Model For Scalar Dissipation Rate Research Articles

A self-consistent extension of flamelet theory for partially premixed combustion

Orthogonal coordinate systems represent an attractive alternative for the formulation of two-dimensional composition space equations for partially premixed combustion: They avoid the need of closure models for a cross scalar dissipation rate and allow for a direct recovery of the corresponding flamelet equations in the asymptotic limits of non-premixed and premixed combustion. Despite these remarkable features, this kind of coordinate system still presents some important unsolved issues, which have limited their application so far. These difficulties are mainly associated with i) the lack of an appropriate formalism for the definition of two variables having orthogonal gradients in the entire flame domain and ii) the absence of corresponding closure models for the gradients of these variables in two-dimensional composition space. In the present work, it is shown how a Lagrangian interpretation of the flamelet derivative allows solving both problems. More specifically, after the mixture fraction, Z, is adopted as first coordinate, the proposed approach allows to derive i) two-dimensional composition space equations for all reactive scalars, ii) a transport equation for a modified reaction progress variable, φ, satisfying the desired orthogonality condition, ∇Z·∇φ=0, and iii) two-dimensional composition space equations for gZ=|∇Z| and gφ=|∇φ|. The obtained set of two-dimensional equations in orthogonal composition space is general and it can describe different flames of interest. In order to illustrate the capabilities of the formulation, the equations are then specialized for planar flames with unity Lewis number, obtaining in this way a solvable set of composition space equations in orthogonal coordinates. After an appropriate numerical approach is introduced, the resulting 2D equations are solved to analyze the interaction between premixed flamelets with a strain rate prescribed along the Z-dimension controlling the interaction. Both flame structures and budgets of the scalar gradient equations are studied and the results provide new insights into the physics of scalar gradients in two-dimensional composition space. Finally, conceivable coupling strategies of the present formulation with CFD codes for the simulation of turbulent flames are discussed.

Statistical Behaviour and Modelling of Variances of Reaction Progress Variable and Temperature During Flame-Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The statistical behaviour of the transport of reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} have been analysed using three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame-wall interaction with isothermal inert walls within turbulent boundary layers for (i) an unsteady head-on quenching of a statistically planar flame propagating across the boundary layer, and (ii) a statistically stationary oblique wall quenching of a V-flame. It has been found that the reaction rate contribution acts as a leading order source term to the transport of both reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} whereas the molecular dissipation term remains the leading order sink term for both configurations analysed here. With the progress of flame wall interaction, the magnitude of all the source terms for the transport equations of both reaction progress variable and non-dimensional temperature variances vanish in the near-wall region with the onset of flame quenching. However, the molecular dissipation term continues to act as a sink term. The performances of the existing models for turbulent scalar flux, reaction rate and scalar dissipation rate contributions have been assessed for both flame-wall interaction configurations based on a priori DNS analysis. The existing available models for scalar dissipation rate for temperature and the reaction rate contribution in the variance transport equations even with the previously proposed wall corrections do not adequately predict the behaviour in the near-wall region. Modifications have been suggested to the existing closure models for the scalar dissipation rate and the reaction rate contribution to the scalar variance transport equations to improve the predictions in the near-wall region. Furthermore, the recommended closures for the unclosed terms of both reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} are shown to accurately capture the corresponding variations obtained from DNS data for both near to and away from the wall.

A Comparison between Statistical Behaviours of Scalar Dissipation Rate between Homogeneous MILD Combustion and Premixed Turbulent Flames

