Laminar diffusion flamelet models in non-premixed turbulent combustion

Turbulent dispersed multiphase flows are common in many engineering and environmental applications. The stochastic nature of both the carrier-phase turbulence and the dispersed-phase distribution makes the problem of turbulent dispersed multiphase flow far more complex than its single-phase counterpart. In this article we first review the current state-of-the-art experimental and computational techniques for turbulent dispersed multiphase flows, their strengths and limitations, and opportunities for the future. The review then focuses on three important aspects of turbulent dispersed multiphase flows: the preferential concentration of particles, droplets, and bubbles; the effect of turbulence on the coupling between the dispersed and carrier phases; and modulation of carrier-phase turbulence due to the presence of particles and bubbles.

Turbulent Dispersed Multiphase Flow

The laminar flamelet concept covers a regime in turbulent combustion where chemistry (as compared to transport processes) is fast such that it occurs in asymptotically thin layers—called flamelets—embedded within the turbulent flow field. This situation occurs in most practical combustion systems including reciprocating engines and gas turbine combustors. The inner structure of the flamelets is one-dimensional and time dependent. This is shown by an asymptotic expansion for the Damkohler number of the rate determining reaction which is assumed to be large. Other non-dimensional chemical parameters such as the nondimensional activation energy or Zeldovich number may also be large and may be related to the Damkohler number by a distinguished asymptoiic limit. Examples of the flamelet structure are presented using onestep model kinetics or a reduced four-step quasi-global mechanism for methane flames. For non-premixed combustion a formal coordinate transformation using the mixture fraction Z as independent variable leads to a universal description. The instantaneous scalar dissipation rate χ of the conserved scalar Z is identified to represent the diffusion time scale that is compared with the chemical time scale in the definition of the Damkohler number. Flame stretch increases the scalar dissipation rate in a turbulent flow field. If it exceeds a critical value χ q the diffusion flamelet will extinguish. Considering the probability density distribution of χ , it is shown how local extinction reduces the number of burnable flamelets and thereby the mean reaction rate. Furthermore, local extinction events may interrupt the connection to burnable flamelets which are not yet reached by an ignition source and will therefore not be ignited. This phenomenon, described by percolation theory, is used to derive criteria for the stability of lifted flames. It is shown how values of ∋ q obtained from laminar experiments scale with turbulent residence times to describe lift-off of turbulent jet diffusion flames. For non-premixed combustion it is concluded that the outer mixing field—by imposing the scalar dissipation rate—dominates the flamelet behaviour because the flamelet is attached to the surface of stoichiometric mixture. The flamelet response may be two-fold: burning or non-burning quasi-stationary states. This is the reason why classical turbulence models readily can be used in the flamelet regime of non-premixed combustion. The extent to which burnable yet non-burning flamelets and unsteady transition events contribute to the overall statistics in turbulent non-premixed flames needs still to be explored further. For premixed combustion the interaction between flamelets and the outer flow is much stronger because the flame front can propagate normal to itself. The chemical time scale and the thermal diffusivity determine the flame thickness and the flame velocity. The flamelet concept is valid if the flame thickness is smaller than the smallest length scale in the turbulent flow, the Kolmogorov scale. Also, if the turbulence intensity v′ is larger than the laminar flame velocity, there is a local interaction between the flame front and the turbulent flow which corrugates the front. A new length scale L G =v F 3 /∈ , the Gibson scale, is introduced which describes the smaller size of the burnt gas pockets of the front. Here v F is the laminar flame velocity and ∈ the dissipation of turbulent kinetic energy in the oncoming flow. Eddies smaller than L G cannot corrugate the flame front due to their smaller circumferential velocity while larger eddies up to the macro length scale will only convect the front within the flow field. Flame stretch effects are the most efficient at the smallest scale L G . If stretch combined with differential diffusion of temperature and the deficient reactant, represented by a Lewis number different from unity, is imposed on the flamelet, its inner structure will respond leading to a change in flame velocity and in some cases to extinction. Transient effects of this response are much more important than for diffusion flamelets. A new mechanism of premixed flamelet extinction, based on the diffusion of radicals out of the reaction zone, is described by Rogg. Recent progress in the Bray-Moss-Libby formulation and the pdf-transport equation approach by Pope are presented. Finally, different approaches to predict the turbulent flame velocity including an argument based on the fractal dimension of the flame front are discussed.

