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.     

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.     

Unsteady flamelet/progress variable approach for non-premixed turbulent lifted flames

The unsteady flamelet/progress variable approach has been developed for the prediction of a lifted flame to capture the extinction and re-ignition physics. In this work inclusion of the time variant behavior in the flamelet generation embedded in the large eddy simulation technique, allows better understanding of partially premixed flame dynamics. In the process sufficient simulations to generate unsteady laminar flamelets are performed, which are a function of time. These flamelets are used for the generation of the look-up table and the flamelet library is produced. This library is used for the calculation of temperature and other species in the computational domain as the solution progresses. The library constitutes filtered quantities of all the scalars as a function of mean mixture fraction, mixture fraction variance and mean progress variable. Mixture fraction and progress variable distributions are assumed to be β-PDF and δ-PDF respectively. The technique used here is known as the unsteady flamelet progress variable (UFPV) approach. One of the well known lifted flames is considered for the present modeling which shows flame lift-off. The results are compared with the experimental data for the mixture fraction and temperature. Lift off height is predicted from the numerical calculations and compared with the experimentally given value. Comparisons show a reasonably good agreement and the UFPV combustion model appears to be a promising technique for the prediction of lifted and partially premixed flames.     

Problems of predicting turbulent burning rates

Different approaches to the modelling of turbulent combustion first are reviewed briefly. A unified, stretched flamelet approach then is presented. With Reynolds stress modelling and a generalized probability density function (PDF) of strain rate, it enables a source term, in the form of a probability of burning function, P_b, to be expressed as a function of Markstein numbers and the Karlovitz stretch factor. When P_b is combined with some turbulent flame fractal considerations, an expression is obtained for the turbulent burning velocity. When it is combined with the profile of the unstretched laminar flame volumetric heat release rate plotted against the reaction progress variable and the PDF of the latter, an expression is obtained for the mean volumetric turbulent heat release rate. Through these relationships experimental values of turbulent burning velocity might be used to evaluate P_b and hence the CFD source term, the mean volumetric heat release rate.

Different theoretical expressions for the turbulent burning velocity, including the present one, are compared with experimental measurements. The differences between these are discussed and this is followed by a review of CFD applications of these flamelet concepts to premixed and non-premixed combustion. The various assumptions made in the course of the analyses are scrutinized in the light of recent direct numerical simulations of turbulent flames and the applications to the flames of laser diagnostics. Remaining problem areas include a sufficiently general combination of strain rate and flame curvature PDFs to give a single PDF of flame stretch rate, the nature of flame quenching under positive and negative stretch rates, flame responses to changing stretch rates and the effects of flame instabilities.     

小火焰模型在贫燃预混火焰中的研究

由层流小火焰库引入详细化学反应机理,通过简化的PDF方法计算组分浓度、平均温度和密度等变量,以钝体火焰稳定燃烧室和某燃气轮机上的燃烧室为例,模拟甲烷/空气贫燃条件下预混燃烧的平均火焰位置和火焰厚度,计算结果与实验结果吻合良好,这表明此方法能够较好计算出平均湍流火焰的主要特征。     

Modelling compression ignition engines by incorporation of the flamelet generated manifolds combustion closure

Tabulated chemistry models allow to include detailed chemistry effects at low cost in numerical simulations of reactive flows. Characteristics of the reactive fluid flows are described by a reduced set of parameters that are representative of the flame structure at small scales so-called flamelets. For a specific turbulent combustion configuration, flamelet combustion closure, with proper formulation of the flame structure can be applied. In this study, flamelet generated manifolds (FGM) combustion closure with progress variable approach were incorporated with OpenFOAM® source code to model combustion within compression ignition engines. For IC engine applications, multi-dimensional flamelet look-up tables for counter flow diffusive flame configuration were generated. Source terms of non-premixed combustion configuration in flamelet domain were tabulated based on pressure, temperature of unburned mixture, mixture fraction, and progress variable. A new frozen flamelet method was introduced to link one dimensional reaction diffusion space to multi-dimensional Computational Fluid Dynamics (CFD) physical space to fulfill correct modelling of thermal state of the engine at expansion stroke when charge composition was changed after combustion and reaction rates were subsided. Predictability of the developed numerical framework were evaluated for Sandia Spray A (constant volume vessel), Spray B (light duty optical Diesel engine), and a heavy duty Diesel engine experiments under Reynolds averaged Navier Stokes turbulence formulation. Results showed that application of multi-dimensional FGM combustion closure can comprehensively predict key parameters such as: ignition delay, in-cylinder pressure, apparent heat release rate, flame lift-off , and flame structure in Diesel engines.     

