Development of diagnostic techniques for the investigation of instabilities in annular liquid sheets

This thesis is concerned with the development of experimental diagnostic techniques for the study of nonlinear instabilities in annular liquid sheets. An axisymmetric annular sheet of varying thickness with no swirl and parallel injection of gas and liquid phases (i.e. no impingement) is considered. In this flow, break-up of the sheet is due to aerodynamic shear forces at the interfaces. Highly resolved velocity measurements of the phase interface from high speed digital images are achieved via a specialised sub-pixel image correlation algorithm. Metrics for image quality based on defocus and image noise are defined, and the effect on the uncertainty in the measured velocity is investigated. The image correlation approach is benchmarked against a number of alternative algorithms with regard to error sensitivity. Decomposition of spatial instability modes is achieved via a novel application of Koopman Mode analysis via the Dynamic Mode Decomposition (DMD). A synthetic error analysis is applied to the DMD to estimate the propagation of uncertainty as a function of data quantity and quality. DMD provides a spatially resolved amplification profile which yields a novel characterisation of the evolution of the non-linear instability. With these techniques, some new insight is obtained into the behaviour of the instability. An unexpectedly rapid onset of nonlinearity in the near-field is observed. In concert with DMD, a novel application of Hilbert-Huang decomposition allows a new theory of modulated nonlinear instability in the far-field of the spray to be proposed. A parametric analysis over an order of magnitude variation in Reynolds number, Weber number and gas momentum is undertaken. From this, a temporal scaling behaviour is observed which shows reasonable agreement with other studies. Using the DMD results, a new scaling behaviour for the effects of the sheet thickness on the convective nonlinear instability is proposed.