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.     

湍流分层燃烧的直接数值模拟和小火焰模型研究

湍流分层燃烧广泛应用于工业燃烧装置,但是目前还比较缺乏适用于湍流分层燃烧的高精度数值模型。本文利用直接数值模拟数据库,对高Karlovitz数分层射流火焰的小火焰模型表现进行了先验性评估。考虑了两种小火焰模型,一种是基于自由传播层流预混火焰的小火焰模型M1,另一种是基于分层对冲小火焰的小火焰模型M2。研究发现M1和M2在c-Z空间的结果与直接数值模拟在定性上是一致的。在物理空间,M2对过程变量反应速率脉动值的预测结果要优于M1.     

Evolution and scaling of the peak flame surface density in spherical turbulent premixed flames subjected to decaying isotropic turbulence

The peak flame surface density within the turbulent flame brush is central to turbulent premixed combustion models in the flamelet regime. This work investigates the evolution of the peak surface density in spherically expanding turbulent premixed flames with the help of direct numerical simulations at various values of the Reynolds and Karlovitz number. The flames propagate in decaying isotropic turbulence inside a closed vessel. The effects of turbulent transport, transport due to mean velocity gradient, and flame stretch on the peak surface density are identified and characterized with an analysis based on the transport equation for the flame surface density function. The three mechanisms are governed by distinct flow time scales; turbulent transport by the eddy turnover time, mean transport by a time scale related to the pressure rise in the closed chamber, and flame stretch by the Kolmogorov time scale. Appropriate scaling of the terms is proposed and shown to collapse the data despite variations in the dimensionless groups. Overall, the transport terms lead to a reduction in the peak value of the surface density, while flame stretch has the opposite effect. In the present configuration, a small imbalance between the two leads to an exponential decay of the peak surface density in time. The dimensionless decay rate is found to be consistent with the evolution of the wrinkling scale as defined in the Bray-Moss-Libby model.     

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。     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

An assessment of large eddy simulations of premixed flames propagating past repeated obstacles

This paper presents an assessment of Large Eddy Simulations (LES) in calculating the structure of turbulent premixed flames propagating past solid obstacles. One objective of the present study is to evaluate the LES simulations and identify the drawbacks in accounting the chemical reaction rate. Another objective is to analyse the flame structure and to calculate flame speed, generated overpressure at different time intervals following ignition of a stoichiometric propane/air mixture. The combustion chamber has built-in repeated solid obstructions to enhance the turbulence level and hence increase the flame propagating speed. Various numerical tests have also been carried out to determine the regimes of combustion at different stages of the flame propagation. These have been identified from the calculated results for the flow and flame characteristic parameters. It is found that the flame lies within the ‘thin reaction zone’ regime which supports the use of the laminar flamelet approach for modelling turbulent premixed flames. A submodel to calculate the model coefficient in the algebraic flame surface density model is implemented and examined. It is found that the LES predictions are slightly improved owing to the calculation of model coefficient by using submodel. Results are presented and discussed in this paper are for the flame structure, position, speed, generated pressure and the regimes of combustion during all stages of flame propagation from ignition to venting. The calculated results are validated against available experimental data.     

Nonlinear hydrodynamic and thermoacoustic oscillations of a bluff-body stabilised turbulent premixed flame

Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier–Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various physical mechanisms. This has implications in selecting the operating conditions for such flames and for devising proper control strategies for the avoidance of thermoacoustic instability.     

Sound emission by non-isomolar combustion at low Mach numbers

This paper shows that the change in the number of moles of species during combustion can make a strong contribution to the acoustic power radiated by turbulent flames and cannot be systematically neglected. Starting from standard conservation equations, we derive an expression for the acoustic pressure radiated in the far field of a compact region of fluid where low Mach number non-isomolar combustion takes place. In this formulation, the contributions from ‘molar’ and thermal expansion appear explicitly. We also give a formulation in which the sound emission arising from purely non-stationary and from purely convective effects appear independently. As an application of the theory, we derive the acoustic power emitted by a premixed flame in the flamelet regime. Numerical evaluations show that the contribution of molar expansion to the acoustic power is between 2 and 5.6 dB (260% increase) for some common hydrocarbon-oxygen flames.     

Modelling of turbulent lifted jet flames using flamelets: a priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z–c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z–c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.     

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.     

Comparison of a spectral model for premixed turbulent flame propagation to DNS and experiments

A recently developed spectral model for premixed turbulent combustion in the flamelet regime (based on the EDQNM turbulence theory) has been compared with both direct numerical simulations (DNS) and experimental data. The 128³ DNS is performed at a Reynolds number of 223 based on the integral length scale. Good agreement is observed for both single- and two-point quantities (i.e. ratio of the turbulent to laminar burning velocities, scalar autocorrelation, dissipation and scalar-velocity cross correlation spectra) for the two different values of u′/s _L0 considered. The model also predicts the rapid transient behaviour of the flame at early times. An experimental set-up is then described for generating a lean methane-air flame and measuring two-point spatial correlations along the midpoint of the flame brush (i.e. along the C¯=0.5 contour). The experimental measurements in the flamelet regime take the form of a discontinuous or ‘telegraph’ signal. The EDQNM model, in contrast, describes an ‘ensemble’ of flames, and thus is based solely on continuous variables. A theoretical relationship between the correlation obtained from the EDQNM model and the equivalent correlation for a discontinuous (experimental) flame is derived. The relationship is used to enable a meaningful comparison between experimentally observed and model correlations. In general, the agreement is good for the three different cases considered in this study, with most of the error occurring at the lowest Reynolds number (Re _L =22). Furthermore, it is shown that considerably more error would result if no attempt is made to convert the ensemble representation in the model to an equivalent single-flame or ‘telegraph’ signal.     

