Concurrent shape and topology optimization for steady conjugate heat transfer

Topology optimization is typically used to discover an optimized material distribution which implicitly defines the external shape of a body. The work presented here considers the case when both the external shape of a body and its internal material distribution are both designable. A potential application would be the concurrent shape optimization of an aircraft's wing skin with topology optimization of its internal structure. This concept is applied to optimization of steady-state conjugate heat transfer between an incompressible flow and a heated rigid body. Separate shape, topology, and concurrent shape with topology optimization is performed on the heated body to optimize cooling. The average temperature at the applied heat flux boundary is the objective, the maximum mass of the body is an inequality constraint, and an optional maximum aerodynamic drag inequality constraint is considered. Optimized geometries with an alternative approximate maximum temperature objective, which is useful when considering operation of electronics with strict operating temperature limits, are shown for topology optimization. It is shown that the number of shape parameters leads to significantly different optimized geometries unless the problem is constrained through a maximum allowable drag inequality constraint. The wide set of optimized geometries emphasizes the importance of using coupled physics-based optimization with well-defined realistic parameterizations and constraints, in contrast to relying on intuitive trends from highly idealized models.