Turbulent combustion modeling

Large-eddy simulation (LES) of turbulent combustion is a relatively new research field. Much research has been carried out over the past years, but to realize the full predictive potential of combustion LES, many fundamental questions still have to be addressed, and common practices of LES of nonreacting flows revisited. The focus of the present review is to highlight the fundamental differences between Reynolds-averaged Navier-Stokes (RANS) and LES combustion models for nonpremixed and premixed turbulent combustion, to identify some of the open questions and modeling issues for LES, and to provide future perspectives.

/pdf/large-eddy-simulation-of-turbulent-combustion-39umcykkan.pdf

Large-eddy simulation of turbulent combustion

http://staff.mechmining.uq.edu.au/klimenko/pub/pdf/Prog_Energy_Combust_Sci_1999_p.pdf

Conditional moment closure for turbulent combustion

Equations governing the variation through the flow field of averages of quantities such as species mass fractions, conditional on mixture fraction, are derived and modeled. The conditioning variable adds to the independent dimensions of the problem, but it is found that this is offset in some cases by reduction in the spatial dimensionality needed. Predictions are made for the reacting scalar mixing layer, and these show good agreement with experiment. The methodology effectively decouples the kinetics from the large inhomogeneity or macromixing aspects of the flow while preserving the input from the scalar dissipation or micromixing. Arbitrarily complex kinetics may be used within reasonable computational cost.

Conditional moment closure for turbulent reacting flow

The Extended Coherent Flame Model of Colin et al. (2003) developed to model combustion in perfectly or partially mixed mixtures is adapted to also account for unmixed combustion. The ECFM model is based on a flame surface density equation which takes into account the wrinkling of the flame front surface by turbulent eddies and a conditioning averaging technique which allows precise reconstruction of local properties in fresh and burned gases even in the case of high levels of local fuel stratification. This model has been used with success in gasoline engines (Duclos et al., 1996; Duclos and Zolver, 1998; Lafossas et al., 2002; Henriot et al., 2003; Kleemann et al., 2003). In order to adapt the model to unmixed combustion for Diesel application, a description of the mixing state has been added. It is represented by three mixing zones: a pure fuel zone, a pure air plus possible residual gases zone and a mixed zone in which the ECFM combustion model is applied. A mixing model is presented which allows progressive mixing of the initially unmixed fuel and air. This new combustion model, called ECFM3Z (3-Zones Extended Coherent Flame Model), can therefore be seen as a simplified CMC (Conditional Moment Closure) type model where the mixture fraction space would be discretized by only three points. The conditioning technique is extended to the three mixing zones and allows to reconstruct, like in the ECFM model, the gas properties in the unburned and burned gases of the mixed zone. Application of the model to internal combustion engine calculations implies the necessity of auto-ignition modelling coupled to premixed and diffusion flames description. Auto-ignition is modelled following (Colin et al., 2004), while the premixed turbulent flame description is given by the ECFM. The diffusion flame is now accounted for thanks to the three zones mixing structure which represents phenomenologically the diffusion of fuel and air towards the reactive layer, that is the mixed zone. The ECFM3Z combustion model has already been presented (Beard et al., 2003) in a comparative work between Diesel experiments and corresponding calculations covering different engine operating points. Here, the model is presented in all its details and its behavior is analysed when the relative duration of injection and auto-ignition delay are varied in a direct injection Diesel engine. It is shown that the model is able to reproduce the relative importance of auto-ignition and diffusion flame on the total heat release, depending on the engine operating point considered.

/pdf/the-3-zones-extended-coherent-flame-model-ecfm3z-for-xfe9a586nc.pdf

The 3-Zones Extended Coherent Flame Model (Ecfm3z) for Computing Premixed/Diffusion Combustion

Averaged equations describing the turbulent diffusion of a chemically active admixture in coordinates tied to the instantaneous values of the concentration of another passive admixture are obtained. The results can be readily extended to the case of an arbitrary number of different chemically active admixtures. An advantage of this approach is the separation of the scales of the fluctuating and average motions, which makes the proposed average diffusion relations applicable even at times on the inertial interval.

