Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES

This work investigates the structure of a diffusion flame in terms of lengthscales, scalar dissipation, and flame orientation by using large eddy simulation. This has been performed for a turbulent, non-premixed, piloted methane/air jet flame (Flame D) at a Reynolds-number of 22,400. A steady flamelet model, which was represented by artificial neural networks, yields species mass fractions, density, and viscosity as a function of the mixture fraction. This will be shown to suffice to simulate such flames. To allow to examine scalar dissipation, a grid of 1.97 × 10⁶ nodes was applied that resolves more than 75% of the turbulent kinetic energy. The accuracy of the results is assessed by varying the grid-resolution and by comparison to experimental data by Barlow, Frank, Karpetis, Schneider (Sandia, Darmstadt), and others. The numerical procedure solves the filtered, incompressible transport equations for mass, momentum, and mixture fraction. For subgrid closure, an eddy viscosity/diffusivity approach is applied, relying on the dynamic Germano model. Artificial turbulent inflow velocities were generated to feature proper one- and two-point statistics. The results obtained for both the one- and two-point statistics were found in good agreement to the experimental data. The PDF of the flame orientation shows the tilting of the flame fronts towards the centerline. Finally, the steady flamelet approach was found to be sufficient for this type of flame unless slowly reacting species are of interest.     

Flamelet modeling of coal particle ignition

This paper numerically investigates the ignition of a single coal particle during the devolatilization phase in a laminar entrained-flow reactor, for which experimental data are available from Molina and Shaddix [3]. Different numerical approaches are combined to evaluate the non-premixed flamelet approach for coal particle ignition. First, the particle trajectory and the particle heating are simulated with a Lagrangian–Eulerian approach using a detailed pyrolysis model. In a second step, these results are used as transient boundary conditions for a simulation fully resolving the flow, the mixing field and the chemical reactions around the particle. Finally, in combination with the boundary conditions the time-dependent scalar dissipation rate profiles from the resolved particle calculation are used in a flamelet calculation for the particle up- and downstream directions. Very good agreement is obtained in terms of ignition delay as well as temperature and chemical species distributions in the mixture fraction space when the resolved particle calculation and the unsteady flamelet calculation are compared in the downstream direction. Good agreement is obtained when the numerical results for the ignition time and the time-averaged OH distribution are compared with the available experimental data. The results show the capability of the laminar flamelet approach to correctly predict coal particle ignition during devolatilization using accurate scalar dissipation rate profiles.     

Conditional Moment Closure (CMC) applied to autoignition of high pressure methane jets in a shock tube

Autoignition of non-premixed methane–air mixtures is investigated using first-order Conditional Moment Closure (CMC). Turbulent velocity and mixing fields simulations are decoupled from the CMC calculations due to low temperature changes until ignition occurs. The CMC equations are cross-stream averaged and finite differences are applied to discretize the equations. A three-step fractional method is implemented to treat separately the stiff chemical source term. Two detailed chemical kinetics mechanisms are tested as well as two mixing models. The present results show good agreement with published experimental measurements for the magnitude of both ignition delay and kernel location. The slope of the predicted ignition delay is overpredicted and possible sources of discrepancy are identified. Both scalar dissipation rate models produce comparable results due to the turbulent flow homogeneity assumption. Further, ignition always occurs at low scalar dissipation rates, much lower than the flamelet critical value of ignition. Ignition is found to take place in lean mixtures for a value of mixture fraction around 0.02. The conditional species concentrations are in qualitative agreement with previous research. Homogeneous and inhomogeneous CMC calculations are also performed in order to investigate the role of physical transport in the present autoignition study. It is found that spatial transport is small at ignition time. Predicted ignition delays are shown to be sensitive to the chemical kinetics. Reasonable agreement with previous simulations is found. Improved formulations for the mixing model based on non-homogeneous turbulence are expected to have an impact.     

Analysis of auto-ignition of heated hydrogen–air mixtures with different detailed reaction mechanisms

Auto-ignition processes of hydrogen, diluted with nitrogen, in heated air are numerically investigated by means of an unsteady laminar flamelet approach in mixture fraction space. The focus is on the auto-ignition delay time and the most reactive mixture fraction as obtained with five chemical mechanisms. Two strongly different levels of dilution, corresponding to experiments in the open literature, are considered. This concerns low-temperature chemistry at atmospheric pressure. The temperature of the air stream is much higher than the temperature of the fuel stream in the cases under study. We extensively investigate the effect of the co-flow temperature, the conditional scalar dissipation rate and the resolution in mixture fraction space for one case. With respect to the conditional scalar dissipation rate, we discuss the Amplitude Mapping Closure (AMC) model with imposed maximum scalar dissipation rate at mixture fraction equal to 0.5, as well as a constant conditional scalar dissipation rate value over the entire mixture fraction value range. We also illustrate that an auto-ignition criterion, based on a temperature rise, leads to similar results as an auto-ignition criterion, based on OH mass fraction, provided that the hydrogen is not too strongly diluted.     

