Non-premixed turbulent combustion modeling based on the filtered turbulent flamelet equation

In turbulent combustion simulations, the flow structure at the unresolved scale level needs to be reasonably modeled. Following the idea of turbulent flamelet equation for the non-premixed flame case, which was derived based on the filtered governing equations(L. Wang, Combust. Flame 175, 259(2017)), the scalar dissipation term for tabulation can be directly computed from the resolved flowing quantities, instead of solving species transport equations. Therefore, the challenging source term closure for the scalar dissipation or any assumed probability density functions can be avoided;meanwhile the chemical sources are closed by scaling relations. The general principles are discussed in the context of large eddy simulation with case validation. The new model predictions of the bluff-body flame show sufficiently improved results, compared with these from the classic progress-variable approach.     

LES of supersonic combustion in a scramjet engine model

In this study, Large Eddy Simulation (LES) has been used to examine supersonic flow and combustion in a model scramjet combustor. The LES model is based on an unstructured finite volume discretization, using total variational diminishing flux reconstruction, of the filtered continuity, momentum, enthalpy, and passive/reactive scalar equations, used to describe the combustion process. The configuration used is similar to the laboratory scramjet at the Institute for Chemical Propulsion of the German Aerospace Center (DLR) and consists of a one-sided divergent channel with a wedge-shaped flameholder at the base of which hydrogen is injected. Here, we investigate supersonic flow with hydrogen injection and supersonic flow with hydrogen injection and combustion. For the purpose of validation, the LES results are compared with experimental data for velocity and temperature at different cross-sections. In addition, qualitative comparisons are also made between predicted and measured shadowgraph images. The LES computations are capable of predicting both the non-reacting and reacting flowfields reasonably well—in particular we notice that the LES model identifies and differentiates between peculiarities of the flowfields found in the experiments.     

Prediction of NO in turbulent diffusion flames using Eulerian particle flamelet model

The combustion characteristics for the turbulent diffusion flames using the unsteady flamelet concept have been numerically investigated. The Favre-averaged Navier–Stokes equations are solved by a finite volume method of SIMPLE type that incorporates the laminar flamelet concept with a modified k ? ε turbulence model. The NO formation is estimated by solving the Eulerian particle transport equations in a postprocessing mode. Two test problems are considered: CH₄/H₂/N₂ jet flame and CH₄/H₂ stabilised bluff body flame. The temperature and species profiles are well captured by the flamelet model. Two different chemical mechanisms (GRI 2.11 and 3.0) give nearly identical results for temperature and species except NO. The GRI 3.0 gives significantly higher NO levels compared to the GRI 2.11. This is mainly attributed to the difference in NO formation by the prompt mechanism. The NO formation is sensitive to the number of flamelet particles. The NO levels for two test flames do not change when the flamelet particle number exceeds six.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

超声速气流中液体横向射流的非定常特性与振荡边界模型

针对液体圆柱射流垂直喷入超声速横向气流中的非定常分布特性开展实验研究, 并建立穿透深度方向上的射流振荡分布模型. 利用脉冲激光背景成像方法“冻结”拍摄马赫2.1(Ma=2.1)气流中煤油射流/喷雾瞬态图像, 结合最大类间方差法(Otsu)和Canny算法提取瞬态图像特征, 基于统计方法并引入间歇因子(γ)定量描述射流振荡分布特性; 通过研究多参数协同作用下的射流振荡分布规律, 提出振荡分布数学模型, 研究的参数变量包括超声速来流总压(642-1010 kPa)、 液体喷注压降(0.36-4.61 MPa)、液体喷嘴流道直径 (0.48 mm/1.0 mm/1.25 mm/1.52 mm)、距离喷嘴的流向距离(10-125 mm)以及液气动量通量比(0.11-7.49). 研究中利用射流振荡分布模型成功预测出水射流在Ma=2.1气流中的的振荡分布, 预测分布与实验结果符合良好.     

Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data

The interaction between turbulence and reactive scalar fields is discussed for the wrinkled flamelets regime of turbulent premixed combustion. Emphasis is placed on the effects associated with the turbulent straining term. In the regime of turbulent combustion under consideration, which corresponds to Karlovitz and Damköhler numbers such that Ka < 1 and Da > 1, a clear and simple formulation is proposed to explain and to model the influence of the correlation between velocity and reactive scalar gradients. This formulation is based on the conservative variables budget across one-dimensional premixed laminar flamelets. The analysis firmly confirms the dependence on both the Damköhler number and the expansion factor, a feature already foreseen in recent studies. Nevertheless, in contrast with previous work, (i) the scaling arguments used in the present contribution are different from those used in other recent proposals, and (ii) the proposed closures are not only deduced from dimensional arguments but also from the consideration of conservative variable budgets across laminar flamelets. The resulting functional dependence on the expansion factor is found to be influenced by the underlying one-dimensional flamelet representation and two possible closures are put forward to take this dependence into account. (iii) The two closures do not exhibit a proportionality to the mean scalar dissipation rate as suggested in previous studies but to the square of this quantity. This results in the presence of a second contribution proportional to in the modelled transport equation for the mean scalar dissipation rate, in addition to the modelled molecular dissipation term. (iv) Since previous Direct Numerical Simulation (DNS) studies have been essentially devoted to the influence of the Damköhler number, the present DNS validation step is focused on the effects of the expansion rate. To this purpose, the proposed models are validated against three available DNS databases obtained for turbulent premixed flames with different values of the density ratio between unburned and fully burned gases.     

