Conditional Scalar Dissipation Research Articles

Analysis of auto-ignition of heated hydrogen–air mixtures with different detailed reaction mechanisms

Auto-ignition processes of hydrogen, diluted with nitrogen, in heated air are numerically investigated by means of an unsteady laminar flamelet approach in mixture fraction space. The focus is on the auto-ignition delay time and the most reactive mixture fraction as obtained with five chemical mechanisms. Two strongly different levels of dilution, corresponding to experiments in the open literature, are considered. This concerns low-temperature chemistry at atmospheric pressure. The temperature of the air stream is much higher than the temperature of the fuel stream in the cases under study. We extensively investigate the effect of the co-flow temperature, the conditional scalar dissipation rate and the resolution in mixture fraction space for one case. With respect to the conditional scalar dissipation rate, we discuss the Amplitude Mapping Closure (AMC) model with imposed maximum scalar dissipation rate at mixture fraction equal to 0.5, as well as a constant conditional scalar dissipation rate value over the entire mixture fraction value range. We also illustrate that an auto-ignition criterion, based on a temperature rise, leads to similar results as an auto-ignition criterion, based on OH mass fraction, provided that the hydrogen is not too strongly diluted.

Direct numerical simulations and analysis of three-dimensional n-heptane spray flames in a model swirl combustor

Three-dimensional n-heptane spray flames in a swirl combustor are investigated by means of direct numerical simulation (DNS) to provide insight into realistic spray evaporation and combustion as well as relevant modeling issues. The variable-density, low-Mach number Navier–Stokes equations are solved using a fully conservative and kinetic energy conserving finite difference scheme in cylindrical coordinates. Dispersed droplets are tracked in a Lagrangian framework. Droplet evaporation is described by an equilibrium model. Gas combustion is represented using an adaptive one-step irreversible reaction. Two different cases are studied: a lean case that resembles a lean direct injection combustion, and a rich case that represents the primary combustion region of a rich-burn/quick-quench/lean-burn combustor. The results suggest that premixed combustion contribute more than 70% to the total heat release rate, although diffusion flame have volumetrically a higher contribution. The conditional mean scalar dissipation rate is shown to be strongly influenced, especially in the rich case. The conditional mean evaporation rate increases almost linearly with mixture fraction in the lean case, but shows a more complex behavior in the rich case. The probability density functions (PDF) of mixture fraction in spray combustion are shown to be quite complex. To model this behavior, the formulation of the PDF in a transformed mixture fraction space is proposed and demonstrated to predict the DNS data reasonably well.

Simulation of Hydrogen Auto-Ignition in a Turbulent Co-flow of Heated Air with LES and CMC Approach

Large-Eddy Simulations (LES) with the first order Conditional Moment Closure (CMC) approach of a nitrogen-diluted hydrogen jet, igniting in a turbulent co-flowing hot air stream, are discussed. A detailed mechanism (nine species, 19 reactions) is used to represent the chemistry. Our study covers the following aspects: CFD mesh resolution; CMC mesh resolution; inlet boundary conditions and conditional scalar dissipation rate modelling. The Amplitude Mapping Closure for the conditional scalar dissipation rate produces acceptable results. We also compare different options to calculate conditional quantities in CMC resolution. The trends in the experimental observations are in general well reproduced. The auto-ignition length decreases with an increase in co-flow temperature and increases with increase in co-flow velocity. The phenomena are not purely chemically controlled: the turbulence and mixing play also affect the location of auto-ignition. In order to explore the effect of turbulence, two options were applied: random noise and turbulence generator based on digital filter. It was found that stronger turbulence promotes ignition.

Capturing localised extinction in Sandia Flame F with LES–CMC

A Large Eddy Simulation (LES) using the Conditional Moment Closure (CMC) as a sub-grid turbulence-chemistry model has been applied to piloted jet diffusion flames (Sandia D&F). A 3D CMC grid was used which allowed different CMC boundary conditions to be applied in the jet and pilot streams. The code was found to give very good agreement with experiment in the low extinction case of Flame D. For Flame F transient extinction and re-ignition events were observed with LES–CMC which lead to reductions in averaged unconditional and conditional temperature consistent with experimental observations. Further analysis revealed that the CMC extinction/ignition events were the result of a combination of high conditional scalar dissipation rate and transport in the CMC grid.