Three-dimensional Direct Numerical Simulations (DNS) data has been utilised to analyse statistical behaviours of the scalar dissipation rate (SDR) and its transport for homogeneous methane-air mixture turbulent Moderate or Intense Low oxygen Dilution (MILD) combustion for different O2 dilution levels and turbulence intensities for different reaction progress variable definitions. Additional DNS has been conducted for turbulent premixed flames and passive scalar mixing for the purpose of comparison with the SDR statistics of the homogeneous mixture MILD combustion with that in conventional premixed combustion and passive scalar mixing. It has been found that the peak mean value of the scalar dissipation rate decreases with decreasing O2 concentration for MILD combustion cases. Moreover, SDR magnitudes increase with increasing turbulence intensity for both MILD and conventional premixed combustion cases. The profiles and mean values of the scalar dissipation rate conditioned upon the reaction progress variable are found to be sensitive to the choice of the reaction progress variable definition. This behaviour arises due to the differences in the distributions of the species mass fractions within the flame. The strain rate contribution and the molecular dissipation term are found to be the leading order contributors in the scalar dissipation rate transport for MILD combustion; whereas, in conventional premixed flames, the terms rising from density variation and reaction rate gradient also play leading roles in addition to the strain rate and molecular dissipation contributions. By contrast, the terms due to density gradient and reaction rate gradient remain negligible in comparison to the leading order contributors in MILD combustion cases due to small density variation because of moderate temperature rise and small reaction rate gradient magnitudes. Furthermore, the qualitative behaviour of the strain rate contribution to the SDR transport in premixed flames is significantly different to that in the case of MILD combustion and passive scalar mixing. The findings of the current analysis indicate that the scalar dissipation rate statistics in MILD combustion show several qualitative similarities to the passive scalar mixing despite major differences with the SDR transport in conventional turbulent premixed flames. This further suggests that the scalar dissipation rate models, which were originally proposed in the context of passive scalar mixing, have the potential to be applicable for MILD combustion but the models for the premixed turbulent combustion may not be applicable for MILD combustion of homogeneous mixtures.

Structure-based transient models for scalar dissipation rate in homogeneous turbulence

We present, for the first time, transient models for scalar-dissipation rate that carry information about the morphology of the turbulence structures. The proposed models are derived from a structure-sensitized transient model for the large-scale field of enstrophy. Special attention is given to the model equation of Yoshizawa (1988), from which alternative closures for scalar-dissipation rate are derived. Assuming negligible transient variations of the turbulent anisotropies, lead to an expression similar to the one used by traditional transient models for scalar dissipation rate. To reduce model uncertainties, the turbulent scalar-flux vector and the turbulence structure tensors are obtained from the same closure models for all cases considered. The estimation performance of the models is evaluated on eight cases of deformation in both fixed and rotating frames, showing encouraging results. The proposed models achieve fair agreement with homogeneous Direct Numerical Simulations (DNS) predictions in the presence of either transverse or streamwise mean scalar gradient.

Large Eddy Simulation of lifted turbulent flame in cold air using Doubly Conditional Source-term Estimation

The present study is focused on Large Eddy Simulation with Doubly Conditional Source-term Estimation (DCSE) applied to a series of lifted turbulent flames in cold air without autoignition. DCSE is formulated for partially-premixed turbulent combustion. Predictions for time-averaged methane concentration and its root mean square (rms), Probability Density Function (PDF), flame width, lift-off height and some qualitative observations are presented and compared with experimental data. The predicted methane concentrations are in good agreement with the experiments. Discrepancies for the rms are observed and several sources of discrepancies are identified. PDF of methane concentration and flammability region are also in good agreement. The lift-off heights are predicted very well. Some edge flame characteristics are visible in the simulated flames. The progress variable scalar dissipation rate model does not have a significant impact on methane concentration predictions, while it has a larger effect on predicted lift-off height and temperature. Inclusion of the non-premixed mode in the closure of the progress variable transport equation has a small effect on the current lift-off height predictions, but has a larger impact on the temperature profiles.

