# Turbulent Flow over Confined Backward-Facing Step: PIV vs. DNS
## 4 PIV Experiment and Data Processing  
The PIV system consisted of an Nd:YLF double cavity pulsed laser (100 ns pulse) from Litron and a Phantom camera with a maximum resolution of 1280 \(\times\) 800 pixels. With a Tokina 100 mm Macro F2.8 lens, we achieved a resolution of roughly 10 pixels per mm length and an active field of the images around 1250 \(\times\) 450 pixels. To improve the resolution, flow downstream the step was measured in two separated runs, where each of them covered a streamwise length of around 13 cm. Both results were merged in the post-processing phase, where combined fields covered sufficient length to capture the flow behind the step up to the reattachment line, which is around 15-20 cm downstream the step. Camera positioning was performed with 3 mm (~2%) accuracy, which was roughly halved in the post-processing length calibration phase. Hollow glass spheres with a diameter of 9-13 \(\upmu\)m were dispersed in the water to provide particle seeds. With a density of 1.1 g/cm\({}^{3}\) they are close to neutrally buoyant in water. PIV measurements of 2D velocity fields were performed in several planes, as described in Table 1. Two of these planes are also shown in the top-right drawing of Figure 1. The positions of the measured planes in Table 1 are given with respect to the origin of the coordinate system shown in Figure 1.  
The laser sheet was around 1 mm thick. The laser sheet positioning uncertainty was around 0.5 mm (0.04 dimensionless units). PIV algorithm calculates velocity field from cross correlation maps while shifting whole image parts (windows), making it more robust to blurriness and optical distortions. The standard PIV algorithm was used with velocities reconstructed from two consecutive images on the 24 \(\times\) 24 pixel surfaces with 50% overlap. With the optics used, a velocity field spatial resolution of about one vector per 1.2 mm (0.1 dimensionless unit) was achieved. Uncertainties of the PIV technique were analyzed according to [33], and key uncertainties were found to be in positioning of the camera and related scaling of the images. An additional relevant factor was position of the laser sheet. Due to the Cartesian geometry of the test section, and therefore, minimal optical distortions, a simple linear calibration was performed to transform the distances in pixels into the metric units. Known channel widths in combination with calibration plates immersed in vessels parallel to the test section were used as the calibration lengths. Contributions of the uncertainties related to the image quality and PIV data processing accuracy were found to be lower. Due to the 3D nature of the observed flow, a priori uncertainty quantification was not possible. Uncertainty of the observed quantity depends on the local properties of the flow; in particular, on the gradients of the observed quantity. The easiest way to demonstrate that is to observe the influence of the laser sheet positioning uncertainty in measurements of the mean streamwise velocity \(u\) in two planes: \(z=0\), the symmetry plane of the BFS section, and in the plane \(z=1.36\), which is already in the boundary layer region. In the first order approximation, the mean streamwise velocity uncertainty \(\sigma_{u}\) and the laser sheet positioning uncertainty are related:  
\[\sigma_{u}=\frac{\Delta u}{\Delta z}\sigma_{laser}\]  
If the gradients \(\Delta u/\Delta z\) are estimated from our measurement at \(z=0\) and at \(z=1.36\), and 0.04 dimensionless laser sheet position uncertainty is taken into account, we obtain the following:  
\[\sigma_{u}(z=0)\ \sim\ 0\times 0.04\ \sim\ 0\sigma_{u}(z=1.36)\ \sim\ \frac{0.1}{0.2}\times 0.04\ \sim\ 0.02\ (\sim\ 2\%)\]  
These results show that the particular systematic uncertainty, which is negligible in one measurement plane, becomes important in the other plane due to the flow structure. Consequently, a priori uncertainty quantification in the particular flow cannot be performed without at least a rough quantification of the 3D field of the observed variable.