Conditional Moment Closure Model Research Articles

Large eddy simulation and finite-volume conditional moment closure modelling of a turbulent lifted H2/N2 flame

Large eddy simulations with three-dimensional finite-volume Conditional Moment Closure (CMC) model are performed for a hydrogen/nitrogen lifted flame with detailed chemical mechanism. The emphasis is laid on the influences of mesh resolution and convection scheme of finite-volume CMC equations on predictions of reactive scalars and unsteady flame dynamics. The results show that the lift-off height is underestimated and the reactive scalars are over-predicted with coarser CMC mesh. It is also found that further refinement of the CMC mesh would not considerably improve the results. The time sequences of the most reactive and stoichiometric hydroxyl radical mass fractions indicate that finer CMC mesh can capture more unsteady details than the coarser CMC mesh. Moreover, the coarse CMC mesh has lower conditional scalar dissipation rate, which would promote the earlier auto-ignition of the flame base. Besides, the effects of the convection scheme for the CMC equations (i.e., upwind, central differencing and their blends) on the lifted flame characteristics are also investigated. It is shown that different convection schemes lead to limited differences on the time-averaged temperature, mixture fraction and species mass fractions. Moreover, the root-mean square values of hydrogen and hydroxyl mass fractions show larger deviation from the measurements with hybrid upwind and central differencing scheme, especially around the flame base. Furthermore, the distributions of the numerical fluxes on the CMC faces also show obvious distinctions between the upwind and blending schemes. The budget analysis of the individual CMC terms shows that a sequence of CMC faces has comparable contributions with upwind scheme. However, with the hybrid schemes, the instantaneous flux is dominantly from limited CMC faces. The reactivity of a CMC cell is more easily to be affected by its neighbors when the upwind scheme is used.

Localized conditional source-term estimation model for turbulent combustion

A novel functional form for approximating the conditional scalars in turbulent reacting flows is introduced based on the Bernstein polynomial. Multi-scalar measurement data of turbulent premixed and non-premixed flames are used to demonstrate that the new functional form provides an excellent reduced-order model for the conditional scalars. This model order reduction technique can be used to improve the accuracy, reduce the computational cost and enhance the spatial localization of the Conditional Source-term Estimation (CSE) model. CSE is a turbulence-chemistry interaction model similar to the Conditional Moment Closure (CMC) model, except that the conditional scalars are estimated from the filtered field in an ensemble of LES cells using an integral equation. An a priori analysis using the DNS data of a series of statistically planar turbulent premixed flames shows that using Bernstein polynomials as the presumed functional form for the conditional scalars provides better regularization than the conventional CSE approach. Furthermore, the ensemble size – that was previously kept on the order of thousands of LES cells in the singly-conditioned CSE – can be reduced to as low as 16 LES cells. This enhanced localization approach reduces the modelling error and the computational cost compared to the conventional CSE approach for tabulated and reduced chemistry models.

Numerical investigation of the autoignition of underexpanded methane jets

This work constitutes a numerical investigation of the autoignition of underexpanded methane jets at high-pressure conditions. Injection pressures from 125 to 500bar, back pressures from 40 to 125bar, and pressure ratios between 2.5 and 10 have been targeted. The aim is to identify the effect of the main control variables of gas injection on the autoignition delay and location. To this end, Reynolds-Averaged Navier-Stokes simulations with the k-ωSST model have been carried out for five broad parametric variations. The computational domain represents a Constant Volume Cell with a prototype gas injector. A two-stage workflow enables proper thermodynamic treatment of the conservation equations with real-gas modeling, sufficient resolution for shock structures in the near nozzle area, detailed kinetics described by the San Diego mechanism and treatment of turbulence-chemistry interaction with elliptic Conditional Moment Closure model. The results are interpreted conceptually as an interplay of jet reactivity, effectively described by an exponential dependence on ambient temperature and a power law dependence on ambient pressure, and of jet aerodynamics, empirically described by a quadratic dependence on pressure ratio. Injection temperature is introduced by defining an appropriate characteristic system temperature and a correlation is constructed, whose predictions are juxtaposed against a modified Arrhenius model and measurements from independent experimental studies in literature. The effect of injection variations on ignition location in physical space is also examined.

