A priori analysis of sub-grid variance of a reactive scalar using DNS data of high Ka flames

Direct numerical simulations (DNS) of low and high Karlovitz number (Ka) flames are analysed to investigate the behaviour of the reactive scalar sub-grid scale (SGS) variance in premixed combustion under a wide range of combustion conditions (regimes). An order of magnitude analysis is performed to assess the importance of various terms in the variance evolution equation and the analysis is validated using the DNS results. This analysis sheds light on the relative behaviour among turbulent transport and production, scalar dissipation and chemical processes involved in the evolution of the SGS variance at different Ka. The common expectation is that the variance equation shifts from a reaction-dissipation balance at low Ka to a production–dissipation balance at high Ka with diminishing reaction contribution. However, in large eddy simulation (LES), a high Ka alone does not make the reaction term negligible, as the relative importance of the reaction term has a concurrent increase with filter size. The filter size can be relatively large compared with the Kolmogorov length scale in practical LES of high Ka flames, and as a consequence a reaction–production–dissipation balance may prevail in the variance equation even in a high Ka configuration, and this possibility is quantified using the DNS analysis in this work. This has implications from modelling perspectives, and therefore two commonly used closures in LES for the SGS scalar dissipation rate are investigated a priori to estimate the importance of the above balance in LES modelling. The results are explained to highlight the interplay among turbulence, chemistry and dissipation processes as a function of Ka.     

Experimental study of velocity-scalar filtered joint density function for LES of turbulent combustion

The velocity-scalar filtered joint density function (FJDF) used in large eddy simulation (LES) of turbulent combustion is experimentally studied. Measurements are made in the fully developed region of an axisymmetric turbulent jet using an array consisting of three X-wires and resistance-wire temperature sensors. Filtering in the cross-stream and streamwise directions is realized by using the array and by invoking Taylor’s hypothesis, respectively. The means of the FJDF conditional on the subgrid-scale (SGS) turbulent kinetic energy and the SGS scalar variance at a given location range from close to joint normal to bimodal with the peaks separated in both velocity and scalar spaces, which correspond to qualitatively different mixing regimes. For close to joint normal FJDFs, the SGS fields are well mixed. For bimodal FJDFs, the conditionally filtered scalar diffusion and dissipation strongly depend on the SGS velocity and scalar, consistent with a combination of diffusion layers and plane strain in the SGS fields, which is similar to the counter-flow model for laminar flamelets. The results suggest that in LES, both mixing regimes could potentially be modeled accurately. The velocity field affects the SGS variance and the filtered scalar dissipation rate primarily by changing the degree of nonequilibrium of the SGS scalar and the SGS time scale, respectively. This study further demonstrates the importance of including velocity in mixing models.     

Conditional dissipation of scalars in homogeneous turbulence: Closure for MMC modelling

While the mean and unconditional variance are to be predicted well by any reasonable turbulent combustion model, these are generally not sufficient for the accurate modelling of complex phenomena such as extinction/reignition. An additional criterion has been recently introduced: accurate modelling of the dissipation timescales associated with fluctuations of scalars about their conditional mean (conditional dissipation timescales). Analysis of Direct Numerical Simulation (DNS) results for a passive scalar shows that the conditional dissipation timescale is of the order of the integral timescale and smaller than the unconditional dissipation timescale. A model is proposed: the conditional dissipation timescale is proportional to the integral timescale. This model is used in Multiple Mapping Conditioning (MMC) modelling for a passive scalar case and a reactive scalar case, comparing to DNS results for both. The results show that this model improves the accuracy of MMC predictions so as to match the DNS results more closely using a relatively-coarse spatial resolution compared to other turbulent combustion models.     

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.     

A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

An appraisal is made of several subgrid scale (SGS) viscous/scalar dissipation closures via a priori analysis of direct numerical simulation data in a temporally evolving compressible mixing layer. The effects of the filter width, the compressibility level and the Schmidt number are studied for several models. Based on the scaling of SGS kinetic energy, a new formulation for SGS viscous dissipation is proposed. This yields the best overall prediction of the SGS viscous dissipation within the inertial subrange. An SGS scalar dissipation model based on the proportionality of the turbulent time scale with the scalar mixing time scale also performs the best for the filter widths in the inertial subrange. Two dynamic methods are implemented for the determination of the model coefficients. The one based on the global equilibrium of dissipation and production is shown to be more satisfactory than the conventional dynamic model.     

