# Numerical Insight into the Kelvin-Helmholtz Instability Appearance in Cavitating Flow
## 4 Results  
First, we assess the capability of the numerical simulation to capture the general cavitation dynamics which was observed inside the microchannel--more specifically the onset of the Kelvin-Helmholtz instability (Figure 4). The flow is from the left to the right, the time difference between the images is 100 \(\upmu\)s.  
The experiment and simulation both reveal the same story, but in the case of simulation, the Kelvin-Helmholtz instability is more pronounced and can be understood better and described more in detail. In Figure 5, the development of the Kelvin-Helmholtz instability is shown with velocity profiles drawn over at cross-sections at horizontal intervals of 3 mm in the downstream direction, starting at the wedge apex. Fluid flow velocity at the throat of the Venturi microchannel is 30 m/s, where liquid flows over the cavity and descents afterward towards the bottom wall of the channel, where the flow divides into the upstream and downstream flow (1). Vapor fraction \(\alpha\) profiles for both phases are approximately uniform in both the fluid and vapor layers. They are however discontinuous at the straight interface between the two (step 1). Shear stress acts on the fluids due to discontinuity of the velocity gradient (velocity gradients are shown by the black line in Figure 5), while vapor gradient locally promotes the generation of instabilities and vorticity. The backflow due to the presence of the adverse pressure gradient at 6 mm downstream from the throat in the vapor phase increases from a peak value of 5 m/s to 13 m/s (step 2), which further increases shear stress. Increased shear stress between the liquid and cavity interface results in the formation of ripples on the interface, while the reentrant jet progresses further upstream. The attached cavity expands and reaches its full size (step 2) and shortly thereafter (100 \(\upmu\)s) in step (3) one can see the first beginnings of ripples on the upper edge area of the vapor phase (approx. 6 mm from the Venturi throat). This promoting the formation of instabilities (step 3) in addition to the already present vertical shear stress between the liquid flow and the cavity interface enables the formation of Kelvin Helmholtz instability. Figure 4: Separation of cavitation clouds and Kelvin-Helmholtz instability formation (experiment: m = 9.15 g/s, \(\Delta\)p = 4.00 bar, \(\sigma\) = 1.24; simulation: m = 9.03 g/s, \(\Delta\)p = 3.71 bar, \(\sigma\) = 1.26). The time difference between the images is \(\Delta\)t = 100 \(\upmu\)s.  
In step (4), 300 us after the start of the instability formation process, we already observe the formation of unstable local turbulent structures approx. 6 mm from the Venturi throat, which are now confined to the shear layer. Due to their limited size, velocity gradients in step (4) are still unchanged in comparison to step (1) and the rolling motion of turbulent structures is not yet recognized. With time, the surface becomes more and more deformed from the original straight boundary interface, and turbulent structures grow in size and number (step 5). It seems that the vapor region is affected by the formation of turbulent structures, here velocity, density, and momentum are low. Velocity profiles in the vapor region change with instabilities continuously protruding deeper in the vapor region, finally leading to the situation in step (5). Instabilities in the vapor phase continue to grow from step (5), and the region of high pressure between the cavities moves in the opposite direction to the main flow towards the Venturi throat, from approx. 4 mm in step (5) to approx. 2 mm in step (6). Advance in the direction opposite is related to the presence of the adverse pressure gradient (step 6), with instabilities and turbulent eddies in later steps reaching the Venturi throat section and causing full cavity separation and partial destruction of the vapor region in the vicinity of the throat. The vapor phase in the vicinity of the throat does not reappear until step (10) 900 us after the start of the process.