LES/PDF Modeling of Turbulent Premixed Flames with Locally Enhanced Mixing by Reaction

Large-eddy simulations (LES) combined with the transported probability density function (PDF) method are carried out for two turbulent piloted premixed methane-air jet flames (flame F1 and flame F3) to assess the capability of LES/PDF for turbulent premixed combustion. The conventionally used model for the sub-filter scale mixing time-scale (or the mixing frequency) fails to capture the premixed flames correctly. This failure is expected to be caused by the lack of the sub-filter scale premixed flame propagation property in the sub-filter scale mixing process when the local flame front is under-resolved. It leads to slower turbulent premixed flame propagation and wider flame front. A new model for specifying the sub-filter scale mixing frequency is developed to account for the effect of sub-filter scale chemical reaction on mixing, based on past development of models for the sub-filter scale scalar dissipation rate in premixed combustion. The new model is assessed in the two turbulent premixed jet flames F1 and F3. Parametric studies are performed to examine the new model and its sensitivity when combined with the different mixing models. Significantly improved performance of the new mixing frequency model is observed to capture the premixed flame propagation reasonably, when compared with the conventional model. The sensitivity of the flame predictions is found be relatively weak to the different mixing models in conjunction with the new mixing frequency model.

A Conditional Moment Closure Study of Chemical Reaction Source Terms in SCCI Combustion

The objective of this study is to evaluate conditional moment closure (CMC) approaches to model chemical reaction rates in compositionally stratified, autoigniting mixtures, in thermochemical conditions relevant to stratified charge compression ignition (SCCI) engines. First-order closure, second-order closure and double conditioning are evaluated and contrasted as options in comparison to a series of direct numerical simulations (DNSs). The two-dimensional (2D) DNS cases simulate ignitions in SCCI-like thermochemical conditions with compositionally stratified n-heptane/air mixtures in a constant volume. The cases feature two different levels of stratification with three mean temperatures in the negative-temperature coefficient (NTC) regime of ignition delay times. The first-order closure approach for reaction rates is first assessed using hybrid DNS-CMC a posteriori tests when implemented in an open source computational fluid dynamics (CFD) package known as OpenFOAM $^{{\circledR }}$ . The hybrid DNS-CMC a posteriori tests are not a full CMC but a DNS-CMC hybrid in that they compute the scalar and velocity fields at the DNS resolution, thus isolating the first-order reaction rate closure model as the main source of modelling error (as opposed to turbulence model, scalar probability density function model, and scalar dissipation rate model). The hybrid DNS-CMC a posteriori test reveals an excellent agreement between the model and DNS for the cases with low levels of stratification, whereas deviations from the DNS are observed in cases which exhibit high level of stratifications. The a priori analysis reveals that the reason for disagreement is failure of the first-order closure hypothesis in the model due to the high level of conditional fluctuations. Second-order and double conditioning approaches are then evaluated in a priori tests to determine the most promising path forwards in addressing higher levels of stratification. The a priori tests use the DNS data to compute the model terms, thus directly evaluating the model assumptions. It is shown that in the cases with a high level of stratification, even the second-order estimation of the reaction rate source term cannot provide a reasonably accurate closure. Double conditioning using mixture-fraction and sensible enthalpy, however, provides an accurate first-order closure to the reaction rate source term.

Dynamic Closure of Scalar Dissipation Rate for Large Eddy Simulations of Turbulent Premixed Combustion: A Direct Numerical Simulations Analysis

Dynamic algebraic closure of scalar dissipation rate (SDR) of reaction progress variable in the context of Large Eddy Simulations (LES) of turbulent premixed combustion has been addressed here using a power-law based expression and a model, which was originally proposed for Reynolds Averaged Navier Stokes (RANS) simulations, but has recently been extended for LES. The performances of these models have been assessed based on a-priori analysis of a Direct Numerical Simulations (DNS) database of statistically planar turbulent premixed flames with a range of different values of heat release parameter t, turbulent Reynolds number R e t and global Lewis number L e. It has been found that the power-law model with a single constant exponent a D does not adequately capture the volume-averaged behaviour of density-weighted SDR and this problem is particularly severe especially for L e < < 1 flames. The deficiency of the power-law model with a single power-law exponent arises due to multi-fractal nature of SDR. The dynamic evaluation of the model parameter for the algebraic model, which was originally proposed in the context of RANS and has been extended here for LES, has been shown to capture the local behaviour of SDR better than the power-law model. It has been demonstrated that the empirical parameterisation of a model parameter for the static version of the RANS-extended SDR model can be avoided using a dynamic formulation which captures the local behaviour of SDR either comparably or better than the static formulation for a range of different values of t, L e and R e t , without sacrificing the prediction of the volume-averaged SDR.

