## 4 General Flow Description  
Figure 5 illustrates the flow evolution over a period \(T\) of the piston motion, for the lab-scale configuration with no turbulence injection. Upstream of the first row of perforations, the grazing flow boundary layer as well as the wall shear stress present similar evolutions for the four considered instants: the boundary layer thickens, leading to a decreasing wall shear stress. This is characteristic of a classical flat plate. Around the first row of perforations, the flow is then completely disturbed by the synthetic jets and its evolution is no longer comparable to that of a flat plate. Two time phases have to be distinguished: the ejection and suction mid-period. The ejection mid-period is characterised by the interaction of the jets and the grazing flow boundary layer, which is destabilised by unstable shear layers. The turbulence levels rise and the formation of several coherent flow structures can be observed (cf. Figure 6). Horseshoe vortices are formed upstream of the first perforations, due to a blockage effect, and counter-rotating vortex pairs (CRVP) can be observed downstream the perforations. The greatest observable structures are hairpins, which have been found to interact with the boundary layer and to affect the wall heat transfer [13; 14; 15; 16]. The upstream structures are more coherent than those that are formed downstream, where all the structures interact and the flow transitions to turbulence. The impact of flow structures on the plate can be noticed through the wall shear stress. This impact is similar all along the perforated zone, except for the first row of perforations where the flow is laminar. Contrarily, the aspiration phase is characterised by a heterogenous wall shear stress, and two regions can be identified: the jet axis and the in-between-jets axis. In the jet axis, the boundary layer is sucked through the perforations. A boundary layer is then established after each perforation. This leads to significant wall shear stress. Between jet lines, the flow behaviour is totally different. The decreasing evolution of the wall shear stress corresponds to a thickening boundary layer. Overall, the boundary layer is deeply impacted by the synthetic jets, which, through the wall shear stress modifications, leads to a wall temperature decrease [19]. Concerning wall heat transfer, since the vortical structures impact the whole perforated surface from the third perforation row in a similar way during the ejection mid-period, the temperature is more homogeneous on the last portion of the plate compared to the upstream part where the flow is mainly laminar (Figure 7). During the suction phase, two different behaviours are observed. In the jet axis, the heat transfer is particularly efficient due to the formation of new, thin boundary layers. However, the thickening of these boundary layers in between the jets decreases the heat transfer. The wall temperature is hence highly heterogenous: the plate is efficiently cooled down in the jet axis but not in between them. Figure 5: Flow evolution along a period \(T\) for the lab-scale configuration without turbulence injection: instantaneous axial velocity field in the symmetry plane and wall shear stress along the perforated plate. To illustrate the unsteadiness of the the flow, Figure 8 presents the different values that can be taken by the temperature through several periods of the piston motion along two axes: the jet axis and the in-between-jets axis. The time-averaged values are provided for the whole period (\"global mean\") as well as the ejection mid-period (\"ejection mean\") and the aspiration mid-period (\"suction mean\"). To complement this statistical view of the profiles, PDF distributions are obtained by recording, for each position \(x/D\), all of the temperature values that can be reached over time. The sampling chosen here is 40 savings per period \(T\).