Turbulent Non-premixed Combustion Research Articles

Conditional velocity statistics in the double scalar mixing layer – A mapping closure approach

In this work we use 3D direct numerical simulations (DNS) to investigate the average velocity conditioned on a conserved scalar in a double scalar mixing layer (DSML). The DSML is a canonical multistream flow designed as a model problem for the extensively studied piloted diffusion flames. The conditional mean velocity appears as an unclosed term in advanced Eulerian models of turbulent non-premixed combustion, like the conditional moment closure and transported probability density function (PDF) methods. Here it accounts for inhomogeneous effects that have been found significant in flames with relatively low Damköhler numbers. Today there are only a few simple models available for the conditional mean velocity and these are discussed with reference to the DNS results. We find that both the linear model of Kutznetzov and the Li and Bilger model are unsuitable for multi stream flows, whereas the gradient diffusion model of Pope shows very close agreement with DNS over the whole range of the DSML. The gradient diffusion model relies on a model for the conserved scalar PDF and here we have used a presumed mapping function PDF, that is known to give an excellent representation of the DNS. A new model for the conditional mean velocity is suggested by arguing that the Gaussian reference field represents the velocity field, a statement that is evidenced by a near perfect agreement with DNS. The model still suffers from an inconsistency with the unconditional flux of conserved scalar variance, though, and a strategy for developing fully consistent models is suggested.

A-priori analysis of conditional moment closure modeling of a temporal ethylene jet flame with soot formation using direct numerical simulation

Modeling soot formation in turbulent nonpremixed combustion is a difficult problem. Unlike most gaseous combustion species, soot lacks a strong state relationship with the mixture fraction due to unsteady formation rates which overlap transport timescales, and strong differential diffusion between gaseous species and soot. The conditional moment closure model (CMC) has recently been applied to the problem of turbulent soot formation. A challenge in CMC modeling is the treatment of differential diffusion. Three-dimensional direct numerical simulation (DNS) of a nonpremixed ethylene jet flame with soot formation has been performed using a 19 species reduced ethylene mechanism and a four-step, three-moment, semi-empirical soot model. The DNS provides full resolution of the turbulent flow field and is used to perform a-priori analysis of a recent CMC model derived from the joint scalar PDF transport equation. Unlike other approaches, this CMC model does not require additional transport equations to treat differentially diffusing species. A budget of the terms of the CMC equation for both gaseous species and soot is presented. In particular, exact expressions for unclosed terms are compared to typical closure models for scalar dissipation, cross-dissipation, differential diffusion, and reactive source terms. The differential diffusion model for gaseous species is found to be quite accurate, while that for soot requires an additional model for the residual term.

Examination of laminar-flamelet concept using vortex/flame interactions

The laminar-flamelet concept for turbulent non-premixed combustion is examined through a study of vortex/flame interactions in a hydrogen/air, opposing-jet non-premixed flame. Vortices with sizes ranging from centimeter to sub-millimeter are injected toward the flame surface. The vortex-injection velocity is selected such that every interaction results in (1) flame extinction and (2) the ratio between the vortex-turnaround and the chemical time scales falling in the laminar-flamelet regime of turbulent combustion. The dynamic changes that occur to the flame structure during its interaction with the vortex are mapped onto a scalar-dissipation-rate scale. It is found that not only the scalar-dissipation rate but also the size of the vortex (eddy) is required for describing the flame-stretching process. The large centimeter-size vortex, irrespective of the propagation velocity, wrinkles and strains the flame before causing local extinction, which represents typical laminar-flamelet behavior. On the other hand, the small sub-millimeter-size vortex replaces the local fluid in the flame zone with fresh air and destroys the flame structure without causing any wrinkling or stretching of the reaction zone, which represents non-flamelet behavior. Interactions with millimeter-size vortices are found to deviate gradually from the flamelet behavior as the vortex size decreases. Vortex/flame interactions that do not follow laminar-flamelet behavior produce very high heat-release rates that are not observed in stretched planar flames. Similar deviations from flamelet behavior are observed in methane and ethylene flames. Since turbulent eddies are two to three orders of magnitude smaller than a millimeter-size vortex, caution must be exercised when applying laminar-flamelet theory to turbulent-combustion modeling.

Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model: 1. A priori study and presumed PDF closure

Previously conducted studies of the flamelet/progress variable model for the prediction of nonpremixed turbulent combustion processes identified two areas for model improvements: the modeling of the presumed probability density function (PDF) for the reaction progress parameter and the consideration of unsteady effects [Ihme et al., Proc. Combust. Inst. 30 (2005) 793]. These effects are of particular importance during local flame extinction and subsequent reignition. Here, the models for the presumed PDFs for conserved and reactive scalars are re-examined and a statistically most likely distribution (SMLD) is employed and tested in a priori studies using direct numerical simulation (DNS) data and experimental results from the Sandia flame series. In the first part of the paper, the SMLD model is employed for a reactive scalar distribution. Modeling aspects of the a priori PDF, accounting for the bias in composition space, are discussed. The convergence of the SMLD with increasing number of enforced moments is demonstrated. It is concluded that information about more than two moments is beneficial to accurately represent the reactive scalar distribution in turbulent flames with strong extinction and reignition. In addition to the reactive scalar analysis, the potential of the SMLD for the representation of conserved scalar distributions is also analyzed. In the a priori study using DNS data it is found that the conventionally employed beta distribution provides a better representation for the scalar distribution. This is attributed to the fact that the beta-PDF implicitly enforces higher moment information that is in excellent agreement with the DNS data. However, the SMLD outperforms the beta distribution in free shear flow applications, which are typically characterized by strongly skewed scalar distributions, in the case where higher moment information can be enforced.

PDF modeling and simulation of premixed turbulent combustion

The use of probability density function (PDF) methods for turbulent combustion simulations is very attractive because arbitrary finite-rate chemistry can be exactly taken into account. PDF methods are well developed for non-premixed turbulent combustion. However, many real flames involve a variety of mixing regimes (non-premixed, partially-premixed and premixed turbulent combustion), and the development of PDF methods for partially-premixed and premixed turbulent combustion turned out to be a very challenging task. The paper shows a promising way to overcome this problem by extending existing PDF methods such that a variety of mixing regimes can be covered. The latter is done by a generalization of the standard scalar mixing frequency model. The generalized scalar mixing frequency model accounts for several relevant processes in addition to velocity-scalar correlations that are represented by the standard model for the mixing of scalars. The suitability of the new mixing frequency model is shown by applications to several premixed turbulent Bunsen flames which cover various regimes ranging from flamelet to distributed combustion. Comparisons to existing concepts focused on the inclusion of reaction effects in mixing frequency models for non- reacting scalars reveal the advantages of the new mixing frequency model. It is worth noting that the same methodology can be used in correspondingfilter density function (FDF) methods.

A combustion model sensitivity study for CH4/H2 bluff-body stabilized flame

The objective of the current work is to assess the performance of different combustion models in predicting turbulent non-premixed combustion in conjunction with the k-∊ turbulence model. The laminar flamelet, equilibrium chemistry, constrained equilibrium chemistry, and flame sheet models are applied to simulate combustion in a CH4/H2 bluff-body flame experimentally studied by the University of Sydney. The computational results are compared to experimental values of mixture fraction, temperature, and constituent mass fractions. The comparison shows that the laminar flamelet model performs better than other combustion models and mimics most of the significant features of the bluff-body flame.

A Eulerian PDF scheme for LES of nonpremixed turbulent combustion with second-order accurate mixture fraction

Monte Carlo simulations of joint probability density function (PDF) approaches have been developed in the past largely with Reynolds averaged Navier Stokes (RANS) applications. Current interests are in the extension of PDF approaches to large eddy simulation (LES). As LES resolves accurately the large scales of turbulence in time, the Monte Carlo simulation and the flow field need to be tightly coupled. A tight coupling can be achieved if the consistency between the scalar field solution obtained via finite-volume (FV) methods and that from the stochastic solution of the PDF is ensured. For nonpremixed turbulent flames with two distinct streams, the local reactive mixture is described by the mixture fraction. A Eulerian Monte Carlo method is developed to achieve a second-order accuracy in the instantaneous filtered mixture fraction that is consistent with the corresponding FV. The performances of the proposed scheme are extensively evaluated using a one-dimensional model. Then, the scheme is applied to two cases with LES. The first one is a non-reacting mixing flow of two different fluids. The second case is the Sandia piloted turbulent flame D with a steady state flamelet model. Both results confirm the consistency of the proposed method to the level of filtered mixture fraction.

