Investigation of conditional source-term estimation applied to a non-premixed turbulent flame

A turbulent combustion model, Conditional Source-term Estimation (CSE) is applied to a non-premixed turbulent jet methane flame. The conditional chemical source terms are determined on the basis of first order closure and the conditional averaged species concentrations are obtained by inverting an integral equation. The Tikhonov method is implemented for regularisation. Detailed chemistry is tabulated using the trajectory generated low-dimensional manifold method. Radiation due to the gaseous species is included. Reynolds Averaged Navier–Stokes calculations are performed using two different turbulence models. The objectives of the paper are (i) assessment of the impact of the main numerical parameters in CSE and (ii) comparison of the CSE numerical predictions with available experimental data and results from previous simulations for the selected flame. The number of CSE domains and the number of points in each CSE domain are shown to have a significant impact on the results if not selected appropriately. The present CSE calculations always converge to unique and stable predictions. The corrected k–ε model yields mixture fraction profiles in good agreement with the experimental data values for axial locations in the first half of the flame. Farther downstream, the RNG k–ε model performs better. Overall, the current predictions for the mixture fraction are in good agreement with the experimental data. The predicted temperatures using CSE and the k–ε turbulence model with a modified value of C_ε1 = 1.47 are found to be in very good agreement with the experimental data. Further, the current CSE results are of comparable quality with previous simulations using the flamelet model and conditional moment closure. Future work may include further investigation on optimal determination of the regularisation parameter and alternative regularisation techniques, soot modelling within the CSE formulation, and improved formulation of radiation.     

Conditional moment closure modelling of turbulent methanol jet flames

Conditional moment closure (CMC) predictions for a turbulent piloted jet diffusion flame of methanol in air at velocities of 66.2 and 90.3 m s^?1 are presented. Predictions are compared with the experimental joint Raman-Rayleigh-LIF results of Masri et al and laminar flamelet calculations. Three comprehensive chemical mechanisms (SKELETAL, GRI-Mech and SUBGRI) are used to represent the chemistry of the methanol flame. The SKELETAL mechanism shows the best agreement among the various mechanisms employed. It is found that the SUBGRI mechanism reduces computational cost in terms of memory and CPU time without compromising results where the focus is on the main reactive chemistry.

The k-ε-g turbulence model underpredicts the rate of mixing and the predicted flames are somewhat longer than that reported by experiment. In general, the CMC predictions for conditional mean temperature and species mass fractions are very good and show qualitative agreement with experiment. At downstream locations, the overall trends of predicted temperature and species concentration levels are similar to the upstream ones with the latter showing better agreement with the conditional measured levels. CMC predictions show the same order of agreement at higher velocities.

It is believed that the discrepancies on the fuel-rich side may be due to lack of consideration of the conditional fluctuations. The absence of a radially dependent CMC formulation, excluding differential diffusion effects and the inadequacy of the chemical mechanism may also account, partly, for the degree of discrepancy in the predictions.     

Flow and mixing fields of turbulent bluff-body jets and flames

The mean structure of turbulent bluff-body jets and flames is presented. Measurements of the flow and mixing fields are compared with predictions made using standard turbulence models. It is found that two vortices exist in the recirculation zone; an outer vortex close to the air coflow and an inner vortex between the outer vortex and the jet. The inner vortex is found to shift downstream with increasing jet momentum flux relative to the coflow momentum flux and gradually loses its circulation pattern. The momentum flux ratio of the jet to the coflow in isothermal flows is found to be the only scaling parameter for the flow field structure. Three mixing layers are identified in the recirculation zone. Numerical simulations using the standard k-? and Reynolds stress turbulence models underpredict the length of the recirculation zone. A simple modification to the C₁ constant in the dissipation transport equation fixes this deficiency and gives better predictions of the flow and mixing fields. The mixed-is-burnt combustion model is found to be adequate for simulating the temperature and mixing field in the recirculation zone of the bluff-body flames.     

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.     

Time-averaging strategies in the finite-volume/particle hybrid algorithm for the joint PDF equation of turbulent reactive flows

The influence of time-averaging on bias is investigated in the finite-volume/particle hybrid algorithm for the joint PDF equation for statistically-stationary turbulent reactive flows. It is found that the time-averaging of the mean fluctuating velocity (TAu) leads to the same variances of the fluctuating velocity before and after the velocity correction, whereas without TAu the estimates are different, and an additional numerical dissipation rate is introduced for the turbulent kinetic energy (TKE). When 100 particles per cell are used without TAu, a large bias error is found to be involved in the unconditional statistics of the statistically-stationary solutions of two tested turbulent flames, the Cabra H₂/N₂ lifted flame and the Sandia piloted flame E. The use of TAu reduces this bias dramatically for the same number of particles per cell. The conditional statistics in these flames, however, are hardly affected by TAu. To a large extent, the effect of the bias error on the unconditional statistics is similar to the effect of increasing the model constant C _{ω 1} in the stochastic turbulence frequency model.     

