## 6 Upstream Turbulence Impact
First, the PDFs for both the jet axis and between the jets are narrower in the turbulent case than in the laminar one, indicating a lower temperature standard deviation. The second point is that higher temperatures can be reached in the reference case than in the turbulent case. This is particularly visible in the jet axis plane between the first and second perforations, where a temperature peak around 360 K is found for the reference case while it reaches only 350 K in the turbulent one. This lower peak is linked to the fact that the upstream turbulence  
Figure 14: Phase-averaged wall shear stress along the perforated plate, with and without turbulence at inlet, for three axes: the symmetry line (jets), in between the jets (IB) and far from the jets (FP: “flat plate”). Lab scale. contributes to lower synthetic jets at the first perforation rows and lower hairpins. Such a difference in temperature can also be observed between the jets. For \(x/D>25\), the maximum temperature reaches around 380 K in the reference case while it does not get higher than 360 K with upstream turbulence. This can be attributed to the development of the hairpins, which were shown to widen in the presence of turbulence, leading to lower temperatures farther from the jets. Moreover, the higher turbulence levels also lead to an increased mixing and therefore lower wall temperatures. The previous results on wall shear stress and temperature with and without upstream turbulence show that the synthetic jets drive the flow most of the time but upstream turbulence can become preponderant in some specific locations and at specific instants. As a result, the wall heat transfer coefficient \(h\) differs with the two inlet flow conditions. Figure 16 compares the heat transfer coefficient along the jet axis (Figure 16a) and between the jets (Figure 16b), for lab-scale simulations with and without upstream turbulence, with the experimental data. On the jet axis, the simulation without upstream turbulence is already really close to the experimental data. This is consistent with the conclusions obtained from the wall shear stress analysis: the synthetic jets drive the flow at this location. However, there is still one difference along the first two perforation rows, where the results are even closer to the experimental data for the turbulent case. The upstream jets are directly bent by the grazing flow, and thus by the upstream turbulence, while the downstream jets are impacted by the upstream jets, which impose their dynamics to the flow. Between the jets, the effect of the upstream turbulence is much more important than for the jet axis. In particular, the heat transfer coefficient gets higher in the turbulent case from the third perforation and remains higher until the end of the plate. This higher value matches that of the experimental data downstream of the perforations, while the simulation without upstream turbulence is characterised by an underpredicted heat transfer coefficient. Here again, this observation is consistent with the wall shear stress analysis: between the jets, the flow behaviour is no longer driven by the synthetic jets but rather by the upstream conditions. It is thus logical to better predict heat transfer at this location with the appropriate numerical upstream conditions. To conclude this analysis, the flow is mainly driven by two different mechanisms: the synthetic jets and the upstream conditions. In the specific operating point considered for the present study, the synthetic jets are the dominant mechanism most of the time, especially along the jet axis. Neglecting the upstream turbulence does not strongly affect the numerical results. However, between the jets the upstream turbulence does have an impact and should not be neglected. The importance of upstream conditions regarding the jets is characterised by the velocity ratio \(M=\overline{W}/U_{0}\), which is here equal to 0.16.