## 3 Optical Analysis  
Early flame front propagation was investigated through cycle resolved digital imaging. Visualization was performed with a high-speed CMOS camera (CamRecord 5000, 8-bit, 16 \(\upmu\)m x16 \(\upmu\)m pixel size by Optronis, Kehl, Germany) equipped with a 50 mm Nikon objective. The camera worked in full chip configuration (512 x 512 pixel) detecting 5000 frames per second with 200 \(\upmu\)s fixed as exposure time. The f-stop of the objective was set at 2.8 to improve the signal-to-noise ratio without extensive saturation effects. Therefore, the set-up allowed the acquisition of the images with a dwell time of 2.4 CAD at 2000 rpm and a spatial resolution of 0.188 mm per pixel. The optical trials related to each engine operative condition consisted in the acquisition of 100 frames per cycle after spark timing, during 30 consecutive engine cycles. A consolidated image processing procedure allowed the evaluation of macroscopic parameters related to flame morphology by a routine developed in Vision of National Instruments; details are reported in [16; 25; 28]. Briefly, a mask was built around the images of each sequence to delineate the limit of the optical window (Figure 3-left). Then, after applying a function for the optimization of brightness and contrast, binary images were achieved by fixing the threshold at 35/256 (Figure  
Figure 2: Fuel injection strategies listed with respect to the position of the second injection pulses: -250 CAD ATDC (**a**) and -200 CAD ATDC (**b**). 3-right). Advanced morphology functions applied to the binary images allowed the estimation of several flame parameters such as area, speed, distortion and preferential propagation. Flame area (A) corresponded to the number of pixels included in the foreground of binary images. Propagation speed (m/s) was calculated as the incremental ratio of the equivalent flame diameter (\(\textbf{D}=\sqrt{\textbf{4}\textbf{ \emph{A}}/\textbf{\emph{n}}}\)) between two frames with respect to the dwell time (\(\delta\)t = 0.2x10\({}^{\circ}\) s). Previous studies identified preferential directions for flame propagation, due to fluid motion phenomena (tumble and swirl) as well as temperature gradients and non-homogeneity of the mixture inside the combustion chamber [28]. This determined a flame distortion that was quantified by the Heywood circularity factor (HCF) corresponding to the ratio between the perimeter P of the image and the circumference of a perfect circle with the same area \(\left(\text{HCF}=\frac{P}{\pi\text{D}}\right)\). To better characterise the previously mentioned effect, a new concept was introduced based on the quantitative analysis of the preferential propagation, evaluated by the ratio between flame size towards intake and exhaust, and left to right with respect to the position of spark plug. In addition, the size in horizontal and vertical axes was estimated. These parameters were calculated using Equations (1-4),  
\[Intake/Exhaust=\left(\frac{L_{intake}}{L_{exhaust}}\right) \tag{1}\]  
\[Left/Right=\left(\frac{L_{left}}{L_{right}}\right) \tag{2}\]  
\[clamp_{y}=L_{intake}+L_{exhaust} \tag{3}\]  
\[clamp_{x}=L_{left}+L_{right} \tag{4}\]  
where \(L_{intake},L_{exhaust},L_{left},and\)\(L_{right}\) indicated the distance between the extreme side of the flame front in each direction with respect to the spark plug (see Figure 3). The tool for the automatic evaluation of distances was inserted in the image processing procedure for morphological analysis of flame propagation. Moreover, a supplementary routine was developed for post-processing; for each sequence, the images with the same flame size along the vertical axis direction (\(clamp_{y}=35.0\pm 0.5 mm\), 45% of the piston diameter) were selected and then the ratio between the distances along \(x\) and \(y\) were calculated. This clamp size was chosen because it is representative of an intermediate phase of flame propagation, without any interference with the optical limit.