# Heat Release Rates of Straight Soybean and Diesel Oil Blends in a Compression Ignition Engine
## 3 Results and Discussion
### Atomization Analysis  
The jet pattern is a significant factor in the combustion process. It is influenced by the injection parameters and the physical fuel properties. The primary disintegration or break-up regime of the fuel jet in diesel engines must be the atomization regime. The Ohnesorge diagram permits the identification of the break-up regime, relating the Ohnesorge number with the Reynolds number of the spray. The dimensionless numbers required to build the Ohnesorge diagram are  
\[Re_{sp}=\frac{\rho_{f}u_{sp}d_{o}}{\mu_{f}} \tag{11}\]  
\[We_{sp}=\frac{\rho_{f}u_{sp}^{2}d_{o}}{\sigma_{f}} \tag{12}\]  
\[Oh=\frac{\sqrt{We_{sp}}}{Re_{sp}} \tag{13}\]  
where \(Re_{sp}\), \(We_{sp}\), and \(Oh\) are Reynolds, Weber, and Ohnesorge dimensionless numbers of the spray, respectively; \(u_{sp}\) is the spray velocity; \(d_{o}\) is the injector nozzle hole diameter; and \(\rho_{f}\), \(\mu_{f}\), and \(\sigma_{f}\) are the density, dynamic viscosity, and surface tension of the fuel, respectively. The \begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{**Fuel**} & \multicolumn{2}{c}{**Mass Fraction Burned (mg Burned/mg Injected)**} \\ \cline{2-3}  & **1800 rpm** & **2100 rpm** \\ \hline
100D(25) & 0.650 & 0.657 \\
505/50D(25) & 0.675 & 0.683 \\
505/50D(85) & 0.687 & 0.705 \\
80S/20D(85) & 0.689 & 0.746 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mass fraction burned at 444\({}^{\circ}\) CA for all fuels at the two speeds tested. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Fuel**} & \multicolumn{2}{c}{**Stoichiometric**} & \multicolumn{2}{c}{**Global Equivalence Ratio**} \\ \cline{2-3}  & **Air/Fuel Ratio (AF)s** & \multicolumn{2}{c}{\(\phi_{gl}\)} \\ \cline{2-3}  & \multicolumn{2}{c}{**1800 rpm**} & **2100 rpm** \\ \hline
100D(25) & 14.92 & 0.83 & 0.81 \\
505/50D(25) & 14.23 & 0.77 & 0.76 \\
505/50D(85) & 14.23 & 0.74 & 0.74 \\
80S/20D(85) & 12.82 & 0.70 & 0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Stoichiometric air/fuel ratio and global equivalence ratio for all fuels at the two speeds tested. injector nozzle hole diameter was 0.3 mm, and the fuel properties were calculated at respective injection temperatures using the correlations previously reported in [PERSON] et al. [37]. In order to help understand the combustion process, the break-up regime (Ohnesorge diagram), _SMD_ (Sauter mean diameter), droplet Reynold number, and oxygen content were estimated for all fuels tested at 1800 rpm. The results are shown in Figure 5 and Table 9. The _SMD_ was calculated using the correlation proposed by [PERSON] and [PERSON] [46]. Thus,  
\[\frac{SMD}{d_{o}}=0.38\text{Re}_{sp}^{0.25}W\text{e}_{sp}^{-0.32}\left(\frac{H _{f}}{\mu_{g}}\right)^{0.37}\left(\frac{\rho_{f}}{\rho_{g}}\right)^{-0.47} \tag{14}\]  
where \(\mu_{g}\) and \(\rho_{g}\) are the dynamic viscosity and density of the gas, respectively. The gas dynamic viscosity was calculated as \(\mu_{g}=4.57\times 10^{-7}\)[645], according to [PERSON] [47]. The droplet Reynold number was calculated as follows:  
\[\text{Re}_{D}=\frac{\rho_{g}\left(u_{sp}-S_{p}\right)SMD}{\mu_{g}} \tag{15}\]  
where \(S_{p}\) is the piston velocity (gas velocity). According to Ohnesorge diagram, the blend 50S/50D(25) does not present the atomization regime required for diesel engine combustion, and the break-up regime of the blend 80S/20D(85) is between second-wind-induced and atomization regimes. In the case of the blend 50S/50D(85), the heating favored the break-up, reaching the atomization regime. Concerning the results shown in Table 9, the blend 50S/50D(25) presents the highest _SMD_, being 15.5% higher than the _SMD_ of 100D(25). The highest droplet Reynold number  
Figure 5: Ohnesorge diagram for all fuels tested at 1800 rpm and full load condition.