基于二阶矩燃烧模型的液雾燃烧大涡模拟

采用亚网格动能(k方程)应力模型、二阶矩(SOM)燃烧模型和欧拉拉氏两相流模型,对乙醇-空气液雾燃烧进行了大涡模拟(LES)。瞬态结果显示:在火焰的高温区域,旋涡强度较大;在高温区边缘附近存在的拟序结构有脱落的趋势。在燃烧装置的燃料进口附近,近喷嘴中心区域,大量液滴聚集在条状湍流拟序结构的周围。LES模拟的统计结果给出的温度分布与实验结果吻合较好。说明SOM燃烧模型适用于液雾两相湍流燃烧研究,计算结果经过和实验数据对比发现,LES-SOM燃烧模型优于RANS-PDF及LES-FA计算结果。数值计算结果与实验结果的误差主要是由于采用统观一步反应机理引起的,表明燃烧模型还有待进一步改进。     

New sub-grid stochastic acceleration model in LES of high-Reynolds-number flows

The experimental observations of intermittent dynamics of Lagrangian acceleration in a “free” high-Reynolds-number turbulence are shown to be consistent with the Kolmogorov-Oboukhov theory. In line with Kolmogorov-Oboukhov’s predictions, a new sub-grid scale (SGS) model is proposed and is combined with the Smagorinsky model. The new SGS model is focused on simulation of the non-resolved total acceleration vector by two stochastic processes: one for its norm, another for its direction. The norm is simulated by stochastic equation, which was derived from the log-normal stochastic process for turbulent kinetic energy dissipation rate, with the Reynolds number, as the parameter. The direction of the acceleration vector is suggested to be governed by random walk process, with correlation on the Kolmogorov’s timescale. In the framework of this model, a surrogate unfiltered velocity field is emulated by computation of the instantaneous model-equation. The coarse-grid computation of a high-Reynolds-number stationary homogeneous turbulence reproduced qualitatively the main intermittency effects, which were observed in experiment of ENS in Lyon. Contrary to the standard LES with the Smagorinsky eddy-viscosity model, the proposed model provided: (i) non-Gaussianity in the acceleration distribution with stretched tails; (ii) rapid decorrelation of acceleration vector components; (iii) “long memory” in correlation of its norm. The turbulent energy spectra of stationary and decaying homogeneous turbulence are also better predicted by the proposed model.     

Analysis of a dynamic model for subfilter scalar dissipation rate in large eddy simulation based on the subfilter scalar variance transport equation

Accurate prediction of non-premixed turbulent combustion using large eddy simulation (LES) requires detailed modelling of the mixing between fuel and oxidizer that occurs at scales smaller than the LES filterwidth. The small-scale mixing process can be quantitatively characterized by two related variables, the subfilter scalar variance and the subfilter scalar dissipation rate. A recently proposed alternative dynamic modelling procedure for the subfilter scale dissipation rate, designed for use with transport equation based models for subfilter scalar variance, is analysed in this work. This new dynamic non-equilibrium modelling approach produces a nonlinear interaction between variance and dissipation rate predictions that makes it difficult to isolate the performance of any single modelling component in a conventional LES simulation. To gain a better understanding of the new model, a three-part study is undertaken here. The first part of the study uses a priori analysis to examine some novel aspects of the model’s computation and guide its practical implementation. In the second part of the study, detailed a posteriori analysis of the model is performed. This analysis suggests that the dynamic estimate of the dissipation rate model coefficient helps to compensate for over-prediction of variance production rates and improves the accuracy of variance prediction. However, improved modelling of the variance production term, which in turn depends on the accuracy of models for the subfilter scalar flux, is necessary to allow both the scalar variance and dissipation rate to be predicted accurately. Therefore, the third part of the study examines the effect of the scalar flux model on the predictions of the dynamic non-equilibrium model. Use of a mixed model for the fluxes, rather than a gradient-diffusion-only model, is found to improve variance predictions in some cases.     

Role of radicals on MILD combustion inception

The criterion used to define MILD combustion in non-premixed condition is analysed using Direct Numerical Simulation (DNS) of MILD combustion of methane-diluted air established with internal exhaust gas recirculation. The simulations reveal multiple interacting reaction zones in MILD combustion which are extremely different from conventional combustion. Furthermore, DNS deduced S-curves highlight the role of chemically active species. Specifically, the temperature rise is accompanied with an increase in the scalar dissipation rate of mixture fraction, which is quite contrasting to the classical S-curve from the classical flame theories. This observation is explained on a physical basis.     

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.     

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.     

