Cluster-based analysis of cycle-to-cycle variations: application to internal combustion engines


We define and illustrate a cluster-based analysis of cycle-to-cycle variations (CCV). The methodology is applied to engine flow but can clearly be valuable for any periodically driven fluid flow at large Reynolds numbers. High-speed particle image velocimetry data acquired during the compression stroke for 161 consecutive engine cycles are used. Clustering is applied to the velocity fields normalised by their kinetic energy. From a phase-averaged analysis of the statistics of cluster content and inter-cluster transitions, we show that CCV can be associated with different sets of trajectories during the second half of the compression phase. Conditional statistics are computed for flow data of each cluster. In particular, we identify a particular subset associated with a loss of large-scale coherence, a very low kinetic energy of the mean flow and a higher fluctuating kinetic energy. This is interpreted as a good indicator of the breakdown of the large-scale coherent tumbling motion. For this particular subset, the cluster analysis confirms the idea of a gradual destabilisation of the in-cylinder flow during the final phase of the compression. Moreover, inter-cycle statistics show that the flow states near TDC and in the measurement zone are statistically independent for consecutive engine cycles. It is important to point out that this approach is generally applicable to very large sets of data, e.g. generated by PIV or LES, and independent of the considered type of information (velocity, concentration, etc.).

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The PhD grant of Y. CAO is financed by Renault. The work is partially funded by the ANR Chair of Excellence TUCOROM. E. Kaiser acknowledges additional funding from region Poitou–Charentes, France, ANR Project “SePaCoDe” (Étude de la Physique du Décollement et Réalisation de son Contrôle) and NSF PIRE Grant OISE-0968313.

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Correspondence to Jacques Borée.

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Cao, Y., Kaiser, E., Borée, J. et al. Cluster-based analysis of cycle-to-cycle variations: application to internal combustion engines. Exp Fluids 55, 1837 (2014).

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  • Proper Orthogonal Decomposition
  • Proper Orthogonal Decomposition Mode
  • Engine Cycle
  • Compression Stroke
  • Crank Angle Degree