Kelvin-Helmholtz Rayleigh-Taylor model

Beale, J.C., and R. D. Reitz. 1999. Modeling spray atomization with the Kelvin-Helmholtz/Rayleigh-Taylor hybrid model. Atomization Sprays 9(6) 623-50. 

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. 

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. 

The Kelvin-Helmholtz instability is similar to the Rayleigh-Taylor instability, except that the former allows a relative velocity between the fluids, u. Using the same concept of Grace et al. (1978), Kitscha and Kocamustafaogullari (1989) applied the Kelvin-Helmholtz instability theory to model the breakup of large bubbles in liquids. Wilkinson and van Dierendonck (1990) applied the critical wavelength to explain the maximum stable bubble size in high-pressure bubble columns ... 

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. 

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