Kelvin-Helmholtz instability, surface

The proposed approach will also represent an advance in multiphase fluid flow numerics. The numerical treatment of the interface will use the highly accurate approach of Nallapati [13]. The free surface will be a true interface, maintained coincidentally with cell faces on a deforming unstructured mesh. This approach allows the possibility of capturing the rapid velocity change near the interface that may play a pivotal role in spray behavior. This gradient controls the Kelvin-Helmholtz instability. 

Figure 10. One frame from the calculation of the evolution of a Kelvin-Helmholtz instability at the surface of a round jet of air into an air background. Cylindrical symmetry -was used and the axis of symmetry is. the left-hand bo mdary. The inflow speed is about 10 cm/s, and the outer co-flow is about 10 cm/s.

This instability mechanism can lead to turbulence. Kelvin-Helmholtz instability is a form commonly observed in the presence of a strongly sheared flow in the interior of a fluid. Turbulent surface layers can also develop by this mechanism. 

As described above, instability of the interface between the electrolyte and molten metal is a significant problem that is one root cause of the energy inefficiency of Hall cells. Expressed simply, the interface is deformed by the electromagnetic body forces arising from the interaction between currents in the cell and the magnetic field. The currents are themselves affected by the interface position because it determines the distance between the top surface of the aluminum and the bottom of the anode. There is therefore the possibility that interface deformation leads to further interface deformation. Other mechanisms for generating waves at the interface may be significant, for example, the Kelvin-Helmholtz... 

Figure 6.1 Three regimes of canopy flow. Three scales of turbulence are present. The smallest scale (black circles) is set by the canopy morphology, specifically the diameter of and spacing between individual canopy elements, such as stems and branches. Drag discontinuity at the canopy interface generates a shear-layer that produces vortices via Kelvin-Helmholtz (K-H) instability (shown as solid, black ovals). Boundary layer vortices are present above the canopy (dashed gray). When H/h is small the water surface constrains the boundary layer eddy scale.

A review of the past literature on the available correlations on the mean droplet size produced by splash plate nozzles shows that there are large discrepancies between the results. The prediction of the droplet sizes generated by splash plate nozzles is based on the Kelvin-Helmholtz (K-H) instability theory for a liquid sheet. Dombrowski and Johns [14], Dombrowski and Hooper [18] and Fraser et al. [13] developed such a theoretical model to predict droplet sizes from the breakup of a liquid sheet. They considered effects of liquid inertia, shear viscosity, surface tension and aerodynamic forces on the sheet breakup and ligament formation. Dombrowski and Johns [14] obtained the following equation for droplets produced by a viscous liquid sheet ... 

The Kelvin-Helmholtz (KH) instability causes the sheared interface between two fluids that move horizontally at different velocities to form waves (Figure 1.4d). Below a threshold value, surface tension stabilizes the interface. Above the threshold, waves of small wavelength become unstable and finally lead to the formation of drops (liquid-liquid flows) or bubbles (gas-liquid flows), defined by the microchannel dimensions. Surface tension will suppress the KFl instability if [57]... 

This arises when two layers of fluids (may not be of same species or density) are in relative motion. Thus, this is an interfacial instability and the resultant flow features due to imposed disturbance will be much more complicated due to relative motion. Physical relevance of this problem was seized upon by Helmholtz (1868) who observed that the interface as a surface of separation tears the flow asunder. Sometime later Kelvin (1871) posed this problem as one of instability and solved it. We follow this latter approach here. The basic equilibrium flow is assumed to be inviscid and incompressible - as two parallel streams having distinct density and velocity - flowing one over the another, as depicted in figure below. 

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