Investigation of an inhomogeneous turbulent mixing model for conditional moment closure applied to autoignition

The present paper examines the case of autoignition of high pressure methane jets in a shock tube over a range of pre-heated air temperatures in engine-relevant conditions. The two objectives of the present paper are: (i) to examine the effect of the inhomogeneous mixing model on the autoignition predictions relative to the results obtained using homogeneous mixing models and (ii) to see if the magnitude of the change can explain the discrepancy between the predictions of ignition delay previously obtained with homogeneous mixing models and the experimental data. The governing equation of the scalar dissipation rate is solved for transient conditions and two different formulations of the same model are tested and compared: one using the linear model for the conditional velocity and one including the gradient diffusion model. The predicted ignition kernel location and time delay over a range of pre-combustion air temperatures are compared with results obtained using two homogeneous turbulent mixing models and available experimental data. The profiles of conditional velocity and the conditional scalar dissipation rate are examined. Issues related to the conditional velocity model are discussed. It is found that the differences in the predictions are due to the mixing model only. The inhomogeneous model using the gradient conditional velocity model produces much larger ignition delays compared to the other models, whereas the inhomogeneous form including the linear model does not produce any significant differences. The effect of the turbulent inhomogeneous model is larger at high air temperatures and decreases with decreasing air temperatures. In comparison with the measured ignition delays, the inhomogeneous-Gradient model brings a small improvement at high air temperatures over the results from the turbulent homogeneous models. At low air temperatures, other parameters need to be investigated in order to bring the predicted ignition delays and locations within the experimental data scatter.

Implementation Issues of the Conditional Moment Closure Model in Large Eddy Simulations

Different ways of transferring information regarding the mixture fraction, its sub-grid scale variance and the scalar dissipation rate are examined in terms of a Large Eddy Simulation (LES)/Conditional Moment Closure (CMC) calculation. In such a simulation, information must be transferred from a fine LES grid to a usually coarser CMC grid. Different options of calculating conditional and unconditional quantities in the CMC resolution are assessed by filtering experimental mixture fraction and scalar dissipation rate data at various resolutions. It was found that when a presumed shape for the Filtered Density Function at the CMC resolution is used, special care must be given to the mixture fraction variance. It was also found that the Amplitude Mapping Closure model can be used for the conditional scalar dissipation rate. LES/CMC with detailed chemistry of a bluff-body stabilised burner was performed using two different ways of calculating the turbulent diffusivity. The structure of the flame is realistic, with little difference noticed when using the two diffusivities.

Gradient trajectory analysis of a scalar field with external intermittency

The passive scalar field of a temporally evolving shear layer is investigated using gradient trajectories as a means to analyse the scalar probability density function and the conditional scalar dissipation rate in the presence of external intermittency. These results are of significance for turbulent combustion, where improved predictions of the statistics of the conditional dissipation rate are needed in several models. First, the variation of the conventional first and second moments of the conditional dissipation rate across the layer is quantitatively documented in detail. A strong dependence of the conditional dissipation rate on the lateral position and on the conditioning value of the scalar is observed. The dependence on the transverse distance to the centre-plane partially explains the double-hump profile usually reported when this dependence is ignored. The variation with the scalar observed in the ratio between the second and first moments would invalidate certain assumptions commonly done in turbulent combustion. It is also seen that conditioning on the scalar does not reduce the fluctuation of the dissipation rate with respect to unconditional values. Next, the role of external intermittency in these results is investigated. For that purpose, the flow is partitioned into different zones based on different types of gradient trajectories passing through each point, thereby introducing non-local information in comparison with the standard turbulent/non-turbulent separation based on the conventional intermittency function. In addition to the homogeneous outer regions, three zones are identified: a turbulent zone, a turbulence interface and quasi-laminar diffusion layers. The relative contribution from each of these zones to the conventional intermittency factor is reported. The statistics are then conditioned on each of these zones, and the spatial variation of the scalar distribution and of the conditional scalar dissipation rate is explained in terms of the observed zonal statistics. For the Reynolds numbers of the present simulation, between 1500 and 3000 based on the vorticity thickness and the velocity difference, and a Schmidt number equal to 1, it results that the major contribution to both statistics is due to the turbulence interfaces. At the same time, the turbulent zone shows a distinct behaviour, being approximately homogeneous but anisotropic.

