Machine Learning-Assisted Discovery of Flow Reactor Designs

TL;DR

This work tackles the challenge of discovering high‑performing, highly parameterised flow reactors by integrating additive manufacturing with an augmented‑intelligence framework that couples polar Gaussian process–driven cross‑sections, coil‑path parameterisation, CFD via OpenFOAM, and multi‑fidelity Bayesian optimisation (DARTS). The approach identifies design features that induce Dean vortices at low Reynolds numbers, achieving significant plug‑flow improvements validated by 3D‑printed prototypes and Villermaux–Dushman mixing tests. Key contributions include two novel parameterisations, a robust multi‑fidelity optimisation strategy, and an emphasis on interpretability, with the authors releasing benchmarks and code to promote broader use. The findings demonstrate that data‑driven design, guided by flow dynamics, can yield superior reactor performance, with potential benefits for sustainability and manufacturing efficiency. The work provides a general workflow for designing highly parametric reactors and offers a practical path toward accelerated discovery and deployment of advanced flow reactors.

Abstract

Additive manufacturing has enabled the fabrication of advanced reactor geometries, permitting larger, more complex design spaces. Identifying promising configurations within such spaces presents a significant challenge for current approaches. Furthermore, existing parameterisations of reactor geometries are low-dimensional with expensive optimisation limiting more complex solutions. To address this challenge, we establish a machine learning-assisted approach for the design of the next-generation of chemical reactors, combining the application of high-dimensional parameterisations, computational fluid dynamics, and multi-fidelity Bayesian optimisation. We associate the development of mixing-enhancing vortical flow structures in novel coiled reactors with performance, and use our approach to identify key characteristics of optimal designs. By appealing to the principles of flow dynamics, we rationalise the selection of novel design features that lead to experimental plug flow performance improvements of 60% over conventional designs. Our results demonstrate that coupling advanced manufacturing techniques with `augmented-intelligence' approaches can lead to superior design performance and, consequently, emissions-reduction and sustainability.

Figures (5)

• Figure 1: Overview of optimal reactor characteristics.a, The conventional coiled-tube reactor (i) alongside optimal coiled tube reactors generated by parameterising the cross-section (ii), the coil path (iii), and a joint parameterisation (iv). b, Velocity streamlines coloured with velocity magnitude within a standard coil (i) and within optimal joint parameterisation (ii). c, Secondary flow streamlines at various cross-sections of the coil. d, Cross-sectional plane across the coil demonstrating streamwise velocities e, The presence of induced Dean vortices within the optimal joint parameterisation coil (ii) compared with a standard coil (i).
• Figure 2: Analysis of residence time distributions and optimisation convergence.a, The optimisation objective against iteration (i) and wall-clock time (ii). The objective has been normalised. The initial data set generated via design-of-experiments is denoted as negative iterations and wall-clock time. Hence, optimisation begins at the 0th iteration and at $t=0$. b, Gaussian process dimension lengthscales throughout Bayesian optimisation iterations (i) alongside histograms demonstrating the distribution of GP lengthscales changing throughout optimisation (ii). c, t-SNE analysis of the data generated throughout optimisation in design parameter space ($\mathcal{X}$), reducing the dimensionality of design parameters to two dimensions, and labelled with different respective quantities. d, Parameter variability, defined as a function of the GP lengthscale corresponding to each parameter, plotted for each inducing parameter on a nominal coil.
• Figure 3: The nominal coiled tube (left, R1) alongside extrapolated steady-flow coil designs containing aspects from the optimal cross-section (centre, R2) and both cross-section and coil path (right, R3).
• Figure 4: Data generated across three experiments for each reactor configuration, designed to maximise equivalent tanks-in-series and minimise non-symmetric RTDs. A tanks-in-series model is used to estimate the performance of each reactor across the experiments performed. Dimensionless concentration at the outlet of the reactor ($E(\theta)$) is plotted against dimensionless time ($\theta$).a, the control reactor (R1). b, the reactor with variable cross-section (R2). c, the reactor with variable cross-section and path (R3).
• Figure 5: Aspects of the methodology.a, Left: Polar Gaussian process parameterisation of coil cross section, demonstrating samples from a Gaussian process prior with a polar kernel. a, Right: The posterior distribution after the polar Prior distribution has been conditioned on data. In this demonstration we assume noiseless observations. b, Examples of sets of inducing points at given locations along the length of a coil. A polar Gaussian process is used to interpolate between points, where each data point's radial value is a parameter. c, A flow-diagram of the main aspects of the methodology of this article.