Large Eddy Simulation of a turbulent lifted flame using multi-modal manifold-based models: Feasibility and interpretability

A general model for multi-modal turbulent combustion is achievable with two-dimensional manifold equations that use the mixture fraction and a generalized progress variable as coordinates. Information about the underlying mode of combustion is encoded in three scalar dissipation rates that appear as parameters in the two-dimensional equations. In this work, Large Eddy Simulation (LES) of a multi-modal turbulent lifted hydrogen jet flame in a vitiated coflow is performed using this new turbulent combustion model, leveraging both convolution-on-the-fly and In-Situ Adaptive Tabulation for computational tractability. The simulation predicts a lifted flame consistent with observations from past experiments. The feasibility of such a model implemented in LES is examined, and the cost per timestep is found to be comparable to conventional one-dimensional manifold-based models describing one asymptotic mode of combustion. Additionally, the model provides clear interpretability, allowing for combustion mode analysis to be performed with ease by evaluating the scalar dissipation rates and generalized progress variable source term. This analysis is used to show that the flame is stabilized by autoignition and has a trailing nonpremixed flame. Furthermore, transport of progress variable from the most reactive mixture fraction towards richer mixtures at the centerline is found to be important.     

不可压反应流动直接模拟和亚网格模型的检验

本文用谱方法对三维槽道不可压湍流反应流动进行了直接模拟,用直接模拟数据对大涡模拟亚网格质量流和燃烧模型进行了检验,结果发现,引入壁面阻尼修正的模型与精确值的符合比较好.     

Large eddy simulation of a turbulent nonpremixed piloted methane jet flame (Sandia Flame D)

Large eddy simulation (LES) is conducted of the Sandia Flame D [Proc. Combust. Inst. 27 (1998) 1087, Sandia National Laboratories (2004)], which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology [J. Fluid Mech. 401 (1999) 85]. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities [Turbulent Flows (2000)]. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme. This is the first LES of a realistic turbulent flame using the transported PDF method as the SGS closure. The results via this method capture important features of the flame as observed experimentally.     

A priori evaluation of large eddy simulation subgrid-scale scalar flux models in isotropic passive-scalar and anisotropic buoyancy-driven homogeneous turbulence

Direct numerical simulation (DNS) of passive (non-buoyant) and active (buoyant) scalar homogeneous turbulence is carried out using a standard pseudo-spectral numerical method. The flow settings simulated include stationary forced and decaying passive-scalar turbulence, as well as decaying anisotropic active-scalar turbulence. The Schmidt number is unity in all cases. The results are compared with, and are found to be in very good agreement with, previous similar DNS studies. The well-validated DNS data are divided into 19 sets, and are employed to study different large eddy simulation (LES) subgrid-scale (SGS) models for the SGS scalar flux. The models examined include three eddy-viscosity-type models (Smagorinsky, Vreman and Sigma with a constant SGS Schmidt number), a Dynamic Structure model and two versions of the Gradient (Gradient and Modulated Gradient) model. The models are investigated with respect to their ability to predict the orientation, and the magnitude, of the SGS scalar flux. Eddy-viscosity models are found to predict the magnitude of the SGS scalar flux accurately, but are poor at predicting the orientation of the SGS scalar flux. The Dynamic Structure and Gradient models are better than eddy-viscosity models at predicting both the magnitude and direction. However, neither of them can be realised in an actual LES, without carrying additional transport equations. Based on these observations, four new models are proposed – combining directions from Dynamic Structure and Gradient models, and magnitudes from Smagorinsky and Vreman eddy-viscosity models. These models are expected to be better than eddy-viscosity and Modulated Gradient models, and this is confirmed by preliminary a posteriori tests.     

Large Eddy Simulation composition equations for single-phase and two-phase fully multicomponent flows

The Large Eddy Simulation (LES) equations for multicomponent (MC) fuel single-phase (SP) flow and two-phase (TP) flow with phase change are derived from the Direct Numerical Simulation (DNS) equations by filtering the DNS equations using a top-hat filter. Additional to the equations solved for single-component (SC) fuels, composition equations enter the formulation. The species composition is represented through a Probability Distribution Function (PDF), and DNS equations for the PDF moments are solved to find the composition. The TP filtered equations contain three categories of subgrid-scale (SGS) terms: (1) SGS–flux terms, (2) filtered source terms (FSTs) and (3) terms representing the ‘LES assumptions’. For SP flows no FSTs exist. The SGS terms in the LES equations must be either shown negligible or modeled. It is shown that for the composition equations, two equivalent forms of the DNS equations lead to two non-equivalent forms of the LES equations. Criteria are proposed to select the form best suited for LES. These criteria are used in conjunction with evaluations based on a DNS database portraying mixing and phase change, and lead to choosing one of the LES forms which satisfies all criteria. It is shown that the LES assumptions lead to additional SGS terms which require modeling. Further considerations are made for reactive flows.     

