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Numerical stability studies of one-phase and immiscible two-phase jets and wakes

Author Document Type Year Download File size
Outi Tammisola Doctoral thesis 2011 Download 25 Mb
Id
ISSN 0348-467X
ISRN KTH/MEK/TR--11/07--SE

Abstract

The initial linear instability growth of two-dimensional plane wakes and jets is investigated, by temporal two-dimensional global modes, and local spatial stability analysis. Comparisons are also made to experiments, direct numerical simulations, and methods designed for weakly-non-parallel flows. The studies proceed through three different flow setups with increasing complexity.
The first flow analysed is a convectively unstable liquid sheet surrounded by a stagnant or co-flowing gas. The experimentally measured growth rates are found to be in excellent agreement with spatial stability calculations, if the air boundary layer is taken into account, and not otherwise. The stabilizing effect of moderate air co-flow is quantified in the numerical study, and the governing parameters found to be the speed difference between water and air, and the shear from air at the water surface (inversely proportional to the air boundary layer thickness).
The second flow case is a one-phase confined wake, i.e. a wake in a channel. The effect of confinement (wall distance) on the global stability of wakes is analysed by linear global modes, and compared to the results from DNS and weakly-non-parallel theory. At Re = 100, confinement is globally stabilizing, mostly due to a faster development towards a parabolic profile for confined flows. The stabilizing effect of confinement almost disappears at Re =400. However, when the structural sensitivity of the wakes is analysed by an adjoint- based approach, fundamental di?erences are seen in the global wavemakers of confined and unconfined wakes at Re =400.
The third and most complex flow case is immiscible two-fluid wakes and jets. A parallel multi-domain spectral code is developed, where the kinematic and dynamic conditions on the interface are imposed as coupling conditions. It is shown that intermediate values of surface tension can destabilize stable wakes and jets. In addition, surface tension has a considerable in?uence on the global oscillation frequency and spatial shape of the global mode for unstable wakes. The character of the mode is gradually changed from a wake instability to a global shear layer instability. Both symmetric and antisymmetric modes are encountered for both wakes and jets, depending on the strength of the surface tension (value of the Weber number) and the flow case.