## 3 Results and Discussions
### Data Processing and Validation  
#### 3.2.1 PIV Processing  
The instantaneous velocity field is first derived from the captured PIV images using commercial software from Dantec Dynamics. The range of the interrogation areas for considerations are \(16\times 16\), \(32\times 32\) and \(64\times 64\) at 0.046 mm per pixels. The vector results of the TDC flow-field at different interrogation areas are shown in Figure 5. If the normalized vector residuals \(r_{0}\) calculated by the following equation exceeds the detection threshold, that vector is defined as an error vector. \[r_{0}=\frac{|U_{0}-U_{m}|}{r_{m}+\varepsilon} \tag{1}\]  
Figure 4: (**a**) The effects of difference seeds amount on the clarity and feasibility of the information that can be measured, (**b**) variation of PIV intensity from BDC to TDC of a firing cycle. Figure 5: Validity of in-cylinder flow-field vectors from PIV processing with different interrogation areas: \(16\times 16\), \(32\times 32\), and \(64\times 64\) with images on left side and valid vectors % plot on the right side. Here, \(U_{0}\) is the displacement vector, \(U_{m}\) is the median vector calculated using neighborhood vectors, \(r_{m}\) is the median residual calculated using the neighborhood residuals and \(\varepsilon\) is the minimum normalization level. The normalized vector residuals \(r_{0}\) was calculated using \(7\times 7\) neighborhood vectors and the detection threshold was set to 1.2. Both \(32\times 32\) and \(64\times 64\) areas allow for \(\sim\)95% valid vectors while the \(16\times 16\) interrogation area has more than 87% valid vectors, with most of the error vectors coming from high scattered region near piston. While 87-90% valid vectors might be enough for interpretation of the flow-field behavior, for the rest of the discussion in the current articles, we will select \(32\times 32\). The instantaneous velocity is further processed for mean velocity, velocity fluctuations and turbulence characteristics using in-house developed MATLAB software. The most common method to derive these specific flow-field characteristics from the instantaneous velocity is to use Fourier transformation to split it into the mean velocity (\(\overline{u}\), \(\overline{v}\)) and the fluctuation of velocity (\(u^{\prime}\), \(v^{\prime}\)). The instantaneous velocity (\(u\), \(v\)) and turbulence intensity are described as following equations. \[u(\theta,n)=\overline{u}(\theta,n)+u^{\prime}(\theta,n) \tag{2}\]  
\[v(\theta,n)=\overline{v}(\theta,n)+v^{\prime}(\theta,n) \tag{3}\]  
\[k(\theta,n)=\frac{1}{2}\sqrt{\left[u^{\prime}(\theta,n)\right]^{2}+\left[v^{ \prime}(\theta,n)\right]^{2}} \tag{4}\]  
Here, \(\theta\) is crank angle and \(n\) is cycle number. While spatial filter is commonly used for PIV, high-speed PIV allows the use of temporal filter. Many studies have investigated the selection of the temporal cutoff frequency for turbulent velocity estimation in internal combustion engines, which is still a relatively arbitrary process. In this study, we selected four points in the important regions of the measurement area, with three points A, B, and C surrounding the spark plug and point D near the squish area to assess the derived temporal cutoff frequency at different spatial location. The power spectrum calculated from fast Fourier transform at the four selected measurement points is shown in Figure 6. The power spectrum was calculated from the instantaneous velocity of each 19 cycle, then the ensemble-averaged power spectrum was obtained. Around the frequency of 300 Hz, all power spectra have an inflection point which indicate that the variability characteristic of velocity changed at this frequency. For LDV measurement in the same optical engine under near engine operating condition, the inflection point in the power spectrum was also around 300 Hz [4]. Therefore, the cutoff frequency of this engine operating condition has been selected to be 300 Hz. Figure 6: The power spectrum of the instantaneous velocity from PIV of different points in the measurement area.