Gradient trajectory analysis in a Jet flow for turbulent combustion modelling

Based on planar high-speed Rayleigh scattering measurements of the mixture fraction Z of propane discharging from a turbulent round jet into co-flowing carbon dioxide at nozzle-based Reynolds numbers Re ₀ = 3000–8600, we use scalar gradient trajectories to investigate the local structure of the turbulent scalar field with a focus on the scalar turbulent/non-turbulent interface. The latter is located between the fully turbulent part of the jet and the outer flow. Using scalar gradient trajectories, we partition the turbulent scalar field into these three regions according to an approach developed by Mellado et al. (J.P. Mellado, L. Wang, and N. Peters, Gradient trajectory analysis of a scalar field with external intermittency, J. Fluid Mech. 626 (2009), pp. 333–365.). Based on these different regions, we investigate in a next step zonal statistics of the scalar probability density function (pdf) P(Z) as well as the scalar difference along the trajectory ΔZ and its mean scalar value Z_m , where the latter two quantities are used to parameterize the scalar profile along gradient trajectories. We show that the scalar pdf P(Z) can be reconstructed from zonal gradient trajectory statistics of the joint pdf P(Z_m , ΔZ). Furthermore, on the one hand we relate our results for the scalar turbulent/non-turbulent interface to the findings made in other experimental and numerical studies of the turbulent/non-turbulent interface, and on the other hand discuss them in the context of the flamelet approach and the modelling of pdfs in turbulent non-premixed combustion. Finally, we compare the zonal statistics for P(Z) with the composite model of Effelsberg and Peters (E. Effelsberg and N. Peters, A composite model for the conserved scalar pdf, Combust. Flame 50 (1983), pp. 351–360) and observe a very good qualitative and quantitative agreement.     

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

In the past three decades, considerable progress has been made in the investigation of incompressible turbulent boundary layer through experiments, DNS and theoretical works, including: (1) the statistics characteristic and structure of turbulence; (2) the co-herent structures in turbulent flows; (3) turbulence modeling and the large eddy simula-tion (LES). In contrast, the progress was very slow for the compressible, in particular, the super-sonic turbulent boundary layer. Recent works on d…     

A comparison of different approaches to integrate flamelet tables with presumed-shape PDF in flamelet models for turbulent flames

Flamelet models for turbulent combustion modelling make use of presumed-shape probability density functions (PDFs) for integrating laminar flamelet solutions to obtain an integrated flamelet table that can readily be used for turbulent flame calculations. The existence of non-unique approaches for such an integration has rarely been investigated before. For the first time, this work studies systematically the non-uniqueness of the flamelet table integration approaches. A flamelet model called the flamelet/progress variable model is used in the study, although the issue exists generally in many other flamelet models. Two classes of table integration approaches are investigated, one preserving the laminar flamelet structures during integration and the other not. Three different table integration approaches are examined and compared in detail to provide a thorough understanding of the different approaches. A partially stirred reactor is used as a test case for examining the different approaches. A method based on the transported PDF method is also employed to provide a reference for the assessment of the different flamelet table integration approaches. It is found in general that the flamelet preserving integration approach yields a more reasonable joint PDF of the mixture fraction and the progress variable, and the prediction results are closer to the referenced transported PDF results.     

Comparison of well-mixed and multiple representative interactive flamelet approaches for diesel spray combustion modelling