Simulation of diesel spray combustion using LES and a multicomponent vapourisation model

Diesel spray and combustion in a constant-volume engine cylinder was simulated by a large eddy simulation (LES) approach coupling with a multicomponent vapourisation (MCV) modelling. The simulation focused on the inclusion of the interaction between fuel spray and gas-phase turbulence flow at the sub-grid scale. The LES was based on the dynamic structure sub-grid model, and an additional source term was added to the filtered momentum equation to account for the effect of drop motion on the gas-phase turbulence. The multicomponent drop vapourisation modelling was based on the continuous thermodynamics approach using a gamma distribution to describe the complex diesel fuel composition and was capable of predicting a more complex drop vapourisation process. The effect of gas-phase turbulence flow on the fuel drop vapourisation process was evaluated through the solution of the gas-phase moments of the distribution in the present LES framework. A non-evaporative spray in a constant-volume engine cylinder was first simulated to examine the behaviours of LES, in comparison with a Reynolds-averaged Navier–Stokes (RANS) simulation based on the RNG k–? model. More realistic diesel spray structures and improved agreement on liquid penetration length with the corresponding experimental data were predicted by the LES, using a grid resolution close to that of RANS. A more comprehensive simulation of diesel spray and combustion in cylindrical combustor was also performed. Predicted distributions of soot particles were compared to the experimental image, and improved agreement with the experimental data was also observed by using the present LES and MCV models. Consequently, results of the present models proved that improved overall performance of the fuel spray simulation can be achieved by the LES without a significant increase in the computational load compared to the RANS.     

H_2/N_2/O_2射流扩散火焰的直接数值模拟

直接数值模拟(DNS),大涡模拟(LES)与雷诺时均模拟(RANS)是数值模拟燃烧流动的三大主要方法,而射流扩散火焰在燃烧理论,实验研究与数值模拟中都扮演着十分重要的角色,本文采用完全可压缩的Naive-Stokes方程,对喷口直径为D=1 mm,Re=2000的射流扩散火焰进行了直接数值模拟.本文首先分析了冷态时H_2,O_2的混合,发现燃料与氧气在流向长度大于6D后的区域混合得十分充分.随后本文分析了燃烧后的统计特性,主要包括速度场,密度,温度以及主要组分与混合分数的分布,并将DNS结果与实验结果进行对比分析.     

An a priori assessment of the Partially Stirred Reactor (PaSR) model for MILD combustion

Moderate or Intense Low-oxygen Dilution (MILD) combustion has drawn increasing attention as it allows to avoid the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from Direct Numerical Simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the Partially Stirred Reactor (PaSR) combustion model in MILD conditions is a priori assessed on Direct Numerical Simulations (DNS) of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, are compared to the corresponding filtered quantities extracted from the DNS. Different submodels for the key model parameters, i.e., the chemical time scale τ_c and the mixing time scale τ_mix, are considered and their influence on the results is evaluated. The results show that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms is achieved by the PaSR model that employs a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurs in limited zones of the computational domain, characterized by low heat release rates.     

Flame characterisation of gas-assisted pulverised coal combustion using FPV-LES

A multiphase flamelet/progress variable (FPV) model for the large eddy simulation (LES) of gas-assisted pulverised coal combustion (PCC) is developed. The target of the simulation is the Darmstadt turbulent gas-assisted swirling solid fuel combustion chamber. The coal particles are treated as Lagrangian point particles, the position, momentum and energy of which are tracked. The gas phase is described by the low-Mach Navier-Stokes equations alongside the Eulerian transport equations of the governing variables for the FPV model. The set of chemical states of the PCC flame is pre-tabulated in a six-dimensional flamelet table and determined by the mixing of the primary fuel stream, volatiles and char off-gases with the oxidising air, the progress of chemical reactions, the interphase heat transfer, as well as sub-grid scale variations. A presumed $\beta$-PDF approach for the total mixture fraction is applied to capture sub-grid scale effects. The discrete ordinate method (DOM) with the weighted sum of grey gases model (WSGGM) is employed to model radiation. The FPV-LES results are validated against the experimental evidence and a good agreement of the predicted mean and RMS velocities, as well as the mean gas temperature between experiments and simulations is obtained. The contributions of the pilot, volatile and char off-gas fuel streams to the coal flame are analysed. It is found that most regions of the furnace are dominated by either pilot or volatile combustion, while char conversion only occurs in the far downstream and outer furnace regions. The pilot gas dominates the near-wall region inside the quarl, whereas the volatile gas mainly released from small particles dominates a first volatile combustion zone in the interior of the internal recirculation zone. Larger particles heat up more slowly and release their volatile content further downstream, leading to a secondary volatile combustion zone.