The present study is devoted to the analysis of the behaviour of the flow through an effusion-cooled aeronautical combustor model. High-fidelity calculations are performed on an experimental model of a combustion chamber multi-perforated wall and compared to experimental measurements. The effect of combustion instability on the effusion-cooling system is investigated by studying the interaction of an acoustic wave with the jets-in-crossflow issued from the cooling plate. It is shown that the mass-flow rate through the plate can be drastically reduced by the acoustic wave, which demonstrates the destructive effect that such instability may have on the cooling of an aeronautical combustion chamber.