A priori assessment of algebraic flame surface density models in the context of large eddy simulation for nonunity lewis number flames in the thin reaction zones regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimension D and inner cut-off scale η i have been studied in detail. It has been found that D is strongly affected by Lewis number and increases significantly with decreasing Le. By contrast, η i remains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation of D is proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD. © 2012 Mohit Katragadda et al.

DNS of EGR-type turbulent flame in MILD condition

Three-dimensional direct numerical simulation (DNS) of exhaust gas recirculation (EGR)-type turbulent combustion operated in moderate and intense low-oxygen dilution (MILD) condition has been carried out to study the flame structure and flame interaction. In order to achieve adequate EGR-type initial/inlet mixture fields, partially premixed mixture fields which are correlated with the turbulence are carefully preprocessed. The chemical kinetics is modelled using a skeletal mechanism for methane-air combustion. The results suggest that the flame fronts have thin flame structure and the direct link between the mean reaction rate and scalar dissipation rate remains valid in the EGR-type combustion with MILD condition. However, the commonly used canonical flamelet is not fully representative for MILD combustion. During the flame-flame interactions, the heat release rate increases higher than the maximum laminar flame value, while the gradient of progress variable becomes smaller than laminar value. It is also proposed that the reaction rate and the scalar gradient can be used as a marker for the flame interaction. © 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Comment and reply on the 'assessment of combustion and submodels for turbulent nonpremixed hydrocarbon flames'

In deriving the flamelet model for nonpremixed combustion certain terms, but not the unsteady term, are assumed to be negligible. This results in a relation between all reacting scalars and the mixture fraction as independent variable. An ideal test of the flamelet assumption can be based on direct numerical simulation (DNS) data, if all reacting scalars are conditioned on mixture fraction and conditional moments are evaluated. The fundamental assumption of the flamelet model are unwillingly justified. The unsteady and steady formulations of the same equations are compared and found that unsteadiness is important in an unsteady simulation.

On computing the physical sources of jet noise

We derive a closed system of equations that relates the acoustically radiating flow variables to the sources of sound for homentropic flows. We use radiating density, momentum density and modified pressure as the dependent variables which leads to simple source terms for the momentum equations. The source terms involve the non-radiating parts of the density and momentum density fields. These non-radiating components are obtained by removing the radiating wavenumbers in the Fourier domain. We demonstrate the usefulness of this new technique on an axi-symmetric jet solution of the Navier-Stokes equations, obtained by direct numerical simulation (DNS). The dominant source term is proportional to the square of the non-radiating part of the axial momentum density. We compare the sound sources to that obtained by an acoustic analogy and find that they have more realistic physical properties. Their frequency content and amplitudes are consistent with. We validate the sources by computing the radiating sound field and comparing it to the DNS solution. © 2010 by S. Sinayoko, A. Agarwal.

Effects of Lewis number on scalar variance transport in premixed flames

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le = 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study. © 2010 Springer Science+Business Media B.V.

Statistics and modelling of turbulent kinetic energy transport in different regimes of premixed combustion

The statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames is analysed using data from three-dimensional Direct Numerical Simulation (DNS) of freely propagating turbulent premixed flames under decaying turbulence. For flames within the corrugated flamelets regime, it is observed that turbulent kinetic energy is generated within the flame brush. By contrast, for flames within the thin reaction zones regime it has been found that the turbulent kinetic energy decays monotonically through the flame brush. Similar trends are observed also for the dissipation rate of turbulent kinetic energy. Within the corrugated flamelets regime, it is demonstrated that the effects of the mean pressure gradient and pressure dilatation within the flame are sufficient to overcome the effects of viscous dissipation and are responsible for the observed augmentation of turbulent kinetic energy in the flame brush. In the thin reaction zones regime, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation, resulting in a monotonic decay of turbulent kinetic energy across the flame brush. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient (gradient) transport wherever the turbulent scalar flux is counter-gradient (gradient) in nature. A new model has been proposed for the turbulent flux of turbulent kinetic energy, and is found to capture the qualitative and quantitative behaviour obtained from DNS data for both the corrugated flamelets and thin reaction zones regimes without the need to adjust any of the model constants. © 2010 Springer Science+Business Media B.V.

