Asymptotic studies of unsteady non-premixed flamelets and buoyancy-induced swirling flows

Asymptotic techniques are used to investigate two different phenomena, namely, acoustically driven counterflows and the flow field surrounding fire whirls. In Part I of the dissertation, the interaction of non-premixed flamelets with acoustic waves of large characteristic wavelength, central to the development of acoustic instabilities in liquid-propellant rocket engines, is investigated using as model the counterflow diffusion flame subject to harmonic pressure and strain variations, with the presentation given in this work proceeding with increasing levels of complexity, outlined below. In order to relate to typical experimental realizations of counterflow diffusion flames, the presentation begins with the investigation of the high-Reynolds and low-Mach number collision of two chemically frozen gaseous streams of different density. The self-similarity of the stagnation-point region is analyzed, with the strain-rate and stagnation point location, amongst other properties relevant for counterflow-flame studies, given as functions of the macroscopic properties of the experimental setup, including the nozzle-separation to semi-width ratio, for irrotational and rotational flows, with explicit formulas given for the former. A general formulation is then provided for reacting mixing layers in counterflows subject to both time-varying strain and pressure using an inverse-thermal-conductivity-weighted coordinate which is shown to have benefits when compared to the classic Howarth-Dorodnitzyn variable. The formulation is applied to the interaction of acoustic waves with non-premixed flamelets by consideration of small amplitude harmonic oscillations of the pressure or strain-rate, with the amplitude serving as small parameter in the perturbative analysis for model one-step Arrhenius chemistry. First, the limit of infinitely fast reaction for non-unity Lewis numbers is considered. It is shown that differential-diffusion effects promote fluctuations of the flame location and