Topology optimization of external compressible flow

The problem of an immersed body interacting with the surrounding fluid flow belongs to the category of external flows, wherein, despite the importance of a plethora of applications, previous papers have only undertaken incompressible or inviscid compressible flows. This is the first topology optimization work for viscous compressible external flows. Topology optimization is hereby employed to distribute solid and fluid to feature designs that are free from shape restrictions and independent of the initial guess. Fluid-flow governing equations are solved numerically, and sensitivities are obtained by automatic differentiation. Energy dissipation, vorticity, lift, and drag forces are considered and combined into five different objective functions, with a prescribed upper bound on the fluid volume and a drag constraint. Flow-physics considerations are given to advance the understanding of topology optimization for maximization of lift forces and minimization of drag, and limitations are highlighted on the use of vorticity as an objective function, linked to boundary-layer physics. Among our findings, intricately-curved, sharp-edged, and non-intuitive designs are produced, and the resulting flows exhibit superior behavior in most instances when contrasted with a renowned airfoil. In a particular case, a topology reminiscent of a well-known airfoil structure emerges from the application of our method—called “Gurney flap,” capable of maximizing lift and minimizing drag—previously inspected through trial-and-error approaches and physical intuition, rather than systematically generated through topology optimization, as is revealed here.