Topology optimization method applied to flow machines design considering two-phase flow

• Grant number: 25/06223-9
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: June 01, 2025
• End date: November 30, 2026
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Emílio Carlos Nelli Silva
• Grantee: Thomaz Garcia Faccioli
• Host Institution: Centro de Pesquisa para Inovação em Gases de Efeito Estufa. Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Company: Universidade de São Paulo (USP). Escola Politécnica (EP)
• Associated research grant: 20/15230-5 - Research Centre for Greenhouse Gas Innovation - RCG2I, AP.PCPE

Abstract

This work involves the development of a Topology Optimization (TO) methodology for the design of flow machines considering two-phase flow. Specifically, the optimization of pumps is studied, considering the flow of bubbles dispersed in the liquid fluid. In various flow machine applications, it is common to find bubbles in the flow admitted by the pump, which can significantly affect the performance of these devices. TO is the most versatile strategy among optimization approaches, as it allows for the addition and removal of material in any part of the computational domain. In the context of flow machine design, the advantage of using TO is highlighted in the creation of splitters and unconventional blade geometries generated by the optimizer. The polydisperse flow will be analyzed through computational fluid dynamics with the Euler-Euler approach and the population balance equation. The applied multiphase model was chosen considering the feasibility of sensitivity calculation for TO and the capacity to capture the dynamics of liquid flow with bubbles inside flow machines. The equations describing the two-phase flow in the rotor-stator assembly are solved using the multiple reference frame formulation. Furthermore, the Wray-Agarwal turbulence model is used, assuming incompressible and steady-state flow. The optimization objectives are: minimization of relative energy dissipation, maximization of pressure rise, and minimization of power consumption. The material model to be used in topology optimization is based on the density method. The implementation will be done on the open-source platform FEniCS, using the adjoint method for derivative calculation and interior point optimization algorithm. This work is part of the FAPESP research grant Engineering Research Centers Program "Research Centre for Greenhouse Gas Innovation - RCGI", no. 2020/15230-5 (05/2021 to 04/2026). (AU)