Research Fellows
James Koch
Early Stage Researcher 8 at National Technical University of Athens
The processes of topology and shape optimization (TopO and ShpO) are well known methods in the field of fluid mechanics and can use adjoint sensitivity information to progress their individual design variable set toward the optimum solution according to defined objective function(s). In fluid mechanics specifically, TopO is commonly used to develop optimal flow paths between prescribed inlets and outlets by altering a solidification parameter in each cell of the simulation geometry which tells the fluid-flow equations how easily flow through that cell may occur. Thus, the TopO process requires a design variable for each cell in a simulation and can be prone to local solutions. ShpO, although robust and requiring a smaller set of design variables (usually one for every active (able to be moved) controlling parameter of the scheme used to define the parameterized boundaries of the shape optimization case: i.e. the control points (CPs) of a non-uniform rational b-splines (NURBS) curve) is only capable of altering known boundaries of a geometry. My research pertains to the automated linking of these two distinct processes: although successful in their own rights, it is conceivable that the two methods will find choicest solutions in tandem, with ShpO either improving a topological solution or being given starting geometries which were not known a-priori.
To allow TopO to definitively prescribing a surface which can be converted into a boundary for a shape optimization case, the level set (LS) method is used to control its solidification field. A novel transitional method has been proposed to process these LS-TopO solutions such that ShpO can be initialized and run to ultimately produce a refined, parameterized solution. After pre-processing steps, the topological fluid-to-solid interface is fitted with NURBS curves which are used to define the boundary geometry of a ShpO case. The internal, boundary-fitted mesh is generated, and the case is run using the same constraints (if any) and objective function(s) used in the TopO simulation.
The following is a set of 2D laminar internal-flow solutions to exemplify the proposed topology to shape transition (or TtoST) process.
A) A LS-TopO optimization process solution to minimize total pressure losses. For the case shown, TopO seeks to find the optimal connection between an entrance and two exits. The black 'level-set' line acts as a wall between the blue/solid and red/fluid topological domains.
B) The wall-solution of topology (see A) is fitted with parameterized curves known as 'NURBS', as parameterization is useful for engineering design and manufacture. In the case of NURBS curves, parameterization and curve-shape is defined by (black) control points.
C) The parameterized fiting solution found in B, plotted in red, is used to start a ShpO process. The the total pressure loss-solution of shape is plotted in black.
D) The graphed pressure losses for both optimization processes. Oscillatory behavior for topology is attributed to the inclusion of a volume constraint (1/3 of the topology solution in A should be red/fluid) which fights expansion of the solution's channel. Due to the laminar nature of the case's flow, large deformations in ShpO yield relatively low improvements.