# Development of Attached Cavitation at Very Low Reynolds Numbers from Partial to Super-Cavitation
## 2 Experimental Study Overview
### Control Parameters, Flow Visualization and Measured Quantities  
The inlet and outlet test section absolute pressure, named \(P_{1}\) and \(P_{2}\), are measured with two pressure transducers located respectively at 103 mm upstream and 201 mm downstream of the Venturi throat. The discharge throat velocity \(V_{in}\) at \(S_{in}\) is computed from flow rate measurements. The viscosity and density have been measured as a function of the temperature [32]. The following dimensionless numbers are defined based on these values: a Reynolds number \(Re\), an inlet and an outlet cavitation numbers \(\sigma_{1}\) and \(\sigma_{2}\) and a capillary number \(Ca\). The definition of these parameters, together with the ranges that have been explored in the present article and the associated uncertainties, can be found in Table 1. Please note that the outlet cavitation number \(\sigma_{2}\) has not been considered in the previous study [28]. It is used in the present article as it seems to be more significant for analyzing the results. We also introduce a dimensionless pressure coefficient \(K_{p}\). Please note that \(K_{p}\) is simply \(K_{p}=\sigma_{1}-\sigma_{2}\). Two Optronis CR1000x3 high-speed cameras are used to visualize the cavities. The two cameras allow synchronized pictures from the top and from the side of the test section, with a field of view of \(1280\times 512\) pixels. Image sequences of 2 to 3 seconds are recorded at 1500 Hz or 1000 Hz. The flow is illuminated from the bottom and the backside with two continuous white LED plate from Phlox and consequently, the gaseous cavities appear as black features in the images. A typical result obtained at \(Re\simeq 1300\) is displayed in Figure 2.  
Figure 1: Sketch of the Venturi geometry. The width of the test section is \(w=10\) mm and its height at the inlet section is \(h_{in}=20\) mm. In the following of the article the axes origin is positioned at the Venturi throat edge in the middle of test section along the width. Reprinted with permission from [PERSON], Ph.D. dissertation [32]. The height of the Venturi throat \(h_{throat}=10\) mm is chosen as the reference length scale for the dimensionless coordinates \(X^{*}\), \(Y^{*}\) and \(Z^{*}\) (see also the bottom right part in Figure 1 for the definition of the coordinate system). The origin of the positions is on top of the wedge, in the symmetry plane of the flow vein. The diverging part of the Venturi section thus extends from \(X^{*}=0\) ; \(Z^{*}=0\) to \begin{table}
\begin{tabular}{l l r r r} \hline
**Symbol** & **Parameters** & **Definition** & **Range** & **Unit** & **Uncertainty** \\ \hline \(P_{1}\) & Inlet pressure & \([146;708]\) & mbar & \(\pm 1\) \\ \(P_{2}\) & Outlet pressure & \([2;294]\) & mbar & \(\pm 1\) \\ \(T\) & Operating temperature & \([18.0;22.0]\) & \({}^{\circ}\)C & \(\pm 0.1\) \\ \(V_{in}\) & Inlet velocity & \([2.12;5.68]\) & m\(\cdot\)s\({}^{-1}\) & \(\pm 0.02\) \\ \(\rho\) & Oil density & \([960.6;962.9]\) & kg\(\cdot\)m\({}^{-3}\) & \(\pm 0.2\) \\ \(\
u\) & Oil kinematic viscosity & \([52.5;56.9]\) & mm\({}^{2}\cdot\)s\({}^{-1}\) & \(\pm 2\)\% \\ \hline \(Ca\) & Capillary number & \(\frac{\rho v\,V_{in}}{S}\) & \([5.4;15.1]\) & \(\leqslant\)3\% \\ \(K_{p}\) & Pressure loss coefficient & \(\frac{P_{1}-P_{2}}{\frac{1}{2}\rho V_{in}^{2}}\) & \([3.11;6.50]\) & \(\leqslant\)4\% \\ \(Re\) & Inlet Reynolds number & \(\frac{V_{in}h_{in}}{\
u}\) & \([797;2056]\) & \(\leqslant\)3\% \\ \(\sigma_{1}\) & Inlet cavitation number & \(\frac{P_{1}-P_{2}}{\frac{1}{2}\rho V_{in}^{2}}\) & \([4.42;7.61]\) & \(\leqslant\)2\% \\ \(\sigma_{2}\) & Outlet cavitation number & \(\frac{P_{2}-P_{2}}{\frac{1}{2}\rho V_{in}^{2}}\) & \([0.02;3.50]\) & \(\leqslant\)2\% \\ \hline \end{tabular}
\end{table} 
Table 1: Flow parameters, ranges and estimated uncertainties for silicone oil 47V50. The surface tension is \(S\simeq 20\) mN\(\cdot\)m\({}^{-1}\) and the vapor pressure is \(P_{v}\simeq 1.3\) Pa according to the oil data file. Figure 2: **(a)** Typical side (left column) and top (right column) instantaneous views.