湍流扩散燃烧的数值研究-PDF方法和火焰面模型的性能比较

采用标量概率密度函数(PDF)方法、稳态和非稳态火焰面模型三种方法对一个值班湍流CH_4/O_2/N_2射流扩散火焰(Sandia Flame D)进行数值计算,以比较不同燃烧模型的性能。PDF方法通过计算反应标量的PDF输运方程来得到标量分布,而火焰面模型只求解单标量混合物分数的PDF方程,组分和温度分布通过火焰面方程的求解或者火焰面数据库的插值得到。计算结果和实验数据对比表明PDF方法计算结果最好但计算量相当大,稳态火焰面模型则反之。综合而言,非稳态火焰面模型的预测结果相对稳态模型有了非常大的改进,而计算量仍然容易接受,非常适合工程应用。     

A quantitative method for a priori evaluation of combustion reaction models

In recent years, direct numerical simulations have been used increasingly to evaluate the validity and performance of combustion reaction models. This study presents a new, quantitative method to determine the ideal model performance attainable by a given parameterization of the state variables. Data from direct numerical simulation (DNS) of unsteady CO/H₂–air jet flames is analysed to determine how well various parameterizations represent the data, and how well specific models based on those parameterizations perform. Results show that the equilibrium model performs poorly relative to an ideal model parameterized by the mixture fraction. The steady laminar flamelet model performs quite well relative to an ideal model parameterized by mixture fraction and dissipation rate in some cases. However, at low dissipation rates or at dissipation rates exceeding the steady extinction limit, the steady flamelet model performs poorly. Interestingly, even in many cases where the steady flamelet model fails (particularly at low dissipation rate), the DNS data suggests that the state may be parameterized well by the mixture fraction and dissipation rate. A progress variable based on the CO₂ mass fraction is proposed, together with a new model based on the CO₂ progress variable. This model performs nearly ideally, and demonstrates the ability to capture extinction with remarkable accuracy for the CO/H₂ flames considered.     

Measurements of flame orientation and scalar dissipation in turbulent partially premixed methane flames

Three turbulent flames were studied using a new experimental facility developed at Sandia National Laboratories. Line imaging of Raman and Rayleigh scattering and CO laser-induced fluorescence (LIF) yielded information on all major species, temperature, mixture fraction, and a 1D surrogate measure of scalar dissipation. Simultaneously, crossed planar OH LIF imaging provided information on the instantaneous flame orientation, allowing estimation of the full 3D (flame-normal) scalar dissipation rate. The three flames studied were methane–air piloted jet flames (Sandia flames C, D, and E), which cover a range in Reynolds number from 13,400 to 33,600. The statistics of the instantaneous flame orientation are examined in the different flames, with the purpose of studying the prevailing kinematics of isoscalar contours. The 1D and 3D results for scalar dissipation rate are examined in detail, both in the form of conditional averages and in the form of probability density functions. The effect of overall strain and Reynolds number on flame suppression and eventual extinction is also investigated, by examining the doubly conditional statistics of temperature in the form of S-shaped curves. This latter analysis reveals that double conditioning of temperature on both mixture fraction and scalar dissipation does not collapse the data from these flames onto the same curve at low scalar dissipation rates, as might be expected from simple flamelet concepts.     

Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

In this work, the first flamelet analysis is conducted of a highly resolved DNS of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction. A novel method is proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. The state-of-the-art DNS database generated by Rieth et al. (US National Combustion Meeting, 2019) for a multi-injection flame in a Diesel engine environment is investigated. Three-dimensional flamelets are extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process are investigated by varying the species composition boundary conditions of the transient flamelet equations. Budget analyses of the generalized flamelet equations show that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.     

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.     

