Application of Conditional Source-term Estimation to two turbulent non-premixed methanol flames

Conditional Source-term Estimation (CSE) is a turbulent combustion model that uses conditional averages to close the chemical source term. Previous CSE studies have shown that the model is able to predict the flame characteristics successfully; however, these studies have only focused on simple hydrocarbon fuels mostly composed of methane. The objective of the present paper is to evaluate the capabilities of CSE applied to turbulent non-premixed methanol flames, which has never been done previously. The current study investigates two different types of methanol flames: piloted and bluff-body flames. For the piloted flame, the standard k–ε model is used for turbulence modelling, while the Shear Stress Transport (SST) k–ω model is applied to the bluff-body case. Different values of empirical constants within the turbulence models were tested, and it was found that C_ε1 = 1.7 for the piloted flame and γ₂ = 0.66 for the bluff-body flame provided the best agreement with experimental measurements for the mixing field. Detailed chemistry is included in tabulated form using the Trajectory Generated Low-Dimensional Manifold (TGLDM) method. The predictions including both the Favre-averaged and conditional mass fraction of reactive species and temperature are compared with available experimental data and previous numerical results. Overall, the CSE predictions of conditional and unconditional quantities are in good agreement with the experimental data except for hydrogen. Sources of discrepancies are identified such as the chemical kinetics and neglect of differential diffusion. Large eddy simulations may also help to improve the velocity and mixing field predictions.     

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.     

Simulations of turbulent lifted jet flames with two-dimensional conditional moment closure

Simulations of H₂ air lifted jet flames are presented, obtained in terms of two-dimensional, first-order conditional moment closure (CMC). The unsteady CMC equation with detailed chemistry is solved without the need for operator splitting, while the accompanying flow field is determined using commercial CFD software employing a k − ε turbulence model. Computed lift-off heights and Favre-averaged species mole fractions are found to be very close to values obtained experimentally for a wide range of jet velocities and fuel–air mixtures. Simulations for which the initial condition is an attached flame and the jet velocity gradually increased do not result in lift-off, a result fully consistent with experimental observation and capturing the hysteresis behaviour of lifted flames. The stabilisation mechanism is explored by quantifying the balance of terms comprising the CMC in the lift-off region. In line with experimental data, it is found that the scalar dissipation rate at the stabilisation height is well below the extinction value, and that axial transport and molecular diffusion play a major role. The radial components of spatial convection and diffusion are always small, fully justifying the alternative approach of employing a cross-stream averaged CMC.     

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.     

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.     

Application of the Lagrangian CMC method in elliptic bluff body and swirl flames

The Lagrangian CMC method was implemented in the open source programme OpenFOAM and applied to turbulent nonpremixed bluff body and swirl flames. Lagrangian CMC is more efficient than Eulerian CMC with the number of Lagrangian flame groups much less than the number of computational cells for Eulerian CMC equations in general. It is based on the conditional flame structure depending on the residence time of the fuel of fixed Lagrangian identity from the nozzle. According to sensitivity study the injected fuel was divided into ten flame groups according to the injection sequence with the resulting conditional profiles between those by ISR and Eulerian CMC. Minor deviation from Eulerian CMC was attributed to the flame structure that is difficult to be characterised by the residence time only in elliptic recirculating flows of the bluff body and swirl flames. The Eulerian and Lagrangian CMC showed the same trend of deviation from measurements for conditional temperature, H₂O, OH, CO and H₂ mass fractions. The significant deviation of H₂ was due to uncertainty in the reaction chemistry, as observed in the previous works based on other reaction mechanisms for methane and methanol.     

