Session 4 - Theme: Computational Fluid Dynamics (2)

Confined impinging jets (CIJs) mixers are a class of efficient mixing devices known for their ability to achieve rapid mixing at the micro-scale. These devices are widely explored in the chemical industry, particularly in processes involving non-Newtonian fluids, such as reaction injection molding (RIM) and emulsification. However, fundamental studies addressing the flow behavior of non-Newtonian fluids in CIJ configurations remain limited. In this work, Computational Fluid Dynamics (CFD) simulations were performed to study the hydrodynamics of a shear-thinning fluid described by a power-law model, with a flow behavior index n=0.8229 and a consistency index K=0.0849 Pa s^n. A 2D model corresponding to an axial section of the 3D chamber was used to assess the conditions for the onset of chaotic mixing regimes. Reynolds numbers in the range 300-500 were analyzed, leading to the identification of two flow regimes: steady and chaotic. The critical Reynolds number that marks the transition between the two flow regimes occurs at 400-500, where a self-sustained chaotic flow regime characterized by the formation of vortices is observed, which is the main factor for the efficient mixing of fluids in CIJs. The validation of the 2D CFD model was done by comparison with fully resolved 3D CFD simulations. Furthermore, a spectral analysis was carried out to examine the characteristic jet oscillations at different locations within the chamber, demonstrating that the 2D model can accurately predict the main flow features when a corrective factor accounting for geometric differences is applied.

Liquid–liquid mixing in mechanically agitated tanks produces drop size distributions governed by the interplay of turbulent stresses, interfacial tension, and viscosity. This work presents a simplified population balance framework for predicting drop size distributions under turbulent agitation. The reactor hydrodynamics is decoupled from drop scale dynamics by deriving a 0D population balance, with the distribution of turbulent dissipation rates obtained from validated single-phase CFD. The averaged breakup frequency is evaluated by integrating the breakup kernel over the full dissipation distribution using a cumulative distribution formulation, which avoids sensitivity to histogram binning. Numerical tests show that the cumulative distribution formulation reduces integration error by about two orders of magnitude relative to a probability density-based discretization and provides stable results with fewer Gauss–Legendre nodes. In addition, a flexible daughter distribution function is introduced as a weighted sum of two-beta functions, preserving mass and enabling asymmetric or multimodal fragmentation outcomes. Model assessment is performed using a dedicated experimental dataset spanning nine operating conditions obtained by combining three dispersed phase viscosities with three impeller speeds, in terms of both drop size distributions and mean diameters. Conventional kernel/daughter distribution combinations provide the closest agreement at low viscosity, whereas higher viscosity conditions exhibit pronounced small diameter tails associated with satellite drops. The two-beta daughter distribution improves the representation of the small diameter region, but remaining discrepancies indicate that further refinement of the breakup frequency model is required.

Inline rotor–stator mixers are widely used in consumer goods manufacturing to accelerate mixing and control microstructure, both critical for product performance and consumer satisfaction. Power input in these mixers is typically described using a two term correlation that separates tank type and flow driven contributions, from which the coefficients Poz and k1 are obtained by regressing experimental or CFD data. Although these coefficients vary significantly with geometry, industrial scale up practice often applies fixed values based on limited data for specific mixer designs, leading to inaccurate power predictions and inconsistent product quality. Given the wide variation in geometries across manufacturing sites, direct measurements or CFD simulations for every configuration is impractical. This work presents an integrated approach combining validated CFD simulations, geometry parameterisation, and data driven modelling to predict Poz and k1 across diverse inline high shear mixer designs. Building on the geometric combinations described in literature, this study replaces design specific investigations with a generalised parameter space that systematically represents key rotor-stator features, including rotor diameter, rotor and stator open area, gap width and stator thickness across multiple scales. Reduced order models are developed using several machine learning methods, with Gaussian process modelling selected for its accuracy and uncertainty quantification. Bayesian optimisation is used to guid additional simulations and enhance predictive capability. The resulting models reproduce literature-reported values and capture the nonlinear influence of geometric parameters on Poz and k1, providing a scalable and reliable workflow for predicting mixer power behaviour and improving scale up fidelity.

Predicting the performance of high-pressure homogenization (HPH) remains a significant challenge in CFD due to the complex coupling of high-shear turbulence and transient cavitation. While cavitation has an essential impact on droplet breakup and cell lysis in food and biotech applications, its stochastic nature often complicates process control and energy efficiency. This study presents a numerical and experimental framework to characterize these cavitation-driven mixing dynamics. The CFD modeling approach utilizes a multiphase mixture formulation incorporating the Schnerr-Sauer and Zwart-Gerber-Belamri mass transfer models to map vapor volume fractions and macroscopic flow behavior across varying orifice geometries. To ensure numerical reliability, simulations were validated against high-speed shadow-graphic images, enabling a direct comparison between predicted cavitation zones and experimental flow regimes. The study systematically investigates the influence of pressure gradients and flow rates on local stress fields. These CFD-derived insights are correlated with macroscopic process parameters, specifically droplet size distributions and protein release yields from cell disruption. By evaluating the advantages and limitations of different cavitation models, this work provides a robust tool for the digital twin-based design of HPH systems. The results offer the mixing community a deeper understanding of how to bridge the gap between microscopic phase-change phenomena and industrial-scale process optimization.