Theoretical analysis of receptivity stability and receptivity of multi-fluid flows

This thesis presents a theoretical investigation of interfacial flows behaviour and their interactions with surrounding perturbation fields in the conditions typical of aerodynamic applications. An analytical method is formulated to extend the fluid stability theory to viscous multi-fluid flows, focusing on surface tension effects. Liquid surface tension is modelled by utilising the pressure jump across the interface which occurs due to viscosity contrast between two fluids while in motion. This work is restricted to the cases where viscosity and density ratios of fluids are small. The conditions which indicate whether a flow is stable or unstable are found by deriva- tion of dispersion equation. The stability analysis of different flow regimes including incompressible and compressible flows outside a liquid film are investigated. Then, a de- tailed examination of multi-fluid receptivity analysis is rendered with the surface tension being the crux infusion of the mathematical model. The theoretical analysis on excitement of instability waves is conducted by modelling the synergy between Tollmien-Schlichting waves with surrounding disturbances. The main focus of this thesis is on the process that the external disturbances convert into instability waves in different flow regimes with objective of advancing our understanding of multi-fluid flow laminar-turbulent transition at its early stage. Further analysis of the boundary layer receptivity to external disturbances such as acoustic waves interacting with a short wall roughness and vibrations of the wing itself is presented in this work. The last chapter on receptivity analysis is devoted to the application of the attained mathematical model to transonic regime. The boundary layer receptivity analysis to the vibrating wall disturbances is conducted based on an assumption that the flow in the free-stream is in the transonic region as it pertains to commercial aeroplanes. The boundary-layer instability is described by the triple-deck theory and viscous-inviscid interaction theory. Other mathematical tools such as complex analysis and asymptotic approach based on large Reynolds number are employed to find solutions in analytical form. The work presented here concludes that the surface tension forces and initial film thick- ness play imperative roles regarding the airflow stability and amplitude of instability waves in flight conditions. It is found that the unconditional unstable incompressible flow becomes stable for certain wavenumber by including the liquid surface tension in the mathematical formulation. It is also shown that a supersonic flow is stable for a certain wavenumber regardless of inclusion of surface tension however the flow becomes stable for a smaller wavenumber when the surface tension is formulated in the model. The su- personic flow is not receptive and the focus of receptivity analyses is on incompressible, subsonic and transonic flows. Finally, the amplitude of Tollmien-Schlichting waves have been expressed in terms of the receptivity coefficients.Open Acces