CMC simulations of lifted turbulent jet flame in a vitiated coflow

Lifted turbulent jet diffusion flame is simulated using Conditional Moment Closure (CMC). Specifically, the burner configuration of Cabra et al. [R. Cabra, T. Myhrvold, J.Y. Chen, R.W. Dibble, A.N. Karpetis, R.S. Barlow, Proc. Combust. Inst. 29 (2002) 1881–1887] is chosen to investigate H₂/N₂ jet flame supported by a vitiated coflow of products of lean H₂/air combustion. A 2D, axisymmetric flow-model fully coupled with the scalar fields, is employed. A detailed chemical kinetic scheme is included, and first order CMC is applied. Simulations are carried out for different jet velocities and coflow temperatures (T_c). The predicted liftoff generally agrees with experimental data, as well as joint-PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for T_c=1025 and 1080 K reveal that (1) Inside the flame zone, the chemical term balances the molecular diffusion term, and hence the structure is of a diffusion flamelet for both cases. (2) In the pre-flame zone, the structure depends on the coflow temperature: for the 1025 K case, the chemical term being small, the advective term balances the axial turbulent diffusion term. However, for the 1080 K case, the chemical term is large and balances the advective term, the axial turbulent diffusion term being small. It is concluded that, lift-off is controlled (a) by turbulent premixed flame propagation for low coflow temperature while (b) by autoignition for high coflow temperature.     

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.     

Modeling evaporation effects in conditional moment closure for spray autoignition

Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in the mixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective–reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected.     

Analysis of second-order conditional moment closure applied to an autoignitive lifted hydrogen jet flame

The timing and location of autoignition can be highly sensitive to turbulent fluctuations of composition. Second-order Conditional Moment Closure (CMC) provides transport equations for conditional (co)variances in turbulent reacting flows. CMC equations accounting for compressibility and differential diffusion are analyzed using data from direct numerical simulation of an autoignitive lifted turbulent hydrogen jet flame [C.S. Yoo, R. Sankaran, J.H. Chen, Three-dimensional direct numerical simulation of turbulent lifted hydrogen/air jet flame in a heated coflow. Part 1. J. Fluid. Mech., (2008)]. At the flame base, second-order moments were required to accurately model the conditional reaction rates. However, over 80% of the second-order reaction rate component was obtainable with a small subset (16%) of the species-temperature covariances. The balance of the second-order CMC equation showed that turbulent transport across spatial composition gradients initiates generation of conditional variances.     

The role of cool-flame chemistry in quasi-steady combustion and extinction of n-heptane droplets

Experiments on the combustion of large n-heptane droplets, performed by the National Aeronautics and Space Administration in the International Space Station, revealed a second stage of continued quasi-steady burning, supported by low-temperature chemistry, that follows radiative extinction of the first stage of burning, which is supported by normal hot-flame chemistry. The second stage of combustion experienced diffusive extinction, after which a large vapour cloud was observed to form around the droplet. In the present work, a 770-step reduced chemical-kinetic mechanism and a new 62-step skeletal chemical-kinetic mechanism, developed as an extension of an earlier 56-step mechanism, are employed to calculate the droplet burning rates, flame structures, and extinction diameters for this cool-flame regime. The calculations are performed for quasi-steady burning with the mixture fraction as the independent variable, which is then related to the physical variables of droplet combustion. The predictions with the new mechanism, which agree well with measured autoignition times, reveal that, in decreasing order of abundance, H₂O, CO, H₂O₂, CH₂O, and C₂H₄ are the principal reaction products during the low-temperature stage and that, during this stage, there is substantial leakage of n-heptane and O₂ through the flame, and very little production of CO₂ with no soot in the mechanism. The fuel leakage has been suggested to be the source of the observed vapour cloud that forms after flame extinction. While the new skeletal chemical-kinetic mechanism facilitates understanding of the chemical kinetics and predicts ignition times well, its predicted droplet diameters at extinction are appreciably larger than observed experimentally, but predictions with the 770-step reduced chemical-kinetic mechanism are in reasonably good agreement with experiment. The computations show how the key ketohydroperoxide compounds control the diffusion-flame structure and its extinction.     

Characteristics of microjet methane diffusion flames

Characteristics of microjet methane diffusion flames stabilized on top of the vertically oriented, stainless-steel tubes with an inner diameter ranging from 186 to 778 μ m are investigated experimentally, theoretically and numerically. Of particular interest are the flame shape, flame length and quenching limit, as they may be related to the minimum size and power of the devices in which such flames would be used for future micro-power generation. Experimental measurements of the flame shape, flame length and quenching velocity are compared with theoretical predictions as well as detailed numerical simulations. Comparisons of the theoretical predictions with measured results show that only Roper's model can satisfactorily predict the flame height and quenching velocity of microjet methane flames. Detailed numerical simulations, using skeletal chemical kinetic mechanism, of the flames stabilized at the tip of d = 186, 324 and 529 μ m tubes are performed to investigate the flame structures and the effects of burner materials on the standoff distance near extinction limit. The computed flame shape and flame length for the d = 186 μm flame are in excellent agreement with experimental results. Numerical predictions of the flame structures strongly suggest that the flame burns in a diffusion mode near the extinction limit. The calculated OH mass fraction isopleths indicate that different tube materials have a minor effect on the standoff distance, but influence the quenching gap between the flame and the tube.     