Conditional moment closure and transient flamelet modelling for detailed structure and NO x formation characteristics of turbulent nonpremixed jet and recirculating flames

This study has been mainly motivated to assess computationally and theoretically the conditional moment closure (CMC) model and the transient flamelet model for the simulation of turbulent nonpremixed flames. These two turbulent combustion models are implemented into the unstructured grid finite volume method that efficiently handles physically and geometrically complex turbulent reacting flows. Moreover, the parallel algorithm has been implemented to improve computational efficiency as well as to reduce the memory load of the CMC procedure. Example cases include two turbulent CO/H₂/N₂ jet flames having different flow timescales and the turbulent nonpremixed H₂/CO flame stabilized on an axisymmetric bluff-body burner. The Lagrangian flamelet model and the simplified CMC formulation are applied to the strongly parabolic jet flame calculation. On the other hand, the Eulerian particle flamelet model and full conservative CMC formulation are employed for the bluff-body flame with flow recirculation. Based on the numerical results, a detailed discussion is given for the comparative performances of the two combustion models in terms of the flame structure and NO _x formation characteristics.     

Turbulent scalar fluxes in H2-air premixed flames at low and high Karlovitz numbers

The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion have been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen-air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multispecies system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two-dimensional anisotropy due to strong heat release whereas a three-dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multispecies systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sub-grid scalar flux closures, a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray–Moss–Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of large eddy simulations.     

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)     

Partially premixed flamelet in LES of acetone spray flames

An effective partially premixed flamelet model for large eddy simulation (LES) of turbulent spray combustion is formulated. Different flame regimes are identified with a flame index defined by budget terms in a 2-D multi-phase flamelet formulation, and the application in LES of partially pre-vaporized spray flames shows a favorable agreement with experiments. Simulations demonstrate that, compared to the conventional single-regime flamelets, the present partially premixed flamelet formulation shows its ability in capturing the subgrid regime transitions, yielding a well prediction of peak gas temperature and the downstream flame spreading. A propagating premixed flame front is found coupled with a trailing diffusion burning through the spray evaporation, and the spray effect on regime discrimination is manifested with transport budget analysis. A two-phase regime indicator is then proposed, by which the evaporation-dictated regime is properly described. Its intended use will rely on both gas and spray flamelet structures.     

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.     

Flame front analysis of high-pressure turbulent lean premixed methane–air flames

An experimental study on lean turbulent premixed methane–air flames at high pressure is conducted by using a turbulent Bunsen flame configuration. A single equivalence ratio flame at Φ = 0.6 is explored for pressures ranging from atmospheric pressure to 0.9 MPa. LDA measurements of the cold flow indicate that turbulence intensities and the integral length scale are not sensitive to pressure. Due to the decreased kinematic viscosity with increasing pressure, the turbulent Reynolds numbers increase, and isotropic turbulence scaling relations indicate a large decrease of the smallest turbulence scales. Available experimental results and PREMIX code computations indicate a decrease in laminar flame propagation velocities with increasing pressure, essentially between the atmospheric pressure and 0.5 MPa. The u′/S_L ratio increases therefore accordingly. Instantaneous flame images are obtained by Mie scattering tomography. The images and their analysis show that pressure increase generates small scale flame structures. In an attempt to generalize these results, the variance of the flamelet curvatures, the standard deviation of the flamelet orientation angle, and the flamelet crossing lengths have been plotted against which is proportional to the ratio between the integral and Taylor length scales, and which increases with pressure. These three parameters vary linearly with the ratio between large and small turbulence scales and clearly indicate the strong effect of this parameter on premixed turbulent flame dynamics and structure. An obvious consequence is the increase in flame surface density and hence burning rate with pressure, as confirmed by its direct determination from 2D tomographic images.     

Premixed flames for arbitrary combinations of strain and curvature

Many modeling strategies for combustion rely on laminar flamelet concepts to determine structure and properties of multi-dimensional and turbulent flames. Using flamelet tabulation strategies, the user anticipates certain aspects of the combustion process prior to the simulation and selects a flamelet model which mimics local flame conditions in the more complex configuration. Flame stretch, which can be decomposed into contributions from strain and curvature, is one of the conditions influencing a flame’s properties, structure, and stability. The objective of this work is to study premixed flame structures in the strain-curvature space using a recently published composition space model (CSM) and three physical space models for canonical flame configurations (stagnation flame, spherical expanding flame and inwardly propagating flame). Flames with effective Lewis numbers both smaller and larger than unity are considered. For canonical laminar flames, the stretch components are inherently determined through boundary conditions and their specific flame configuration. Therefore, canonical flames can only represent a certain sub-set of stretch effects experienced by multi-dimensional and turbulent flames. On the contrary, the CSM allows arbitrary combinations of strain and curvature to be prescribed for premixed flames exceeding the conditions attainable with the canonical flame setups. Thereby, also influences of negative strain effects and large curvatures can be studied. A parameter variation with the CSM shows that flame structures still significantly change outside the region of the canonical flame configurations. Furthermore, limits in the strain-curvature space are discussed. The present paper highlights advantages of composition space modeling which is achieved by detaching the representation of the flame structure from a specific canonical flame configuration in physical space.     

Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity–reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity–reaction rate correlation term were also modelled, and these models mimicked DNS well.