Diffusion-flame flickering as a hydrodynamic global mode

Abstract

The present study employs a linear global stability analysis to investigate buoyancyinduced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude-number/Reynolds-number plane for different fuel-jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

Global instability of low-density jets

“…The discrepancies between the two analyses can be attributed to the rapid spatial development of the flow (see figure 2(a)) that violates the parallel flow hypothesis on which the local analysis is based. An clear example of this was found recently by Moreno-Boza et al (2016) when studying buoyancy-driven flickering in diffusion flames.…”

On the critical conditions for pool-fire puffing

“…Recent analyses have shown that the flickering of low-density jets [36] , jet diffusion flames [30] , and buoyant plumes [37,38] is a manifestation of a hydrodynamic global instability, the onset of which can be computed with a linear global stability analysis. The same type of global instability is anticipated to be responsible for the puffing of liquid-pool fires.…”

“…It is known that the buoyant acceleration of the flow in the central region of the flame causes the radial profiles of axial velocity to exhibit inflection points along the flame envelope, a region characterized by low values of the advection velocity [30,42,43] . From a local stability point of view, this scenario allows for the possibility of an absolutely unstable flow.…”

“…The physically similar problem of flickering jet diffusion flames has been recently shown [30] to correspond to a hydrodynamic global instability of the flow. Since the resulting instability modes have wavelengths that are comparable to the flame height, stability analyses based on the quasi-parallel approximation give quantitatively poor predictions.…”

“…Since the resulting instability modes have wavelengths that are comparable to the flame height, stability analyses based on the quasi-parallel approximation give quantitatively poor predictions. To overcome this difficulty, a global stability analysis was used in [30] to characterize the flickering dynamics near the bifurcation, giving results in excellent agreement with those of direct numerical simulations. A global linear stability analysis will also be used below to investigate the physically similar problem of puffing of a round liquid-pool fire, as is appropriate,…”