Body Shape Optimisation for Enhanced Aerodynamic Cooling

Abstract

The study considers a two-dimensional flow of a viscous perfect gas around thermally insulated bodies. Using a composite Bézier curve to describe various body shapes and leveraging a reinforcement learning algorithm, we identify optimal shapes that minimise two distinct objective functions reflecting local or global surface temperature. We show that even at the Reynolds number \({\text{Re}} = 200\), Mach number M = 0.4, and Prandtl number \({\text{Pr}} = 0.72\), one can observe surface temperatures dropping below the free-stream value—a phenomenon known as aerodynamic cooling or the Eckert–Weise effect. The lowest local temperatures are attained at the rear of slender cross-flow plates, exhibiting a time-averaged recovery factor of –0.26, contrasting with 0.31 observed in the canonical flow around a circular cylinder. However, such shapes are not optimal in terms of the surface-averaged temperature of the body—boomerang-like shapes yield the lowest overall temperatures, with a global recovery factor of 0.34, in contrast to 0.63 for the circular cylinder. By independently varying the frontal and rear parts of the body, we propose a rationale behind these optimal shapes.