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.     

钝体驻定湍流扩散火焰的数值研究——燃烧模型比较

分别采用标量联合的概率密度函数方法、稳态火焰面模型、Euler非稳态火焰面模型和基于有限体积/Monte Carlo混合算法的完备PDF模型对钝体驻定的Sydney湍流扩散火焰HM1进行数值模拟,以比较不同燃烧模型的性能,并比较标量联合的概率密度函数方法和Euler非稳态火焰面模型对氮氧化物排放预测的差异.计算结果和实验数据的比较表明,采用概率密度函数方法计算化学反应可以得到更好的结果但计算量较大,而用火焰面模型求解计算量较小,在接近完全燃烧的情形下,其计算结果比较合理.     

湍流扩散火焰的非稳态火焰面模拟

采用稳态的和非稳态的火焰面模型同时对一个湍流甲烷射流扩散火焰进行了数值模拟,比较了两者对湍流平均火焰结构、活性自由基和污染物(氮氧化物)排放的模拟效果。速度场采用κ-ε模型计算,守恒标量混合物分数的分布通过其概率密度函数(PDF)输运方程的求解得到。稳态的火焰面结构由查询火焰面数据库得到,而非稳态的火焰面结构由火焰面方程和流场方程耦合求解来计算。采用详细的GRI—Mech 3.0机理描述甲烷的氧化和氮氧化物的形成。数值模拟结果和实验数据作了广泛的对比,验证了火焰面模型对湍流扩散燃烧的定量模拟能力。     

A generalized flame surface density modelling approach for the auto-ignition of a turbulent non-premixed system

Auto-ignition of turbulent non-premixed systems is encountered in practical devices such as diesel internal combustion engines. It remains a challenge for modellers, as it exhibits specific features such as unsteadiness, flame propagation and combustion far from stoichiometric conditions. In this paper, a two-dimensional DNS database of an igniting H₂/O₂/N₂ mixing layer, including detailed chemistry and transport, is extensively post-processed in order to gain physical insight into the flame structure and dynamics during auto-ignition. The results are used as a framework for the development of a generalized flame surface density modelling approach by integrating the equations over all possible mixture fraction values. The mean reaction rate is split into two contributions: a generalized flame surface density and a mean reaction rate per unit generalized flame surface density. The unsteadiness of the ignition phenomenon is accounted for via a generalized progress variable. Closures for the generalized surface average of the reaction rate and for the generalized progress variable are proposed, and the modelling approach is tested a priori versus the DNS data. The use of a laminar database for the chemistry coupled to the mean turbulent field via the generalized progress variable shows very promising results, capturing the correct ignition delay and the premixed peak in the turbulent mean heat release rate evolution. This allows confidence in future inclusion and validation of this approach in a RANS-CFD code.     

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k–? model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC.     

氢气扩散火焰中辐射源项湍流脉动特征的PDF模拟

采用κ-ε湍流模型、标量联合的概率密度函数(PDF)输运方程和层流火焰面模型相结合,模拟氢气自由扩散火焰中辐射源项湍流脉动特征.给出了主燃区内辐射源项湍流脉动的频率图.辐射源项的样本点分布集中,大约95%以上的样本落在其系综的±3倍方差以内,频谱图为单峰.     

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.     

Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

Detailed measurements of local scalar front structures in stagnation-type turbulent premixed flames

Local scalar front structures of OH mole fraction, reaction progress variable, and its three-dimensional gradient have been measured in stagnation-type turbulent premixed flames. The reaction progress variable front is observed to change with increasing turbulence from parallel iso-scalar contours but reduced progress variable gradients, called the lamella-like front, to disrupted non-parallel iso-contours that deviate substantially from those of wrinkled laminar flamelets, called the non-flamelet front. This transition is attributed to the different scales of interaction between the flame internal structure and a spectrum of turbulence extending from the integral scale to the Kolmogorov scale. The lamella-like front pattern occurs when the length scales of interaction are smaller than the laminar flame thickness but the time scales are greater than the flame residence time. The non-flamelet front pattern occurs when the length scales of interaction are greater than the laminar flame thickness but the time scales are smaller than the flame residence time. This difference corresponds to the change of combustion regime from complex-strain flame front to turbulent flame front on a revised regime diagram. A correlation is also proposed for the turbulent flame brush thickness as a function of turbulent Reynolds number and heat release parameter. The heat release parameter is considered to arise from the non-passive effects of flame-surface wrinkling.     

A priori investigation of subgrid correlation of mixture fraction and progress variable in partially premixed flames

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z–c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z–c correlation effect is included.     

Assessment of dynamic closure for premixed combustion large eddy simulation

Turbulent piloted Bunsen flames of stoichiometric methane–air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter β_c representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of β_c obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.     

Simulation of flame lift-off on a diesel jet using a generalized flame surface density modeling approach

A generalized flame surface density modelling approach is presented to simulate the transient ignition and flame stabilization of a diesel jet flame, for which experimental data are available. The approach consists of four submodels: a mixing model, a generalized flame surface density model, a generalized progress variable model, and a chemistry model. A database containing the laminar model reaction rates per unit generalized flame surface density is generated by solving the unsteady flamelet equations. The RANS-CFD code solves for the mean flame surface density and mean progress variable. The coupling of the models is done via the progress variable and the scalar dissipation rate. The proposed approach is found to be adapted to simulate such a lifted flame and yields good trend agreement for ignition delay and flame lift-off vs. liquid penetration. These first promising results are encouraging to further explore and to apply this method to a more industrial configuration such as a diesel engine.     

A DNS assessment of linear relations between filtered reaction rate,flame surface density,and scalar dissipation rate in a weakly turbulent premixed flame

Linear relations between (i) filtered reaction rate and filtered flame surface density (FSD) and (ii) filtered reaction rate and filtered scalar dissipation rate (SDR), which are widely used in Large Eddy Simulation (LES) research into premixed turbulent combustion, are examined by processing DNS data obtained from a statistically 1D planar flame under weakly turbulent conditions that are most favourable for the two approaches (flamelet combustion regime, single-step chemistry, equidiffusive mixture, adiabatic burner, and low Mach number). The analysis well supports the former approach provided that the filtered reaction rate is combined with filtered molecular transport term. In such a case, both the RANS and LES FSD approaches are based on local relations valid within weakly perturbed flamelets. Accordingly, simply recasting RANS expressions to a filtered form works well. On the contrary, while the FSD and SDR approaches appear to be basically similar at first glance, the analysis does not support the latter one, but shows that a ratio of the filtered reaction rate to the filtered SDR is strongly scattered within the studied flame brush, with its conditionally mean value varying significantly with Favre-filtered combustion progress variable. As argued in the paper, these limitations of the LES SDR approach stem from the fact that it is based on a relation valid after integration over weakly perturbed flamelets, but this relation does not hold locally within such flamelets. Consequently, when a sufficiently small filter is applied to instantaneous fields, the filter may contain only a part of the local flamelet, whereas the linear relation holds solely for the entire flamelet and may not hold within the filtered flamelet volume. Thus, the present study implies that straightforwardly recasting well-established RANS equations to a filtered form is a flawed approach if the equations are based on integral features of local burning.