In this article, different manifold reduction techniques are implemented for the post-processing of Particle Image Velocimetry (PIV) images from a Spark Ignition Direct Injection (SIDI) engine. The methods are proposed to help make a more objective comparison between Reynolds-averaged Navier-Stokes (RANS) simulations and PIV experiments when Cycle-to-Cycle Variations (CCV) are present in the flow field. The two different methods used here are based on Singular Value Decomposition (SVD) principles where Proper Orthogonal Decomposition (POD) and Kernel Principal Component Analysis (KPCA) are used for representing linear and non-linear manifold reduction techniques. To the authors’ best knowledge, this is the first time a non-linear manifold reduction technique, such as KPCA, has ever been used in the study of in-cylinder flow fields. Both qualitative and quantitative studies are given to show the capability of each method in validating the simulation and incorporating CCV for each engine cycle. Traditional Relevance Index (RI) and two other previously developed novel indexes: the Weighted Relevance Index (WRI) and the Weighted Magnitude Index (WMI), are used for the quantitative study. The results indicate that both POD and KPCA show improvements in capturing the main flow field features compared to ensemble-averaged PIV experimental data and single cycle experimental flow fields while capturing CCV. Both methods present similar quantitative accuracy when using the three indexes. However, challenges were highlighted in the POD method for the selection of the number of POD modes needed for a representative reconstruction. When the flow field region presents a Gaussian distribution, the KPCA method is seen to provide a more objective numerical process as the reconstructed flow field will see convergence with an increasing number of modes due to its usage of Gaussian properties. No additional criterion is needed to determine how to reconstruct the main flow field feature. Using KPCA can, therefore, reduce the amount of analysis needed in the process of extracting the main flow field while incorporating CCV.

在本文中，为火花点火直接喷射（SIDI）引擎的粒子图像测速（PIV）图像的后处理实现了不同的歧管缩减技术。提出这些方法是为了帮助在流场中存在逐周期变化（CCV）时，在雷诺平均Navier-Stokes（RANS）模拟和PIV实验之间进行更客观的比较。此处使用的两种不同方法是基于奇异值分解（SVD）原理的，其中正确的正交分解（POD）和核主成分分析（KPCA）用于表示线性和非线性流形缩减技术。据作者所知，这是首次将非线性歧管减少技术（例如KPCA）用于缸内流场的研究。定性和定量研究均显示了每种方法在验证仿真和结合每个发动机循环CCV方面的能力。传统关联指数（RI）和其他两个先前开发的新颖指数：加权关联指数（WRI）和加权幅度指数（WMI）用于定量研究。结果表明，与整体平均PIV实验数据和单周期实验流场同时捕获CCV相比，POD和KPCA在捕获主要流场特征方面均表现出改进。当使用这三个指标时，两种方法都具有相似的定量准确性。但是，在POD方法中突出了选择代表性重建所需的POD模式数量的挑战。当流场区域呈现高斯分布时，由于使用了高斯性质，重构的流场将随着越来越多的模态收敛，因此KPCA方法被认为提供了更为客观的数值过程。无需其他准则即可确定如何重建主要流场特征。因此，在合并CCV的同时，使用KPCA可以减少提取主流场过程中所需的分析量。