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. Computed probability distributions agree well with measurements, and a detailed comparison of the modeled conditional and mean scalar dissipation with experimental data and conventional closures demonstrate MMC’s potential. Predictions of reactive species and temperature are in good agreement with experimental data and similar in quality to singly conditioned, first-order CMC predictions. MMC therefore provides an attractive-since consistent-alternative approach for the modeling of scalar mixing in turbulent reacting flows.

Direct numerical simulation of diluted combustion by evaporating droplets

Diluted combustion has been studied using DNS in a three-dimensional temporally developing reacting shear-layer with the oxidizer stream laden with evaporating droplets. The gaseous phase is described in the Eulerian frame while the discrete droplet phase is treated in the Lagrangian frame, with strong two-way coupling between the two phases through mass, momentum and energy exchange. Grid-resolution-independent results have been obtained in cases without and with droplets. A comprehensive parametric study has been conducted by varying the initial Stokes number ( St 0) and mass loading ratio (MLR 0). Detailed field analysis has been conducted to examine the complex nonlinear interactions among droplet dynamics, evaporation, turbulence and combustion, and so on. Effects of evaporating droplets on averaged flow and combustion quantities have also been presented. In particular, the conditional scalar dissipation rate is found to be enhanced by evaporating droplets, which suggests that they can promote micromixing and combustion under certain conditions, in addition to their roles in combustion suppression. The transport equation for the mixture fraction variance Z ″ 2 ∼ has been analyzed, with a focus on the vaporization-related source terms. Such source terms exhibit more complex local variations in the present shear-flow non-premixed flame configuration, compared with the case in the homogeneous decaying turbulence configuration of Réveillon and Vervisch (2000).

Multiple mapping conditioning of turbulent jet diffusion flames

The multiple mapping conditioning (MMC) approach is applied to two non-piloted CH 4 / H 2 / N 2 turbulent jet diffusion flames with Reynolds numbers of Re = 15,200 and 22,800. The work presented here examines primarily the suitability of MMC to simulate CH 4 / H 2 flames with varying Re numbers. The equations are solved in a prescribed Gaussian reference space with only one stochastic reference variable emulating the fluctuations of mixture fraction. The mixture fraction is considered as the only major species on which the remaining minor species are conditioned. Fluctuations around the conditional means are ignored. It is shown that the statistics of the mapped reference field are an accurate model for the statistics of the physical field for both flames. A transformation of the Gaussian reference space introduced in previous work on MMC is used to express the MMC model in the same form as CMC. The most important advantage of this transformation is that the conditionally averaged scalar dissipation term is in a closed form. The corresponding temperature and reactive species predictions are generally in good agreement with experimental data. The application to real laboratory flames and the assessment of the new conditional scalar dissipation model for the closure of the singly conditioned CMC equation is the major novelty of this paper. The results are therefore primarily examined with respect to changes of the conditionally averaged quantities in mixture fraction space.

Modelling of autoignition for methane-based fuel blends using Conditional Moment Closure

First-order Conditional Moment Closure (CMC) is applied to investigate the autoignition of high pressure CH4, CH4/C2H6, CH4/H2, and CH4/N2 jets injected into lower pressure heated air over a wide range of pre-combustion temperatures. Detailed and optimized chemical kinetics mechanisms are used for each fuel blend. The turbulent flow field and CMC calculations are decoupled based on the frozen mixing assumption. The standard k–ε turbulence model is used to perform the velocity and mixing fields calculations. The CMC equations are cross-stream averaged due to the small radial dependence of the conditional scalars in shear flows, and are solved elliptically. A three-step fractional method is implemented to treat the stiff chemical source term separately. Two formulations are implemented to model the conditional scalar dissipation term. The numerical results are compared to shock tube experiments. Predicted ignition delays and locations are found to be in reasonable agreement with the experiments. Further analysis is provided.