Conditional moment closure modelling of turbulent jet diffusion flames of helium-diluted hydrogen

First-order conditional moment closure (CMC) modelling of NO in non-premixed flames has met with limited success due to the need to consider turbulence influences on the conditional production rate of chemical species. This paper presents results obtained using a second-order approach where such effects are incorporated through solution of a transport equation for the conditional variance. In contrast to earlier work, second-order chemistry is implemented using a more robust numerical technique, with predictions obtained using a Reynolds stress turbulence model. First-order CMC and k–? turbulence model predictions are presented for comparison purposes. For the hydrogen flames examined, results demonstrate small differences between first- and second-order calculations of major species and temperature, although second-order corrections reduce NO and OH levels. Additionally, variations occur between results for these species derived using the two turbulence models due to differences in conditional variance predictions. This and the numerical solution method employed are responsible for deviations with earlier results. It is concluded that while the higher-order CMC model does not significantly improve NO predictions, agreement with OH data is superior. Physical space predictions are sufficiently accurate for assessing flame characteristics, with the Reynolds stress model providing superior results.     

Large eddy simulations of turbulent flames using the filtered density function model

Large eddy simulations (LES) of the Sandia/Sydney swirl burners (SM1 and SMA1) and the Sandia/Darmstadt piloted jet diffusion flame (Flame D) are performed. These flames are part of the database of turbulent reacting flows widely considered as benchmark test cases for validating turbulent-combustion models. In the simulations presented in this paper, the subgrid scale (SGS) closure model adopted for turbulence-chemistry interactions is based on the transport filtered density function (FDF) model. In the FDF model, the transport equation for the joint probability density function (PDF) of scalars is solved. The main advantage of this model is that the filtered reaction rates can be exactly computed. However, the density field, computed directly from the FDF solver and needed in the hydrodynamic equations, is noisy and causes numerical instability. Two numerical approaches that yield a smooth density field are examined. The two methods are based on transport equations for specific sensible enthalpy (h_s) and RT, where R is the gas constant and T is the temperature. Consistency of the two methods is assessed in a bluff-body configuration using Reynolds averaged Navier-Stokes (RANS) methodology in conjunction with the transported PDF method. It is observed that the h_s method is superior to the RT method. Both methods are used in LES of the SM1 burner. In the near-field region, the h_s method produces better predictions of temperature. However, in the far-field region, both methods show deviation from data. Simulations of the SMA1 burner and Flame D are also presented using the h_s method. Some deficiencies are seen in the predictions of the SMA1 burner that may be related to the simple chemical kinetics model and mixing model used in the simulations. Simulations of Flame D show good agreement with data. These results indicate that, while further improvements to the methodology are needed, the LES/FDF method has the potential to accurately predict complex turbulent flames.     

Level set simulations of turbulent thermonuclear deflagration in degenerate carbon and oxygen

We study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing. The fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the Chandrasekhar limit. The level set method is applied to represent the flame fronts numerically. The computational domain for the numerical simulations is cubic, and periodic boundary conditions are imposed. The goal is the development of a suitable flame speed model for the small-scale dynamics of turbulent deflagration in thermonuclear supernovae. Because the burning process in a supernova explosion is transient and spatially inhomogeneous, the localized determination of subgrid scale closure parameters is essential. We formulate a semi-localized model based on the dynamical equation for the subgrid scale turbulence energy k _sgs. The turbulent flame speed s _t is of the order √2k _sgs. In particular, the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales, which has been successfully applied to combustion problems in engineering. The options of either including or suppressing inverse energy transfer in the turbulence production term are compared. In combination with the piece-wise parabolic method for the hydrodynamics, our results favour the latter option. Moreover, different choices for the constant of proportionality in the asymptotic flame speed relation, s _t∝√2k _sgs, are investigated.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

Effects of Lewis number,density ratio and gravity on burning velocity and conditional statistics in stagnating turbulent premixed flames

DNS is performed to analyse the effects of Lewis number (Le), density ratio and gravity in stagnating turbulent premixed flames. The results show good agreement with those of Lee and Huh (Combustion and Flame, Vol. 159, 2012, pp. 1576–1591) with respect to the turbulent burning velocity, S_T, in terms of turbulent diffusivity, flamelet thickness, mean curvature and displacement speed at the leading edge. In all four stagnating flames studied, a mean tangential strain rate resulting in a mean flamelet thickness smaller than the unstretched laminar flame thickness leads to an increase in S_T. A flame cusp of positive curvature involves a superadiabatic burned gas temperature due to diffusive–thermal instability for an Le less than unity. Wrinkling tends to be suppressed at a larger density ratio, not enhanced by hydrodynamic instability, in the stagnating flow configuration. Turbulence is produced, resulting in highly anisotropic turbulence with heavier unburned gas accelerating through a flame brush by Rayleigh–Taylor instability. Results are also provided on brush thickness, flame surface density and conditional velocities in burned and unburned gas and on flame surfaces to represent the internal brush structures for all four test flames.     