Multicomponent diffusion of various admixtures in turbulent flow

The accuracy of the method of calculating turbulent reacting flows [1–3] which is based on the use of the conditional mean concentrations of the reacting components is analyzed. The effect of large-scale fluctuations of the dissipation of passive admixture concentration [4–6] on the accuracy of the equations for the conditional means is considered and the corresponding corrections are computed. By means of numerical calculations the models for the conditional moment and traditional calculation methods are compared, as are the various approaches to the computation of the coefficients of the equations for the conditional means.

Conditional moment closure and large-scale fluctuations of scalar dissipation

Turbulent isobaric vapor-air jet flows with homogeneous condensation are examined. A general system of equations, including the gas dynamic and kinetic equations, the thermodynamic relations and the equations for the turbulence model, is formulated. The moment kinetic equations valid for the free-molecular regime of drop growth in the surrounding medium are extended to other drop mass transfer regimes. The structure of the condensation shock, which includes the nucleation zone and the zone of drop growth on pre-existing nuclei, is investigated on the basis of a general asymptotic approach. Additional conditions at the nucleation and condensation shocks, the need for which follows from the requirement that the shocks be evolutionary, are obtained. Certain problems of averaging of the source terms in the moment equations are discussed, and with reference to the simple example of averaging of the “frozen” nucleation rate it is shown that the latter is nonzero for a mean supersaturation less than unity and that the condensation zone is displaced upstream. Condensation in a turbulent jet into which condensation-intensifying charged particles (corona discharge ions) are introduced is studied. A numerical method of analyzing homogeneous condensation in turbulent jets, which makes it possible to obtain the gas dynamic and disperse flow characteristics for various temperature conditions with allowance for the averaging of the source terms, is developed.

Homogeneous condensation in turbulent submerged isobaric jets

A methodology of continuous description of the motion of inertial particles in hydrodynamic flows has been developed. This methodology involves the following main elements: the equations of motion for a single particle in a given velocity field of the carrier medium in the presence of a random disturbing force such as white noise; the Fokker-Planck equation with a diffusion term in velocity space, which is treated as an instantaneous equation relative to the large-scale motion; the moment (for the Fokker-Planck equation) relations which are treated as instantaneous continuous equations in physical space; the closing of the continuous equations on the basis of phenomenological relations or by means of an approximate asymptotic solution of the Fokker-Planck equation for a short particle dynamic relaxation time. The direct interaction of the particles and their reciprocal action on the motion of the carrier medium are not taken into account. In the case of laminar motion, the random disturbing force results from Brownian fluctuations (the interaction between the particles and the molecules of the carrier medium) and the Fokker-Planck equation for this situation can be written in a natural way. For turbulent motion of the carrier medium it is assumed that the fluctuating field can be broken down into small- and large-scale motions (in relation to the particle dynamic relaxation time); in the random force, besides Brownian perturbations the small-scale turbulent fluctuations are included, while the velocity field is averaged over the small scales. In this case the Fokker-Planck equation (and its moment analogs) becomes an instantaneous equation with respect to the large-scale turbulent fluctuations. The continuous equations are analyzed and in the case of the turbulent motion elementary closing methods are proposed. Estimates of the small-scale turbulent particle diffusion coefficient are given.

Continuous models of the motion of inertial particles in laminar and turbulent flows based on the Fokker-Planck equations

An asymptotic method is proposed for reducing the order of the equations of condensation kinetics not only in the region of gradual droplet growth but also where diffusion in the space of sizes is important. This method makes it possible to extend the class of problems of determining the unsteady nucleation rate that have analytic solutions and to weaken the constraints imposed on the rate of variation of the gas dynamic parameters. Effects associated with the rapid variation of the critical droplet size are investigated. For this purpose the concept of a threshold dimension, in whose neighborhood the clusters go over into the droplet growth regime, is introduced. In the highly nonstationary case the threshold size differs from the critical size. Examples of simple calculations are presented.

A. Yu. Klimenko

Papers

Multicomponent diffusion of various admixtures in turbulent flow

Conditional moment closure and large-scale fluctuations of scalar dissipation

Homogeneous condensation in turbulent submerged isobaric jets

Continuous models of the motion of inertial particles in laminar and turbulent flows based on the Fokker-Planck equations

Asymptotic analysis of the nucleation rate for rapidly varying gas dynamic parameters