A Closer Look at Linear Stability Theory in Modeling Spray Atomization

Abstract

The common Lagrangian-Eulerian modeling of liquid sprays is largely based on linear stability theory, where the associated growth rates and most unstable wavelengths are used in prescribing initial Lagrangian droplet characteristics. Using highly-resolved VoF simulations, the present work is aimed at examining the extent to which this linear stability and associated flow characteristics hold in a realistic spray configuration under normal operating conditions using the ECN spray A geometry. This involves a comparison between linear stability wavelength predictions, originating from two-phase Orr-Sommerfeld solutions, and those obtained from the VoF simulations. The results show that within the first 4 diameters beyond the orifice, the non-linear components of the Navier-Stokes have grown to 10% of the corresponding linear part in both the liquid and the gas phase, and continue to grow exponentially. The non-axial and non-fully developed flow profiles are particularly significant even within one diameter but do not develop as strongly as the non-linear components. Linear stability theory is able to adequately capture the initial surface disturbances, and there is reasonable agreement with VoF simulations, despite the fact that the base flow is not exactly the conventional one. A main finding from the work shows that while the most unstable modes are captured in the simulations and agree with theoretical predictions, these modes are not directly responsible for fragmenting the liquid core or causing primary atomization. Their action is limited to breaking up the surface of the jet, while the liquid core of the jet remains intact for another 20 jet diameters downstream.