The effect of timescale variation in multiple mapping conditioning mixing of PDF calculations for Sandia Flame series D–F

A stochastic implementation of the multiple mapping conditioning (MMC) model has been used for the modelling of turbulence–chemistry interactions in a series of turbulent jet diffusion flames with varying degrees of local extinction (Sandia Flames D–F). The mapping function approximates the cumulative probability distribution of mixture fraction and the corresponding variance can be controlled by a standard implementation of the scalar mixing timescale. The conditional fluctuations are controlled by a minor dissipation timescale, τ_min. The results show a clear dependence of the conditional fluctuations on the choice of the minor timescale, and the appropriate value for turbulent jet flames is similar to values determined in related direct numerical simulation (DNS) studies of homogeneous turbulent reacting flows. The predictions of means and variances of temperature and species mass fractions are very good for all flames, indicating an appropriate modelling of the conditional variances. Further sensitivity studies with respect to particle number density demonstrate a relative insensitivity of the results to the particle number in the numerical solution procedure. Good results can be obtained with as few as 10 particles per cell, allowing for a computationally inexpensive implementation of a Monte Carlo/probability density function (PDF) method.     

Studies of the flow and turbulence fields in a turbulent pulsed jet flame using LES/PDF

A turbulent piloted jet flame subject to a rapid velocity pulse in its fuel jet inflow is proposed as a new benchmark case for the study of turbulent combustion models. In this work, we perform modelling studies of this turbulent pulsed jet flame and focus on the predictions of its flow and turbulence fields. An advanced modelling strategy combining the large eddy simulation (LES) and the probability density function (PDF) methods is employed to model the turbulent pulsed jet flame. Characteristics of the velocity measurements are analysed to produce a time-dependent inflow condition that can be fed into the simulations. The effect of the uncertainty in the inflow turbulence intensity is investigated and is found to be very small. A method of specifying the inflow turbulence boundary condition for the simulations of the pulsed jet flame is assessed. The strategies for validating LES of statistically transient flames are discussed, and a new framework is developed consisting of different averaging strategies and a bootstrap method for constructing confidence intervals. Parametric studies are performed to examine the sensitivity of the predictions of the flow and turbulence fields to model and numerical parameters. A direct comparison of the predicted and measured time series of the axial velocity demonstrates a satisfactory prediction of the flow and turbulence fields of the pulsed jet flame by the employed modelling methods.     

Simulations and experiments on the ignition probability in turbulent premixed bluff-body flames

The ignition characteristics of a premixed bluff-body burner under lean conditions were investigated experimentally and numerically with a physical model focusing on ignition probability. Visualisation of the flame with a 5 kHz OH* chemiluminescence camera confirmed that successful ignitions were those associated with the movement of the kernel upstream, consistent with previous work on non-premixed systems. Performing many separate ignition trials at the same spark position and flow conditions resulted in a quantification of the ignition probability P_ign, which was found to decrease with increasing distance downstream of the bluff body and a decrease in equivalence ratio. Flows corresponding to flames close to the blow-off limit could not be ignited, although such flames were stable if reached from a richer already ignited condition. A detailed comparison with the local Karlovitz number and the mean velocity showed that regions of high P_ign are associated with low Ka and negative bulk velocity (i.e. towards the bluff body), although a direct correlation was not possible. A modelling effort that takes convection and localised flame quenching into account by tracking stochastic virtual flame particles, previously validated for non-premixed and spray ignition, was used to estimate the ignition probability. The applicability of this approach to premixed flows was first evaluated by investigating the model's flame propagation mechanism in a uniform turbulence field, which showed that the model reproduces the bending behaviour of the S_T-versus-u′ curve. Then ignition simulations of the bluff-body burner were carried out. The ignition probability map was computed and it was found that the model reproduces all main trends found in the experimental study.     

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.     

Reaction zone structures and mixing characteristics of partially premixed swirling CH4/air flames in a gas turbine model combustor

The mixing, reaction progress, and flame front structures of partially premixed flames have been investigated in a gas turbine model combustor using different laser techniques comprising laser Doppler velocimetry for the characterization of the flow field, Raman scattering for simultaneous multi-species and temperature measurements, and planar laser-induced fluorescence of CH for the visualization of the reaction zones. Swirling CH₄/air flames with Re numbers between 7500 and 60,000 have been studied to identify the influence of the turbulent flow field on the thermochemical state of the flames and the structures of the CH layers. Turbulence intensities and length scales, as well as the classification of these flames in regime diagrams of turbulent combustion, are addressed. The results indicate that the flames exhibit more characteristics of a diffusion flame (with connected flame zones) than of a uniformly premixed flame.     

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.     

PDF方法模拟钝体驻定的湍流扩散火焰

采用标量联合的概率密度函数方法,对钝体驻定的湍流射流扩散Sydney火焰HM1进行数值模拟,结合当地自适应建表方法加速化学反应计算,用修正的LRR-IP雷诺应力模型求解速度场.首次对3种不同规模的甲烷化学反应动力学机理进行研究,并与实验数据进行比较,结果表明,模型和反应机理很好地预测了速度场和标量场的变化及局部熄火现象,而考虑反应机理中的C2化学对火焰HM1的影响不大.     

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.