approximately 180 CAD and approximately 540 CAD are caused by throttling the flow in the connecting passage between the expansion cylinders 2 and 3. The pressure

value obtained for 540 CAD occurs when the exhaust goes to the additional expansion cylinder No. 3 from the adjacent fired cylinder No. 4, in which the in-cylinder pressure is also measured. The pressure registered at 180 CAD resulted from filling the assembly of the cylinders of additional expansion by exhaust gases from cylinder No. 1. In this case, the exhaust gases were first delivered into cylinder 2, then through the connecting channel in the cylinder head to cylinder No. 3, where the measurement was carried out. During the calculation of the indicated work of the additional expansion cylinders, its value was determined in consideration of the fact that in the cylinders of additional expansion, the pressure is variable in a cyclic manner as described above.

In Figure 10, the in-cylinder pressure curves are shown as a function of cylinder volume (Vc) for the fired and additional expansion cylinders registered for a full load of 123 Nm at 3000 rpm rotational speed.

**Figure 10.** p-V diagrams for the fired cylinder and additional expansion cylinder recorded at 3000 rpm and a torque equal to 123 Nm.

The assembly of additional expansion cylinders of the engine works in a two-stroke mode, therefore the in-cylinder pressure waveform shown in the above chart includes two complete processes of additional expansion and the exhaust process, as shown in the p-CA diagram. The values of the indicated mean effective pressure in the fired cylinder (IMEPfrd) and in the additional expansion cylinders (IMEPadd) were calculated by numerical integration of relevant areas of the p-V chart. These values were: IMEPfrd was equal to 1.72 MPa, and IMEPadd was equal to 0.08 MPa. The indicated power in the working cylinders (Pi\_frd) was then calculated using Formula (1):

$$P\_{\rm i\\_frd} = \frac{2 \cdot \text{IMEP}\_{\rm frd} \cdot \text{V}\_{\rm frd} \cdot \text{n}}{120000}, \text{ kW} \tag{1}$$

The formula presented above takes into account the used units, including the speed and four-stroke nature of the work of the two working cylinders. Similarly, the formula for calculating the indicated power of the cylinder of additional expansion (Pi\_add) is presented as Formula (2):

$$\text{P}\_{\text{i\\_add}} = \frac{\text{IMEP}\_{\text{add}} \cdot \text{V}\_{\text{add}} \cdot \text{n}}{60000}, \text{ kW} \tag{2}$$

This formula takes into account that both cylinders of additional expansion work in a two-stroke mode as a single working volume. The calculated value of the indicated power of the fired cylinders at this operating point is 42.77 kW, and the value of the indicated power in the cylinders of additional expansion is approximately 3.98 kW, which is more than 9% of the Pi\_frd value.

A similar analysis of the waveforms of in-cylinder pressure for the fired and additional expansion cylinders was carried out for the results obtained in the other measuring points. This made it possible to determine the relationship between IMEPfrd and IMEPadd. This is shown graphically in the form of a plot in Figure 11.

**Figure 11.** The Indicated Mean Effective Pressure in the cylinders of additional expansion as a function of the Indicated Mean Effective Pressure in the fired cylinders.

The course has been approximated by a straight line, and the equation is presented in the chart. The achieved value for the IMEPadd/IMEPfrd ratio is greater when the IMEPfrd is higher. The highest value (the last point on the top of the graph) is 0.063. With regards to the relations of the indicated power, the mentioned ratio will be about 12.6%, as the additional expansion cylinders operate in a two-stroke mode. This is an important energy recovery ratio in the additional expansion process of the working medium.

In order to determine the load of the five-stroke engine from which the cylinders of additional expansion start to give power to the output, the dependence of the Brake Mean Effective Pressure (BMEP) as a function of the Indicated Mean Effective Pressure of the additional expansion cylinders (IMEPadd) was defined. Figure 12 shows a graph of this function. Similarly, as in the previous case, the obtained waveform is approximated by a straight line whose equation is given in the chart.

**Figure 12.** The Brake Mean Effective Pressure of the five-stroke engine as a function of the Indicated Mean Effective Pressure of the additional expansion cylinders.

BMEP values were determined from the value of the torque, taking into account the displacement volume of the fired cylinders (2 × Vfrd = 992 cm3). The volume of the cylinders of additional expansion cannot be taken into account while calculating BMEP, because there is no combustion process in these cylinders. The determination of this function was aimed at finding a load limit before which the additional expansion cylinders take power from the engine instead of delivering power to the engine. The value of the intercept of the function from Figure 12 is equal to about 0.6. This means that if the BMEP is lower than 0.6 MPa, then additional expansion cylinders require power from the engine. Above this value, the additional expansion process becomes positive for the engine work. Taking into account the volume of the cylinder, the engine, and the mechanical efficiency, this means that the assembly of the cylinders of additional expansion transmit additional power to the engine output from the time when the measured torque exceeds 60 Nm. This fact means that the five-stroke engine would be most suitable for applications where it would work mainly in the field of medium and high loads.

### *3.3. Brake Specific Fuel Consumption and Effective Power*

The results of this research also allow us to determine the effective power (Pe) and Brake Specific Fuel Consumption (BSFC) of the engine. In Figure 13, the curves of BSFC and effective power as a function of engine rotational speed at wide open throttle (WOT) are presented. A stoichiometric air-fuel mixture composition was maintained.