Presumed Joint-PDF Modelling for Turbulent Stratified Flames

Turbulence–chemistry interaction models such as the conditional moment closure and various flamelet models require a presumed Probability Density Function (PDF) model of the conditioning variables. In turbulent stratified flames, a joint-PDF model for a reaction progress variable and the mixture fraction is required. The joint-PDF is often modelled by two beta functions using the first and second moments of the two conditioning variables. In this work, the performance of a joint-PDF model based on the flamelet PDF approach is compared to the double beta-PDF model. The conditional PDF of the reaction progress variable conditioned on mixture fraction is modelled with the flamelet PDF. Unlike the beta PDF, the flamelet functional form for the conditional PDF varies with the local mixture fraction. The two PDF models are coupled with a two-dimensional premixed flamelet-generated manifold chemistry model. Two stratified flames of the Cambridge–Sandia bluff-body burner are simulated using a Reynolds-Averaged Navier–Stokes (RANS) approach. The results indicate that the flamelet PDF model has a superior, albeit marginal, predictions of the temperature, major and minor species mass fractions.

Assessment of Tabulated Premixed Conditional Moment Closure Model Using Direct Numerical Simulation

ABSTRACT The Conditional Moment Closure (CMC) is a proven methodology to model non-premixed flames, but an emerging technique for analyzing turbulent premixed flames. However, solving a full set of CMC equations is a time-consuming process. The Tabulated Premixed CMC (TPCMC) model is a modification of the premixed CMC model that seeks to reduce the time consumed in solving equations by making the premixed CMC model amenable to the tabulation of chemistry. TPCMC model considers the effect of small scale mixing of reactants and products using the scalar dissipation rate and effect of large scale turbulence on the flame using the beta probability density function. The validation of TPCMC model using Direct Numerical Simulation (DNS) data has been attempted in this paper. DNS of growth of an ignition kernel in a turbulent medium was performed for this purpose. Two sets of simulations, namely 3D DNS with three-step reduced chemistry and 2D DNS with multi-step chemistry, have been carried out in this study using PENCIL code. The Favre averaging of this DNS data was performed on the surfaces of constant radius to assess the accuracy of TPCMC model. The variations in turbulence intensity and integral length scale were considered to generate DNS database. TPCMC model accurately predicted the variation of fuel mass fraction and temperature for all the cases considered in this study and captured the qualitative trends in the CO mass fraction where a negligible deviation from the actual values was observed. The influence of initial parameters related to turbulence considered in this study was negligible on the accuracy of predictions obtained from the model.

OpenFOAM based conditional moment closure (CMC) model for solving non-premixed turbulent combustion: Integration and validation

This article presents a direct integration of conditional moment closure (CMC), an advanced combustion model with a computational fluid dynamics (CFD) package, OpenFOAM (Open-source Field Operation And Manipulation) to solve non-premixed turbulent combustion. Earlier our group (Roy and Sreedhara, 2016) had coupled CMC code with FLUENT to model non-premixed turbulent combustion, but it was through manual two-way coupling method where CFD and CMC codes were sequentially solved one after the other until the steady state is reached. The extensible and flexible framework of OpenFOAM encouraged us to build a CFD-CMC solver called cmcFoam. This fully-coupled solver solves CMC equations internally in OpenFOAM along with flow-field equations. Major advantages of this solver are (1) it is built in the open-source framework, (2) it can predict the transient behavior of flames, and (3) one can benefit from all features of OpenFOAM. The validity of the proposed solver has been thoroughly demonstrated by accurately predicting experimental data published for the Sandia syngas (CO/H2/N2) flame. Two-dimensional axisymmetric simulations were performed with a modified k-ε turbulence model and using a chemical kinetic scheme having 21 species and 84 chemical reactions (DRM 19). Results predicted by the solver showed an excellent agreement with the published data, both in mixture fraction and physical space. This benchmarked coupled code may be useful to analyze fairly complex industrial problems.

Numerical investigation of methanol bluff-body flame using variants of RANS turbulence models with conditional moment closure model

In this article, conditional moment closure model (CMC) along with four variants of RANS turbulence models is used for investigating a methanol bluff-body flame. This work attempts to establish the accuracy of turbulence models in predicting the mixing fields, which results in improved predictions of the mean and variance of mixture fraction. This ensures an accurate probability density function (pdf) of the mixture fraction field which is used to obtain unconditional quantities from the conditional quantities calculated from CMC closure. The flow and mixing field are calculated using ANSYS Fluent software by incorporating four different turbulence models viz. standard k-ε (SKE), modified k-ε (MKE), RNG k-ε and Reynolds stress turbulence models. Flow field simulations have been coupled with an in-house CMC solver to obtain the mean flame structure. Profiles of mixture fraction showed an excellent agreement with the experimental data when Reynolds stress turbulence model was used. The unconditional mean temperature and species mass fraction obtained from the CMC model shows improved predictions when coupled with the Reynolds stress turbulence models. Because of inaccurate mixing field and hence the pdf predicted from SKE, MKE and RNG k-ε models, the unconditional quantities showed significant deviations from the experimental results.