Numerical investigation of turbulent non-premixed combustion of a wood pyrolysis gas

A fully compressible database of turbulent non-premixed flames of a wood pyrolysis gas is developed by means of direct numerical simulation (DNS). A reduced kinetic mechanism is used to model the combustion of a pyrolysis gas-air mixture. The instantaneous flame surface density evolution equation based on the concept of a displacement speed is examined. The normal component of the displacement speed is nearly constant with respect to curvature, while the curvature-related component tries to restore the flame front to a planar shape. The strain-rate term is mainly a source as the flame is mostly extended. The normal displacement is responsible for both positive and negative contributions to the flame area. The displacement/curvature term is primarily a sink, since it is dominated by its curvature component. Effects of strain and curvature are analyzed by considering their correlations with reaction rates. Reaction rates are enhanced with increased positive strain rates owing to an increase in the flame surface area and to a decrease in curvature. The analyzed results aid in the development of turbulent combustion models. Finally, a new model for a mean variance of the scalar dissipation rate, based on a scale similarity approach, is proposed and examined. A comparison with DNS results shows that the proposed model provides a significant improvement over existing models.

LES OF THE SYDNEY SWIRL FLAME SERIES: AN INITIAL INVESTIGATION OF THE FLUID DYNAMICS

The non-premixed turbulent Sydney Swirl Burner is a target of the workshop series on turbulent non-premixed flames (TNF). Thorough experimental investigations in Sydney and Sandia provided experimental data for 10 different configurations. This flame series allows for the examination of various fuel compositions, flow rates and swirl numbers and its computation by Large Eddy Simulation (LES) promises detailed insight into turbulent non-premixed swirl combustion. To improve the reliability of these simulations elaborate preliminary studies must be carried out, which are detailed in this paper. Spatial resolution requirements are discussed and an appropriate sampling period for statistics is determined. The paper presents first and second moments for the velocity components in the non-reactive flow and preliminary mixture fraction results for one flame of the series. Results are in reasonable agreement with experimental data, while some deficiencies indicate the need for further grid refinement and more accurate inflow data before the simulation of the entire flame series can be attempted.

Multiple mapping conditioning for extinction and reignition in turbulent diffusion flames

The newly developed multiple mapping conditioning (MMC) approach for turbulent non-premixed combustion is applied to a series of flames with varying levels of extinction and reignition. This is one of the first applications of MMC to reacting flows and results for mixture fraction, normalised temperature and reactive species are compared with DNS data. MMC is a generalised approach applying mapping closure to a prescribed reference space. The dimensions of the reference space are problem specific; here reference spaces with a single mixture-fraction-like variable and up to three dissipation-like variables are used. The results for two flame cases show an improvement in accuracy over those obtained from conditional moment closure singly conditioned on mixture fraction or doubly conditioned on mixture fraction and scalar dissipation. Results for another case suggest that the essential physics of the problem may not be fully described by this modelling.

Modelling of burner stabilised oxy-fuel flames by using non-premixed and partially-premixed turbulent combustion models

The turbulent flow and combustion process of oxy-fuel flames are studied in the wake behind a burner rim separating fuel and oxidiser inlet channels. A range of conditions was considered, from stably attached flames, via lifted flames to blow-off. It was found that the chemical equilibrium model did not predict the chemical composition well. The laminar flamelet model performed better. It appeared that extinction is not the mechanism that leads to a lifted flame and therefore partial premixing was considered. It appeared that lifted oxy-fuel flames can be predicted fairly well by adjusting a turbulent burning velocity constant.

Matching conditional moments in PDF modelling of nonpremixed combustion

The rate of generation of fluctuations with respect to the scalar values conditioned on the mixture fraction, which significantly affects turbulent nonpremixed combustion processes, is examined. Simulation of the rate in a major mixing model is investigated and the derived equations can assist in selecting the model parameters so that the level of conditional fluctuations is better reproduced by the models. A more general formulation of the multiple mapping conditioning (MMC) model that distinguishes the reference and conditioning variables is suggested. This formulation can be viewed as a methodology of enforcing certain desired conditional properties onto conventional mixing models. Examples of constructing consistent MMC models with dissipation and velocity conditioning as well as of combining MMC with large eddy simulations (LES) are also provided.

