Data-driven optimisation of two-phase problems using composite fidelities

Design optimisation plays a crucial role across industries, including chemical engineering, to enhance performance, sustainability, and energy efficiency. It is necessary to develop computationally inexpensive methods that can quickly evaluate and select optimal designs, particularly for processes involving multiphase flows. In this study, we present a framework that addresses this challenge by employing multi-fidelity Bayesian optimisation. This framework is integrated with the OpenFOAM solver using the PyFoam library, allowing for low to high-fidelity simulations that balance cost and accuracy in exploring the design parameter space. The fidelities considered in this work include variations in mesh sizes in the continuous space and different multiphase flow models, such as Eulerian-Eulerian, geometric VOF, and algebraic VOF, in the discrete space. To demonstrate the effectiveness of our framework, we apply it to a ‘toy problem’ involving two immiscible fluids (water and silicon oil) in a channel. The goal is to shape-parameterise the channel to maximise mixing efficiency. By formulating a cost-based acquisition function, our framework automatically selects the combination of fidelities for function evaluations based on the expected value of the objective function. This approach leads to the achievement of near-optimal designs in a computationally efficient manner. We anticipate that this low-cost modelling framework can be extended to a wide range of industrial problems involving multiphase flows to address design optimisation challenges.