Fluid-flow topology optimization methods feature the ability to find optimal shapes and flow-channel layouts for a wide range of fluid flows. Fluid-flow topology optimization was first explored through density-based methods considering Stokes flow. The solid region of the design domain is implemented into the flow regime by dampening their velocities with an inverse permeability term or by considering them as a porous medium governed by Darcy's law. These approaches were later expanded to consider laminar and turbulent Navier-Stokes flows. While fluid-flow topology optimization efforts have greatly expanded their methods to consider a wide range of flow types defined by the Reynolds number, a study on the effects of the Reynolds number on the topology optimization of Naiver-Stokes flows has yet to be presented. In this work, a parametric study of the Reynolds number is performed to investigate its effects on the results of a density-based topology optimization method for incompressible Navier-Stokes flow. To this end, an in-house finite element analysis code is developed along with an optimization framework. The nonlinear Navier-Stokes equations are solved using a trust-region Newton's method, while the sensitivity analysis is carried out using the adjoint method. The optimization process is updated using the method of moving asymptotes so that the flow's compliance is maximized. To showcase the effects of the Reynold's number on the results of the fluid-flow topology optimization method, two numerical examples are solved with their corresponding velocity and pressure profiles. The implications of the Reynold's number is discussed, with a special interest given to the differences and similarities between problems under Stokes flow and Navier-Stokes flow.


A Parametric Study on the Effects of Reynolds Number on the Topology Optimization of Navier-Stokes Flows

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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