TANDEM TOPOLOGY AND SHAPE OPTIMIZATION IN FLUID MECHANICS USING CONTINUOUS ADJOINT

In the field of fluid mechanics, the two main classifications of optimization are topology (TopO) and shape (ShpO). TopO, enhanced with the level set (LS) method in this paper, is used to define an optimal geometric solution when only the inlets, outlets and bounding design domain of a flow problem are known. Alternatively, ShpO, utilizing differentiated turbulence models and the Enhanced Surface Integral (E-SI) formulation to obtain accurate derivatives (based on the recent, original work by the same group), finds a physically accurate optimal shape for a predefined connectivity between inlets and outlets. In this paper, both techniques employ the continuous adjoint method to drive design variables toward the optimal value-set. Although generally treated as mutually exclusive, a recently developed Topology to Shape Transition (TtoST) method is used to conjoin the two optimization techniques, allowing shape to be run from a topological solution by automatically parameterizing the interface between the solid and fluid domains and using it to generate a parameterized, boundary-fitted grid. This form of ‘tandem’ optimization is useful for problems in which inlet-outlet connectivity is either unknown or free to be re-defined by TopO. The 3D internal-flow cases presented in this work and the in-house code pertaining to the optimization and transition process are implemented within OpenFOAM 2.2.1. Portions of this research were funded by the People Programme (ITN Marie Curie Actions) of the European Union’s H2020 Framework Programme (MSCA-ITN-2014-ETN) under REA Grant Agreement no. 642959 (IODA project). The first author is an IODA Early Stage Researcher.