Effects of heat release on triple flames

Heat release effects on laminar flame propagation in partially premixed flows are studied. Data for analysis are obtained from direct numerical simulations of a laminar mixing layer with a uniformly approaching velocity field. The structure that evolves under such conditions is a triple flame, which consists of two premixed wings and a trailing diffusion flame. Heat release increases the flame speed over that of the corresponding planar premixed flame. In agreement with previous analytical work, reductions in the mixture fraction gradient also increase the flame speed. The effects of heat release and mixture fraction gradients on flame speed are not independent, however; heat release modifies the effective mixture fraction gradient in front of the flame. For very small mixture fraction gradients, scaling laws that determine the flame speed in terms of the density change are presented. © 1995 American Institute of Physics

Triple flame structure and diffusion flame stabilization

The stabilization of diffusion ñames is studied using asymptotic techniques and numerical tools. The configuration studied corresponda to parallel streams of cold oxidizer and fuel initially separated by a splitter píate. It is shown that stabilization of a diffusion flame may only occur in this situation by two processes. First, the flame may be stabilized behind the flame holder in the wake of the splitter píate. For this case, numerical simulations confirm scalings previously predicted by asymptotic analysis. Second, the flame may be lifted. In this case a triple flame is found at longer distanees downstream of the flame holder. The structure and propagation speed of this flame are studied by using an actively controlled numerical technique in which the triple flame is tracked in its own reference frame. It is then possible to investigate the triple flame structure and velocity. It is shown, as suggested from asymptotic analysis, that heat reléase may induce displacement speeds of the triple flame larger than the laminar flame speed corresponding to the stoichiometric conditions prevailing in the mixture approaching the triple flame. In addition to studying the characteristics of triple flames in a uniform flow, their re-sistance to turbulence is investigated by subjecting triple flames to different vortical configurations

Laminar Craya-Curtet jets

This Brief Communication investigates laminar Craya-Curtet flows, formed when a jet with moderately large Reynolds number discharges into a coaxial ducted flow of much larger radius. It is seen that the Craya-Curtet number, C=(J/sub c//J/sub j/)/sup 1/2/, defined as the square root of the ratio of the momentum flux of the coflowing stream to that of the central jet, arises as the single governing parameter when the boundary-layer approximation is used to describe the resulting steady slender jet. The numerical integrations show that for C above a critical value C/sub c/ the resulting streamlines remain aligned with the axis, while for C<C/sub c/ the entrainment demands of the jet cannot be satisfied by the coflow, and a toroidal recirculation region forms. The critical Craya-Curtet number is determined for both uniform and parabolic coflow, yielding C/sub c/=0.65 and C/sub c/=0.77, respectively. The streamlines determined numerically are compared with those obtained experimentally by flow visualizations, yielding good agreement in the resulting flow structure and also in the value of C/sub c

The quasi-cylindrical description of submerged laminar swirling jets

TThe quasi-cylindrical approximation is used to describe numerically the structure of a submerged swirling jet for subcritical values of the swirl ratio S<Sc . The emerging flow structure is affected by the swirling motion, which enhances the entrainment rate of the jet and induces an adverse pressure gradient that reduces its momentum flux. The effect is more pronounced as the swirl ratio S is increased, yielding for sufficiently large values of S a jet with an annular structure. The integration describes the smooth transition towards the far-field self-similar solution for all values of S smaller than a critical value S5Sc , at which the numerical integration fails to converge at a given downstream location. The comparisons with previous experimental results confirm the correspondence between the onset of vortex breakdown and the failure of the quasi-cylindrical approximation

Critical radius for hot-jet ignition of hydrogen-air mixtures

This study addresses deflagration initiation of lean and stoichiometric hydrogen–air mixtures by the sudden discharge of a hot jet of their adiabatic combustion products. The objective is to compute the minimum jet radius required for ignition, a relevant quantity of interest for safety and technological applications. For sufficiently small discharge velocities, the numerical solution of the problem requires integration of the axisymmetric Navier–Stokes equations for chemically reacting ideal-gas mixtures, supplemented by standard descriptions of the molecular transport terms and a suitably reduced chemical-kinetic mechanism for the chemistry description. The computations provide the variation of the critical radius for hot-jet ignition with both the jet velocity and the equivalence ratio of the mixture, giving values that vary between a few tens microns to a few hundred microns in the range of conditions explored. For a given equivalence ratio, the critical radius is found to increase with increasing injection velocities, although the increase is only moderately large. On the other hand, for a given injection velocity, the smallest critical radius is found at stoichiometric conditions