Direct numerical simulation of a supersonic lifted hydrogen jet flame: A priori study on combustion models

In this study, a systematic assessment of turbulent combustion submodels of conditional moment closure (CMC) has been conducted using DNS data of a three-dimensional spatially-developing supersonic lifted hydrogen flame with a Mach number of 1.2 at the jet injection. It has been found that Beta pdf of mixture fraction can well capture the mixing space of the high speed reacting flow. The linear model exhibits a good performance for the axial velocity predictions. Girimaji׳s model for scalar dissipation rate performs well at upstream, while the AMC model presents better further downstream. The first order closure for the conditional reaction rate deviates a lot from the DNS extracted results. Second-order corrections made to temperature only or to the two rate-limiting reaction steps induce improvement, still with much discrepancy. Second order closure considering fluctuations of all the reacting species and temperature can accurately reproduce the DNS results.

Conditional statistics of a laboratory-scale lifted turbulent H2/N2 flame using direct numerical simulation

The direct numerical simulation (DNS) database of a lifted turbulent H2/N2 flame is used to validate models in the framework of conditional moment closure (CMC). The cross-stream dependency of the reactive scalars, the presumed PDF, and the conditional means of the velocity, scalar dissipation rate and turbulent flux are investigated. It is found that in the stabilization region, the conditional mean of YOH varies significantly in the radial direction, indicating CMC grids should be considered in the radial direction. The performances of the β-PDF for both of the mixture fraction and the progress variable are generally satisfactory. However, the PDFs of the DNS results are more complex. The two conditioning variables are proved to be dependent, which makes it more difficult to model the joint PDF. The conditional velocity and scalar dissipation rate are closed with the linear model and AMC model, respectively. The linear model captures the variations of the conditional velocity very well. As for the conditional scalar dissipation rate model, further improvements could be taking into account the skew and bimodal distribution. The gradient diffusion approximation is used for the conditional turbulent flux, the performance of which is found to depend on the estimate of the diffusivity.

Algebraic Closure of Scalar Dissipation Rate for Large Eddy Simulations of Turbulent Premixed Combustion

An a-priori analysis of the filtered reaction rate closure based on Favre-filtered scalar dissipation rate (SDR) for large eddy simulations (LES) of turbulent premixed combustion has been conducted using a direct numerical simulation (DNS) database of freely propagating statistically planar flames for a range of different values of heat release parameter τ, global Lewis number Le, and turbulent Reynolds number Ret. It has been found that an existing SDR based reaction rate closure for Reynolds averaged Navier–Stokes (RANS) simulations is also valid for LES, when the filter width is larger than the flame thickness. This RANS-based reaction rate closure has been extended here for LES, and a satisfactory performance of this LES closure is observed for the values of filter widths, τ, Le, and Ret investigated here. A-priori DNS assessment of the SDR closures based on passive scalar mixing model and a power-law has been conducted. Moreover, an existing algebraic model of Favre-averaged SDR for RANS simulations has been extended here for LES. The performances of the algebraic closures of have been assessed with respect to Favre-filtered SDR extracted from the DNS data. It has been found that the newly proposed model for , which was extended here for LES from an existing RANS-based closure, predicts both local and volume-averaged behaviors of SDR satisfactorily for a range of for flames with different values of τ, Le, and Ret. The sensitivity of sub-grid turbulent velocity fluctuation modeling on the newly developed algebraic SDR closure has also been analyzed and it has been observed that the modeling does not significantly affect the performance of the algebraic SDR model proposed in this study.

