On-the-Fly Dual Reduction for Optimal Design of Transient Responses in Thermal Energy Storage

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The objective of this project is to develop a computational design method that enables efficient topology optimization (TO) for tailored transient physical responses. Many physical phenomena are transient in nature, such as unsteady flow, transient heat transfer, and elastodynamic and time-dependent viscoelastic creep responses. TO is a computational design method that can automatically determine material distribution for tailored physical responses. Although TO for time-dependent problems has been conducted in the past, lack of computer methods for effectively handling computational and storage obstacles in transient problems has restricted the design optimization to mostly two-dimensional space, thus limiting its practical use. This research aims to fill the knowledge gap by developing a novel reduced-order, model-based efficient TO method for three-dimensional time-dependent problems, with targeted applications in topological design of latent heat-based thermal energy storage devices. The resulting designs from this new model reduction-based TO method will be synergistically complemented with data-driven designs that will be undertaken by groups of undergraduate researchers from diverse disciplines. Successful completion of this project will lead to technological advances in a host of products where transient physical responses are critical, such as energy storage applications. This project will result in optimized designs for latent heat-based thermal energy storage with increased power density and improved charging/discharging efficiency. This project will also broaden research opportunities for undergraduates from diverse disciplines. It will enhance their interest in STEM careers and increase the likelihood for them to pursue advanced degrees in STEM disciplines.This project fills an intellectual gap in computer methods that can enable efficient time-dependent TO in three-dimensional settings. It will lead to a novel reduced-order model (ROM) based approach for time-dependent TO through on-the-fly dual reduction with moving local basis. In this approach, snapshots and basis required for constructing ROMs are dynamically updated during the optimization without any extraneous computing of full-order solutions. Instead of constructing linear ROMs with global basis vectors, the PI plans to construct moving local basis based on backward and forward snapshot strategies. Instead of developing adjoint sensitivity to approximated ROMs for primal equilibrium equations, the PI will develop a dual reduction method where reduction of primal and adjoint equations are conducted independently. In order to overcome potential reduction challenges due to strong non-linearity in time-dependent partial different equations, it is also planned to apply a deep learning approach through deep neural networks for model reduction. Completion of this research will lead to a new ROM-based optimization methodology that overcomes both computational and storage obstacles in time-dependent TO. Further, this project will develop a team-based experiential learning approach to broadening research opportunities for undergraduates. Teams of undergraduates from diverse disciplines will be conducting data-driven design research and applying it in energy storage device design. The designs from the new TO method and the data-driven design method will be compared to improve the efficacy of both methods in energy storage device design.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.