Carrier-phase direct numerical simulations (CP-DNS) of a three-dimensional turbulent shear- and mixing-layer are presented. DNS enables detailed investigation of complex multiphase turbulent reacting systems that are difficult to study experimentally; however, the reliability and reproducibility of such simulations remain uncertain and are potentially sensitive to the underlying numerical treatment. Given this, the simulations are cross-validated against DNS data by Luu et al. (Flow Turbul. Combust. 2024), first in a statistical sense and then, for the first time, by direct comparison of the instantaneous realizations of the two DNS. A further DNS is then presented for a higher Reynolds number at twice the grid resolution. This represents the most resolved carrier-phase DNS of such systems to date and enables higher turbulence conditions that better represent realistic burner operating conditions. The new simulations confirm the previously observed overall system behavior and further demonstrate the influence of Reynolds number on the combustion process. Higher turbulence intensity leads to a broader ignition zone, enhanced oxygen entrainment, and increased ignition and conversion rates, while the particle-scale oxidation behavior remains largely unchanged, indicating weak coupling between gas-phase turbulence and individual particle combustion.

This study performs a comparative assessment of three Machine Learning (ML) models to determine their robustness in data-sparse industrial environments for predicting and optimising the performance and energy consumption of an immersion mill. By employing active learning strategies that target high-variance regions in process space, a limited experimental dataset (15 batches) was found sufficient to accurately predict mill performance, provided the correct model architecture is chosen. Three models were used: Random Forest Regression (RFR), Gradient Boosted Trees (GBT) and Symbolic Regression (SR). Based on performance when used on completely unseen data, as well as interpretability and usability, the SR models were found to be the most effective for this application. The simple algebraic form of the SR models allowed for direct use in exploring 'what-if' scenarios, and equally allowed either model to serve as a constraint for the other to minimise energy use to achieve a target particle size. An unexpected finding during this work was that the relationship between final particle size and impeller speed and grinding media content is weaker than for classic vertical stirred mill designs owing to transport and/or mixing mechanisms novel to this particular mill design. The result of this study is a set of predictive models that can be used in optimising the immersion milling process, and effectively responding to changes in feed Particle Size Distribution (PSD) whilst minimising energy use.