Dynamics of circulation-controlled firewhirls and periodically-forced jets

Abstract

This thesis consists of two parts, viz. the circulation-controlled firewhirls for the first part and periodically-forced jet for the second part. The first part of this thesis progressively presents our theoretical studies on circulation-controlled firewhirls. The circulation-controlled firewhirls was reproduced by Chuah et al. in laboratory (Proc. Combust. Inst. 33, 2011). The theory proposed by Chuah et al. yielded an underestimation to the flame height due to the oversimplified assumptions, e.g., constant physical properties (density and mass diffusivity), Burgers vortex, and unity Lewis number. The revised theory by Klimenko and Williams (Combust. Flame 160, 2013) in which the Burges vortex was replaced by strong vortex interpreted well with the Chuah et al.'s experimental observed flame heights. Through a series of theoretical studies, we proposed a generalized flame height theory in which the effect of variable physical properties was taken into account by introducing the Howarth-Dorodnitsyn-like coordinate transformations, converting the formulation into "density-implicit" form, the effect of differential diffusion was considered by constructing a mass-diffusivity-ratio-model correction, which is verified by the non-unity Lewis number asymptotic analysis, and moreover the strong vortex model proposed by Klimenko was appropriately implemented in our generalized flame height theory by generalizing its mathematical form. Our generalized flame height formula agrees well with the Chuah et al.'s experiments, and in the meanwhile provides further understandings in non-premixed flames of fundamental combustion problems. In second part of the thesis, the response of compressible axisymmetric jets to external periodic forcing at the jet exit was analyzed based on the energy integral method with emphasis on identifying the optimal forcing frequency that can maximize the spreading of the shear layer surrounding the jet potential core. The non-monotonic variation of optimal forcing frequency with respect to the jet Mach numbers is investigated systematically. The results show that the identified optimal Strouhal number, Stp, decreases first with increasing M0 due to stronger suppression of the flow compressibility on the growth of high-frequency perturbations than that of low-frequency ones. As M0 increases to above a critical value, the suppression is of approximately the same extent to all the frequencies, and thus Stp starts to increase because the jet development favors high-frequency perturbations, which have higher rates of energy transfer from the base jet flow and hence larger growth rates. With further increasing M0, Stp decreases again mainly because the viscous dissipation suppresses the development of high-frequency forced perturbation more significantly than that of low-frequency ones.