A. Kronenburg

Modeling soot formation in turbulent methane–air jet diffusion flames

Abstract The modeling of soot formation and oxidation by the conditional moment closure (CMC) method is considered. It is particularly focused on the influence of differential diffusion of the soot particles on soot predictions. Most importantly, no changes are made to the soot models that were derived from laminar flame experiments and calculations. Good to excellent predictions are achieved in lightly sooting turbulent methane–air jet diffusion flames at atmospheric and elevated pressure when differential diffusion is taken into account. Unity Lewis number assumptions yield underpredictions of soot volume fractions by about 40%. Soot oxidation by OH and O2 can be treated accurately and both oxidation mechanisms are found to be important for soot burnout in downstream regions.

Double conditioning of reactive scalar transport equations in turbulent nonpremixed flames

Double conditioning of reactive scalar transport equations on mixture fraction and sensible enthalpy is presented as a promising extension to conventional conditional moment closure (CMC) methods. Simple first order, singly conditioned CMC cannot accurately predict combustion phenomena such as partially premixed flames and flames with local extinction and reignition. CMC is applied to turbulent flames with significant temperature fluctuations that bring to light the deficiencies of the conventional CMC approach. Fluctuations of temperature and species around their conditional means cannot be neglected when these quantities are conditioned on mixture fraction only. Comparison with direct numerical simulation (DNS) results demonstrates, however, the great potential for doubly conditioned CMC. Doubly conditioned CMC gives excellent agreement with DNS at all times and it captures phenomena like local extinction and the onset of reignition accurately.

Second-order conditional moment closure for turbulent jet diffusion flames

The limited success in predicting nitric oxide concentrations in turbulent hydrogen-air diffusion flames using conditional first-moment closure indicates the importance of the correlations of the conditional fluctuations. Hence, a second-order closure for the chemical reaction rate term is suggested. Correction terms that account for moments of higher order are introduced. They are derived from a global one-step mechanism for hydrogen-air combustion. Assuming the radicals O, H, and OH to be in partial equilibrium and the minor radicals such as HO2 and H2O2 in steady state, chemical reaction rates can be represented by a two-variable formalism for a given enthalpy. Then, second-order moments of combined variables can be used to find more accurate solutions of the conditionally averaged chemical source terms. The model is complemented by a conditional variance transport equation. The validity of the model has been verified by comparison with experimental data, and good to excellent predictions of nitric oxide levels are achieved in undiluted and helium-diluted hydrogen jet flames.

Modelling of differential diffusion effects in nonpremixed nonreacting turbulent flow

The modelling of differential diffusion with a conditional moment closure (CMC) method is considered. Direct numerical simulations for scalar fields in homogeneous isotropic decaying turbulence are used to quantify the non-unity Schmidt number effects. Unlike the equal molecular diffusion case, where terms involving deviations from the conditional average usually make a negligible contribution, these terms contribute significantly to the equations governing the evolution of the conditional average scalar in the presence of different molecular diffusion coefficients. Together with the conditional scalar dissipation they come to balance conditional scalar diffusion, the driving force of the differential diffusion effects. The shape of the conditional averages of these terms in mixture fraction space coincides with the approximate shape of the conditional average differential diffusion, Qz. Therefore, dividing by Qz they are only functions of time. Conditional moment closure leads to good predictions of Qz p...

A simple model for the filtered density function for passive scalar combustion LES

LES models for turbulent non-premixed combustion usually require knowledge of the filtered density function of the conserved scalar, and we propose to use a simple top-hat function. Such top-hat distributions were developed as probability density functions for RANS applications in the 1970s but were soon surpassed by the β function. We find that in the context of LES, the top-hat distribution provides an excellent alternative to the now much more common β function. The top-hat function is assessed through a phenomenological analysis of Direct Numerical Simulation (DNS) data from a planar jet and of experimental data from a turbulent opposed jet. The approach is then tested a posteriori for a piloted diffusion flame (Sandia Flame D). Advantages of the top-hat function are the ease of implementation and the reduced dimensionality of look-up tables. The present paper also discusses inconsistencies of sub-grid β-FDFs, the FDFs sensitivity on implicit filtering, and the regime in which a β assumption can be a valid filtered density function for LES.

Computation of Conditional Average Scalar Dissipation in Turbulent Jet Diffusion Flames

The modelling of conditional scalar dissipation in locally self-similar turbulent reacting jets is considered. The streamwise dependence in the transport equation of the conserved scalar pdf is represented by a function solely dependent on centreline mixture fraction. This procedure provides a simple model suitable for non-homogeneous flows and ensures positive values for conditional scalar dissipation. It has been tested in pure hydrogen-air jet diffusion flames using a Conditional Moment Closure method with detailed 12species, 23 reactions chemistry. The calculations show good agreement of the averaged scalar dissipation with reference values and the model proves to be superior to previous models based on homogeneous flows if the distribution of the conditional scalar dissipation in mixture fraction space is compared with experimental results. A dependence of NO predictions on the model of conditional scalar dissipation can be observed.

