Kelvin-Helmholtz mechanism

As described previously, in the atomization sub-model, 232 droplet parcels are injected with a size equal to the nozzle exit diameter. The subsequent breakups of the parcels and the resultant droplets are calculated with a breakup model that assumes that droplet breakup times and sizes are proportional to wave growth rates and wavelengths obtained from the liquid jet stability analysis. Other breakup mechanisms considered in the sub-model include the Kelvin-Helmholtz instability, Rayleigh-Taylor instability, 206 and boundary layer stripping mechanisms. The TAB model 310 is also included for modeling liquid breakup. 

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... 

It is anticipated that the results of calculations will show the governing mechanisms of primary atomization. They will indicate the relative importance of turbulence, the Kelvin-Helmholtz instability, the Rayleigh-Taylor instability, the initial perturbation level (attributable to cavitation or oscillations in fuel injection equipment), and other phenomena. The quantitative detail of the simulations will provide information and inspiration for the construction of a new generation of spray models. The proposed code can be used for other kinds of simulations, including wall impingement, liquid film flow, and impinging injections. 

Crapper, G.D., N. Dombrowski, W. P. Jepson, and G. A.D. Pyott. 1973. A note on the growth of Kelvin-Helmholtz waves on thin liquid sheets. J. Fluid Mechanics 57 671-72. 

Fig. 9.1 Schematic illustration of a drop breakup caused by Kelvin-Helmholtz (KH) or Rayleigh-Taylor (R-T) instabilities. The breakup mechanisms are ciassified with respect to the (increasing) Weber number as bag, stripping (shear) and catastrophic breakup...

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. 

T. Funada, D.D. Joseph, Viscous potential flow analysis of Kelvin-Helmholtz instability in a channel. Journal of Fluid Mechanics, 2001, 445, 263-283. 

The comparison of experimental maximum bubble sizes and the predictions by various instability theories is shown in Fig. 11. The internal circulation model can reasonably predict the observed pressure effect on the maximum bubble size, indicating that the internal circulation model captures the intrinsic physics of bubble breakup at high pressures. The comparison of the predictions by different models further indicates that bubble breakup is governed by the internal circulation mechanism at high pressures over 1.0 MPa, whereas the Rayleigh-Taylor instability or the Kelvin-Helmholtz instability is the dominant mechanism at low pressure. 

Instabilities caused by the flow of matter have been known for a long time and their study constitutes a central task of hydrodynamics and its applications [1], The driving force of these instabilities are the spatial gradients of the flow velocity field when spatially separated elements are in relative motion, they exert destabilizing mechanical, electrical or electromagnetic forces on each other. The hydrodynamic system may be just a single species which is often simply referred to as matter or fluid , regardless of its chemical nature. Perhaps the simplest example of a hydrodynamic instability is the Kelvin-Helmholtz instability of in viscid shear flow [1]. 

In contrast to mechanics, electromagnetic field theory, or relativity, where the names of Newton, Maxwell, and Einstein stand out uniquely, the foundations of thermodynamics originated from the thinking of over half a dozen individuals Carnot, Mayer, Joule, Helmholtz, Rankine, Kelvin, and Clausius [1]. Each person provided cmcial steps that led to the grand synthesis of the two classic laws of thermodynamics. 

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