Multi-Stage Optimal Design for Turbulent Pipe Systems by Data-Driven Morphological Exploration and Evolutionary Shape Optimization

Abstract Turbulence fields typically cause cumbersome multimodality in their solution space and the optimal shape of flow paths could be strongly dependent on a huge number of branch patterns. These features hinder gradient-based structural optimization frameworks from finding promising solutions for turbulent pipe systems. In this paper, we propose a multi-stage framework that integrates data-driven morphological exploration and evolutionary shape optimization to address the challenges posed by the complexity of turbulent pipe systems. Our framework begins with data-driven morphological exploration, aiming to find promising topologies as well as shapes for selecting a reasonable number of candidates for the next shape refinement stage. Herein, we employ data-driven topology design, a gradient-free and multiobjective optimization methodology incorporating a deep generative model and the concept of evolutionary algorithms to generate promising arrangements. Subsequently, representative shapes are extracted through a deep clustering strategy. The final stage involves refining these shapes through shape optimization using a genetic algorithm. Focusing on a two-dimensional turbulent pipe system with a min/max objective, our numerical results show the effectiveness of the proposed framework in delivering high-performance solutions for the turbulent flow optimization problem with branching.