Concurrent shape and topology optimization for unsteady conjugate heat transfer

This work explores topology optimization under unsteady conditions on a fundamental design problem to gain design insights between steady and unsteady regimes. A previously studied steady conjugate heat transfer problem at a Reynolds number of 20 is extended to unsteady conditions at a Reynolds number of 100 exhibiting vortex shedding. Interesting non-intuitive optimized shapes and internal topologies for a heated body are computed that do not qualitatively match optimized designs generated with a Reynolds number of 20. Shape optimization under unsteady conditions with a solid interior relies on vortex shedding to improve heat transfer while shape optimization under steady conditions increased the exposed surface area near cool fluid. Concurrent shape and topology optimization with two shape parameter spaces are considered and show that the higher parameter space leverages a higher frequency of vortex shedding to improve cooling. The internal optimized topologies with concurrent shape and topology optimization prioritize heat transfer near the flow separation point biased towards the leading or trailing edge of the body, dependent on the location of most efficient convection. Computing reasonably converged time-averaged objectives and constraints for the presented unsteady case requires 4000 time steps while the steady case requires one time step, leading to a large marginal computational cost increase.