Robust Fluid Topology Optimization Using Polynomial Chaos Expansions: TOffee

Abstract

The paper presents an innovative solution to robust topology optimization developed for components that can be manufactured by additive manufacturing. Topology optimization has been used in fluid dynamics to optimize geometries based on a target set of performances required for the flow paths. These target performances can be defined as pressure losses or heat exchanges for example, and multiple optimized geometries can be found in the literature. However, none of these cases considered the impact of stochastic variations and are based on a deterministic optimization. It means the optimization has been done for a single boundary condition value. Would this boundary be random, as it is the case in real life gas turbines, then the optimized geometry, optimized for a single set of boundary conditions, will underperform. Robust topology optimization obtains a geometry able to cope with these random variations. The robust optimization method has been implemented in an in-house solver TOffee and relies on a multi-objective function. 2D and 3D robust optimized geometries are obtained and their performance compared to deterministic cases over a range of boundary conditions. Superiority of robust geometries as compared to deterministic geometries is shown. Robust topology optimization presents a great interest in the gas turbine industry due to the greater performance obtained by the optimized geometries while taking into consideration random variations of boundary conditions, making the simulations closer to real life conditions. For the first time in this work it is shown a fluid topology optimization solution with sedimentation that are inherently able to cope with uncertainty.