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Current simulations of turbulent flames are instrumented with particles to capture the dynamic behavior of combustion in next-generation engines. Categorizing the set of many millions of particles, each of which is featured with a history of its movement positions and changing thermo-chemical states, helps understand the turbulence mechanism. We introduce a dual-space method to analyze such data, starting by clustering the time series curves in the phase space of the data, and then visualizing the corresponding trajectories of each cluster in the physical space. To cluster time series curves, we adopt a model-based clustering technique in a two-stage scheme. In the first stage, the characteristics of shape and relative position are particularly concerned in classifying the time series curves, and in the second stage, within each group of curves, clustering is further conducted based on how the curves change over time. In our work, we perform the model-based clustering in a semi-supervised manner. Users' domain knowledge is integrated through intuitive interaction tools to steer the clustering process. Our dual-space method has been used to analyze particle data in combustion simulations and can also be applied to other scientific simulations involving particle trajectory analysis work.