# Turbulent Flow over Confined Backward-Facing Step: PIV vs. DNS
## 5 Results and Discussion
### Inlet Boundary Conditions  
Comparison of the measurement and DNS starts in the inlet part of the test section. In the fully developed DNS, statistically steady turbulence is established through the implementation of the streamwise periodic boundary conditions on a short part (six dimensionless units) of the inlet section. In the experiments, fully developed flow is established with sufficiently long inlet section. The requirement for entrance length can be reduced if the large-scale turbulent structures are destroyed on the inlet. In the present test section, this was achieved with a diffusor: an acrylic piece covering the 20 mm \(\times\) 45 mm\({}^{2}\) cross-section entrance with 15 holes of 1 mm diameter distributed over the inlet surface. The preliminary analysis performed by [PERSON] et al. (2018), according to the guidelines of [PERSON] (2014), resulted in the inlet part of the test section, which is 68 cm long (\(\sim\)25 hydraulic diameters). Inlet section streamwise velocity profiles and velocity RMS fluctuations are extracted from four measurements and compared with the DNS in Figure 4. All measurements and simulation results are taken 10 mm upstream of the step, which corresponds to x = \(-\)0.8 plane. Positions of the line segments where the profiles are taken are shown in the inset images. The two graphs at the top of Figure 4 show the u velocity and u and w velocity  
Figure 3: Time history of the streamwise velocity component u in point #46. PIV: (5.83, \(-\)0.16, 0), DNS: (6, \(-\)0.2, 0). **Top-left**: experiment, case ‘z \(-\) 0’, **Bottom-left**: DNS. **Bottom-right**: frequency spectra of PIV and DNS time histories in point #46. RMS fluctuation profiles extracted from the measurement case 'y + 0.8', while the bottom row of Figure 4 contains the profiles from the measurement cases 'z - 1.36', 'z - 0', and 'z + 1.36', together with two DNS profiles taken at x = \(-\)0.8, z = 0 and x = \(-\)0.8, z = +1.36. DNS profiles at x = \(-\)0.8, z = \(-\)1.36 are not given due to the symmetry of the z = \(-\)1.36 and z = +1.36 results. Uncertainty bands in the top graphs of Figure 4 mark the magnitude of the measurement uncertainties in mean velocities and velocity fluctuations. Quantification of these uncertainties was performed a posteriori and is described in Section 5.5. A rough estimate is that the total measurement uncertainties are around two times larger than the statistical uncertainties of the measurements and DNS. Several other observations follow from Figure 4:  
* Measured mean streamwise velocity profile is slightly flatter in the central region of the inlet section (Figure 4, top-left) than in the DNS. Maximum velocity in the axis of the inlet section DNS is higher than in the experiment, despite having the same Reynolds number and mass flow rate. On the other hand, measured mean velocities are higher near the walls (Figure 4, both left graphs: \(\sim\)0.6 length units of the near-wall regions). We can see that uncertainty bands of both profiles overlap in most of the central region; however, the measurement and DNS seem to be consistent, and they both show very smooth profiles with clearly distinguishable difference. The same behavior is observed in the z direction and in y direction measurements. Thus, we believe that the flat measured profile, which is somewhat different than  
Figure 4: **Top**: profiles of u (**left**), uRMS, wRMS (**right**) at line segment x = \(-\)0.8, case ’y + 0.8’ in Table 1 (green line on top inset drawing). **Bottom**: profiles of u (**left**), uRMS (**right**) at line segments x = \(-\)0.8 in cases ’z – 0’, ’z – 1.36’, ’z + 1.36’ (green lines on bottom inset drawing). Symbols: PIV, lines: DNS. in the DNS, comes as a consequence of a slightly too short inlet section of around 25 hydraulic diameters based on the guidelines of [34].