Computational and experimental study of JP-8, a surrogate, and its components in counterflow diffusion flames

Non-sooting counterflow diffusion flames have been studied both computationally and experimentally, using either JP-8, or a six-component JP-8 surrogate mixture, or its individual components. The computational study employs a counterflow diffusion flame model, the solution of which is coupled with arc length continuation to examine a wide variety of inlet conditions and to calculate extinction limits. The surrogate model includes a semi-detailed kinetic mechanism composed of 221 gaseous species participating in 5032 reactions. Experimentally, counterflow diffusion flames are established, in which multicomponent fuel vaporization is achieved through the use of an ultrasonic nebulizer that introduces small fuel droplets into a heated nitrogen stream, fostering complete vaporization without fractional distillation. Temperature profiles and extinction limits are measured in all flames and compared with predictions using the semi-detailed mechanism. These measurements show good agreement with predictions in single-component n-dodecane, methylcyclohexane, and iso-octane flames. Good agreement also exists between predicted and measured variables in flames of the surrogate, and the agreement is even better between the experimental JP-8 flames and the surrogate predictions.     

Dynamic adaptive chemistry for turbulent flame simulations

The use of large chemical mechanisms in flame simulations is computationally expensive due to the large number of chemical species and the wide range of chemical time scales involved. This study investigates the use of dynamic adaptive chemistry (DAC) for efficient chemistry calculations in turbulent flame simulations. DAC is achieved through the directed relation graph (DRG) method, which is invoked for each computational fluid dynamics cell/particle to obtain a small skeletal mechanism that is valid for the local thermochemical condition. Consequently, during reaction fractional steps, one needs to solve a smaller set of ordinary differential equations governing chemical kinetics. Test calculations are performed in a partially-stirred reactor (PaSR) involving both methane/air premixed and non-premixed combustion with chemistry described by the 53-species GRI-Mech 3.0 mechanism and the 129-species USC-Mech II mechanism augmented with recently updated NO _x pathways, respectively. Results show that, in the DAC approach, the DRG reduction threshold effectively controls the incurred errors in the predicted temperature and species concentrations. The computational saving achieved by DAC increases with the size of chemical kinetic mechanisms. For the PaSR simulations, DAC achieves a speedup factor of up to three for GRI-Mech 3.0 and up to six for USC-Mech II in simulation time, while at the same time maintaining good accuracy in temperature and species concentration predictions.     

Monte Carlo PDF modelling of a turbulent natural-gas diffusion flame

A piloted turbulent natural-gas diffusion flame is investigated numerically using a 2D elliptic Monte Carlo algorithm to solve for the joint probability density function (PDF) of velocity and composition. Results from simulations are compared to detailed experimental data: measurements of temperature statistics, data on mean velocity and turbulence characteristics and data on OH. Conserved-scalar/constrained-equilibrium chemistry calculations were performed using three different models for scalar micro-mixing: the interaction by exchange with the mean (IEM) model, a coalescence/dispersion (C/D) model and a mapping closure model. All three models yield good agreement with the experimental data for the mean temperature. Temperature standard deviation and PDF shapes are generally predicted well by the C/D and mapping closure models, whereas the IEM model gives qualitatively incorrect results in parts of the domain. It is concluded that the choice of micro-mixing model can have a strong influence on the quality of the predictions. The same flame was also simulated using reduced chemical kinetics obtained from the intrinsic low-dimensional manifold (ILDM) approach. Comparison with the constrained-equilibrium results shows that the shape of the OH concentration profiles is recovered better in the ILDM simulation, and that the ILDM reduced chemical kinetics can correctly predict super-equilibrium OH.     