Exact solutions for transient mixing of two gases of different densities

This Brief Communication presents a number of exact solutions describing the transient mixing of two gases of different molecular weights. Descriptions are given for both the concentration field and the associated induced motion in one-dimensional spherical, cylindrical, and planar configurations, including mixing layers, pockets, coflow jets, and concentrated mass sources

The New Political Economy of EU State Aid Policy

Despite its importance and singularity, the EU’s state aid policy has attracted less scholarly attention than other elements of EU competition policy. Introducing the themes addressed by the special issue, this article briefly reviews the development of EU policy and highlights why the control of state aid matters. The Commission’s response to the current economic crisis notably in banking and the car industry is a key concern, but the interests of the special issue go far beyond. They include: the role of the European Commission in the development of EU policy, the politics of state aid, and a clash between models of capitalism. The special issue also examines the impact of EU policy. It investigates how EU state aid decisions affect not only industrial policy at the national level (and therefore at the EU level), but the welfare state and territorial relations within federal member states, the external implications of EU action and the strategies pursued by the Commission to limit any potential disadvantage to European firms, and the conflict between the EU’s expanding legal order and national

The virtual origin as a first-order correction for the far-field description of laminar jets

The far-field velocity and composition fields of a submerged laminar jet are known to approach a self-similar solution corresponding to the flow induced by a point source of momentum and scalar. Previous efforts to improve this far-field description have introduced a virtual origin for the streamwise coordinate to remedy the singular behavior of the self-similar solution near the jet origin. The purpose of this note is to show, by means of a perturbative analysis of the point-source solution, that this virtual origin is in fact the first-order correction to the leading-order description. The perturbative analysis, which uses the ratio x of the streamwise distance to the length of jet development as an asymptotically large quantity, also indicates that the displaced point source provides the description in the far field with small relative errors of order x-3 for the round jet and of order x-10/3 for the plane jet. The values of the virtual origin are obtained by numerical integration of the boundary-layer equations in the region of jet development, giving values that depend on the shape of the jet velocity profile at the exit

On the interaction of vortices with mixing layers

We describe the perturbations introduced by two counter-rotating vortices - in a two-dimensional configuration - or by a vortex ring - in an axisymmetric configuration - to the mixing layer between two counterflowing gaseous fuel and air streams of the same density. The analysis is confined to the near stagnation point region, where the strain rate of the unperturbed velocity field, A0, is uniform. We restrict our attention to cases where the typical distance 2r0 between the vortices - or the characteristic vortex ring radius r0 - is large compared to both the thickness, δv, of the vorticity core and the thickness, δm∼(ν/A0)1/2, of the mixing layer. In addition, we consider that the ratio, Γ/ν, of the vortex circulation, Γ, to the kinematic viscosity, ν, is large compared to unity. Then, during the interaction time, A0,-1, the viscous and diffusion effects are confined to the thin vorticity core and the thin mixing layer, which, when seen with the scale r0, appears as a passive interface between the two counterflowing streams when they have the same density. In this case, the analysis provides a simple procedure to describe the displacement and distortion of the interface, as well as the time evolution of the strain rate imposed on the mixing layer, which are needed to calculate the inner structure of the reacting mixing layer as well as the conditions for diffusion flame extinction and edge-flame propagation along the mixing layer. Although in the reacting case variable density effects due to heat release play an important role inside the mixing layer, in this paper the analysis of the inner structure is carried out using the constant density model, which provides good qualitative understanding of the mixing layer response

The role of separation of scales in the description of spray combustion

The present paper deals with the description of the interacting multiscale processes governing spray vaporization and combustion downstream from the near-injector atomization region in liquid-fueled burners. One of the main objectives is to emphasize the progress made in the mathematical description and understanding of reactive spray flows by incorporation of rationally derived simplifications based on the disparity of length and time scales present in the problem. In particular, we aim to show how the disparity of the scales that correspond – with increasing values of their orders of magnitude – to the droplet size, interdroplet spacing, and width of the spray jets, ensures the validity of their homogenized description. The two-way coupling associated with exchanges of mass, momentum, and energy between the gas and the liquid phases is dominated by the homogenized exchanges with the gas provided collectively by the droplets, and not by the direct interaction between neighboring droplets. The formulation is used as a basis to address nonpremixed spray diffusion flames in the Burke-Schumann limit of infinitely fast chemical reactions, with the conservation equations written in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor. Laminar canonical problems that have been used in the past to shed light on different aspects of spray-combustion phenomena are also discussed, including spherical spray clouds and structures of counterflow spray flames in mixing layers. The presentation ends with a brief account of some open problems and modeling challenges