Assessment of the Eulerian particle flamelet model for nonpremixed turbulent jet flames

Although the Eulerian particle flamelet model (EPFM) recently proposed by Barths et al. [Proc. Combust. Inst. 27 (1998) 1841–1847] has shown the potential capabilities to realistically predict detailed pollutant (NO x , soot) formation in a turbulent reacting flow occurring within practical combustion devices, there still exists room to improve the predicative capability in terms of local flame structure and turbulence–chemistry interaction. In this study, the EPFM approach was applied to simulate two turbulent nonpremixed jet flames of CO/H 2/N 2 fuel having the same jet Reynolds number but different nozzle diameters, and the capability of predicting the NO x formation as well as both similarity of major species and sensitivity of minor species to fluid-dynamic scaling for the two flames has been assessed deeply in terms of both conditional and unconditional mean structures. The present results indicate that the original EPFM substantially overpredicts the conditional scalar dissipation rate at the downstream region and consequently underpredicts the streamwise decay of superequilibrium radical concentrations to the equilibrium state. In this study, in order to correctly estimate the averaged conditional scalar dissipation rate, a new modeling of the conditional scalar dissipation rate based on a least-squares fit through a mass weighted spatial distribution has been devised. In terms of both conditional and unconditional means, the EPFM utilizing this new procedure yields nearly the same results as the Lagrangian flamelet model, and provides closer agreement with experimental data than the original EPFM approach.

A mixing model providing statistics of the conditional scalar dissipation rate

AbstractJoint composition probability density function (PDF) methods are used for the numerical simulation of turbulent reactive flows. Here, other than in classical Reynolds averaged Navier–Stokes (RANS) or large eddy simulation (LES) approaches, the highly non‐linear chemical source term appears in closed form. On the other hand, mixing models are required for the closure of the molecular diffusion term. In the present work, the joint statistics of the scalar and the scalar dissipation rate provided by the parameterized scalar profile (PSP) mixing model are validated. The goal is to combine the PDF method with a flamelet approach, where the scalar dissipation rate plays a crucial role in determining the contribution of the chemical source term. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of submodels for conditional velocity and scalar dissipation in CMC simulation of piloted jet and bluff-body flames

No meaningful difference is observed between the predictions with the conditional velocity modeled by linear scaling and gradient diffusion assumption for the test flames under consideration. The AMC and Girimaji's model for CSDR show similar results, while the pdf integration method results in an asymmetric profile with some deviation from the other two. The difference tends to decrease as mixing proceeds, to result in a lower level of scalar dissipation at downstream locations. Reasonable agreement is achieved with measured scalar dissipation rates at different axial locations for the Sandia Flame D, while direct comparison is difficult due to radially averaged pdfs and no measured scalar dissipation rates being available for the Sydney bluff-body flame.

Direct numerical simulations of the double scalar mixing layer: Part II: Reactive scalars

The reacting double scalar mixing layer (RDSML) is investigated as a canonical multistream flow and a model problem for simple piloted diffusion flames. In piloted diffusion flames, the reacting fuel and oxidizer streams are initially separated by a central pilot stream at stoichiometric composition. The primary purpose of this pilot is to delay the mixing of the pure streams until a stable flame base can develop. In such multistream systems, the modeling of turbulent scalar mixing is complicated by the multiple feed streams, leading to more complex fine-scale statistics, which remain as yet an unmet modeling challenge compared to the simpler two-feed system. In Part I we described how multimodal mixture fraction probability density functions (PDFs) and conditional scalar dissipation rates can be modeled with a presumed mapping function approach. In this work we present an efficient and robust extension of the modeling to a general multistream reacting flow and compare predictions to three-dimensional direct numerical simulations (DNS) of the RDSML with a single-step reversible chemistry model and varying levels of extinction. With high extinction levels, the interaction with the pilot stream is described. Additionally, state-of-the-art combustion modeling calculations including conditional moment closure (CMC) and stationary laminar flamelet modeling (SLFM) are performed with the newly developed mixing model. Excellent agreement is found between the DNS and modeling predictions, even where the PDF is essentially a triple-delta shape near the flame base, so long as extinction levels are moderate to low. The suggested approach outlined in this paper is strictly valid only for flows that can be described by a single mixture fraction. For these flows the approach should provide engineers with fine-scale models that are of accuracy comparable to those already available for binary mixing, at only marginally higher complexity and cost.