Conditional filtering method for large-eddy simulation of turbulent nonpremixed combustion

The conditional filtering method is proposed as a subfilter combustion model for large-eddy simulation (LES) of turbulent nonpremixed combustion. The novel method is based on conditional filtering of a reactive scalar field and an extension of conditional moment closure (CMC) for LES. Filtering conditioned on isosurfaces of the mixture fraction is adopted to resolve small-scale mixing and chemical reactions in nonpremixed combustion. The conditionally filtered equations are derived and the closure assumptions are discussed. A priori tests are performed using direct numerical simulation data for reacting mixing layers. The primary closure assumption on the subfilter flux in mixture fraction space is shown to work much better than the corresponding closure for the Reynolds averaged CMC due to resolved large-scale fluctuations of the scalar dissipation rate and of reactive scalars. Results show that first-order closure of the reaction rate performs well except for the boundaries of flame holes. In the boundaries of flame holes, fluctuations of reactive scalars around the conditionally filtered values are large enough for the effects of higher-order correlations to be significant. The accuracy of the first-order closure is less sensitive to the level of local extinction than that of first-order CMC, since large-scale fluctuations of reactive scalars on isosurfaces of the mixture fraction are resolved. This shows that extinction processes occur primarily over length scales comparable to the large scales of the turbulence. The integrated conditional filtering approach is introduced to reduce the computational cost and to resolve the low probability problem in the conditional filtering method. While the assumption of homogeneity in the integration direction is not as good as in the conditional average, the integrated formulation is shown to represent the extinction process caused by large-scale fluctuations of the scalar dissipation rate quite well.

Conditional mixing statistics in a self-similar scalar mixing layer

Conditional scalar mixing statistics from a three-dimensional direct numerical simulation (DNS) of a scalar mixing layer are presented in the context of modeling nonpremixed turbulent combustion. The simulation is closely matched to a particular laboratory experiment but with slight adjustments so that the simulated flow is very nearly self-similar. All statistics commonly used in mixing models are presented, along with comparisons to models and laboratory data where available. A model for the conditional scalar dissipation rate (CSD), recently introduced by Mortensen [“Consistent modeling of scalar mixing for presumed multiple parameter probability density functions,” Phys. Fluids 17, 018106 (2005)], is tested against the data set, as is a Lagrangian stochastic trajectory technique recently published by Sawford [“Conditional scalar mixing statistics in homogenous isotropic turbulence,” New J. Phys. 6, 1 (2004)]. It is concluded that (i) the DNS data set provides an excellent, high-resolution description of the scalar mixing layer that can be used for developing and verifying models for scalar mixing; (ii) the self-consistent CSD model of Mortensen is necessary for consistent implementations of the conditional moment closure, but for the current flow it gives only small adjustments to the more commonly adopted model of Girimaji [“On the modeling of scalar diffusion in isotropic turbulence,” Phys. Fluids A 4, 2529 (1992)]; and (iii) Sawford’s Lagrangian technique very closely predicts the DNS results.

Sensitivity Analysis of a FGR Industrial Furnace for NOx Emission Using Frequency Domain Method

Preliminary study has shown that the flue gas recirculation (FGR) is one of the effective ways to reduce the nitric oxides (NOx) emission in industrial furnaces. The sensitivity of the NOx emission from a FGR industrial furnace to the change in three major furnace input variables—inlet combustion air mass flow rate, inlet combustion air temperature, and pressure head of the FGR fan—is investigated numerically in this study. The investigation is carried out in frequency domain by superimposing sinusoidal signals of different frequencies on to the furnace control inputs around the design operating condition, and observing the frequency responses. The results obtained in this study can be used in the design of active combustion control systems to reduce NOx emission. The numerical simulation of the turbulent non-premixed combustion process in the furnace is conducted using a moment closure method with the assumed β probability density function for the mixture fraction. The combustion model is derived based on the assumption of instantaneous full chemical equilibrium. The discrete transfer radiation model is chosen as the radiation heat transfer model, and the weighted-sum-of-gray-gases model is used to calculate the absorption coefficient.

Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter λ. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of λ lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of λ is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.

