Numerical study of oil–water emulsion formation in stirred vessels: effect of impeller speed

Abstract

The mixing of immiscible oil and water by a pitched blade turbine in a cylindrical vessel is studied numerically. Three-dimensional simulations combined with a hybrid front-tracking/level-set method are employed to capture the complex flow and interfacial dynamics. A large eddy simulation approach, with a Lilly–Smagorinsky model, is employed to simulate the turbulent two-phase dynamics at large Reynolds numbers $Re=1802{-}18\ 026$ . The numerical predictions are validated against previous experimental work involving single-drop breakup in a stirred vessel. For small $Re$ , the interface is deformed but does not reach the impeller hub, assuming instead the shape of a Newton's Bucket. As the rotating speed increases, the deforming interface attaches to the impeller hub which leads to the formation of long ligaments that subsequently break up into small droplets. For the largest $Re$ studied, the system dynamics becomes extremely complex wherein the creation of ligaments, their breakup and the coalescence of drops occur simultaneously. The simulation outcomes are presented in terms of spatio-temporal evolution of the interface shape and vortical structures. The results of a drop size analysis in terms of the evolution of the number of drops, and their size distribution, is also presented as a parametric function of $Re$ .

Liquid–Liquid Dispersion Performance Prediction and Uncertainty Quantification Using Recurrent Neural Networks

“…Specifically, two network architectures, fully connected (FC) and encoder–decoder, with two different RNN cells, LSTM and GRU, have been finely trained and deployed to predict interfacial area growth, drop count, and their size distribution for future time-steps. The RNN models developed herein have been trained with data obtained from high-fidelity, three-dimensional, CFD simulations of two mixing systems, carried out for stirred , and static , mixers. In particular, the RNN model has been assigned the task of learning and capturing the influence of varying physicochemical properties, operational conditions, and mixer geometrical characteristics on dispersion performance.…”

“…to the dissipation term, and second, a direct forcing method is added with the inclusion of a fluid−solid interaction force, F fsi . 28 In the presence of surfactants, the force F is decomposed into its normal (σκn) and tangential components (∇ s σ), as shown in eq 11…”

“…Each mixer operates in a completely different flow regime, with the former handling transitional/turbulent flows (Re = ρND r 2 /μ ≈ [9000, 18,000]) and the latter operating under laminar conditions (Re = ρ U r D r /μ = 1.63). For brevity, specifics on the problem formulation of each system will not be described herein, but readers are encouraged to refer to previous publications detailing the geometrical and operational specifications, fluid properties, numerical considerations (e.g., grid refinement), and validation. − The extracted data sets comprise multidimensional time-series data encompassing three key metrics integral to the dispersion performance: interfacial area growth (IA), drop count (ND), and DSD, calculated as the approximate volume of cells resolving a fully detached structure or “drop”. The choice of these parameters capitalizes on the explicit and robust nature of the interface-tracking scheme [level-contour reconstruction method (LCRM)] embedded in the CFD code used, which furnishes a more accurate and well-resolved representation of the intricate interfacial dynamics compared to other traditional schemes (e.g., level-set methods) …”

“…This Heaviside function is defined to have a value of 1 for the oil phase (subscript o) and 0 for the aqueous phase (subscript a) and is generated through a vector distance function from the interface φ( x ) and solved numerically with a smooth 3–4 grid cells transition. , Additional terms are added to the formulation in eq when dealing with stirred tanks. First, a Smagorinsky–Lilly LES turbulence model is implemented, adding the filter false( μ normalv normali normals + ρ C s 2 Δ 2 | | false) to the dissipation term, and second, a direct forcing method is added with the inclusion of a fluid–solid interaction force, F fsi …”

“…Inspired by the work reviewed before, this study seeks to develop an inexpensive time-series model using RNNs by capitalizing on a comprehensive set of high-fidelity three-dimensional CFD simulations, some of which have been exploited in recent works − to unravel the fundamental governing mechanisms underlying extensively utilized mixing systems handling L–L dispersions across a range of industrially relevant scenarios. These simulations have been conducted with a state-of-the-art DNS code, which comprises a hybrid front-tracking/level-set interface-tracking algorithm, embedded along a well-validated multiphase solver for surfactant transport at the interface and in the bulk phase .…”