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 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.     

Species and temperature predictions in a semi-industrial MILD furnace using a non-adiabatic conditional source-term estimation formulation

A Reynolds-Averaged Navier–Stokes (RANS) simulation of the semi-industrial International Flame Research Foundation (IFRF) furnace is performed using a non-adiabatic Conditional Source-term Estimation (CSE) formulation. This represents the first time that a CSE formulation, which accounts for the effect of radiation on the conditional reaction rates, has been applied to a large scale semi-industrial furnace. The objective of the current study is to assess the capabilities of CSE to accurately reproduce the velocity field, temperature, species concentration and nitrogen oxides (NO_x) emission for the IFRF furnace. The flow field is solved using the standard k–ε turbulence model and detailed chemistry is included. NO_x emissions are calculated using two different methods. Predicted velocity profiles are in good agreement with the experimental data. The predicted peak temperature occurs closer to the centreline, as compared to the experimental observations, suggesting that the mixing between the fuel jet and vitiated air jet may be overestimated. Good agreement between the species concentrations, including NO_x, and the experimental data is observed near the burner exit. Farther downstream, the centreline oxygen concentration is found to be underpredicted. Predicted NO_x concentrations are in good agreement with experimental data when calculated using the method of Peters and Weber. The current study indicates that RANS-CSE can accurately predict the main characteristics seen in a semi-industrial IFRF furnace.     

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.     

Interaction of a Particle‐Laden Gaseous Jet with a Confined Annular Turbulent Flow

A numerical analysis of polydispersed glass particles interacting with a confined turbulent bluff‐body flow was performed by combining the finite‐volume method for the gaseous flow with a mesh‐free Lagrangian approach for the particulate flow. Three turbulence‐closure models, namely the Reynolds‐stress, the standard k‐ϵ, and the nonlinear k‐ϵ models, were first comparatively studied for the single‐phase flow. The second‐moment Reynolds‐stress model was then selected for the prediction of the turbulent gaseous flow in a gas‐particle system, where an improved eddy‐interaction model was used to predict turbulence‐induced particle dispersion. The interaction between the two phases was accounted for through coupling source terms. Numerical predictions of two‐phase mean and fluctuating velocities for particle sizes ranging from 15 to 115 μm were compared with corresponding experimental data. Reasonably good agreement was achieved for the mean properties of both the gaseous and particulate flows.     

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.     

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.     

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 comparative study of turbulence models for non-premixed swirl-stabilized flames

ABSTRACT

The accuracy of turbulent swirl-stabilized flame simulation strongly depends on the choice of turbulence model. In this study, four 3D unsteady turbulence closures, including large eddy simulation, scale-adaptive simulation, and two detached eddy simulation variants, along with four RANS models, including RNG k??, SST k?ω, transition SST, and RSM, are examined for moderate- and high-swirl case studies. It is observed that the scale-adaptive simulation provides the most accurate results for almost all variables and both swirl conditions in the reactive flow. Only the 3D unsteady models predict the vortex breakdown bubble and flame attachment state correctly. However, based on our error analysis, the flow and composition fields predicted by the RANS models are in acceptable agreement with the experimental fields, especially the ones of transition SST when higher swirl number cases or minor species concentration are of interest. Moreover, it is concluded that the viscosity ratio criterion is a better measure of the local LES quality than the turbulent kinetic energy ratio, and the accuracy of a hybrid simulation may be much more dependent on the ability of the model to operate close to the RANS mode where the grid resolution is not sufficient for a resolving simulation than the fraction of the resolved kinetic energy. Finally, the propriety of the base (RANS) model of a DES for the application of interest is important, such that DES with realizable k?? outperforms the commonly used DES with SST k?ω model.     

An Improved Method to Determine Particle Dispersion Width for Efficient Modeling of Turbulent Two‐Phase Flows

An improved approach is presented for the hybrid Eulerian‐Lagrangian modeling of turbulent two‐phase flows. The hybrid model consists of a nonlinear k–ε model for the fluid flow and an efficient Lagrangian trajectory model for the particulate flow. The improved approach avoids an empirical correlation required to determine the dispersion width for the existing Stochastic‐Probabilistic Efficiency Enhanced Dispersion (SPEED) model. The improved SPEED model is validated using experimental data for a poly‐dispersed water spray interacting with a turbulent annular air jet behind a bluff‐body. Numerical results for the number‐mean and Sauter‐mean droplet diameters, as well as mean and fluctuating droplet velocities are compared with the experimental data and with the predictions of other dispersion models. It is demonstrated that higher computational efficiency and smoother profiles of Sauter‐mean diameter can be obtained with the improved stochastic‐probabilistic model than with the eddy‐interaction model.     

