Adjoint based topology optimization of a duct bend

The cooling performance of a duct is a complex interaction between its shape, position inside the surrounding material and the resulting flow. Hence a change in the geometry does effect both the pressure loss as well as the temperature distribution. Due to this coupling of heat transfer and fluid flow a numerical solution is often computationally expensive. Lowering the number of these evaluation steps is therefore crucial. A gradient based optimization method promises high optimization speed if the gradient can be computed effortlessly. The adjoint method in particular offers a low computational cost to calculate this gradient and is hence chosen for the optimization. In this contribution the continuous adjoint equations including conjugate heat transfer are used to optimize a duct bend. A level‐set is used to differentiate the fluid and solid regions. The aim of the optimization is to lower the temperature of a wall inside the heated solid domain. The Reynolds number of the initial design is varied and the effects on the optimization are studied.