Validation and implementation of algebraic LES modelling of scalar dissipation rate for reaction rate closure in turbulent premixed combustion

The closure of the filtered reaction rate of the reaction progress variable using an algebraic model for Favre-filtered Scalar Dissipation Rate (SDR) N∼c in turbulent premixed combustion has been assessed in the context of Large Eddy Simulations (LES). This assessment consists of a priori Direct Numerical Simulation (DNS) analysis based on freely propagating statistically planar turbulent premixed flames and a posteriori analysis, involving the LES simulations of a well-documented rectangular dump combustor configuration with sudden expansion (i.e. ORACLES burner) and a premixed flame stabilised on a triangular bluff body flame holder (i.e. Volvo Rig). It has been found that the newly developed SDR model satisfactorily captures N∼c obtained from explicitly filtered DNS data. The predictions of this SDR based LES closure in the ORACLES burner and Volvo Rig configurations exhibit good agreement with experimental results without requiring any major modification to the model parameters. The predictions of the SDR model for the LES of the ORACLES burner and Volvo Rig have been compared to those of two algebraic Flame Surface Density (FSD) models, which yielded satisfactory agreement with experimental data in a previous analysis. The performance of the SDR based closure remains either comparable to or better than the FSD based closures for the two test configurations considered in this analysis.

Scalar Dissipation Rate Transport in the Context of Large Eddy Simulations for Turbulent Premixed Flames with Non-Unity Lewis Number

The effects of global Lewis number Le on the statistical behaviour of the unclosed terms in the transport equation of the Favre-filtered scalar dissipation rate (SDR) N c have been analysed using a Direct Numerical Simulation (DNS) database of freely propagating statistically planer turbulent premixed flames with Le ranging from 0.34 to 1.2. The DNS data has been explicitly filtered to analyse the statistical behaviour of the unclosed terms in the SDR transport equation arising from turbulent transport T 1, density variation due to heat release T 2, scalar-turbulence interaction T 3, reaction rate gradient T 4, molecular dissipation (−D 2) and diffusivity gradients f(D) in the context of Large Eddy Simulations (LES). It Le has significant effects on the magnitudes of T 1, T 2, T 3, T 4, (−D 2) and f(D). Moreover, both qualitative and quantitative behaviours of the unclosed terms T 1, T 2, T 3, T 4, (−D 2) and f(D) are found to be significantly affected by the LES filter width Δ, which have been explained based on a detailed scaling analysis. Both scaling analysis and DNS data suggest that T 2, T 3, T 4, (−D 2) and f(D) remain leading order contributors to the SDR $\tilde {{N}}_{c} $ transport for LES. The scaling estimates of leading order contributors to the SDR $\tilde {{N}}_{c} $ transport has been utilised to discuss the possibility of extending an existing SDR model for Reynolds Averaged Navier Stokes (RANS) simulation for SDR $\tilde {{N}}_{c} $ closure in the context of LES of turbulent premixed combustion.

Linear-Eddy Model Formulated Probability Density Function and Scalar Dissipation Rate Models for Premixed Combustion

A tabulated, pseudo-turbulent Probability Density Function (PDF) model for premixed combustion is proposed. The Linear-Eddy Model (LEM) is used to construct the PDFs for a temperature-based progress variable in a premixed, turbulent methane/air V-flame produced by the Cambridge slot burner. As a second case study, the LEM PDFs are similarly compared to PDFs extracted from Direct Numerical Simulations (DNS) of a turbulent premixed flame. LEM demonstrates the ability to reproduce the salient features from experimental and DNS PDFs; moreover, it is able to better capture turbulent effects than previously suggested laminar flamelet PDF models. The Scalar Dissipation Rate (SDR) for premixed combustion is likewise investigated. The stochastic nature of LEM enables it to mimic the overall behaviors of turbulent reactions inexpensively and qualitatively. Crucially, LEM appears to be well suited for the preprocessing tabulation of PDF and SDR models for a number of premixed combustion simulation strategies.

