# Numerical Insight into the Kelvin-Helmholtz Instability Appearance in Cavitating Flow
## 4 Results
In steps (7-9) we notice the change of the velocity profiles, caused by the separation of the cavity from the Venturi throat and hence smoothing of the velocity profiles in the horizontal direction. The region of constant velocity near the upper Venturi section wall is reduced and the velocity profiles in horizontal direction become skewed. Regions of backflow are reduced in size and intensity. In steps (7-9) generation of Kelvin Helmholtz instabilities increase further downstream of the detached cavitation cavity. Finally, the entire detached cavitation cloud becomes  
Figure 5: Development of Kelvin-Helmholtz instability with velocity profiles at individual cross-sections. The time difference between the images is \(\Delta\)t = 100 μs. engulfed in the border instabilities. In addition to the change of velocity gradient, the vapor fraction \(\alpha\) in the vertical direction becomes non-homogeneous and areas of slightly higher vapor fraction \(\alpha\) can be traced to the region where instabilities were initially formed. The detached cavitation cloud together with all instabilities continues to flow downstream and finally dissipates (not shown in this sequence). In step (10), 900 \(\upmu\)s after the start of the instabilities formation, cavitation cavity is again formed at the Venturi throat section and the entire process is about to continue in a quasi-periodic way. More insight into the instability formation process may be gained from Figure 6, which shows an enlarged segment of the Venturi section relative to Figure 5.  
Velocity vectors reveal the presence of the turbulent eddies within the vapor phase and their interaction with the main flow above the discontinuity of the horizontal velocity. Figure 6 also shows contours of 10% vapor region location. Step (1) shows the initial situation with a turbulent eddy on the right side of the observation region. Just next to the lower limit of 10% vapor region is the turbulent eddy impingement point on the shear layer. On the left of the 10% vapor fraction region, we observe the backflow, while on the right the turbulent eddy rotation causes the flow velocity to be in the direction of the main flow. Impingement point marks the position of the large variation of the shear stress gradient, on the left of the impingement point, the stress is higher than on the right. The horizontal 10% vapor fraction region limit of the velocity discontinuity is just above the impingement point. The transition from step (1) to step (2) is marked with an additional depression of the horizontal 10% vapor fraction region limit. The location of the impingement point and the horizontal 10% vapor fraction region has moved to the right in step (2) relative to step (1), while the lower 10% vapor fraction region has widened from the original location in step (1) to the newly established impingement point of step (2). Figure 6: A close-up view of the initial development of Kelvin-Helmholtz instability. The time difference between the images is \(\Delta\)t = 20 \(\upmu\)s. The black line shows a 10% vapor fraction region limit. As the instability process continues in step (3) we observe gradual folding of the lower 10% vapor fraction limit, even before we notice significant variations in the velocity within the shear layer. We, therefore, speculate that the vapor fraction properties influence the instability process through the variation of the flow density and the transfer of the momentum. In step (3) we notice velocity variations within the main flow, corresponding well to the vapor fraction variations in intensity and location. The process, first observed in step (3) continues with step (4) showing increased spatial variations of the vapor fraction, followed by velocity variations in the main flow. As a consequence, turbulent eddy, first responsible for impinging the shear layer, is decayed into two turbulent eddies with an additional one formed near the location of the original impingement point.