LES/CMC Modelling of a Gas Turbine Model Combustor with Quick Fuel Mixing

The first-order, single-conditioned sub-grid Conditional Moment Closure (CMC) model for Large Eddy Simulation (LES) is applied to simulate a globally lean swirling methane flame in a gas turbine model combustor that has been studied experimentally. The time-averaged velocity, mixture fraction, temperature, major species and OH mass fractions, and the heat release rate are predicted well for most locations. A transient lift-off and flashback of the flame root due to localized extinction near the burner exit is observed that is qualitatively consistent with the experimental measurements. The time-averaged temperature is over-predicted very close to the fuel injection point, while it is accurately reproduced downstream. Comparisons of instantaneous conditionally-filtered temperature in mixture fraction space shows that the LES/CMC reproduces the large scatter of the experimental data points in temperature–mixture fraction plane that span the full range unburnt to fully burnt, but to a smaller extent, suggesting a minor under-prediction of local extinction or the inaccuracy of the present first-order, coarse-grid CMC formulation to capture locally premixed flame propagation behaviour. Periodic variation of the heat release rate is observed with a frequency close to that of the measured Precessing Vortex Core (PVC). In general, the current LES/CMC model captures most features of this high-mixing-rate nominally non-premixed swirl flame in a gas turbine model combustor in agreement with experimental measurements.

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.

Sensible-Enthalpy-Based Conditional Moment Closure Model for Homogeneous Charge Compression Ignition with Temperature Inhomogeneity

This paper presents a sensible-enthalpy-based conditional moment closure (CMC) model for homogeneous charge compression ignition (HCCI) with temperature inhomogeneity. The focus of study is placed on the effects of a conditioning variable on the prediction of heat release rates and developing the mixing models for sensible enthalpy, a reacting scalar. The sensible-enthalpy-based CMC model is validated a priori with 2-D direct numerical simulation (DNS) data for HCCI, and compared with the total-enthalpy-based formulation. Sensible enthalpy is shown to be strongly correlated with temperature, which makes sensible enthalpy well suited for a conditioning variable in CMC for HCCI. Results show that sensible-enthalpy-based CMC performs well for the prediction of heat release rates for all temperature stratification levels investigated in this study, while total-enthalpy-based CMC leads to the overprediction of heat release rates when the temperature stratification level is high. While conditional fluctuations of species mass fractions are substantial, sensible-enthalpy-based CMC is found to accurately estimate heat release rates during ignition, as well as reaction rates of key species, due to substantially suppressed conditional temperature fluctuations. The mapping closure models for the probability density function (PDF) and conditional dissipation rates of sensible enthalpy are proposed. The proposed models are found to capture the characteristics of reactive scalar mixing.

Large-eddy simulation of direct injection natural gas combustion in a heavy-duty truck engine using modified conditional moment closure model with low-dimensional manifold method

This article describes the application of a modified first-order conditional moment closure model used in conjunction with the trajectory-generated low-dimensional manifold method in large-eddy simulation of pilot ignited high-pressure direct injection natural gas combustion in a heavy-duty diesel engine. The article starts with a review of the intrinsic low-dimensional manifold method for reducing detailed chemistry and various formulations for the construction of such manifolds. It is followed by a brief review of the conditional moment closure method for modelling the interaction between turbulence and combustion chemistry. The high computational cost associated with the direct implementation of the basic conditional moment closure model was discussed. The article then describes the formulation of a modified approach to solve the conditional moment closure equation, whose reaction source terms for the conditional mass fractions for species were obtained by projecting the turbulent perturbation onto the reaction manifold. The main model assumptions were explained and the resulting limitations were discussed. A numerical experiment was conducted to examine the validity the model assumptions. The model was then implemented in a combustion computational fluid dynamics solver developed on an open-source computational fluid dynamics platform. Non-reactive jet simulations were first conducted and the results were compared to the experimental measurement from a high-pressure visualization chamber to verify that the jet penetration under engine relevant conditions was correctly predicted. The model was then used to simulate natural gas combustion in a heavy-duty diesel engine equipped with a high-pressure direct injection system. The simulation results were compared with the experimental measurement from a research engine to verify the accuracy of the model for both the combustion rate and engine-out emissions.