Development and application of a diffusion-inertia model for calculating aerosol particle deposition from turbulent flows

Three-dimensional simulation of experiments on aerosol particle deposition in a turbulent flow is carried out. The k — ɛ turbulence model and the diffusion inertia model of particle transport and deposition were used in the simulation. The range of flow velocities and particle sizes is typical for the diffusion and turbophoresis deposition mechanisms. Deposition of particles in a turbulent flow is considered for cases of a direct vertical pipe and for a 90° bend in which the turbophoresis is coupled with centrifugal forces. The calculation results are in good agreement with experimental data. Deviations of results are comparable with those of discrete particle modeling.     

Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

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.     

Simulation of transient turbulent methane jet ignition and combustion under engine-relevant conditions using conditional source-term estimation with detailed chemistry

The ignition and combustion processes of transient turbulent methane jets under high-pressure and moderate temperature conditions were simulated using a computationally efficient combustion model. Closure for the mean chemical source-terms was obtained with Conditional Source-term Estimation (CSE) using first conditional moment closure in conjunction with a detailed chemical kinetic mechanism, which was reduced to a Trajectory-Generated Low-Dimensional Manifold (TGLDM). The accuracy of the manifold was first validated against the direct integral method by comparing the predicted reactive scalar profiles in three methane–air reaction systems: a laminar premixed flame, a laminar flamelet and a perfectly stirred reactor. Detailed CFD simulations incorporating the CSE-TGLDM model were able to provide reasonably good predictions of the experimental ignition delay and initial ignition kernel locations of the methane jets reported in the literature with relatively low computational cost. Nitrogen oxides formed in the methane jet flame were found to be underpredicted by the model by as much as a factor of 2. The discrepancy may be attributable to the inability of the simulation to account for the effects of the rarefaction wave in the shock-tube experiments.     

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.     

Transported PDF simulation of auto-ignition of a turbulent methane jet in a hot,vitiated coflow

In the current work, the auto-ignition of a turbulent round methane jet is studied numerically by means of a transported probability density function (PDF) method. The methane jet is issued into a hot, vitiated coflow, where it ignites to form a steady lifted flame. For this flame, experimental data of hydroxyl, temperature and mixture fraction are provided in the area where the fuel auto-ignites. To model this experiment, the transport equation for the thermochemical PDF is solved using a hybrid finite volume / Lagrangian Monte-Carlo method. Turbulence is modelled using the k-? turbulence model including a jet-correction. Computational results are compared to experimental data in terms of mean quantities, variances and lift-off height. Moreover, the structure of the one-point, one-time marginal PDF of temperature is analysed and compared to experimental data which are provided in this work. It is found that the transported PDF method in conjunction with the k-? model is capable of reproducing these statistical data very well. In particular the effect of ignition on the marginal PDF of temperature can be well reproduced with this approach. To further analyse the relevant processes in the evolution of the temperature PDF, a statistically homogeneous system is studied both numerically and analytically.     

A fractal flame-wrinkling large eddy simulation model for premixed turbulent combustion

Combustion plays an important role in a wide variety of industrial applications, such as gas-turbines, furnaces, spark-ignition engines, and various air-breathing engines. The ability to predict and understand the behavior of reacting flows in practical devices is fundamental to improved combustors with higher efficiency and reduced levels of emissions. At present, large eddy simulation is considered the most promising approach for premixed combustion modeling since the large-scale energy containing flow structures are resolved on the grid. However, the typically thin reaction zone cannot be resolved. To overcome this difficulty flamelet models, in which the reaction is assumed to take place in thin layers, wrinkled by the turbulence can sometimes be used. In these models, the turbulent flame speed can be represented as the product of the laminar flame speed, S_u, corrected for the effects of stretch (strain and curvature) and the flame-wrinkling, Ξ. In this study, we propose to model Ξ using fractal theory. This model requires sub-models for the fractal dimension, and the inner and outer cut-offs—the latter being set by the grid. A model is proposed for the inner cut-off, whereas an empirical parameterization is used to provide the fractal dimension. The proposed model is applied to flame kernel growth in homogeneous isotropic turbulence in a fan-stirred bomb and to a lean premixed flame in a plane symmetric dump combustor. Good qualitative and quantitative agreement with experimental data were obtained for the proposed model in both cases. Comparison with other well-known turbulent flame speed closure models shows that the proposed model behaves at least as good, or even better, than the reference models.     

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

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