Scalar dissipation rate transport in the corrugated flamelets and thin reaction zones regime for turbulent premixed flames

The characteristics of the scalar dissipation rate transport in the corrugated flamelets and the thin reaction zones regimes are studied based on two three-dimensional Direct Numerical Simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames. The turbulent flame parameters are so chosen that the database which represents the corrugated flamelets regime has a global Damköhler number Da>1 whereas the database representing the thin reaction zones regime has Da <1. It is demonstrated that the terms originating from the correlation between fluctuating velocity and scalar gradient T1 shows strong Da dependence. The terms originating from dilatation T2, the scalar inner product of gradients of velocity and scalar fields T3 and the correlation between reaction rate and scalar gradients T4 and the dissipation term D2 remain important for both the flames. However, T3 dissipates scalar dissipation rate in the Da > 1 flame while it produces scalar dissipation rate in the Da < 1 flame. This difference is because of the change in the alignment between scalar and velocity gradients

Spatial correlation of heat release rate and sound emission from turbulent premixed flames

The two-point spatial correlation of the rate of change of fluctuating heat release rate is central to the sound emission from open turbulent flames, and a few attempts have been made to address this correlation in recent studies. In this paper, the two-point correlation and its role in combustion noise are studied by analysing direct numerical simulation (DNS) data of statistically multi-dimensional turbulent premixed flames. The results suggest that this correlation function depends on the separation distance and direction but, not on the positions inside the flame brush. This correlation can be modelled using a combination of Hermite-Gaussian functions of zero and second order, i.e. functions of the form (1-Ax2)e-Bx2 for constants A and B, to include its possible negative values. The integral correlation volume obtained using this model is about 0.2δL3 with the length scale obtained from its cube root being about 0.6δ L, where δ L is the laminar flame thermal thickness. Both of the values are slightly larger than the values reported in an earlier study because of the anisotropy observed for the correlation. This model together with the turbulence-dependent parameter K, the ratio of the root-mean-square (RMS) value of the rate of change of reaction rate to the mean reaction rate, derived from the DNS data is applied to predict the far-field sound emitted from open flames. The calculated noise levels agree well with recently reported measurements and show a sensitivity to K values. © 2012 The Combustion Institute.

Geometry and interaction of structures in homogeneous isotropic turbulence

A strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number Reλ = 141 is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, L. The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, planarity' and filamentarity', obtained using the Minkowski functionals. The planarity increases gradually by a small amount as L is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as L decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale L are most likely to align with the largest extensional strain at a scale 3-5 times larger than L. This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the 5η scale (where η is the Kolmogorov scale) are more concentrated near the ones that are 3-5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures. Copyright © 2012 Cambridge University Press.

A presumed joint pdf model for turbulent combustion with varying equivalence ratio

Modeling of the joint probability density function of the mixture fraction and progress variable with a given covariance value is studied. This modeling is validated using experimental and direct numerical simulation (DNS) data. A very good agreement with experimental data of turbulent stratified flames and DNS data of a lifted hydrogen jet flame is obtained. The effect of using this joint pdf modeling to calculate the mean reaction rate with a flamelet closure in Reynolds averaged Navier-Stokes (RANS) calculation of stratified flames is studied. The covariance effect is observed to be large within the flame brush. The results obtained from RANS calculations using this modeling for stratified jet- and rod-stabilized V-flames are discussed and compared to the measurements as a posteriori validation for the joint probability density function model with the flamelet closure. The agreement between the computed and measured values of flame and turbulence quantities is found to be good. © 2012 Copyright Taylor and Francis Group, LLC.

