# Limiting Conditions for Droplet Fragmentation of Stabilized Suspension Fuels
## 4 Results and Discussion
### Generalization of Experimental Data  
According to the analysis presented in Figures 4-8, droplets of stabilized fuels do not break up unless they contain a flammable liquid. Figure 9 presents the generalized experimental data on the maximum values of \((D/D_{0})^{2}\) (a) and \(\tau/(D_{0})^{2}\) (b) against temperature for different puffing fuel compositions described in this paper together with compositions with a small share of solid components (slurries) and without them (typical two-liquid droplets), as presented in earlier works [52; 53; 54; 55; 56]. The curves show clearly that the value of \((D/D_{0})^{2}{}_{\rm max}\) can reach 3.5 for nonstabilized fuels and does not exceed 1.75 for stabilized ones. The higher values of \((D/D_{0})^{2}{}_{\rm max}\) at low temperatures are also an interesting and important result. In the case of fuels with added solid particles, this is caused by the solid crust formed at high temperatures and preventing the droplets from enlarging before breakup. As for fuels without solid particles, this happens because the total breakup conditions are achieved at smaller critical radii of bubbles. The experimental findings have shown that stabilizing additives have a counter-vailing effect on droplet heating and breakup behavior. In such cases, it is important to determine the droplet breakup efficiency factor reflecting the heating delay, the required ambient gas temperature, the average size and number of secondary fragments, and the increase in the liquid surface area. The corresponding relative efficiency factor of secondary atomization in the microexplosive breakup regime have the maximum values at the minimum breakup delay times, sufficient ambient gas temperature, and  
Figure 9: Generalized experimental data on maximum values of \((D/D_{0})^{2}\) (a) and \(\tau/(D_{0})^{2}\) (b) vs. gas temperature for different fuel compositions in the course of breakup: 1—C50W49 DI (current study); 2—C50W49 RI (current study); 3—diesel [52]; 4—DCe-0.05 [52]; 5—DCe-0.25 [52]; 6—P25 BD75 [53]; 7—P50 BD50 [53]; 8—P75 BD25 [53]; 9—HE30 [54]; 10—E10 [55]; 11—E30 [55]; 12—E50 [55]; 13—water/kerosene [56]; 14—water/diesel [56]; 15—water/rapeseed oil [56]. maximum number of secondary fragments with their minimum size. Using the multi-criteria comparative analysis [15; 57], we generalized the experimental data obtained for the stabilized blends of C50W49D1 and C50W49R1, and the two-liquid droplets of water/kerosene, water/diesel, and water/rapesed oil [56] according to the following formula: \(P=\overline{T_{g}^{min}}\times\overline{\left(D/D_{0}\right)_{max}^{2}}\times \overline{\tau}\), where \(\overline{T_{g}^{min}}=\frac{T_{g}^{min}}{480}\) is the relative gas temperature limit of droplet breakup, \(\overline{\left(D/D_{0}\right)_{max}^{2}}=\frac{\left(D/D_{0}\right)_{max}^{2} }{3.36111}\) is the relative maximum normalized droplet diameter, and \(\overline{\tau}=\frac{1.18356}{\tau}\) is the relative droplet breakup time. Constant values in the equation for \(P\) refer to the case of two-liquid droplets without coal particles [38]. It was established (Figure 10) that the maximum value of the droplet microexplosion efficiency factor was 0.98 and it was typical of the compositions containing water/kerosene. These values correlate with the earlier studied emulsified compositions and two-liquid droplets [42]. The efficiency factor was 0.95-1 for such compositions. The values of this efficiency factor may reach 1 given the required ambient gas temperature, heat flux, initial droplet size, and component composition. Stabilization of fuel slurries is one of the key factors for industrial use. The fuel blends used in the experiments are notable for rather high sedimentation stability providing the required slurry storage time (about four days of fuel reserves for typical power-generating facilities: boiler units and thermal power stations).