Coupled x-ray high-speed imaging and pressure measurements in a cavitating backward facing step flow

The purpose of the present experimental study is to get a better understanding of the dynamics of the vapor phase spatiotemporal repartition in a cavitating backward facing step flow. We provide a refined data base of the use of the void fraction transport equation to model such flows. The backward facing step flow provides a well-known test case to compare vortex dynamics between single and two-phase flow. To evidence the vapor phase dynamics, the flow is probed by high-speed x-ray attenuation techniques and by pressure fluctuation measurements at the walls. Long-time dynamics are also visualized using conventional high-speed imaging synchronized with pressure measurements. Large vortex structures, free shear layer instability, wall interaction and reverse flow are observed. The two-phase structures are studied at different cavitation levels corresponding void fractions ranging from 1% to 50%. The topology of the mean and fluctuating void fraction maps is performed, leading to the establishment of three specific areas in the flow. These areas are distinguished by the underlying mechanisms happening within them: vaporization, transport, and condensation. The statistical analysis underlines the existence of extreme events associated with high void fraction levels and wave propagations. While these events are associated with topological changes from a shear layer to a wake mode that also exist in the single-phase case, they are associated with much lower frequency at high cavitation levels.

Figure 1

(a) Backward facing step test section. The dimensions are $h=51.8$ mm, $w=80$ mm, $H=88.8$ mm, and $L=500$ mm. The orange dots indicate the locations of the pressure probes. P00 is located the step vertical wall, at midheight; P01 to P15 re located after the step, on the test section bottom wall, spaced by h/2. (b)–(f) Representative snapshots of the different cavitation level imaged by a back-lit high-speed camera (see Table 1; the paper focuses on operating conditions CAV1-3).

Figure 2

Experimental setup for high-speed x-ray attenuation measurements.

Figure 3

Example of instantaneous void fraction field (%) for the CAV2 conditions. The step is located at ${\mathrm{x}}^{*}=0$

Figure 4

Mean void fraction (%) for different cavitation cases. Note that the colormap is different for each subfigure as the void fraction changes drastically.

Figure 5

Evolution of the maximum of the mean void fraction field with the longitudinal direction, for different cavitating cases.

Figure 6

Close-up visualizations of the recirculation area, immediately after the step, for different cavitating cases.

Figure 7

Rms values of the void fraction for different cavitation cases. Note that the colormap is different for each subfigure as the void fraction changes drastically.

Figure 8

Spatiotemporal correlation functions for the three developed cavitating cases. The red lines are linear fits of the correlation maxima. The dashed line is a fit of the secondary maxima.

Figure 9

(a) Extreme event in the CAV3 case (top and side views). The two longitudinal vortices are located in the center of the pictures, surrounded by two transverse vortices characterized by high void fraction and circled in red. (b) Corresponding pressure signature at the step wall.

Figure 10

Void fraction power spectra for the three developed cavitating cases. The frequency axis is normalized into a Strouhal number using the inlet mean velocity and the step height.

Figure 11

Spatiotemporal diagrams of void fraction at ${\mathrm{y}}^{*}=0$ and pressure fluctuations (Pa) at the step wall for the CAV3 case. The pressure diagram, obtained on 15 points along $x^{*}$, is interpolated linearly here.

Figure 12

(a), (b) Two instantaneous snapshots of the CAV3 case showing a shear layer (a) and wake mode (b). The red lines delaminate the shear layer expansion. (c), (d) Respective sketches from Hudy et al. 2007.

Figure 13

Temporal evolution of the void fraction for the CAV3 case, centered around the extreme event at ${\mathrm{t}}^{*}=0$.