## 5 Validation of the Similitude  
A preliminary validation of the lab-scale configuration with no turbulence injection was presented in a previous study [28]. It confirmed the key role of the mesh adaptation strategy and the validity of the numerical set-up. In the present study, the goal is now to assess the relevance of the similitude methodology that allows the use of the lab-scale configuration in place of a real geometry and operating condition to perform experiments. To do so, velocity profiles corresponding to both lab and engine scales are compared to the experimental data (Figure 10). Recall that these cases correspond to the simulations without turbulence injection at the inlet. The experimental uncertainty, shown by the error bars in the velocity profiles, is equal to 4% for mean velocities and 8% for _rms_ velocities [18]. The provided profiles coincide with the following positions: \(x/D=0\), \(x/D=8\), \(x/D=16.4\), \(x/D=28.4\), \(x/D=33.2\) and \(x/D=40\), shown in Figure 1b. To clarify the figures, the dimensionless velocity profiles are shifted with the addition of \(x/X_{0}\), where \(X_{0}=0.1\) m for axial velocities and \(X_{0}=0.05\) m for vertical velocities. The first observation is the destabilisation and thickening of the boundary layer due to the synthetic jets. The numerical results are similar for the two scales and the boundary layer thickness is particularly well retrieved, as seen with the axial velocity \(u/U_{0}\) profiles in Figure 10a. Note, nonetheless, that both numerical simulations overpredict the  
Figure 10: Comparison of time-averaged axial (u) and wall-normal (w) velocities and associated RMS values for lab and engine scales with experimental data, without turbulence injection at the locations \(\times\) provided in Figure 1.  
Figure 9: Plate temperature field averaged over five periods obtained with \(\Phi=1500\) W.m\({}^{-2}\). jet penetration within the boundary layer compared to experimental results, as seen in the \(w/\overline{W}\) profiles (Figure 9(b)). This leads to some overprediction of the boundary layer displacement thickness close to the wall, and particularly for the first three perforation rows, observed for \(u/U_{0}\) (Figure 9(a)) and \(u_{rms}/U_{0}\) (Figure 9(c)). As the flow evolves along the plate, the experimental axial and vertical velocity profiles are then better reproduced for both the lab- and the engine-scale simulations. The first profiles present some differences while downstream of the seventh row of jets numerical results reproduce the experimental measurements very well. The normalised wall heat transfer coefficent \(h\) obtained by LES is compared to the experimental results in Figure 11. Here, \(h\) is normalised by \(H_{0}\), which equals 1 W.m\({}^{-2}\).K\({}^{-1}\) for the lab scale and 6.25 W.m\({}^{-2}\).K\({}^{-1}\) for the engine scale. The considered axes correspond to those shown in Figure 9(b). First, the simulations retrieve the right order of magnitude and both the lab scale and the engine scale present similar results. Some differences from the experimental data are nonetheless present. To begin with, upstream of the perforations, the heat coefficient \(h\) profiles present a similar shape for the three data sets, corresponding to a developing boundary layer along a flat plate. The slope is, however, larger for the numerical results than for the experimental data. The perforated area can be divided into two main areas: the jet wakes and the zone between the jets. Along the jet wakes, numerical predictions underestimate the heat transfer coefficient \(h\) close to the first perforation whereas it is well reproduced from the second jet row. This observation is linked to the absence of inlet freestream turbulence in the simulation, which seems to be critical for the first row of jets. On the contrary, between the jets, predicted \(h\) evolutions differ from the experimental data.