## 3 Research Results
### Simulation of the Fuel Mass Stream through the Spray Holes
Relative pressure losses were calculated from the relationship:  
\[\Delta\overline{\omega}=\frac{\Delta\omega}{\Delta p} \tag{16}\]  
where \(\Delta p=p_{i}-p_{c}\)--pressure difference in the nozzle sack and the combustion chamber. The fuel mass flux \(q_{m}\), when flowing through the number of \(i\) spray holes can be determined by the following relationship [9]:  
\[\mu_{r}=k_{1}\,k_{2}\,k_{3}\mu_{o} \tag{6}\]0The value of these features is determined at the production stage. The final formula for the fuel mass flux was calculated by the following dependence:  
\[\mu_{r}=k_{1}\,k_{2}\,k_{3}\mu_{o} \tag{6}\]1  
Experimental measurements of the fuel mass flux and determination of flow characteristics for new and used injector nozzles were carried out on a flow test stand using calibration oil for many years [9; 10]. These measurements made it possible to experimentally determine the flow coefficient \(\mu_{r}\) and the spray holes' average area. The pressure courses in the combustion chamber were calculated and measured using a resistance sensor with digital processing. The mass of the injected fuel as a result of the pressure loss is lower:  
\[\mu_{r}=k_{1}\,k_{2}\,k_{3}\mu_{o} \tag{6}\]2  
Thus, the fuel mass flux, which should be maximized due to flow losses, depends on the following geometrical values and results from the type of fuel and the design of the internal combustion engine, resulting in the parameters of the working medium:  
\[\mu_{r}=k_{1}\,k_{2}\,k_{3}\mu_{o} \tag{6}\]3  
The latter relationship will be used to optimize for surface roughness losses \(\Delta\), the radius of the spray orifices on the inlet side \(r_{k}\), the influence of temperature \(t\) and pressure \(\Delta p\) and pressure losses \(\Delta\omega\). This means that when \(\Delta\overline{\omega}=1\), then there are no friction losses, and when \(\Delta\overline{\omega}=0\), there are such large friction losses that the mass flux of dosed fuel is equal to 0. In the simulation, the change in \(\Delta\overline{\omega}\) was assumed in the range from 0.3 to 1.0, in steps of 0.1. Various functions can approximate such a relationship. From the point of view of friction losses, the value of pressure losses \(\Delta\omega\) is interesting, because the quantity is irretrievably lost, depending on the characteristics of the technical state determined at the production stage and changing during operation:  
\[\mu_{r}=k_{1}\,k_{2}\,k_{3}\mu_{o} \tag{6}\]4  
Based on the presented dependencies, the influence of selected design features on the pressure loss at the flow through the nozzle holes was presented. Figure 4a shows the effect of the number of flows through the nozzle holes on the pressure curve in the nozzle space. The diagram 4a shows that the influence of the spray hole flow coefficient \(\mu_{r}\) on the pressure course in the nozzle space is significant. Therefore, there is a need to build a simulation model due to the optimization goal. \[\mu_{r}=k_{1}\,k_{2}\,k_{3}\mu_{o} \tag{6}\]5 An example of the influence of surface roughness (**a**) and the length of the spray hole (**b**) on pressure losses \(\Delta\omega\). On the other hand, Figure 4b shows the influence of the relative pressure drop on the mass fluid of the dosage fuel. The figure also shows a significant decrease in the mass fluid of the dosed fuel with an increase in the relative pressure loss caused by friction in the geometric profiles of the spray holes. Figure 4b shows the influence of relative pressure losses through the spray holes on the fuel mass fluid. Experimental measurements were also made in the injection subsystem outside the engine and on actual selected internal combustion engines in the Marine Power Plants Laboratory of the Maritime University of Szczecin and on sea-going ships.