Adaptive topology optimization for incompressible laminar flow problems with mass flow constraints

Abstract

This paper presents an adaptive no-slip boundary conditions scheme within the context of topology optimization of incompressible laminar fluid flow problems with mass flow constraints. The flow of fluid is described by the Incompressible Navier–Stokes (INS) equations and the density-based topology optimization methodology together with Heaviside projection is used to optimize the flow layout. Adjoint sensitivity analysis is used to compute the sensitivities of the objective and constraints which are used by a gradient-based optimizer to solve the problem. To accurately capture flow characteristics and improve computational efficiency of the forward analysis, no-slip nodal boundary conditions are adaptively added (and removed) as the design evolves, with these operations guided entirely by the formal sensitivity analysis. Several design examples are presented, including 2-D and 3-D design problems purposely constructed to challenge the proposed algorithm. Presented solutions are shown to achieve crisp (0–1) representations of topology satisfying required flow rates, with no pressure diffusion and flow seepage through the solid material phase. The results reveal the performance and efficiency of the proposed approach for use in such applications as the design of flow manifolds.