Transient topology optimization for efficient design of actively cooled microvascular materials

Microvascular materials containing internal microchannels are able to achieve multi-functionality by flowing different fluids through vasculature. Active cooling is one application to protect structural components and devices from thermal overload, which is critical to modern technology including electric vehicle battery packaging and solar panels on space probes. Creating thermally efficient vascular network designs requires state-of-the-art computational tools. Prior optimization schemes have only considered steady-state cooling, rendering a knowledge gap for time-varying heat transfer behavior. In this study, a transient topology optimization framework is presented to maximize the active-cooling performance and mitigate computational cost. Here, we optimize the channel layout so that coolant flowing within the vascular network can remove heat quickly and also provide a lower steady-state temperature. An objective function for this new transient formulation is proposed that minimizes the area beneath the average temperature versus time curve to simultaneously reduce the temperature and cooling time. The thermal response of the system is obtained through a transient Geometric Reduced Order Finite Element Model (GRO-FEM). The model is verified via a conjugate heat transfer simulation in commercial software and validated by an active-cooling experiment conducted on a 3D-printed microvascular metal. A transient sensitivity analysis is derived to provide the optimizer with analytical gradients of the objective function for further computational efficiency. Example problems are solved demonstrating the method’s ability to enhance cooling performance along with a comparison of transient versus steady-state optimization results. In this comparison, both the steady-state and transient frameworks delivered different designs with similar performance characteristics for the problems considered in this study. This latest computational framework provides a new thermal regulation toolbox for microvascular material designers.