Session 3 - Theme: Computational Fluid Dynamics (1)

Mixing in industrial multiphase systems is commonly modelled using the Two-Fluid (TF) model, an Euler–Euler framework that treats each phase as an interpenetrating continuum coupled through interfacial exchange terms. It enables simulation of stirred tanks, bubble columns, and emulsions at practical scales where interface-resolved approaches are infeasible. However, conventional Navier–Stokes–based discretisations can face stability and scalability challenges. The Lattice Boltzmann (LB) method, with its natural parallelism, offers an attractive alternative. Yet robust and general TF implementations within LB remain limited. Here, we propose two novel LB-based formulations of the TF equations. The primary challenge in realising the TF equations in LB is obtaining the correct pressure term. In the first approach, the built-in pressure term in LB is removed using the well-balanced formulation of LB, and the correct pressure term is subsequently reintroduced using a pressure Poisson equation. This reproduces the full TF equations, albeit with the addition of an expensive Poisson equation. The second approach reformulates the TF equations into a mixture equation and a phase momentum equation with correction terms, assuming an incompressible dilute mixture. This approach provides a more efficient, but approximate alternative. The two proposed models are validated against multiple benchmarks and shown to be accurate within their assumptions. Subsequently, they are used in a large eddy simulation to simulate homogeneous isotropic turbulence using the static Smagorinsky model, and the results are validated against a full direct numerical simulation, showing the stability of the proposed models in highly complex and chaotic flows.

Transport of soluble gases between bubbles and surrounding liquid is an important phenomenon in many industrial processes such as bio-reactor aeration, stripping, absorption, and electrolysis. An effective tool to understand such systems is numerical simulation of the relevant conservation equations coupled with a description of the mixture thermodynamics. We have developed a method for simulations where the soluble gas is approximated as ideal and the liquid is non-ideal (present as liquid and vapour). Since demonstrating the model’s equilibrium behaviour (Byrne and Shardt, Phys. Rev. E 111, 035306, 2025), we have extended the model to describe systems with convection. This model is implemented as a free energy lattice Boltzmann method (LBM), in which the transport equations are solved with LBM and the thermodynamics are incorporated through a free energy functional. This model employs a diffuse interface approach to describe interfaces between phases, which enables straightforward handling of merging and breaking interfaces. The model is stable up to high density ratios, O(1000), between the liquid and vapour phases. Mass transfer characteristics of dissolving soluble gas bubbles have been validated for both static and dynamic cases. Bubble shapes and rise velocities have also been validated up to Reynolds and Eotvos numbers of order one. The model has been used to simulate decomposition of a liquid to form gas bubbles (as during electrolysis of water), showcasing different bubble generation regimes.

This work presents a GPU-accelerated Lattice Boltzmann Method (LBM) coupled with Large Eddy Simulation (LES) to enable high-fidelity analysis of turbulent mixing and liquid-liquid dispersion in stirred tanks. Integrating the Immersed Boundary Method (IBM) for complex geometry modeling, the solver achieves a 1500-fold speedup over 16 CPU cores, supporting efficient simulation of ~10⁷ droplets and up to 1.38×10⁷ grids. A probabilistic droplet breakage model is proposed to eliminate Lagrangian time step dependence, ensuring accurate predictions of Sauter mean diameter (d₃₂) and droplet size distribution (DSD)—critical for optimizing mixing efficiency. The framework resolves >95% of turbulent kinetic energy in high-turbulence regions, capturing key mixing characteristics: increasing impeller speed enhances droplet trajectory tortuosity, strengthens radial/axial circulations, and shifts peak droplet velocity toward the tank wall. This GPU-accelerated LBM approach provides reliable insights into mixing hydrodynamics, offering a practical tool for optimizing stirred tank design in chemical, pharmaceutical, and process engineering applications.