## 3 Results and Discussion
### Fuel Properties
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **FADR** & **HFO** \\ \hline Density (60 \({}^{\circ}\)C), kg/m\({}^{3}\) & 882 & 864 \\ Ignition temperature (open vessel), \({}^{\circ}\)C & 227 & 250 \\ LHV, kJ/kg & 36,619 & 42,251 \\ HHV, kJ/kg & 39,914 & 45,222 \\ Energy density, E\({}_{\text{d, LHV}}\), GJ/m\({}^{3}\) (from LHV) & 32.298 & 36.505 \\ Energy density, E\({}_{\text{d, HHV}}\) GJ/m\({}^{3}\) (from HHV) & 35.20 & 39.07 \\ Ash content, w.\% & 0.28 & 0.36 \\ C, w.\% & 76.6 & 86.1 \\ H, w.\% & 12.45 & 13.61 \\ N, w.\% & 0.85 & 0.56 \\ S, w.\% & 0.16 & 0.62 \\ Cl, w.\% & \textless{0.005\%} & \textless{0.005\%} \\ Distillation beginning, \({}^{\circ}\)C & 98 & 168 \\ to 235 \({}^{\circ}\)C & 1.9 & 2 \\
235–270 \({}^{\circ}\)C & 1 & 1.8 \\
270–300 \({}^{\circ}\)C & 3 & 2.4 \\
300–330 \({}^{\circ}\)C & 52.5 & 5.5 \\
330–360 \({}^{\circ}\)C & 35.9 \\ Distillation residue, \% & 31.9 & 47.5 \\ Distillation loses, \% & 9.7 & 4.9 \\ Viscosity, Pa-s, at temperature & & \\
30 \({}^{\circ}\)C & 0.1954 & \\
40 \({}^{\circ}\)C & 0.0541 & \\
50 \({}^{\circ}\)C & 0.136 \\
60 \({}^{\circ}\)C & 0.0255 & 0.057 \\
70 \({}^{\circ}\)C & 0.034 \\
80 \({}^{\circ}\)C & 0.0142 & 0.0244 \\
90 \({}^{\circ}\)C & 0.0189 \\
100 \({}^{\circ}\)C & 0.0152 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic properties of the fatty acids distillation residues, FADR, and heavy fuel oil, HFO. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pressure** & **Flow Rate** & **Expected Input Power, kW** & **Visual Evaluation of Atomization** \\ \hline
**kPa** & **kg/h** & **kW** & \\ \hline  & & Nozzle 1 mm & \\
56 & 1.1 & 11 & Droplets \\
67 & 1.3 & 13 & Compact flow \\
82 & 4.9 & 50 & Compact flow \\
112 & 11 & 112 & Compact flow \\
150 & 17 & 173 & Compact flow \\
165 & 19.5 & 198 & Compact flow \\
168 & 20 & 203 & Compact flow \\
195 & off the scale & & Compact flow \\ \hline  & & Nozzle 0.5 mm & \\
385 & 7.4 & 75 & Compact flow \\
429 & 8.2 & 83 & Compact flow \\
470 & 9.3 & 95 & Compact flow \\
502 & 9.9 & 101 & Compact flow with spontaneous droplets \\
512 & 10.2 & 104 & Fine droplets \\
528 & 10.3 & 105 & Ultra-fine droplets and fog-like flow \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The flow characteristic of FADR by nozzle, temperature of 70 \({}^{\circ}\)C.  
The required viscosity in terms of temperature is directly related to the energy demand on the fuel transportation and the efficient atomization behind the nozzle spray. The specific heat capacity of animal fat is very close to the specific heat capacity of diesel fuel [37]. At a temperature of 293K and pressure of 0.1 MPa, the heat capacity of diesel is 1.9 kJ/kgK [38; 39]. The average specific heat of crude oil is in a similar range of 2.2 kJ/kgK [40]. The properties of micro wax were taken from [22; 41; 42] (heat capacity [41; 42] \(c_{p}\) at a level of 2.5 kJ/kgK). The specific heat of HFO was assumed on a similar level. The energy demand on fuel transportation has two specific parts: (a) the energy necessary to heat the fuel up to a certain level of enough viscosity; and (b) the energy related to the pressurization of the fuel before its introduction to the nozzle. It is assumed that the energy demand refers to the mass of fuel (i.e., kJ/kg); thus, the energy for fuel heating and fuel pressurization were calculated according to Equations (14) and (15), respectively:  
\[E_{heat}=c_{p}\left(T_{fuel}-T_{room}\right),\ \mathrm{kJ/kg} \tag{14}\]  
\[E_{pressur}=\frac{p}{\rho},\ \mathrm{kJ/kg} \tag{15}\]  
The sum of \(E_{heat}\) and \(E_{pressur}\) is defined as \(E_{total}\). When nominal fuel feed \(\dot{m}_{nominal}\), kg/s at 100 kW\({}_{\mathrm{th}}\), power is calculated from Equation (16)  
\[\dot{m}_{100\mathrm{kW}}=\frac{100}{LHV} \tag{16}\]  
Then power loss, \(P_{loss}\), kW is (Equation (17))  
\[P_{loss}=\frac{\dot{m}_{100\mathrm{kW}}}{\left(E_{heat}+E_{pressur}\right)} \tag{17}\]  
The nominal feed of analyzed fuel at 100 kW\({}_{\mathrm{th}}\) power was in the range of 8.25-9.83 kg/h.