## 7 Conclusions  
The flow dynamics generated by an acoustic liner are characterised by a phenomenon called the synthetic jet: the ambient flow is successively sucked into and ejected from cavities. This mechanism leads to a complex boundary layer development and thus a complex wall heat transfer. In order to better understand wall heat transfer within acoustic liners, numerical simulations were run based on an experimental set-up developed by Institut Pprime (France). The synthetic jets in this configuration are not generated by acoustic resonance, as for acoustic liners, but by pistons. The dimensions and operating points are representative of a classic liner through a similitude methodology. Two sets of numerical simulations were run: one called \"lab scale\", based on the test rig, and one referred to as \"engine scale\" with dimensions and flow conditions directly corresponding to engine conditions. These simulations enabled the validation of the similitude methodology while pointing out its limitations. Although the mechanism is not driven in a similar way (leading notably to a phase lag that appears in the engine scale but not in the lab scale), the synthetic jets are similar for both configurations. In particular, the wall heat transfer coefficients obtained for time-averaged fields are close. The results are in part compared to the \"flat plate\" case by considering the flow dynamics along the plate far from the perforations. Simulations with and without inlet turbulence are compared and analysed for lab scale, and an important element is found to strongly impact the numerical results: the upstream flow turbulence modifies the boundary layer development and thus the wall heat transfer mechanisms. In fact, two competing phenomena are responsible for the flow dynamics: the synthetic jets and the grazing flow. Depending on the velocity ratio \(M=\overline{W}/U_{0}\), one of these two phenomena can become preponderant. As was observed here, the synthetic jets completely drive the flow dynamics in the jet axis, where the upstream conditions do not affect the boundary layer development. However, between the jets, the upstream turbulence is no longer negligible: neglecting it leads to significant errors in wall heat transfer coefficient values. It is assumed that for higher \(M\) values the upstream conditions would tend to become completely negligible, while low \(M\) synthetic jets would be much more driven by the upstream conditions. Figure 16: Time-averaged (over 5 periods) wall heat transfer coefficient \(h\) along different axes. Lab scale. **Author Contributions:** Methodology, S.E., F.D., L.Y.M.G. and S.M. ; Software, S.E. and F.D. ; Validation, S.E. ; Writing--original draft, S.E. ; Writing--review & editing, F.D., L.Y.M.G. and S.M. ; Supervision, F.D., L.Y.M.G. and S.M. ; Project administration, F.D. ; Funding acquisition, F.D. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding  
**Data Availability Statement:** Not applicable  
**Acknowledgments:** The authors acknowledge the DGAC OPTIMA (OPTimisation Thermique de l'Integration des Moteurs d'Avions) project for funding this research and Airbus as a project partner. They also thank Institut Pprime and especially [PERSON] and [PERSON] for the experimental data. This work was granted access by the HPC resources of CINES/IDRIS under the allocation 2018-A0102A06074 made by GENCI. **Conflicts of Interest:** The authors declare no conflict of interest.