## 1 Introduction
Although wall heat transfer has not been much studied within acoustic liners, such issues have been considered for other applications of synthetic jets. Most of the applications treating heat transfer with synthetic jets target impinging jet applications [11] while, in acoustic liners, it is the perforated plate crossed by the jets that is of interest. Such a configuration has been studied by [PERSON] et al. [12], who evidenced an enhanced wall heat transfer with synthetic jets compared to natural convection only. They also pointed out that a multi-perforated configuration is more efficient in increasing wall heat transfer than a single perforation. However, their configuration considered only four perforations in a quiescent environment. Another field of research provided information of interest: flow control, more specifically flow separation delay. In this context, the jets are submitted to a grazing flow. [PERSON] et al. [13] experimentally identified different flow structures. Depending on the synthetic jet Reynolds number, stroke length and velocity ratio, hairpins, tilted vortices or vortex rings can be observed. [PERSON] and [PERSON] [14] determined the flow structure impacts on the wall through thermo-sensitive methods: the tilted vortices are evacuated very early out of the boundary layer, while the two other categories have a greater impact on the wall. [PERSON] and [PERSON] [15] numerically reproduced their experiment and observed similar flow structures. They distinguished two kinds of structures, depending on their footprint on the wall heat flux and wall shear stress that can present one (distorted vortex rings) or two (hairpins and stretched vortex rings) streamwise streaks. More recently, [PERSON] and [PERSON] [16] showed the impact of turbulence on hairpin formation: hairpins are more bent-shaped, asymmetric, and are characterised by a higher velocity and dissipation rate in the turbulent case, leading to a wider but weaker impact on the turbulent boundary layer (visible on velocity and gradient profiles) and wall shear stress. These configurations bring information about wall heat transfer around a synthetic jet but are limited to a single jet and their results cannot be directly extended to liners, where a large number of jets interact with each other. [PERSON] et al. [17] studied two in-line synthetic jets and highlighted the importance of the jet phase difference \(\Delta\phi\) in the jet development: the hairpins can merge into combined vortices (\(\Delta\phi=90^{\circ}\)), partially interact (\(\Delta\phi=0^{\circ}\) or \(180^{\circ}\)) or remain separated (\(\Delta\phi=270^{\circ}\)). A recent experimental study proposed by [PERSON] et al. [18] at Pprime Institute (France) investigated the wall heat transfer on a similitude configuration that matches the different aspects of acoustic liners through a scaling: it is multi-perforated (50 perforations distributed in 10 rows of 5) and submitted to a grazing flow. They evidenced the interest of a multi-perforation configuration and obtained Nusselt increases up to 175% when comparing synthetic jets' results with no jet cases. Moreover, they pointed out the interest of a high \(M=\overline{W}/U_{0}\) value: the higher it is, the higher the heat transfer enhancement that is obtained. The goal of the present study based on the experiment of [PERSON] is twofold. The first objective is to validate the numerical methodology used to simulate heat transfer in acoustic liners. To do so, Large-Eddy Simulation (LES) results are compared to experimental data obtained with the test rig. A previous study [19] has shown promising results and provided a preliminar validation of the numerical set-up. However, the upstream turbulence was not considered in that case while a previous study [3] evidenced that inlet turbulence played a key role in the development of the first rows of perforation. To conclude, the similitude is validated comparing numerical results on the lab-scale configuration with the engine-scale predictions. The paper is organised as follows.