**Figure 13.** Effective power and BSFC as a function of engine rotational speed at WOT and with rel. AFR = 1.0; Brake Specific Fuel Consumption (BSFC); Wide Open Throttle (WOT); Relative Air-to-Fuel Ratio (rel. AFR).

The minimum value of the specific fuel consumption was 240 g/kW·h. This value was obtained at a speed of 3000 rpm and a boost pressure pbst of 0.5 bar. For higher values of the rotational speed, especially for 3600 rpm, the obtained value of the brake specific fuel consumption tended to increase, which resulted in a discontinuation of the tests for higher values of the rotational speed.

### *3.4. Mechanical Efficiency of the Tested Engine*

For conventional internal combustion engines, calculations of the mechanical efficiency (ηm\_cnv) based on the known indicated mean effective pressure do not pose any problems. This is described by Formula (3):

$$
\eta\_{\rm Im\\_env} = \frac{\rm BMEP}{\rm MEP} = \frac{\rm P\_e}{\rm P\_i} \tag{3}
$$

Brake Mean Effective Pressure at a certain rotational speed is determined by measuring the torque of the engine relative to a displacement volume of the engine and to the engine type, i.e., whether it is a two-stroke or four-stroke engine. Indicated Mean Effective Pressure is determined based on the measured in-cylinder pressure as a function of CA. For a multi-cylinder engine, the pressure is typically measured for one cylinder and it is assumed that all the other cylinders operate in the same

way. For obvious reasons, for the classic engine, the BMEP/IMPEP ratio is exactly the same as the ratio of effective power (Pe) to the indicated power of the engine (Pi).

In the case of an engine with the additional expansion of exhaust gas in a separate cylinder, the situation becomes more complicated. Besides the cylinders, where a conventional four-stroke working cycle is carried out, the engine has a cylinder for the additional expansion of the exhaust, which should deliver work to the output of the engine. This cylinder is an integral part of the engine so its effect cannot be ignored in the analysis of the mechanical efficiency of the engine, because the calculated value of the mechanical efficiency would be artificially high and, in particular, the engine operating conditions could prove to be even higher than 1. Under the conditions of a sufficiently high load of the engine, where the cylinder of additional expansion provides additional power to the output, its indicated mean effective pressure is higher than zero. In the case of low engine load when the pressure of the exhaust gas going into the cylinder is low, the additional expansion cylinder requires additional propulsion from the engine, and the value of the indicated mean effective pressure becomes negative; of course, the same thing happens to the value of power indicated from the cylinder. Considering the case above, we conclude that the effect of the operation of the additional expansion cylinder has to be included in a certain way when determining the mechanical efficiency of the five-stroke engine. The values of IMEP for the fired and additional expansion cylinders are not additive. This happens because in a general case they relate the different displacement volumes, and it should be noted that the fired cylinders operate in four-stroke mode, while the cylinders of additional expansion operate in two-stroke mode. Avoiding this problem is possible by calculating the mechanical efficiency from the calculated values of the effective power and the indicated power of the engine. To determine the mechanical efficiency of the five-stroke engine, the author of this paper proposes a summation of the indicated power for the fired cylinders Pi\_frd and indicated power of the cylinders of additional expansion Pi\_add when the indicated power Pi\_add is greater than zero—Formula (4). In contrast, if the indicated power of the cylinder of additional expansion Pi\_add is zero or less than zero, it acts as a load (like the oil pump, water pump, and alternator), and in this situation the indicated power of the cylinder of additional expansion Pi\_add should not be taken into account while calculating the mechanical efficiency of the engine with an additional expansion of exhaust gas in a separate cylinder (ηm)—Formula (5).

$$\text{for } \mathcal{P}\_{\text{i\\_add}} > 0, \quad \eta\_{\text{m}} = \frac{\mathcal{P}\_{\text{e}}}{\mathcal{P}\_{\text{i\\_frd}} + \mathcal{P}\_{\text{i\\_add}}},\tag{4}$$

$$\text{for } \mathcal{P}\_{\text{i\\_add}} \le \text{ 0}, \quad \eta\_{\text{lm}} = \frac{\mathcal{P}\_{\text{e}}}{\mathcal{P}\_{\text{i\\_frd}}},\tag{5}$$

Figure 14 shows curves of the mechanical efficiency of the engine with the additional expansion of the exhaust gases for various values of rotational speed and its dependence on the brake torque.

**Figure 14.** Mechanical efficiency as a function of the load for three different values of the rotational speed.

An analysis of the diagram indicates that the obtained value of the mechanical efficiency of the engine increases with engine load, reaching a value slightly larger than 0.8. This took place at the rotational speed of 3000 rpm, when the boost pressure pbst was 0.5 bar. It is also seen that in the analyzed range of the rotational speed of the engine, the mechanical efficiency does not depend significantly on the rotational speed.

Figure 15 presents charts of the effective efficiency and boost pressure of the tested engine versus the rotational speed at full throttle (WOT) and with a stoichiometric air-fuel mixture composition.

**Figure 15.** Mechanical efficiency and boost pressure as a function of the rotational speed at WOT.

The maximum value of the mechanical efficiency of the tested engine was 85.5% and was recorded at a rotational speed of 3400 rpm. Above this value, the boost pressure increased to 0.9 bar, and the mechanical efficiency began to decrease. The effect of a significant increase in BSFC was also demonstrated (shown in Figure 13). The resulting course of the boost pressure indicates that the used turbocharger starts to work effectively with the tested engine at rotational speeds of 3000–3200 rpm.