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。     

Experimental evaluation of flame observables for simplified scalar dissipation rate measurements in laminar diffusion flamelets

We present a comparative evaluation of the potential of several flame observables to yield a simplified measurement of the scalar dissipation rate (χ). The realization of the importance of this quantity for the structure of diffusion flamelets has led to brilliant experimental efforts targeted to its measurement, with a particular emphasis on χ_stoich, i.e., its value at the stoichiometric surface, which has been shown to control extinction. Such measurements require a significant amount of experimental resources, since they necessitate the simultaneous acquisition of multi-scalar data. The possibility of a simplified measurement stems from the realization that the related gradient of the mixture fraction scales as the inverse of an appropriately defined thickness of the mixing layer. In this paper, we investigate experimentally the utilization of several flame observables for the measurement of this thickness. In a flat, nitrogen diluted, counterflow, methane/oxygen diffusion flame, the scalar dissipation rate was first measured directly using line Raman imaging of major species and a N₂-molecule based definition of the mixture fraction. Additionally, LIF measurements of the hydroxyl radical (OH) and formaldehyde (HCHO) as well as Raman measurements of carbon monoxide (CO) were performed across the flamelet. The precision of χ_stoich estimates based on the thickness of the layers of these three observables as well as the layers corresponding to [HCHO] × [OH] and [CO] × [OH] “overlap” zones was evaluated in terms of following the theoretically expected inverse-square-root dependence on strain rate. Also, the absolute thickness of these layers was recorded, since it may restrict the application of simplified techniques in turbulent flow fields.     

A three mixture fraction flamelet model for multi-stream laminar pulverized coal combustion

A three mixture fraction flamelet model is proposed for multi-stream laminar pulverized coal combustion. The technique of coordinate transformation is utilized to map the flamelet solutions from a unit pyramid space into a unit cubic space to improve the stability of the simulation. The validity of the three mixture fraction flamelet model was assessed on different configurations, including a laminar counterflow pulverized coal/methane flame and a laminar piloted pulverized coal jet flame. The flamelet predictions were compared to the reference results of the detailed chemistry solutions. For the counterflow flame, it was found that the flame temperature and major species mass fractions are correctly predicted by the three mixture fraction flamelet model. However, discrepancies are observed for combustion-mode-sensitive species such as CO and H₂ in the premixed combustion region. The thermo-chemical quantities in the char surface reaction zone cannot be correctly predicted if the mixing between the char off-gas stream and other streams is neglected. For the piloted jet flame, it was shown that the stable thermo-chemical variables can be correctly predicted at the upper and middle stream locations. However, at the downstream location, discrepancies can be observed in certain regions. Overall, the validity of the three mixture fraction flamelet model for multi-stream pulverized coal combustion is confirmed and its performance in turbulent pulverized coal combustion will be tested in future work.     

Numerical simulation and laser-based imaging of mixture formation, ignition, and soot formation in a diesel spray

Laser-based imaging of fuel vapor distribution, ignition, and soot formation in diesel sprays was carried out in a high-pressure, high-temperature spray chamber under conditions that correspond to temperature and pressure in a diesel engine. Rayleigh scattering and laser-induced incandescence are used to image fuel density and soot volume fraction. The experimental results provide data for comparison with numerical simulations. An interactive cross-sectionally averaged spray model based on Eulerian transport equations was used for the simulation of the spray, and the turbulence-chemistry interaction was modeled with the representative interactive flamelet (RIF) concept. The flamelet calculation is coupled to the Kiva3V computational fluid dynamics (CFD) code using the scalar dissipation rate and pressure as an input to the RIF-code. The flamelet code computes the instationary flamelet profiles for every time step. These profiles were integrated over mixture fraction space using a prescribed β-PDF to obtain mean values, which are passed back to the CFD-code. Thereby, the temperature and the relevant species in each CFD-cell were obtained. The fuel distribution, the average ignition delay as well as the location of ignition are well predicted by the simulation. Furthermore, simulations show that the experimentally observed injection-to-injection variations in ignition delay are due to temperature inhomogeneities. Experimental and simulated spatial soot and fuel vapor density distributions are compared during and after second stage ignition.     

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.     

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

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

Geometric features of the mixing of passive scalars at high Schmidt numbers

The mixing of passive scalars of decreasing diffusivity, advected in each case by the same three-dimensional Navier-Stokes turbulence, is studied. The mixing becomes more isotropic with decreasing diffusivity. The local flow in the vicinity of steepest negative and positive scalar gradients is in general different, and its behavior is studied for various values of the scalar diffusivity. Mixing approaches monofractal properties with diminishing diffusivity. We consider these results in the context of possible singularities of scalar dissipation.