After the detonation of an oxygen-deficient homogeneous high explosive, a phase of turbulent combustion, called afterburning, takes place at the interface between the rich detonation products and air. Its modelling is instrumental for the accurate prediction of the performance of these explosives. Because of the high temperature of detonation products, the chemical reactions are mixing-driven. Modelling afterburning thus relies on the precise description of the mixing process inside fireballs. This work presents a joint numerical and experimental study of a non-reacting reduced-scale set-up, which uses the compressed balloon analogy and does not involve the detonation of a high explosive. The set-up produces a flow similar to the one caused by a spherical detonation and allows focusing on the mixing process. The numerical work is composed of 2D and 3D LES simulations of the set-up. It is shown that grid independence can be reached by imposing perturbations at the edge of the fireball. The results compare well with the existing literature and give new insights on the mixing process inside fireballs. In particular, they highlight the fact that the mixing layer development follows an energetic scaling law but remains sensitive to the density ratio between the detonation products and air.