Bodies subject strictly to the effect of the free-stream flow are commonly termed external flows, which span a variety of applications, from small exiting jets all the way to the flow over massive aircrafts. In these cases, flow modelling becomes more complex as the energy equation must be resolved and additional flow variables are necessary to describe the phenomenon, thus rendering the design of these devices more involved. Yet, the literature in topology optimisation is absent in terms of external compressible flows. At present, topology optimisation has focused on creeping and incompressible flows, as well as inviscid fluid, which cannot describe compressible flows. The methodologies developed thereof cannot be used to design external compressible flow devices. We explore this existing gap. Our methodology employs the FEniCS TopOpt Foam framework, which entails finite volume simulations for the direct problem and FEniCS/dolfinadjoint automatic differentiation to attain sensitivities to drive the gradientbased optimisation. For this purpose, we employ a density-based approach, wherein fluid and solid are distributed within the design domain to improve objective functions and satisfy constraints. Here, energy dissipation, vorticity, drag and lift comprise five different objective functions, while upper bounds in fluid volume and drag are imposed. Convergence curves of the objective function and constraints are presented and exhibit favourable behaviour in terms of our methodology. The optimised designs are evaluated in body-fitted grids, and compared with a benchmark NACA 0012 aerofoil. In contrast to previous approaches involving trial-and-error examination, physical intuition and parametric evaluation, our methodology designs a Gurney flap in a systematic fashion with a simple formulation of the optimisation problem. The intricate shapes developed from a simple initial guess demonstrate that our evaluation could not be developed through parametric or shape optimisation, attesting to the capacity of topology optimisation in designing external compressible flows.