Gregory I. Sivashinsky

Diffusional-Thermal Theory of Cellular Flames

abstract It is shown that the formation of cellular structure in a flame is conditioned by diffusion and heat conduction effects and is independent of the hydrodynamics of the perturbed flame. It is proved that cellular flames are formed only when a sufficiently light reactant of the combustible mixture is present in a low concentration. If there is an excess of the light reactant, a plane flame front is absolutely stable (in the framework of the diffusional-thermal model) or shows a noncellular periodic structure (hydrodynamic model)

An Asymptotic Derivation of Two Models in Flame Theory Associated with the Constant Density Approximation

We consider the general equations of combustion theory. By expanding in appropriately chosen small parameters, we derive two simplified models for the leading term of such an expansion. Both are associated with the constant density approximation. In the first model, the equations of fluid dynamics are completely decoupled from the equations governing heat and mass transport. The resulting model is generally referred to as the constant density approximation, or as the diffusional thermal model. In the second model, there is a weak coupling between the equations of fluid dynamics and the equations for temperature and concentration. Specifically the coupling, which enters through the effect of variable density, which in turn is due to the thermal expansion of the gas in which a flame propagates, occurs only in the external forcing term, and not elsewhere in the fluid dynamical equations. Thus, our model is analogous to the Boussinesq model in hydrodynamics.

Weak turbulence in periodic flows

Abstract We consider the stability of a two-dimensional plane-parallel flow of viscous liquid in an external force field which is a periodic function of one of the coordinates. At sufficiently high Reynolds numbers the plane-parallel flow becomes unstable and a two-dimensional secondary flow ensues. Near the stability threshold, the secondary flow turns out to be large-scale and chaotically self-fluctuating in time.

The Effect of Viscosity on Hydrodynamic Stability of a Plane Flame Front

Abstract This paper presents a linear analysis of the hydrodynamic stablity of the plane flame front of a premixed laminar flame. The technique of outer and inner asymptotic expansions is used to calculate the next approximation to the classical long-wave Landau limit. The resulting correction turns out to be independent of the Prandtl number. This implies that, although diffusivity, conductivity and viscosity in gases are of the same order of magnitude, viscosity exerts a secondary influence in comparison with diffusivity and conductivity.

Annular flows can keep unstable films from breakup: Nonlinear saturation of capillary instability

Abstract We consider a fluid film on the inner walls of a capillary. The film surrounds another fluid in the core. It is known that the capillary instability, driven by the surface tension at the fluid-fluid interface, breaks up the film if it is primarily stagnant. In contrast, as we show, a primary flow, in a certain range of parameters, can keep the linearly unstable film from rupturing. This is a result of the nonlinear low-level saturation of the interface instability. This saturation is due to the coordinated action of the destabilizing factors, the shear of flow, and the surface tension at the interface. The resulting state of the interface is, in general, chaotic oscillations, with their amplitude being much less than the unperturbed film thickness. The approximate equation of interface evolution is derived. The saturation mechanism is explained. The characteristic scales of the developed oscillations are found, and the parameter range of the theory applicability is discussed.

Some developments in premixed combustion modeling

Recent theoretical advances in premixed gas combustion are reviewed. The attention is focused on (1) self-acceleration of outward propagating wrinkled flames sustained by the intrinsic flame instability, (2) fragmentation of near-limit cellular flames and formation of self-drifting flame balls, (3) flame acceleration and extinction by large-scale turbulence, (4) multiplicity of detonation regimes in hydraulically resisted flows and the phenomenon of shock-free pressure-driven combustion, and (5) hydraulic resistance as a mechanisms of deflagration-to-detonation transition.

On self-acceleration of outward propagating wrinkled flames

Abstract Numerical simulations of hydrodynamically unstable outward propagating premixed flames are presented. In a qualitative agreement with many experimental observations it is shown that the expanding wrinkled flames enjoy an appreciable acceleration. The morphology of expanding wrinkled flames appears to be essentially different from that occuring in non-expanding flames. In the latter case short-wavelength corrugations merge forming a single cusp, whose scale is controlled by the overall size of the system. In expanding flames the tendency to merge is balanced by the overall stretch. As a result the flame interface appears to be more or less uniformly wrinkled. In contrast to hydrodynamically unstable flames, expanding flames, subject exclusively to the effect of diffusive instability, do not indicate any disposition towards acceleration.

The transition from deflagration to detonation in thin channels

A numerical study of a two-dimensional model for premixed gas combustion in a thin, semi-infinite and thermally-insulated channel is performed. The work is motivated by recent theoretical advances revealing the important role of hydraulic resistance in deflagration-to-detonation transition, one of the central yet still poorly understood phenomena of gaseous combustion. The two-dimensional formulation reproduces the formation of the so-called tulip flame and its predetonational acceleration, well-known experimentally but unattainable within the quasi-one-dimensional approach employed previously. It is shown that the detonation first develops in the boundary layer where the effect of hydraulic resistance is stronger, and thereupon spreads over the channels interior. However, the second stage of the transition does not proceed gradually but rather through a localized auto-ignition within the tulip.

Flame propagation and extinction in large-scale vortical flows

It is shown that the propagation speed of the premixed gas flame spreading through a time-independent, space-periodic array of large-scale vorticities is a nonmonotonic function of their intensity. For moderately strong vorticities their intensification results in the flame speed enhancement accompanied by shedding of islands of unburned gas. Yet there is a certain level of stirring at which the flame speed reaches its maximum. Any further increase in the stirring intensity leads to a drop in the flame speed, followed, for mildly nonadiabatic systems, by flame extinction. The relation of these findings to the classical theory of planar counterflow flames is discussed. The study is motivated by the experimentally known phenomenon of flame extinction by turbulence.

SHORT COMMUNICATION On Flame Propagation Through Periodic Flow Fields

Abstract Flame propagation through a periodic system or time independent eddies is studied. It is shown that at sufficiently low amplitudes of the velocity spatial variation, the effective speed of a passive flame has a global dependence on the underlying flow. However, at high amplitudes, the effective flame speed is determined by the local features of the flow. Simultaneously, the shape of the flame undergoes a transition from a smooth configuration to a cusped one.