UC San Diego

Asymptotic methods and experimental techniques have been used in combination with direct numerical simulations and stability analyses to investigate effects of buoyancy-driven motion in two different reactive problems, namely, flickering of nonpremixed diffusion flames in open atmospheres and slowly reacting combustion of confined mixtures. A brief description of these two separate topics is given below.

Part I of this dissertation deals with the flickering of jet diffusion flames and the puffing of liquid-fuel pool fires. Both phenomena are a manifestation of an axisymmmetric global hydrodynamic instability driven by the interactions of the buoyancy force with the

density differences induced by the chemical heat release, which occurs in the flame sheet separating the fuel and oxidizer domains. For these flows, the predictive capability of local quasi-parallel stability analyses is limited by the non-slender character of the resulting

eigenmodes, so that a biglobal analysis is needed to accurately determine marginal instability conditions and resulting frequencies. The results for jet diffusion flames, including the Froude number/Reynolds number instability boundaries for different fuel-feed dilutions,

are compared with direct numerical simulations, giving good agreement for the range of conditions explored in our study. For liquid-fuel pool fires, the stability analysis provides the critical value of the Rayleigh number at the onset of the puffing instability. The predictions for different liquid fuels are compared with the results obtained in small-scale laboratory experiments.

Part II is concerned with the “slowly reacting” mode of combustion, and its thermal-explosion limits, of an initially cold gaseous mixture enclosed in a spherical vessel with a constant wall temperature, a relevant problem in connection with the safe storage

and transportation of reactant gas mixtures. Following Frank-Kamenetskii’s seminal analysis of this problem, the strong temperature dependence of the effective overall reaction rate is taken into account by using a single-reaction model with an Arrhenius rate having

a large activation energy, resulting in a critical value Da_c of the controlling Damköhler number above which the slowly reacting mode of combustion no longer exists. A Rayleigh number Ra based on the relevant density difference is seen to measure the relative effect of

natural convection. Our numerical computations indicate that the value of Da_c increases with Ra as a result of the enhanced heat-transfer rate. Specific consideration is given to the flow structure in the asymptotic limits Ra << 1 and Ra >> 1, which yield accurate

predictions of critical explosion conditions. For completeness, the application of Frank-Kamenetskii’s ideas to the problem of flow of a reactive mixture in a pipe is presented in an appendix for the case of buoyancy-free conditions.