Conditional statistics of nonreacting and reacting sprays in turbulent flows by direct numerical simulation

Conditional statistics concerning evaporation and combustion of a spray are investigated in homogeneous, isotropic, and decaying two-dimensional (2D) turbulence. Randomly distributed, polydisperse droplets of n-heptane go through single-step combustion chemistry. Attention is focused on parametric effects of initial Sauter mean radius (SMR), turbulence level and droplet velocity in both reacting and nonreacting cases. A simple linear model for the conditional evaporation rate is proposed and validated against DNS data. A conventional β-probability density function (pdf) is shown to be valid with no peak occurring on the fuel side. The amplitude mapping closure (AMC) model works well for the conditional scalar dissipation rate with evaporating and reacting sprays. Parametric study shows that initial SMR and droplet velocity are major factors affecting conditional flame structures, whereas the effect of reaction is not significant except during autoignition.

Mixing characteristics and structure of a turbulent jet diffusion flame stabilized on a bluff-body

Flow dynamics, scalar mixing, and pollutant formation in a turbulent jet diffusion flame stabilized on a bluff-body are investigated using large-eddy simulation. The density weighted filtered equations for the flow and mixing fields are solved using dynamic models for the subfilter quantities. Subfilter combustion processes are modeled by the conditional filtering method. An integrated formulation that considers only axial variation of conditionally filtered quantities is presented. Results show that vortex shedding from the coflow stream and its interaction with the high speed main jet play an important role in the generation of high dissipation layers in the intense mixing region. The mechanisms that generate the high dissipation layers in the intense mixing region are identified. The relatively uniform composition of combustion products in the recirculation zone helps the flame stabilization by maintaining low scalar dissipation rate and high temperature in the vicinity of the stoichiometric surfaces. The present integrated formulation is shown to reproduce these characteristics of the mixing field and to predict the flame structure and NO formation well. The weighted integral formulation of the conditional velocity allows the entrainment of the combustion products in the intense mixing region into the recirculation zone. The proper prediction of low conditional scalar dissipation in the recirculation zone is shown to be crucial for accurately describing the stabilization process. The decrease of NO at the end of the recirculation zone is reproduced due to the well-predicted mixing characteristics.

Measurements and simulations of mixing and autoignition of an n-heptane plume in a turbulent flow of heated air

The autoignition of a gaseous n-heptane plume in heated turbulent air has been investigated experimentally and numerically with the conditional moment closure and a CFD code. It has been demonstrated that, consistent with previous experimental results for hydrogen and acetylene, the increased scalar dissipation rate created by faster co-flowing air delays autoignition, as revealed by a disproportionate increase of ignition length with air velocity. The predicted mean and variance of the mixture fraction, the mixture fraction PDF and the conditional scalar dissipation rate are in good agreement with experimental results obtained with acetone-tracer PLIF. The first-order, spatially averaged CMC model reproduces the experimental trends quite well, despite the neglect of conditional fluctuations and spatial dependence of the conditional averages. This is attributed to the fact that for a significant period of time before autoignition the conditional scalar dissipation rate at the most reactive mixture fraction is much smaller than the critical value above which autoignition is precluded.

Simulations of Turbulent Non-Premixed Counterflow Flames with First-Order Conditional Moment Closure

Simulations of turbulent CH4-air counterflow flames are presented, obtained in terms of zero and two-dimensional first-order Conditional Moment Closure (CMC) to study the flame structure and extinction limits. The CMC equation with detailed chemistry is solved without the need for operator splitting, while the accompanying flow field is determined using a commercial CFD software employing a Reynolds stress turbulence model and additional transport equations for the turbulent scalar flux and for the mean scalar dissipation rate. Two detailed chemical mechanisms and different conditional scalar dissipation rate models have been examined and small differences were found.

Conditional Moment Closure for Large Eddy Simulations

A conditional moment closure (CMC) based combustion model for large-eddy simulations (LES) of turbulent reacting flow is proposed and evaluated. Transport equations for the conditionally filtered species are derived that are consistent with the LES formulation and closures are suggested for the modelling of the conditional velocity, conditional scalar dissipation and the fluctuations around the conditional mean. A conventional β-probability density distribution of the scalar is used together with dynamic modelling for the sub-grid fluxes. The model is validated by comparison of simulations with measurements of a piloted, turbulent methane-air jet diffusion flame.