## 2 Methodology
### Experimental Setup and Measurements
#### 2.2.4 Data Analysis  
For each set of experimental conditions, the combustion pressure and heat release rate were averaged over 200 cycles of the engine running through the combustion analyzer. The heat release rate was calculated using the following formula [19; 20; 21; 38]:  
\[\frac{\mathrm{dQ}}{\mathrm{d\theta}}=\frac{\mathrm{k}}{\mathrm{k-1}}\mathrm{ p}\frac{\mathrm{dV}}{\mathrm{d\theta}}+\frac{1}{\mathrm{k-1}}\mathrm{V}\frac{ \mathrm{dP}}{\mathrm{d\theta}} \tag{1}\]  
Here, k is the specific heat ratio, P is the combustion pressure, and \(\theta\) is the crank angle. The piston cylinder volume (V) can be calculated as a function of crank angle from the compression ratio, bore, stroke and length of connecting rod by sider-crank system. The volume of the cylinder (V) is given by Equation (2) as follows [38]:  
\begin{table}
\begin{tabular}{l l l} \hline
**Test Parameters** & **Unit** & **Condition** \\ \hline Engine Speed & rpm & 750 \(\pm\) 10 (Idle Speed) \\ Engine Load & Nm & 0 and 40 1 \\ Cooling Water Temperature & \({}^{\circ}\)C & 85 \(\pm\) 5 \\ Intake Air Temperature & \({}^{\circ}\)C & 25 \(\pm\) 5 \\ Fuel Injection Pressure & bar & 280 \\ Injection Timing & \({}^{\circ}\)CA & Main BTDC 2/Pilot BTDC 15 and 20 \\ EGR rate & - & 0 \\ \hline \end{tabular}
\end{table}
Table 3: Test Conditions.  
Figure 2: Injection timings and duration of pilot and main. (**a**) Main BTDC 2 \({}^{\circ}\)CA, pilot BTDC 20 \({}^{\circ}\)CA (separation 18 \({}^{\circ}\)CA), (**b**) main BTDC 2 \({}^{\circ}\)CA, pilot BTDC 15 \({}^{\circ}\)CA (Separation 13 \({}^{\circ}\)CA).  
\[\mathrm{V}=\frac{\mathrm{V_{d}}}{\mathrm{r}-1}+\frac{\mathrm{V_{d}}}{2}\Big{[}1+ \mathrm{R}-\cos\theta-\sqrt{\mathrm{R}^{2}-\sin^{2}\theta}\Big{]} \tag{2}\]  
where Vd is the displacement volume, r is the compression ratio and R is the stroke-to-bore ratio.  
The specific fuel consumption (SFC) is calculated using the following formula [19; 38]:  
\[\mathrm{SFC}=\frac{\dot{m_{f}}}{2\pi\mathrm{NT}} \tag{3}\]  
Here, \(\dot{m_{f}}\) is the fuel flow rate, N is the engine speed, and T is the indicated torque calculated based on the indicated mean effective pressure (IMEP) for engine load 0 Nm or the brake torque from the engine dynamometer for an engine load of 40 Nm.  
To check the combustion stability of the diesel engine operation at idle using each test fuel, the coefficient of variation (COV) for the indicated mean effective pressure was used, which is defined as [19]:  
\[\mathrm{COV_{IMEP}}=\frac{\mathrm{S}}{\mathrm{X}} \tag{4}\]  
\[\mathrm{S}=\sqrt{\frac{1}{\mathrm{N}}\sum_{i=1}^{\mathrm{N}}\{\mathrm{IMEP(i) }-\mathrm{X}\}^{2}} \tag{5}\]  
\[\mathrm{X}=\frac{1}{\mathrm{N}}\sum_{i=1}^{\mathrm{N}}\mathrm{IMEP(i)} \tag{6}\]  
Here, S is the standard deviation and X is the average of the IMEP over 200 cycles (here, N = 200), IMEP(i) is the indicated mean effective pressure (here, i = 1, 2, 3,..., 200).  
Particle matter emitted from the diesel engine was collected on a copper grid, and the experiment for soot morphology and particulate analysis was carried out on a TEM and SEM. Particle agglomerates were measured using a SEM at 250 K magnification, and the acceleration voltage of the microscope was 10 kV. The TEM acceleration voltage was 100 kV, and the magnification was 100,000 times. The SEM images were modified using ImageJ software ([[http://imagej.net](http://imagej.net)]([http://imagej.net](http://imagej.net))) to correct the boundary between soot particles to be more certain. The length of the soot particles was measured by randomly selecting a total of 200 particles. The average of the measured particles was calculated, and the distributions of particulate size were analyzed for each test.