A method for topology optimization for high reynolds number flows

Determining the best designs in engineering applications has been the focus of many research endeavors. Over the last century, design optimization techniques have advanced from trial and error tactics to computationally intense numerical schemes. However, even with the high level of computational resources available, tackling highly complex, nonlinear design optimization problems is still problematic. In particular, topology optimization applications in fluid dynamics is a growing field of study and there is little work in high Reynolds number applications. The issues that arise when attempting to apply topology optimization to such a problem are that there may exist many local minima and the design space is very large, topology changes within a high-fidelity flow solver can results in drastically different flow physics in one iteration, and the resulting topology may be lumpy and bumpy creating undesirable effects such as flow separation. The research presented in this paper aims to address these issues by introducing a novel approach for determining a good initial topology that can be used in a high-fidelity flow solver. This new method combines a potential flow solver with a genetic algorithm for fast calculations over a large design space. The problem chosen to test this approach is determining the design and distribution of turning vanes in a 90 degree duct that produce uniform flow at the outlet. Point vortices are used to represent the turning vanes in the potential flow solver. Fifteen test cases are presented: three different problem definitions with five different numbers of points vortices for each problem. First, the vortices are fixed in a conventional turning vane setup and their strengths are held constant among them. Second, the vortices are similarly fixed in space but their strengths can vary. Third, the vortices are free to move in the domain and their strengths are variable. It is shown that allowing the x-and y-coordinates and the vortex strengths to varying produces better results than the conventional setup. The connection between potential flow analysis and physical topologies is explored, as well. Two procedures for creating camber lines from the point vortices are explored and compared. The results support the use of an implicit geometry representation method because the vortices may group together, so the level-set method is investigated. An analysis of two approaches for using the level-set method to represent aerodynamic bodies is presented. Each approach is evaluated based on how well the slopes of a NACA0012 airfoil can be captured.