## 3 Research Results
### Optimization of the Parameters of Multi-Hole Nozzles  
The research subject is multi-hole nozzles, both conventional and with electronically controlled injection, and the aim of the research is the impact of changes in the design of nozzles on fuel flow losses. The research object is a four-stroke medium-speed marine engine. The dependencies of the pressure course in the atomizer well and the fuel stream flowing out through the spraying hole for a given fuel setting can be approximated by various functions. Based on the formulas (8), (14) and (15), the pressure loss \(\Delta\omega\) can be represented as a function of six variables:  
Figure 5: Comparison of the pressure course of the calculated \(p_{ic}\) in the injector nozzle space and measured before the injector valve \(p_{\text{im}}\).  
\[\Delta\omega=f(d_{rt},D_{t},\Delta,l_{rt},p_{i},p_{c})=\frac{\sqrt{1.5\big{(}D_{t}^{4 }-d_{rt}^{4}\big{)}+\frac{\big{(}D_{t}^{4}-d_{rt}^{4}\big{)}l_{rt}}{d_{rt}\big{(} 1.14+2\log\big{(}\frac{d_{t}}{\Delta}\big{)}\big{)}^{2}}}-d_{rt}^{2}}{\sqrt{1.5D_ {t}^{3}(D_{t}-d_{rt})+\frac{D_{t}^{3}\big{(}D_{t}-d_{rt}\big{)}l_{rt}}{d_{rt} \big{(}1.14+2\log\big{(}\frac{d_{t}}{\Delta}\big{)}\big{)}^{2}}+d_{rt}^{2}}}\.\ (p_{i}-p_{c}) \tag{25}\]  
four of which relate to the geometric parameters of the atomizer: hole diameter \(d_{rt}\), the diameter of the inflow channel to the hole \(D_{t}\), surface roughness \(\Delta\) and channel length \(l_{rt}\). These four variables were analyzed in terms of minimizing pressure losses \(\Delta\omega\). As the form of the function \(f\) is too complex, the analytical solution turned out to be impossible to implement. Therefore, in order to optimize the function \(f\), the numerical conjugate gradient method was used. The following restrictions were imposed on the values of the variables: 0.00020 m \(<d_{rt}<\) 0.00032 m; 0.0004 m \(<D_{t}<\) 0.0010 m; 0.001 m \(<l<\) 0.002 m; 2.5 \(\times\) 10\({}^{-8}\) \(<\)\(\Delta\) \(<\) 2.8 \(\times\) 10\({}^{-7}\) m.  
The pressure increase was assumed at the average level: \(\Delta p\) = 2 \(\times\) 108 Pa.  
For the assumed limits of variability, the function \(f\) reached the minimum for the extreme values of the variability ranges of the atomizer geometric parameters: \(\Delta\omega_{min}\) = 5.22858 \(\times\) 10\({}^{7}\) Pa for \(d_{rt}\) = 0.00032 m, \(D_{t}\) = 0.0004 m, \(l_{rt}\) = 0.001 m and \(\Delta\) = 2.5 \(\times\) 10\({}^{-8}\) m.  
The course of the function variability depends on the individual variables, with the values of the remaining variables fixed, witch makes it possible to determine the influence of these variables on the rate of changes in the value of the function \(\Delta\omega\).  
In the case of \(\Delta\), the change in the value of pressure loss \(\Delta\omega\) is the smallest and amounts to 1.03312 \(\times\) 10\({}^{6}\) Pa, which is about 2% of the minimum value of \(\Delta\omega\) (Figure 6).  
In the case of \(l_{rt}\), the change in the value of pressure loss \(\Delta\omega\) amounts to 1.55469 \(\times\) 10\({}^{6}\) Pa, which is about 3% of the minimum value of \(\Delta\omega\) (Figure 7).  
In the case of \(D_{t}\), the change in the value of pressure loss \(\Delta\omega\) is the biggest and amounts to 1.48785 \(\times\) 10\({}^{8}\) Pa, which is about 285% of the minimum value of \(\Delta\omega\) (Figure 8).  
In the case of \(d_{rt}\), the change in the value of pressure loss \(\Delta\omega\) amounts to -1.17087 \(\times\) 10\({}^{8}\) Pa, which is about 240% of the minimum value of \(\Delta\omega\) (Figure 9).  
In the case of the variables \(\Delta\) and \(l_{rt}\), \(D_{t}\), as the variable grows, the values of \(\Delta\omega\) also increase. Only for hole diameter \(d_{rt}\), the values of \(\Delta\omega\) decrease. The variables \(D_{t}\) and \(d_{rt}\) have the greatest influence on the change of the pressure loss value.  
Figure 6: The course of absolute pressure loss \(\Delta\omega\), as a function of surface roughness \(\Delta\).