Second-order conditional moment closure modeling of a turbulent CH4/H2/N2 jet diffusion flame

The second-order CMC model for a detailed chemical mechanism is used to model a turbulent CH₄/H₂/N₂ jet diffusion flame. Second-order corrections are made to the three rate limiting steps of methane–air combustion, while first-order closure is employed for all the other steps. Elementary reaction steps have a wide range of timescales with only a few of them slow enough to interact with turbulent mixing. Those steps with relatively large timescales require higher-order correction to represent the effect of fluctuating scalar dissipation rates. Results show improved prediction of conditional mean temperature and mass fractions of OH and NO. Major species are not much influenced by second-order corrections except near the nozzle exit. A parametric study is performed to evaluate the effects of the variance parameter in log-normal scalar dissipation PDF and the constants for the dissipation term in conditional variance and covariance equations.     

LES/CMC modelling of ignition and flame propagation in a non-premixed methane jet

The Large Eddy Simulation (LES) / Conditional Moment Closure (CMC) model with detailed chemistry is used for modelling spark ignition and flame propagation in a turbulent methane jet in ambient air. Two centerline and one off-axis ignition locations are simulated. We focus on predicting the flame kernel formation, flame edge propagation and stabilization. The current LES/CMC computations capture the three stages reasonably well compared to available experimental data. Regarding the formation of flame kernel, it is found that the convection dominates the propagation of its downstream edge. The simulated initial downstream and radial flame propagation compare well with OH-PLIF images from the experiment. Additionally, when the spark is deposited at off-centerline locations, the flame first propagates downstream and then back upstream from the other side of the stoichiometric iso-surface. At the leading edge location, the chemical source term is larger than others in magnitude, indicating its role in the flame propagation. The time evolution of flame edge position and the final lift-off height are compared with measurements and generally good agreement is observed. The conditional quantities at the stabilization point reflect a balance between chemistry and micro-mixing. This investigation, which focused on model validation for various stages of spark ignition of a turbulent lifted jet flame through comparison with measurements, demonstrates that turbulent edge flame propagation in non-premixed systems can be reasonably well captured by LES/CMC.     

A comparison of computational and experimental lift-off heights of coflow laminar diffusion flames

As a sensitive marker of changes in flame structure, the number densities of excited-state CH (denoted CH^*), and excited-state OH (denoted OH^*) are imaged in coflow laminar diffusion flames. Measurements are made both in normal gravity and on the NASA KC-135 reduced-gravity aircraft. The spatial distribution of these radicals provides information about flame structure and lift-off heights that can be directly compared with computational predictions. Measurements and computations are compared over a range of buoyancy and fuel dilution levels. Results indicate that the lift-off heights and flame shapes predicted by the computations are in excellent agreement with measurement for both normal gravity (1g) and reduced gravity flames at low dilution levels. As the fuel mixture is increasingly diluted, however, the 1g lift-off heights become underpredicted. This trend continues until the computations predict stable flames at highly dilute fuel mixtures beyond the 1g experimental blow-off limit. To better understand this behavior, an analysis was performed, which indicates that the lift-off height is sensitive to the laminar flame speed of the corresponding premixed mixture at the flame edge. By varying the rates of two key “flame speed” controlling reactions, we were able to modify the predicted lift-off heights so as to be in closer agreement with the experiments. The results indicate that reaction sets that work well in low dilution systems may need to be modified to accommodate high dilution flames.     

Multiple mapping conditioning of turbulent jet diffusion flames

The multiple mapping conditioning (MMC) approach is applied to two non-piloted CH₄/H₂/N₂ turbulent jet diffusion flames with Reynolds numbers of Re = 15,200 and 22,800. The work presented here examines primarily the suitability of MMC to simulate CH₄/H₂ flames with varying Re numbers. The equations are solved in a prescribed Gaussian reference space with only one stochastic reference variable emulating the fluctuations of mixture fraction. The mixture fraction is considered as the only major species on which the remaining minor species are conditioned. Fluctuations around the conditional means are ignored. It is shown that the statistics of the mapped reference field are an accurate model for the statistics of the physical field for both flames. A transformation of the Gaussian reference space introduced in previous work on MMC is used to express the MMC model in the same form as CMC. The most important advantage of this transformation is that the conditionally averaged scalar dissipation term is in a closed form. The corresponding temperature and reactive species predictions are generally in good agreement with experimental data. The application to real laboratory flames and the assessment of the new conditional scalar dissipation model for the closure of the singly conditioned CMC equation is the major novelty of this paper. The results are therefore primarily examined with respect to changes of the conditionally averaged quantities in mixture fraction space.