## 3 CFD Simulation Results
### In-Cylinder Pressure and Rate of Heat Release (RoHR)  
The mean in-cylinder pressure and RoHR diagrams for the three various piston bowl types are presented in Figure 9. The results pointed out that, even though the in-cylinder peak pressure insignificantly changed when changing the type of piston bowl, it slightly decreased in the order of the U-type, \(\omega\)-type, and re-entrant type of the engine piston bowls. The decrease in peak pressure in the engine cylinder has the same cause as the decrease in the peak temperature in the cylinder. The more uniform distribution of temperature (thermal energy) within the engine combustion chamber decreased the peak combustion pressure of the engine cylinder. However, it should be noted that a decrease in in-cylinder peak pressure does not imply that engine power will also be reduced. This is because of the following reason:  
The effective work generated by the cylinder in a working cycle (\(W_{c}\)) of the engine is calculated by Formula (2):  
\[W_{c}=\int_{v_{c}}^{v_{a}}Pdv-\int_{v_{a}}^{v_{c}}Pdv\;(J) \tag{2}\]  
where \(P\;(N/m^{2})\) and \(v\;(m^{3})\) are the in-cylinder pressure and the cylinder volume of the engine, respectively. \(v_{c}\) and \(v_{a}\) are the clearance volume and overall volume of the cylinder, respectively. \(v_{a}\) is a sum of \(v_{c}\) and the swept volume \(v_{s}\). In Formula (2), \(\int_{v_{c}}^{v_{a}}Pdv\) is the work carried out during the combustion and expansion strokes of the engine when the piston moves downward from the TDC to the bottom dead center (BDC). Meanwhile, \(\int_{v_{a}}^{v_{c}}Pdv\) is the work consumed to force the piston to move upward from the BDC to the TDC (including all the compression stroke and one part of the combustion stroke when the piston has not passed TDC). The consumed work in a diesel cycle is thus not only the work for the compression process, but also the work consumed to counteract the resistance of the expansion of the combustion gas inside the engine cylinder when the combustion occurred, but the piston has not passed TDC yet. Generally, higher peak pressures could increase the work of the combustion and expansion processes. However, the cycle work of the cylinder may not change or even decrease, even if the peak pressure in one case is higher than the pressure in another case if the work consumed to force the piston to move up from BDC to TDC in this is also higher. A comparison of the cylinder power and indicated specific fuel oil consumption (ISFOC) when using the three types of piston bowls is shown in Section 3.4. The RoHR history in Figure 9 clearly presents the four stages of combustion of the engine. This is a DI diesel engine. In all three cases, the combustion of the engine undertook four stages, including the (1) 1 st stage-ignition delay stage (ID); (2) 2 nd stage-premixed  
Figure 9: In-cylinder mean pressure diagrams. combustion stage; (3) 3 rd stage-diffusion combustion stage; and (4) 4 th stage-late stage of combustion. The 1 st stage began when the fuel was injected directly into the engine cylinder (point A) and finished when the fuel self-ignited (point B). In this stage, the RoHR was zero due to the fuel being under the heat-receiving process for heating and evaporation to prepare for self-ignition. The 2 nd stage began immediately after the self-ignition of the fuel (point B) until the pre-mixed mixture between the fuel injected into the cylinder during the ID time with the charge air finished (point C). In this stage, thermal energy (heat) from the premixed combustion was rapidly released in a very short time leading to a very high RoHR, as shown in Figure 9. At the moment when the combustion of the mixture ended (point C), diffusion combustion began. This 3 rd stage took place until the end of fuel injection (point D). During this stage, the injected fuel was burnt immediately after being injected into a very high-temperature environment inside the engine cylinder caused by the premixed combustion.