Laminar Flamelet Concepts in Turbulent Combustion

A new approach to chemistry modelling for large-eddy simulation of turbulent reacting flows is developed. Instead of solving transport equations for all of the numerous species in a typical chemical mechanism and modelling the unclosed chemical source terms, the present study adopts an indirect mapping approach, whereby all of the detailed chemical processes are mapped to a reduced system of tracking scalars. Here, only two such scalars are considered: a mixture fraction variable, which tracks the mixing of fuel and oxidizer, and a progress variable, which tracks the global extent of reaction of the local mixture. The mapping functions, which describe all of the detailed chemical processes with respect to the tracking variables, are determined by solving quasi-steady diffusion-reaction equations with complex chemical kinetics and multicomponent mass diffusion. The performance of the new model is compared to fast-chemistry and steady-flamelet models for predicting velocity, species concentration, and temperature fields in a methane-fuelled coaxial jet combustor for which experimental data are available. The progress-variable approach is able to capture the unsteady, lifted flame dynamics observed in the experiment, and to obtain good agreement with the experimental data, while the fast-chemistry and steady-flamelet models both predict an attached flame.

Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion

Turbulent combustion modeling

http://oa.upm.es/927/1/Acta_Astronautica(1007-1039).pdf

The asymptotic structure of counterflow diffusion flames for large activation energies

The β-assumed-p.d.f. approximation of Cook & Riley (1994) is tested as a subgrid model for the LES computation of non-premixed turbulent reacting flows, in the limit of infinitely fast chemistry, for two plane constant-density turbulent mixing layers with different degrees of intermittency. Excellent results are obtained in the computation of plane-averaged properties, such as product mass fractions and relatively high powers of the temperature, and even of the p.d.f. of the conserved scalar itself. In all these cases the errors are small enough to be useful in practical applications. The analysis is extended to slightly out-of-equilibrium problems, such as the generation of radicals, and formulated in terms of the p.d.f. of the gradient of the mixture fraction. It is shown that the form of the conditional gradient distribution is universal in a wide range of cases, whose limits are established. Within those limits, engineering approximations to the radical concentration are also possible. It is argued that the experiments in this paper are already in the limit of high Reynolds numbers.

/pdf/a-priori-testing-of-subgrid-models-for-chemically-reacting-705kghpouy.pdf

A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows

In this paper, we study the dynamics of small, spherical, rigid particles in a spatially pe­ riodic array of Stuart vortices given by a steady-state solution to the two-dimensional incompressible Euler equation. In the limiting case of dominant viscous drag forces, the motion of the particles is studied analytically by using a perturbation scheme. This approach consists of the analysis of the leading-order term in the expansion of the 'particle path function' <P, which is equal to the stream function evaluated at the instantaneous particle position. It is shown that heavy particles which remain suspended against gravity all move in a periodic asymptotic trajectory located above the vortices, while buoyant particles may be trapped by the stable equilibrium points located within the vortices. In addition, a linear map for <P is derived to describe the short-term evolution of particles moving near the boundary of a vortex. Next, the assumption of dominant viscous drag forces is relaxed, and linear stability analyses are carried out to investigate the equilibrium points of the five-parameter dynamical system governing the motion of the particles. The five parameters are the free-stream Reynolds number, the Stokes number, the fluid-to-particle mass density ratio, the distribution of vorticity in the flow, and a gravitational parameter. For heavy particles, the equilibrium points, when they exist, are found to be unstable. In the case of buoyant particles, a pair of stable and unstable equilibrium points exist simultaneously, and undergo a saddle-node bifurcation when a certain parameter of the dynamical system is varied. Finally, a computational study is also carried out by integrating the dynamical system numerically. It is found that the analytical and computational results are in agreement, provided the viscous drag forces are large. The computational study covers a more general regime in which the viscous drag forces are not necessarily dominant, and the effects of the various parametric inputs on the dynamics of buoyant particles are investigated.

On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow

This review uses as a vehicular example the jet-flame configuration to examine some phenomena that emerge in nonpremixed gaseous combustion as a result of the interaction between the temperature-sensitive chemical reaction, typical of combustion, and the convective and diffusive transport. These include diffusion-controlled flames, edge flames and their role in flame attachment, triple flames and their role as ignition fronts, and strain-induced extinction, including flame-vortex interactions. The aim is to give an overall view of the fluid dynamics of nonpremixed combustion and to review the most relevant contributions.

Ignition, Liftoff, and Extinction of Gaseous Diffusion Flames

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...

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Amable Liñán

Papers

The asymptotic structure of counterflow diffusion flames for large activation energies

A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows

On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow

Ignition, Liftoff, and Extinction of Gaseous Diffusion Flames

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