The application of detailed chemistry to the computational fluid dynamics simulation of combustion process in diesel engines has many potentials, including the possibility to predict auto-ignition, diffusion flame structure, stabilisation and soot formation in a wide range of operating conditions, also taking into account the effects of different fuel types. Among the approaches that were proposed over the years, the ones that are mostly used in practical calculations can be divided into two main categories: the first assumes each cell to be a well-stirred reactor, while the second employs the flamelet assumption to describe both auto-ignition and turbulent diffusion flame propagation. Despite the fact that both types of model have been widely validated over the years, a detailed comparison between them appears to be very useful in order to understand better the relevant parameters governing auto-ignition, flame stabilisation and the formation of pollutant emissions. This work is focused on a comparison of two different combustion models that were recently implemented by the authors in an open-source code. The first assumes each cell to be a homogeneous reactor and neglects interaction between turbulence and chemistry, while in the second, multiple laminar flamelets are used to represent the structure of a turbulent diffusion flame. Suitable techniques for online reaction rate tabulation and chemical mechanism reduction are also incorporated, to make the use of bigger mechanisms possible (up to 150 species). The two models are compared and validated by simulating constant-volume diesel combustion in a wide range of operating conditions, including variations of ambient temperature and oxygen concentration. Comparison between the computed and experimental data on flame structure, auto-ignition and flame lift-off enables an understanding of the main relevant differences between the models in the way both auto-ignition and flame stabilisation processes are predicted.     

DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion

The linear relation between the mean rate of product creation and the mean scalar dissipation rate, derived in the seminal paper by K.N.C. Bray [‘The interaction between turbulence and combustion’, Proceedings of the Combustion Institute, Vol. 17 (1979), pp. 223–233], is the cornerstone for models of premixed turbulent combustion that deal with the dissipation rate in order to close the reaction rate. In the present work, this linear relation is straightforwardly validated by analysing data computed earlier in the 3D Direct Numerical Simulation (DNS) of three statistically stationary, 1D, planar turbulent flames associated with the flamelet regime of premixed combustion. Although the linear relation does not hold at the leading and trailing edges of the mean flame brush, such a result is expected within the framework of Bray's theory. However, the present DNS yields substantially larger (smaller) values of an input parameter c_m (or K₂ = 1/(2c_m ? 1)), involved by the studied linear relation, when compared to the commonly used value of c_m = 0.7 (or K₂ = 2.5). To gain further insight into the issue and into the eventual dependence of c_m on mixture composition, the DNS data are combined with the results of numerical simulations of stationary, 1D, planar laminar methane–air flames with complex chemistry, with the results being reported in terms of differently defined combustion progress variables c, i.e. the normalised temperature, density, or mole fraction of CH₄, O₂, CO₂ or H₂O. Such a study indicates the dependence of c_m both on the definition of c and on the equivalence ratio. Nevertheless, K₂ and c_m can be estimated by processing the results of simulations of counterpart laminar premixed flames. Similar conclusions were also drawn by skipping the DNS data, but invoking a presumed beta probability density function in order to evaluate c_m for the differently defined c's and various equivalence ratios.     

Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling

In this paper it is investigated whether the Flame Surface Density (FSD) model, developed for turbulent premixed combustion, is also applicable to stratified flames. Direct Numerical Simulations (DNS) of turbulent stratified Bunsen flames have been carried out, using the Flamelet Generated Manifold (FGM) reduction method for reaction kinetics. Before examining the suitability of the FSD model, flame surfaces are characterized in terms of thickness, curvature and stratification.

All flames are in the Thin Reaction Zones regime, and the maximum equivalence ratio range covers 0.1?φ?1.3. For all flames, local flame thicknesses correspond very well to those observed in stretchless, steady premixed flamelets. Extracted curvature radii and mixing length scales are significantly larger than the flame thickness, implying that the stratified flames all burn in a premixed mode. The remaining challenge is accounting for the large variation in (subfilter) mass burning rate.

In this contribution, the FSD model is proven to be applicable for Large Eddy Simulations (LES) of stratified flames for the equivalence ratio range 0.1?φ?1.3. Subfilter mass burning rate variations are taken into account by a subfilter Probability Density Function (PDF) for the mixture fraction, on which the mass burning rate directly depends. A priori analysis point out that for small stratifications (0.4?φ?1.0), the replacement of the subfilter PDF (obtained from DNS data) by the corresponding Dirac function is appropriate. Integration of the Dirac function with the mass burning rate m=m(φ), can then adequately model the filtered mass burning rate obtained from filtered DNS data. For a larger stratification (0.1?φ?1.3), and filter widths up to ten flame thicknesses, a β-function for the subfilter PDF yields substantially better predictions than a Dirac function. Finally, inclusion of a simple algebraic model for the FSD resulted only in small additional deviations from DNS data, thereby rendering this approach promising for application in LES.     

