# Turbulent Flow over Confined Backward-Facing Step: PIV vs. DNS
## 2 Experimental and Computational Geometry  
The first test section used in our laboratory by [PERSON] et al. [28] in 2018 was 1 m long. The most recent test section, used for measurements in the present paper, is 1.2 m long. The length, pump flow rate and the desired Reynolds number constrains resulted in a duct with inlet section with 45 \(\times\) 20 mm\({}^{2}\) cross-section, a step height of 25 mm, and a square duct of 45 \(\times\) 45 mm\({}^{2}\) downstream the step. The geometry has an expansion ratio of 2.25. The part of the section downstream the step was extended from 32 cm in the first test section to 52 cm in the second and the third test section in order to diminish the effects of the constriction at the outflow, where the section is connected to a pipe with a diameter of 10 mm. The complete backward-facing step test section, schematically shown in Figure 1, was manufactured from 10 mm thick polycarbonate plexiglass, to provide the transparency needed for PIV measurements. Water was used as a working fluid at a temperature of 24 \(\pm\) 0.5 \({}^{\circ}\)C in order to minimize the variations of viscosity. The test section was positioned vertically and plumbed as a semi-open (non-pressurized) loop. Pump operating at constant flow rate was delivering water into the test section and into the by-pass loop. A valve was used for accurate setting of the mass flow rate through the main loop. The Coriolis flowmeter (Emerson Micro Motion) was used to measure the mass flow rate with an accuracy of 0.5% of the measured value. The Reynolds number, based on the hydraulic radius of the inflow and the bulk velocity at the inflow was equal to 7100. Fluctuations of the Reynolds number 7120 \(\pm\) 20 were observed in the recorded histories of the mass flow rates during the measurement and are below the uncertainty of the flowmeter. Each experimental case in Table 1 was performed with two separate measurements with position of the camera changed in x direction in each measurement. This approach improved the spatial resolution of each measurement in comparison with the first two experimental campaigns, but required an additional post-processing step where two measurements were merged in a streamwise direction. Small discontinuities are visible in the results of the measurements presented in several of the figures below for most of the cases in Table 1; nevertheless, this approach, with a reduced field of view, increased the spatial resolution of the measurements. The magnitude of the uncertainties related to the merging of images is closely related to the uncertainties of the camera position setting, image scaling and laser sheet position and is discussed in Sections 4 and 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case Name** & **Re** & **z (mm)** & **z Dimensionless** \\ \hline \({}^{\prime}\)z \(-\) 1.36\({}^{\prime}\) & 7120, 7120 & \(-\)17 & \(-\)1.36 \\ \({}^{\prime}\)z \(-\) 0.8\({}^{\prime}\) & 7140, 7120 & \(-\)10 & \(-\)0.8 \\ \({}^{\prime}\)z \(-\) 0\({}^{\prime}\) & 7120, 7120 & 0 & 0 \\ \({}^{\prime}\)z + 0.8\({}^{\prime}\) & 7120, 7120 & 10 & 0.8 \\ \({}^{\prime}\)z + 1.36\({}^{\prime}\) & 7120, 7120 & 17 & 1.36 \\ \({}^{\prime}\)z \(-\) 0a\({}^{\prime}\) & 7130, 7120 & 0 & 0 \\  & & **y (mm)** & **y Dimensionless** \\ \({}^{\prime}\)y + 0.8\({}^{\prime}\) & 7120, 7120 & 10 & 0.8 \\ \({}^{\prime}\)y \(-\) 0.8\({}^{\prime}\) & 7130, 7130 & \(-\)10 & \(-\)0.8 \\ \({}^{\prime}\)y \(-\) 1.6\({}^{\prime}\) & 7110, 7130 & \(-\)20 & \(-\)1.6 \\ \({}^{\prime}\)y \(-\) 1.92\({}^{\prime}\) & 7130, 7120 & \(-\)24 & \(-\)1.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of measurements in the planes z = const. and in the planes y = const. Each case contains two measurements: one with camera at position at x = 4 cm and another at x = 16 cm. Reynolds numbers are given for each of them. Figure 1: **Left:** Test loop configuration. **Top-right:** Schematic of the test-section, coordinate system and measurement planes z = 0 (green) and y = 0 (blue). In parentheses: dimensionless lengths.