Modeling of scalar mixing in turbulent jet flames by multiple mapping conditioning

Multiple mapping conditioning (MMC) combines the probability density function (PDF) and the conditional moment closure (CMC) methods via the application of a generalized mapping function to a prescribed reference space. Stochastic and deterministic formulations of MMC exist, and the deterministic implementation has been applied here to a piloted jet diffusion flame (Sandia Flame D). This paper focuses on the feasibility of MMC and its closures for real (laboratory) flames and a relatively simple one-dimensional reference space that represents mixture fraction has been used. The remaining chemically reactive species are implicitly conditioned on mixture fraction and their fluctuations around the conditional mean are neglected. This work primarily evaluates the ability of the deterministic form of MMC to provide accurate and consistent closures for the mixture fraction PDF and the conditional scalar dissipation which do not rely on presumed shape functions for the PDF such as the commonly used β-PDF. Comput...

The effect of timescale variation in multiple mapping conditioning mixing of PDF calculations for Sandia Flame series D–F

A stochastic implementation of the multiple mapping conditioning (MMC) model has been used for the modelling of turbulence–chemistry interactions in a series of turbulent jet diffusion flames with varying degrees of local extinction (Sandia Flames D–F). The mapping function approximates the cumulative probability distribution of mixture fraction and the corresponding variance can be controlled by a standard implementation of the scalar mixing timescale. The conditional fluctuations are controlled by a minor dissipation timescale, τmin. The results show a clear dependence of the conditional fluctuations on the choice of the minor timescale, and the appropriate value for turbulent jet flames is similar to values determined in related direct numerical simulation (DNS) studies of homogeneous turbulent reacting flows. The predictions of means and variances of temperature and species mass fractions are very good for all flames, indicating an appropriate modelling of the conditional variances. Further sensitivity studies with respect to particle number density demonstrate a relative insensitivity of the results to the particle number in the numerical solution procedure. Good results can be obtained with as few as 10 particles per cell, allowing for a computationally inexpensive implementation of a Monte Carlo/probability density function (PDF) method.

On the spatial length scales of scalar dissipation in turbulent jet flames

Spatial length scales of the rate of dissipation, Χ, of fluctuations of a conserved scalar, Z, are inferred numerically using a DNS database of a turbulent planar jet flame. The Taylor-scale Reynolds numbers lie in the range of 38 to 58 along the centreline of the simulated jet flame. Three different methods are used to study the spatial length scales associated with Χ. First, analysis of the one-dimensional dissipation spectra shows an expected Reδ -3/4 (Kolmogorov) scaling with the outer-scale Reynolds number, Re δ . Secondly, thin sheet-like three-dimensional scalar dissipation structures have been investigated directly. Such structures were identified within the computational domain using level-sets of the Χ-field, and their thicknesses were subsequently computed. The study shows, in accordance with experimental studies, that the captured dissipation-layer thickness also shows a Kolmogorov scaling with Re δ . Finally, spatial filters of varying widths were applied to the instantaneous Z field in order to model the averaging effect that takes place with some experimental measurement techniques. The filtered scalar dissipation rate was then calculated from the filtered scalar field. The peaks in the instantaneous filtered Χ-profiles are observed to decrease exponentially with increasing filter width, yielding estimates of the true value of Χ. Unlike the dissipation length scales obtained from the spectral analysis and the level-set method, the length-scale estimates from the spatial-filtering method are found to be proportional to Re δ -1 . This is consistent with the small-scale intermittency of Χ which cannot be captured by techniques that just resolve the conventional Batchelor/Obukhov-Corrsin scale. These results have implications when considering resolution requirements for measuring scalar dissipation length scales in experimental flows.

Modeling Nanoparticle Agglomeration using Local Interactions

Nanoparticle agglomeration plays an important role in processes such as spray drying and particle flame synthesis. These processes have in common that nanoparticles collide at low concentrations and get irreversibly linked at the point of contact due to plastic deformation. In this article, we investigate several models of irreversible connections, which require only local interactions between the colliding nanoparticles and thus allow for scalable simulations. The models investigated here connect the particles upon collision by non-bonded strongly attractive interactions, bonded interactions or by binding agents placed at the point of contact. Models using spherically symmetric interactions form compact agglomerates and are therefore unsuitable to study agglomeration. In contrast, models that are either based on both central and angular potentials (type one) or on binding agents (type two) efficiently prevent restructuring of the agglomerates, and are therefore useful for modeling contacts formed by plastic deformation. Moreover, both types of models allow to control the rigidity and by that the degree of restructuring. The first type of model is computationally more efficient at low fractional dimensions of the aggregates, while the second gives easy access to local shear forces, which is important when breaking of agglomerates is to be considered. As example applications, we reproduce the well-known diffusion-limited agglomeration (DLA) and report results on soot aggregation. Copyright 2014 American Association for Aerosol Research