Detonation cellular regularity: A data analysis

Detonation cellular regularity describes the spatial organization of the cellular patterns that emerge from the unsteady shock interactions within a propagating detonation. This study introduces the regularity index (RI), a quantitative metric derived from the spatial distribution of triple-point collision locations recorded on soot foils. The RI provides a robust and accessible approach for characterizing cellular regularity and leverages the extensive archive of soot foil measurements in the literature. Over 100 soot foils were analyzed to calculate RI values, enabling a systematic evaluation of the relationship between cellular regularity and key detonation properties. Among the properties considered, the effective activation energy (${\varepsilon }_i$) emerged as the most effective predictor of regularity, with higher ${\varepsilon }_i$ correlating with high RI values, indicating increasingly irregular cellular structures. In contrast, the stability parameter ($\chi$), traditionally used to describe detonation instability, exhibited limited applicability across the broader dataset. The discrepancies originate from large uncertainties in calculating $\chi$ and related properties when different chemical kinetic modes were used, underscoring the need for improved chemical kinetic knowledge under detonation-relevant conditions. New soot foil measurements were performed for acetylene–oxygen, acetylene–oxygen–argon, and hydrogen–oxygen mixtures, where $\chi$ had previously been proposed as an effective measure for regularity. The derived RI values as well as the visual inspection of the new soot foils confirmed the strong correlation between ${\varepsilon }_i$ and cellular regularity. Overall, the regularity index concept was shown to effectively capture cellular regularity, and offers opportunities for future quantitative analyses of detonation dynamics involving regularity.

Novelty and significance statement

This work introduces a new metric, the regularity index (RI), for quantitatively characterizing detonation cellular regularity. By analyzing a comprehensive dataset of over 100 soot foils and conducting new experiments, the study establishes the effective activation energy (${\varepsilon }_i$) as the most reliable predictor of cellular regularity. Moreover, the broader applicability of the stability parameter ($\chi$) to cellular regularity was evaluated, and only a weak correlation, if any, was observed. The previously reported trends were shown to result from chemical kinetic models with significant uncertainties under detonation-relevant conditions. Finally, this research establishes a data-driven framework to connect detonation properties with cellular structures and offers opportunities for future quantitative analyses of detonation dynamics involving cellular regularity.