Reynolds number effects on scalar dissipation rate transport and its modeling in turbulent premixed combustion

The effects of turbulent Reynolds number, Ret, on the transport of scalar dissipation rate of reaction progress variable in the context of Reynolds averaged Navier-Stokes simulations have been analyzed using three-dimensional simplified chemistry-based direct numerical simulation (DNS) data of freely propagating turbulent premixed flames with different values of Ret. Scaling arguments have been used to explain the effects of Ret on the turbulent transport, scalar-turbulence interaction, and the combined reaction and molecular dissipation terms. Suitable modifications to the models for these terms have been proposed to account for Ret effects, and the model parameters include explicit Ret dependence. These expressions approach expected asymptotic limits for large values of Ret. However, turbulent Reynolds number Ret does not seem to have any major effects on the modeling of the term arising from density variation. Copyright © Taylor and Francis Group, LLC.

Nonlinear thermoacoustics of ducted premixed flames: The influence of perturbation convection speed

When a premixed flame is placed within a duct, acoustic waves induce velocity perturbations at the flame's base. These travel down the flame, distorting its surface and modulating its heat release. This can induce self-sustained thermoacoustic oscillations. Although the phase speed of these perturbations is often assumed to equal the mean flow speed, experiments conducted in other studies and Direct Numerical Simulation (DNS) conducted in this study show that it varies with the acoustic frequency. In this paper, we examine how these variations affect the nonlinear thermoacoustic behaviour. We model the heat release with a nonlinear kinematic G-equation, in which the velocity perturbation is modelled on DNS results. The acoustics are governed by linearised momentum and energy equations. We calculate the flame describing function (FDF) using harmonic forcing at several frequencies and amplitudes. Then we calculate thermoacoustic limit cycles and explain their existence and stability by examining the amplitude-dependence of the gain and phase of the FDF. We find that, when the phase speed equals the mean flow speed, the system has only one stable state. When the phase speed does not equal the mean flow speed, however, the system supports multiple limit cycles because the phase of the FDF changes significantly with oscillation amplitude. This shows that the phase speed of velocity perturbations has a strong influence on the nonlinear thermoacoustic behaviour of ducted premixed flames. © 2013 The Combustion Institute.

Scalar gradient behaviour in MILD combustion

The results of three-dimensional Direct Numerical Simulation (DNS) of Moderate, Intense Low-oxygen Dilution (MILD) and conventional premixed turbulent combustion conducted using a skeletal mechanism including the effects of non-unity Lewis numbers and temperature dependent transport properties are analysed to investigate combustion characteristics using scalar gradient information. The DNS data is also used to synthesise laser induced fluorescence (LIF) signals of OH, CH2O, and CHO. These signals are analysed to verify if they can be used to study turbulent MILD combustion and it has been observed that at least two (OH and CH2O) LIF signals are required since the OH increase across the reaction zone is smaller in MILD combustion compared to premixed combustion. The scalar gradient PDFs conditioned on the reaction rate obtained from the DNS data and synthesised LIF signals suggests a strong gradient in the direction normal to the MILD reaction zone with moderate reaction rate implying flamelet combustion. However, the PDF of the normal gradient is as broad as for the tangential gradient when the reaction rate is high. This suggests a non-flamelet behaviour, which is due to interaction of reaction zones. The analysis of the conditional PDFs for the premixed case confirms the expected behaviour of scalar gradient in flamelet combustion. It has been shown that the LIF signals synthesised using 2D slices of DNS data also provide very similar insights. These results demonstrate that the so-called flameless combustion is not an idealised homogeneous reactive mixture but has common features of conventional combustion while containing distinctive characteristics. © 2013 The Combustion Institute.

Modelling of turbulent lifted jet flames using flamelets: A priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z-c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z-c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences. © 2014 Taylor & Francis.

Direct simulation of turbulent entrainment due to a plume impinging on a density interface

The law for turbulent entrainment due to plumes and jets impinging on a density interface is subject to significant uncertainty, with reported differences in entrainment rates up to a factor of 10. We report preliminary results obtained by Direct Numerical Simulation which are part of a PRACE project on turbulent entrainment carried out on JUGENE at Jülich, Germany. Various interface tracking methods are discussed and the entrainment coefficient is determined.