Analysis of a dynamic model for subfilter scalar dissipation rate in large eddy simulation based on the subfilter scalar variance transport equation

Accurate prediction of non-premixed turbulent combustion using large eddy simulation (LES) requires detailed modelling of the mixing between fuel and oxidizer that occurs at scales smaller than the LES filterwidth. The small-scale mixing process can be quantitatively characterized by two related variables, the subfilter scalar variance and the subfilter scalar dissipation rate. A recently proposed alternative dynamic modelling procedure for the subfilter scale dissipation rate, designed for use with transport equation based models for subfilter scalar variance, is analysed in this work. This new dynamic non-equilibrium modelling approach produces a nonlinear interaction between variance and dissipation rate predictions that makes it difficult to isolate the performance of any single modelling component in a conventional LES simulation. To gain a better understanding of the new model, a three-part study is undertaken here. The first part of the study uses a priori analysis to examine some novel aspects of the model’s computation and guide its practical implementation. In the second part of the study, detailed a posteriori analysis of the model is performed. This analysis suggests that the dynamic estimate of the dissipation rate model coefficient helps to compensate for over-prediction of variance production rates and improves the accuracy of variance prediction. However, improved modelling of the variance production term, which in turn depends on the accuracy of models for the subfilter scalar flux, is necessary to allow both the scalar variance and dissipation rate to be predicted accurately. Therefore, the third part of the study examines the effect of the scalar flux model on the predictions of the dynamic non-equilibrium model. Use of a mixed model for the fluxes, rather than a gradient-diffusion-only model, is found to improve variance predictions in some cases.

Investigation of Mixing Models and Conditional Moment Closure Applied to Autoignition of Hydrogen Jets

The present paper is focused on performing a thorough investigation of first order Conditional Moment Closure (CMC) including an inhomogeneous turbulent mixing model for the conditional scalar dissipation rate to predict autoignition. Autoignition of a hydrogen and nitrogen fuel mixture in a heated coflow of air is examined. A sensitivity analysis is proposed for the autoignition length with respect to the mixing field, as well as a comparison of the effects of the inhomogeneous turbulent and Amplitude Mapping Closure (AMC) mixing models. The choice of turbulence constants only change predicted ignition length by approximately 5 % when applied to the AMC mixing model. Predictions of ignition length performed by the inhomogeneous model are lower than that of the AMC model by up to 15 %. The current ignition predictions are in reasonable agreement with the experimental data and previous simulation results. Two of the four regimes observed experimentally are reproduced qualitatively. Further improvement may be gained by using large eddy simulation and a gradient model for the conditional velocity in the inhomogeneous turbulent mixing model.

Large eddy simulation of a lifted ethylene flame using a dynamic nonequilibrium model for subfilter scalar variance and dissipation rate

Accurate prediction of nonpremixed turbulent combustion using large eddy simulation (LES) requires detailed modeling of the mixing between fuel and oxidizer at scales finer than the LES filter resolution. In conserved scalar combustion models, the small scale mixing process is quantified by two parameters, the subfilter scalar variance and the subfilter scalar dissipation rate. The most commonly used models for these quantities assume a local equilibrium exists between production and dissipation of variance. Such an assumption has limited validity in realistic, technically relevant flow configurations. However, nonequilibrium models for variance and dissipation rate typically contain a model coefficient whose optimal value is unknown a priori for a given simulation. Furthermore, conventional dynamic procedures are not useful for estimating the value of this coefficient. In this work, an alternative dynamic procedure based on the transport equation for subfilter scalar variance is presented. This dynamic nonequilibrium modeling approach is used for simulation of a turbulent lifted ethylene flame, previously studied using DNS by Yoo et al. (2011). The predictions of the new model are compared to those of a static nonequilibrium modeling approach using an assumed model coefficient, as well as those of the equilibrium modeling approach. The equilibrium models are found to systematically underpredict both subfilter scalar variance and dissipation rate. Use of the dynamic procedure is shown to increase the accuracy of the nonequilibrium modeling approach. However, numerical errors that arise as a consequence of grid-based implicit filtering appear to degrade the accuracy of all three modeling options. Thus, while these results confirm the usefulness of the new dynamic model, they also show that the quality of subfilter model predictions depends on several factors extrinsic to the formulation of the subfilter model itself.

