# Turbulent Flow over Confined Backward-Facing Step: PIV vs. DNS
## 5 Results and Discussion
### Recirculation Zone, Planes z = Const  
Figure 5 shows the 2D fields measured in the z = 0 plane; case 'z - 0' in Table 1. Case 'z - 0' consists of two separate measurements, which were merged in the post-processing phase. Mild discontinuities can be observed in Figure 5 at x-8, where the fields are glued into a single image, and are a consequence of the uncertainties related to scaling of the images due to the uncertain laser and camera position. These systematic errors dominate the total uncertainty and are quantified for each measurement case in Section 5.5. Measurement data in each plane are available in two separate files, because the coordinates of the rows and columns in the global coordinate system of the experiment do not overlap. The streamwise velocity field shown in Figure 5 shows the expected agreement of the measurements and the black simulation contours. A small vortex can be seen in the bottom left corner (x = 0 and y\(\sim\)\(-\)2) just downstream the step and is visible in both mean velocity components in Figure 5. The large vortex that spans down to the dimensionless length of x\(\sim\)15 (~20 cm behind the step) is clearly visible in the top image of Figure 5. Reattachment point at z = 0 is defined by the point where the contour 0.0 of u velocity touches the y = \(-\)2 plane. Due to the 3D nature of the flow, the reattachment point is actually not a point but a curve on the plane y = \(-\)2. The shape of the reattachment curve can be obtained from the measurements from the different perspective (y = const. planes), and is discussed in the next subsection. Several authors [1; 18; 19; 20] reported that the size of the separation zone in separated flow depends not only on step height but also on the degree of turbulence in the upstream flow. In fact, it has been shown that the length of the separation region decreases with the increasing degree of turbulence in the upstream flow. In particular, [PERSON] and [PERSON] [19] measured the influence of turbulence on the length of the separation region behind the step with height of 40 mm at Reynolds number of 32,000. Our obtained reattachment point at the symmetry plane (i.e., plane z = 0) is 7.5 step heights downstream the step and it corresponds to the turbulence intensity of the inlet flow of about 4%. In general, the length of the separation region behind the step depends on the degree of expansion and asymmetry of the channel, and it varies from 6 to 9 calibers of the step height [1]. Bottom three images of Figure 5 show two components of the velocity fluctuations and one component of Reynolds stress tensor available from 2D measurement in z = 0 planes. One can see that the fluctuations created in the recirculation zone significantly  
Figure 5: Time-averaged velocity field of case ‘z \(-\) 0’: components u and v (**top pair**), u\({}_{\text{RMS}}\),v\({}_{\text{RMS}}\), u’v’ (**bottom triplet**) in plane z = 0. PIV experiment: color-scale and blue contours. DNS—black contours. exceed the fluctuations in the boundary layer of the inlet section: the maximum values of u\({}_{\rm RMS}\) are almost two times higher and the maximum of v\({}_{\rm RMS}\) is roughly three times higher. The first consistency check, which also served as one of the measures of total uncertainty, was a check of the repeatability of the measurements, which was performed in the plane z = 0. Contours shown in Figure 6 compare the measurements of the 'z \(-\) 0' case and the case 'z \(-\) 0a', which was performed 10 days later under the same conditions. The expected agreement has demonstrated the repeatability of the measurements. Only contours of two parameters, u and v\({}_{\rm RMS}\), are shown in Figure 6, with the other three processed quantities showing a similar agreement. Dotted contours in Figure 6 show that positions of the violet contours increased and decreased for 0.03 and 0.01 for u and v\({}_{\rm RMS}\), respectively.