(664e) Geometry-Informed Deep Learning Surrogate Models for Flow Prediction and Optimisation of Flow Reactors

Flow reactors, also known as continuous flow reactors, are used in chemical synthesis, pharmaceutical manufacturing or polymerisation. The shift from batch to continuous processes has led to the development of novel reactor configurations, such as 3D printed mesoscale reactors. These reactor designs, which are otherwise difficult to manufacture through other conventional techniques, have demonstrated high yields [1][2][3]. However, identifying optimal designs requires efficient computational methods to explore the vast design space effectively.

Computational Fluid Dynamics (CFD), CFD-led explorations have been extensively carried out for improving the design of reactors, where design improvements can be identified based on visualisations of the flows [4][5][6]. However, these simulations are expensive and are often based on human intuition to navigate the parameter space, which makes this approach ineffective at balancing the number of evaluations needed to identify truly optimal solutions. To address this, we have previously explored derivative-free Bayesian optimisation models, along with multi-fidelity optimisation techniques integrated with the CFD simulations. These approaches have shown promising results in uncovering crucial flow phenomena, such as Dean vortices, which enhance mixing at low Reynolds numbers [7][8][9]. With an aim to further reduce the costs of exploration, we propose to extend the multi-fidelity Bayesian optimisation by exploring fidelities encompassing full CFD as high-order models and reduced-order models through Geometry-Informed Graph Neural Networks (GNNs). The focus of this work is on developing and applying geometry-informed GNNs to efficiently predict flow dynamics across diverse reactor configurations and operating conditions.

GNNs have been successfully applied within chemical reactors to improve reaction yield prediction using pre-trained models [10]. They have also demonstrated the capability to learn fluid dynamics for various geometries, including airfoils, flow around cylinders [11], shapes generated through Bezier curves [12], and even wind turbine blades [13]. Our approach introduces a geometry-informed deep learning surrogate modeling framework that leverages GNNs to encode topological and geometric information, coupled with Convolutional Autoencoders for compressed flow representations. This framework enables us to replace costly CFD computations with efficient prediction mechanisms, significantly reducing computational overhead. Figure shows the GNN-Autoencoder-OpenFoam framework used in this study.

We pre-train the GNN model on a two-dimensional serpentine reactor with shape variants generated using sinusoidally-parameterised geometries. The geometric parameters varied include the amplitude (p1 = 0.1-0.5), frequency (p2 = 3.0-4.0), and horizontal offset (p3 = 0-Ï€/2) of the sinusoidal curve. Structured meshes for each reactor geometry are created using the blockMesh utility in OpenFOAM v2012. The reactor geometry is defined by two sinusoidal curves representing the upper and lower walls, with smooth transitions at the inlet and outlet regions. Each geometry consists of approximately 4000 cells. We integrate OpenFOAM with Python using the PyFoam library.

We run transient CFD simulations using scalarTransportFoam to track the tracer concentration in the water medium. The flow is governed by the convection-diffusion equation, with convection being the dominant transport mechanism. The plug flow performance is evaluated through the residence time distribution (RTD), obtained from the tracer concentration at the outlet. More than 100 cases are generated using Latin-hypercube sampling. For each transient case, 140 arrays are generated to capture a time period of 7 seconds, with data recorded every 0.05 seconds.

The GNN architecture comprises graph convolution layers that operate on the reactor mesh graph, capturing spatial dependencies and encoding geometric information. The node features include x and y coordinates, tracer concentration, and velocity components. The graph convolution layers are followed by pooling layers to reduce spatial dimensions and extract high-level features. The compressed flow representations are then fed into fully connected layers to predict velocity and tracer concentration fields at future time steps. The model is trained using a combination of mean squared error loss for flow predictions and a reconstruction loss for the autoencoder.

Our integrated framework demonstrates good accuracy and efficiency in flow predictions. On a test set of 10 unseen reactor geometries, the GNN surrogate model achieves low mean squared errors for both tracer concentration and velocity predictions compared to ground truth CFD simulations. Additionally, the GNN surrogate model provides more than a 100-fold speedup in computational time compared to traditional CFD simulations, enabling real-time flow predictions and efficient design space exploration.

This geometry-informed deep learning surrogate modelling approach showcases the potential for accurate and efficient flow predictions, real-time simulations, and uncertainty quantification across complex reactor geometries and can be extended to three-dimensional geometries. Future work will focus on integrating this approach with the multi-fidelity optimisation framework, reporting on optimisation time, and validating the designs through 3D printing and experimental testing of the reactors.

Acknowledgements: This work is supported by the EPSRC PREMIERE (EP/T000414/1) Programme Grant.

References

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