Scalar dissipation rate modelling for Large Eddy Simulation of turbulent premixed flames

The statistical behaviours of scalar dissipation rate (SDR) in the context Large Eddy Simulations (LES) of turbulent premixed combustion have been analysed using a simplified chemistry based Direct Numerical Simulations (DNS) data of a turbulent V-flame. The filter size dependence of the SDR is analysed in detail and it has been demonstrated that the filtered reaction rate can be satisfactorily closed using the Favre filtered SDR provided the filter width, Δ, remains greater than the thermal flame thickness, δth. Due to the close relation between the SDR and generalised Flame Surface Density (FSD), the dependence of the FSD on filter size has also been addressed. It has been found that a fractal dimension based power-law model satisfactorily captures the global and local behaviours of the generalised FSD in the context of LES. The fractal dimension and the inner cut-off scale for flame surface based on the volume-averaged value of the FSD are found to be in good agreement with previous analytical, experimental and DNS studies. The ratio of the volume-integrated filtered value of density-weighted SDR to its resolved component exhibits a power-law in terms of Δ with an inner cut-off scale scaling with δth. A power-law based model with a global exponent and inner cut-off scale is found to be insufficient to capture the local variations of SDR possibly due to its multi-fractal nature. An algebraic model for SDR, which was originally proposed for Reynolds Averaged Navier Stokes simulations, has been extended here for LES, which is found to satisfactorily capture both the global and local behaviours of SDR.

LES model for sooting turbulent nonpremixed flames

In this work, an integrated Large Eddy Simulation (LES) model is developed for sooting turbulent nonpremixed flames and validated in a laboratory scale flame. The integrated approach leverages state-of-the-art developments in both soot modeling and turbulent combustion modeling and gives special consideration to the small-scale interactions between turbulence, soot, and chemistry. The oxidation of the fuel and the formation of gas-phase soot precursors is described by the Flamelet/Progress Variable model, which has been previously extended to account for radiation losses. However, previous DNS studies have shown that Polycyclic Aromatic Hydrocarbons (PAH), the immediate precursors of soot particles, exhibit significant unsteady effects due to relatively slow chemistry. To model these unsteady effects, a transport equation is solved for a lumped PAH species. In addition, due to the removal of PAH from the gas-phase, alternative definitions of the mixture fraction, progress variable, and enthalpy are proposed. The evolution of the soot population is modeled with the Hybrid Method of Moments (HMOM), an efficient statistical model requiring the solution of only a few transport equations describing statistics of the soot population. The filtered source terms in these equations that describe the various formation, growth, and destruction processes are closed with a recently developed presumed subfilter PDF approach that accounts for the high spatial intermittency of soot. The integrated LES model is validated in a piloted natural gas turbulent jet diffusion flame and is shown to predict the magnitude of the maximum soot volume fraction in the flame relatively accurately, although the maximum soot volume fraction is shown to be rather sensitive to the subfilter scalar dissipation rate model.

Scalar and its dissipation in the near field of turbulent lifted jet flame

In this study various scalar dissipation rates and their modelling in the context of partially premixed flame are investigated. A DNS dataset of the near field of a turbulent hydrogen lifted jet flame is processed to analyse the mixture fraction and progress variable dissipation rates and their cross dissipation rate at several axial positions. It is found that the classical model for the passive scalar dissipation rate ϵ ˜ ZZ gives good agreement with the DNS, while models developed based on premixed flames for the reactive scalar dissipation rate ϵ ˜ cc only qualitatively capture the correct trend. The cross dissipation rate ϵ ˜ cZ is mostly negative and can be reasonably approximated at downstream positions once ϵ ˜ ZZ and ϵ ˜ cc are known, although the sign cannot be determined. This approach gives better results than one employing a constant ratio of turbulent timescale and the scalar covariance c ″ Z ″ ∼ . The statistics of scalar gradients are further examined and lognormal distributions are shown to be very good approximations for the passive scalar and acceptable for the reactive scalar. The correlation between the two gradients increases downstream as the partially premixed flame in the near field evolves ultimately to a diffusion flame in the far field. A bivariate lognormal distribution is tested and found to be a reasonable approximation for the joint PDF of the two scalar gradients.