Large eddy simulation of piloted pulverised coal combustion using extended flamelet/progress variable model

An extended flamelet/progress variable (EFPV) model for simulating pulverised coal combustion (PCC) in the context of large eddy simulation (LES) is proposed, in which devolatilisation, char surface reaction and radiation are all taken into account. The pulverised coal particles are tracked in the Lagrangian framework with various sub-models and the sub-grid scale (SGS) effects of turbulent velocity and scalar fluctuations on the coal particles are modelled by the velocity-scalar joint filtered density function (VSJFDF) model. The presented model is then evaluated by LES of an experimental piloted coal jet flame and comparing the numerical results with the experimental data and the results from the eddy break up (EBU) model. Detailed quantitative comparisons are carried out. It is found that the proposed model performs much better than the EBU model on radial velocity and species concentrations predictions. Comparing against the adiabatic counterpart, we find that the predicted temperature is evidently lowered and agrees well with the experimental data if the conditional sampling method is adopted.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)     

RANS predictions of turbulent diffusion flames: comparison of a reactor and a flamelet combustion model to the well stirred approach

The flame stabilisation process in turbulent non-premixed flames is not fully understood and several models have been developed to describe the turbulence–chemistry interaction. This work compares the performance of the multiple Representative Interactive Flamelet (mRIF) model, the Volume Reactor Fraction Model (VRFM), and the Well-Stirred reactor (WS) model in describing such flames. The predicted ignition delay and flame lift-off length of n-heptane sprays are compared to experimental results published within the Engine Combustion Network (ECN). All of the models predict the trend of ignition delay reasonably well. At a low gas pressure (42 bar) the ignition delay is overpredicted compared to the experimental data, but the difference between the models is not significant. However, the predicted lift-off lengths differ. At high pressure (87 bar) the difference between the models is small. All models slightly underpredict the lift-off length compared to the experimental data. At low gas pressure (42 bar) the mRIF model gives the best results. The VRFM and WS models predict excessively short lift-off lengths, but the VRFM model gives better results than the WS model. The flame structures of the models are also compared. The WS model and the VRFM model yield a well defined flame stabilisation point whereas the mRIF model does not. The flame of the mRIF model is more diffuse and the model is not able to predict flame propagation. All models were able to predict the experimental trends in lift-off and ignition delay, but certain differences between them are demonstrated.     

Statistical model for combustion of high-metal magnesium-based hydro-reactive fuel

<正>We investigate experimentally and analytically the combustion behavior of a high-metal magnesium-based hydroreactive fuel under high temperature gaseous atmosphere.The fuel studied in this paper contains 73%magnesium powders.An experimental system is designed and experiments are carried out in both argon and water vapor atmospheres. It is found that the burning surface temperature of the fuel is higher in water vapor than that in argon and both of them are higher than the melting point of magnesium,which indicates the molten state of magnesium particles in the burning surface of the fuel.Based on physical considerations and experimental results,a mathematical one-dimensional model is formulated to describe the combustion behavior of the high-metal magnesium-based hydro-reactive fuel.The model enables the evaluation of the burning surface temperature,the burning rate and the flame standoff distance each as a function of chamber pressure and water vapor concentration.The results predicted by the model show that the burning rate and the surface temperature increase when the chamber pressure and the water vapor concentration increase,which are in agreement with the observed experimental trends.     

Combustion and emission modelling of a direct-injection spark-ignition engine by combining flamelet models for premixed and diffusion flames

The combustion and emission production processes of a DISI (direct-injection spark-ignition) engine were modelled by combining flamelet models for premixed and diffusion flames. A new surrogate fuel was proposed to approximate the complicated composition of real gasoline. In contrast to simpler conventional models, the fuel was modelled as a ternary mixture of three hydrocarbons: iso-octane, n-heptane and toluene. Turbulent flame propagation in a partially premixed field was modelled by a premixed flamelet model. The mass fractions of the detailed composition of species in burnt gas were predicted by a diffusion flamelet model. For the pollutant formation modelling, a two-step oxidation of CO and H₂ was used to simulate the secondary diffusion flame. The extended Zeldovich mechanism was used to model NOx formation, while a phenomenological model was used to model soot formation. This model was initially applied to a simple geometry to investigate the fundamentals of the model's behaviour, after which three-dimensional computational fluid dynamic (CFD) simulations were performed in a realistic engine geometry.     

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.     

A mixing controlled direct chemistry (MCDC) model for diesel engine combustion modelling using large eddy simulation

A mixing controlled direct chemistry (MCDC) combustion model with sub-grid scale (SGS) mixing effects and chemical kinetics has been evaluated for Large Eddy Simulation (LES) of diesel engine combustion. The mixing effect is modelled by a mixing timescale based on mixture fraction variance and sub-grid scalar dissipation rate. The SGS scalar dissipation rate is modelled using a similarity term and a scaling factor from the analysis of Direct Numerical Simulation (DNS) data. The chemical reaction progress is estimated from a kinetic timescale based on local internal energy change rate and equilibrium state internal energy. An optical research engine operating at conventional operating conditions and Low Temperature Combustion (LTC) conditions was used for evaluation of the combustion model. From the simulation results, the effect of SGS scalar mixing is evaluated at different stages of combustion. In the context of LES, the new approach provides improved engine modelling results compared to the Direct Chemistry Solver (DCS) combustion model.