An Analytical Study in Multi-physics and Multi-criteria Shape Optimization

A simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Holder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid's static pressure. For this multi-physical system, it is shown that, under certain conditions, the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with the Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.

Automated summary

This research introduces a simple multi-physical system to model the potential flow of a fluid through a shroud with a mechanical component such as a turbine vane. The study shows that, under certain conditions, the Pareto front of the feasible set is maximal and that the set of optimal forms deforms continuously with respect to preference parameters in scalarization techniques.