# 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 flow is from left to right. \(Re\simeq 1300\), \(\sigma_{1}=5.10\pm 0.04\) and \(\sigma_{2}=0.70\pm 0.03\). **(b)** Illustration of the image processing. The treatment is based on binarization, morphological closing and regions labeling (see text for details). The large region close to the throat is displayed in black in the figure, whereas the other small gaseous cavities are in white and the background in pale gray. A binary image (not shown) is generated that only contain the large region close to the throat. **(c)** Time average of 3000 binary images showing the average attached cavity on the side and top views. The colorbar corresponds to the proportion of time when the cavity is present. \(X^{*}=1/\tan\left(8^{\circ}\right)\simeq 7.1\) ; \(Z^{*}=-1\); the two side walls are at \(Y^{*}=\pm 0.5\) and the upper flat wall is at \(Z^{*}~{}=~{}1\). Time series of 3000 images are recorded for each experiment. A background reference image \(I_{ref}\) is also recorded with the same cameras setting, while the flow is at rest. The instantaneous images \(I_{i}\) are then processed with Python, using the scipy.ndimage and scikit-image libraries [33] in the following way, based on Morphological Image Processing [34]:  
* The images are converted to matrices of floats, the background is subtracted and the result is normalized by the background reference image, giving the \(i\)th normalized image of the time series \(I_{i}^{{}^{\prime}}=\frac{I_{i}-I_{ref}}{I_{ref}}\) (see Figure 2a). The gaseous features that are darker than the background have then gray-level values in the range \(-1\) ; \(0\). * Image \(I_{i}^{{}^{\prime}}\) is then binarized with a threshold of \(-0.4\): \(I_{i}^{b}=\left(I_{i}^{{}^{\prime}}<-0.4\right)\) which gives the position of the interfaces between liquid and cavities with a dimensionless accuracy of \(\pm 0.02\) (see Figure 3b for a gray-level profile on a normalized image). * The holes that could remain inside the cavities are then filled with an algorithm based on invading the complementary of \(I_{i}^{b}\) from the outer boundary of the image with binary dilations. Holes are not connected to the boundary and are therefore not invaded. The result is the complementary subset of the invaded region. A filled binary image \(I_{i}^{f}\) is obtained. * The features are then labeled, and their properties are measured with the scikit-image functions measure.label() and measure.regionprops(). A filter on the bounding box of the labeled regions is then used to keep the region that is the closest to the Venturi throat, resulting in a binary image containing a closed and filled representation of the cavity that is attached to the throat \(I_{i}^{a}\). This process is illustrated in Figure 2b where \(2I_{i}^{a}-I_{i}^{f}\) is displayed. * The mean \(I^{m}\) and standard deviation \(I^{rms}\) of the time series of the filtered images \(I_{i}^{a}\) are then computed. The mean image for the series at \(Re\simeq 1300\), \(\sigma_{1}=5.10\pm 0.04\) and \(\sigma_{2}=0.70\pm 0.03\) is displayed in Figure 2c. The length of the attached cavities is then measured on the mean images of the side view, using a threshold \(I^{m}>0.6\). This value corresponds to the region of space where the attached sheet is present on 60% of the time series. For the case illustrated in Figure 2, it gives a length \(L^{*}\simeq 3.5\). Varying the threshold between 0.5 and 0.7--see the colorbar in Figure 2c--leads to a variation of \(\pm 0.2\) on the measure of \(L^{*}\) which is a relative variation of \(\pm 5\%\). Figure 3: Illustration of image processing for the characterization of the temporal features of the attached cavities. (**a**): Instantaneous normalized side view \(I_{i}^{{}^{\prime}}\) at \(Re=1600\), \(\sigma_{1}=4.97\pm 0.04\) and \(\sigma_{2}=1.17\pm 0.03\). (**b**): Gray level along the dashed blue line displayed in (a); \(s^{*}\) is the dimensionless curvilinear abscissa along the line. (**c**): Spatio-temporal diagram along the line; space is from top to bottom and time is from left to right.