Linear stability of plane wakes and liquid jets: global and local approach

Respondent Huvudhandledare Bihandledare Datum
Outi Tammisola Daniel Söderberg Fredrik Lundell 2009-04-16




In this work, the linear stability of wakes and liquid jets is analysed with global and local methods. The first topic is the global instability of confined wakes, i.e. wakes with near-lying walls. The problem is solved using 2D linear global modes. The base flow, which starts from a wake inlet profile with different velocity ratios between the wake and the surrounding flow, is calculated by a spectral element method. The global linear stability problem is discretised by Chebyshev polynomials in both spatial directions, and solved by using a code based on a parallel version of the Arnoldi Algorithm, with the aim of the mathematical libraries PARPACK and ScaLAPACK. The frequency and growth rate of the most unstable mode, and the spatial shape of the eigenfunction, are compared for confined and unconfined wakes. The confinement is found to be stabilising at Re=100, and this is shown to be an effect of the differences in the streamwise mean flow development between confined and unconfined wakes. For higher Reynolds numbers, this effect disappears and the stability limits of the two types wakes approach each other. The highest Reynolds number studied was 500 to get a good resolution of the modes. The second topic is the effect of air co-flow on the stability of a plane liquid sheet, which is studied theoretically and experimentally. A liquid sheet is a liquid jet with an extent in the spanwise direction much larger than its vertical thickness, so that the problem can be considered to be two-dimensional in Cartesian coordinates. The flow studied is a water sheet in air, and is convectively unstable due to an uniform inlet profile and a high Reynolds number (Re=2850). Therefore the flow can be studied with a local spatial approach. The theoretical and experimental growth rates compare quantitatively well in the case of stagnant air, and qualitatively well when air co-flow is introduced. The largest difference between experimental and theoretical frequency-growth rate curves is 20 %. The growth rate scales with the difference between gas and liqudi velocity. In addition, for a fixed gas velocity the growth rate scales with the square root of the shear from gas at the free surface, or almost equivalently, the gas boundary layer thickness. The third topic is the global modes of a plane spatially developing liquid sheet. The global stability problem is formulated, and preliminary results presented for the special case of an 0.55 mm thick water sheet in air for different Reynolds numbers. Descriptors: Hydrodynamic stability, global modes, wake, liquid jet, confinement, capillary instability, absolute/convective instability, papermaking.