Conditional moment closure modeling of extinction and re-ignition in turbulent non-premixed flames

The conditional moment closure approach is used to describe extinction and re-ignition events in turbulent non-premixed hydrocarbon combustion. It is well known that single conditional moment closure cannot correctly capture these phenomena and a second conditioning variable, sensible enthalpy, needs to be introduced to account for significant fluctuations around the singly conditioned mean. As a first step, the key closure assumptions are validated with the aid of direct numerical simulation with four-step chemistry. Simulations with an increasing degree of local extinction are used to assess the performance of first order closures for the highly non-linear chemical source terms. The results obtained with the doubly conditioned moment closure method are excellent for all cases, and conditional moment closure is capable of accurately predicting local extinction, the onset of re-ignition, and the occurrence of global extinction. Next, it is shown that the conditioned reaction rate terms can be modelled using presumed shape functions for the conditional moments in sensible enthalpy space, thus leading to a new closure for the reaction rate terms in the singly conditioned moment closure equations. Full closure can be based on a presumed β-distribution for the conditional PDF of sensible enthalpy, and the solution of an additional variance equation is needed.

Conditional moment closure modeling of turbulent nonpremixed combustion in diluted hot coflow

The conditional moment closure (CMC) model is applied to predict flame structures and NO formation in the moderate and intense low oxygen dilution combustion mode. The effects of oxygen concentration in a hot diluted oxidant stream are investigated in the experimental condition of Dally et al. [Proc. Combust. Inst. 29 (2002) 1147–1154]. The GRI 2.11 Mech is used for description of chemical reaction including NO x chemistry. The conditional scalar dissipation rate, which describes the effect of turbulent mixing on finite chemistry, is calculated by integrating the transport equation for probability density function (PDF). A new PDF is proposed to describe three stream mixing in terms of a single mixture fraction. The conditional mean predictions of temperature, and CO, OH, and NO mass fractions are in good agreement with measurements. The unconditional Favre mean predictions of CO and NO mass fractions are also in reasonable agreement. Upstream underprediction of OH and NO in the low oxygen concentration case may be attributed to uncertainty in low temperature reaction mechanism and mixing prediction. Differential diffusion effects are shown to be nonnegligible in the present flames. The CMC model is an attractive choice for simulation of MILD combustion in which conditional fluctuations of reactive scalars are small enough for first-order closure of conditional mean reaction rates to remain valid.

Transient dynamics of edge flames in a laminar nonpremixed hydrogen–air counterflow

Dynamics of edge flames encountered upon local quenching of nonpremixed flames is studied numerically considering the detailed chemistry of hydrogen–air combustion. The simulations are performed by superimposing two pairs of counter-rotating vortices on a steady counterflow nonpremixed flame. The density-weighted displacement speed and scalar dissipation rate are found to be appropriate parameters in characterizing the propagation speed of the edge flame with finite thickness and chemical structure, for both steady and transient conditions. It is also found that the edge flame speed strongly depends on the transient and history effects of the imposed flow field in addition to the instantaneous local scalar dissipation rate. A negative edge flame speed is observed during the early phase of the interaction due to the enthalpy loss to the transverse direction in the presence of a large strain. The effects of the fuel Lewis number on the edge flame speed are found to be consistent with the previous theoretical predictions based on the laminar flamelet theory. The results suggest that the transient and history aspects need to be carefully taken into account for an accurate description of the realistic turbulent nonpremixed combustion with partial quenching.

PDF modelling of turbulent non-premixed combustion with detailed chemistry

Although the significant advantage for the probability density function (PDF) methods of the exact treatment of chemical reactions in turbulent combustion problems, a detailed chemistry mechanism (e.g., the GRI mechanism) has not been implemented in the practical calculations by now due to the prohibitive computation of PDF methods. In this work, a detailed mechanism (GRI-Mech 3.0, consisting of 53 species and 325 elemental reactions) is firstly incorporated into the PDF calculation of a turbulent non-premixed jet flame (Sandia Flame D). The flow is formulated in the boundary layer form. The joint composition PDF closure level is applied and a multiple-time-scale (MTS) k– ε turbulence model is combined for the closure of turbulent transport terms. The molecular mixing process is modelled by the Euclidean minimum spanning tree (EMST) mixing model. The solutions are obtained by using the space marching algorithm for turbulence equations and node-based Monte Carlo particle method for PDF evolution equation. The chemical reaction source terms are integrated directly. Extensive comparisons between the predictions and the measurements are made, which involve radial profiles of mean and rms (root mean square), conditional mean, scatter plots of scalars and conditional PDF distribution etc. The flame structures are well represented by the present calculation, including intermediate species (e.g. CO and H 2) mass fractions, pollutant NO emission and local extinction.