Investigation of Flame Structure and Soot Formation in a Single Sector Model Combustor Using Experiments and Numerical Simulations Based on the Large Eddy Simulation/Conditional Moment Closure Approach

In this work, a single sector lean burn model combustor operating in pilot only mode has been investigated using both experiments and computations with the main objective of analyzing the flame structure and soot formation at conditions relevant to aero-engine applications. Numerical simulations were performed using the large eddy simulation (LES) approach and the conditional moment closure (CMC) combustion model with detailed chemistry and a two-equation model for soot. The CMC model is based on the time-resolved solution of the local flame structure and allows to directly take into account the phenomena associated to molecular mixing and turbulent transport, which are of great importance for the prediction of emissions. The rig investigated in this work, called big optical single sector rig, allows to test real scale lean burn injectors. Experiments, performed at elevated pressure and temperature, corresponding to engine conditions at part load, include planar laser-induced fluorescence of OH (OH-PLIF) and phase Doppler anemometry (PDA) and have been complemented with new laser-induced incandescence (LII) measurements for soot location. The wide range of measurements available allows a comprehensive analysis of the primary combustion region and can be exploited to further assess and validate the LES/CMC approach to capture the flame behavior at engine conditions. It is shown that the LES/CMC approach is able to predict the main characteristics of the flame with a good agreement with the experiment in terms of flame shape, spray characteristics and soot location. Finite-rate chemistry effects appear to be very important in the region close to the injection location leading to the lift-off of the flame. Low levels of soot are observed immediately downstream of the injector exit, where a high amount of vaporized fuel is still present. Further downstream, the fuel vapor disappears quite quickly and an extended region characterized by the presence of pyrolysis products and soot precursors is observed. The strong production of soot precursors together with high soot surface growth rates lead to high values of soot volume fraction in locations consistent with the experiment. Soot oxidation is also very important in the downstream region resulting in a decrease of the soot level at the combustor exit. The results show a very promising capability of the LES/CMC approach to capture the main characteristics of the flame, soot formation, and location at engine relevant conditions. More advanced soot models will be considered in future work in order to improve the quantitative prediction of the soot level.

Modelling of Spray Flames with Doubly Conditional Moment Closure

Simulations of a pilot-stabilised flame in a uniformly dispersed ethanol spray are performed using a Doubly Conditional Moment Closure (DCMC) model. The DCMC equation for spray combustion is derived, using the mixture fraction and the reaction progress variable as conditioning variables, including droplet evaporation and differential diffusion terms. A set of closure sub-models is suggested to allow for a first, preliminary application of the DCMC model to the test case presented here. In particular, the DCMC model is used to provide complete closure for the Favre-averaged spray terms in the mean and variance equations of the conditioning variables and the present test case is used to assess the importance of each term. Comparison with experimental data shows a promising overall agreement, whilst differences are related to modelling choices.

Combustion Simulation of a Diesel Engine with Split Injections by Lagrangian Conditional Moment Closure Model

ABSTRACTThe Lagrangian conditional moment closure (CMC) model is applied to combustion simulation of a diesel engine at different load conditions. Calculation is performed by the free open-source computational fluid dynamics (CFD) package, OpenFOAM (Jasak, 1996). In Lagrangian CMC total injected fuel is divided into a given number of fuel groups with each group assumed to have the same residence time, consequently the same conditional flame structure. The Favre mean quantities are obtained by local conditional flame structures weighted by an assumed probability density function (PDF) through the improved beta-PDF integration method. Calculated pressure traces are compared with measurements in five operating conditions involving a single or multiple injections with different fuel mass ratios, rpms, swirl ratios, and exhaust gas recirculation (EGR) rates. The Lagrangian CMC model showed acceptable agreement with measured pressure traces and apparent heat release rates for all test cases. There was no improvement in the results by flame group interaction, which is considered not relevant in the given engine conditions.

Reacting Unsteady Reynolds-Averaged Navier–Stokes with the Tabulated Premixed Conditional Moment Closure Method

The tabulated premixed conditional moment closure model has shown the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable run times in a Reynolds-averaged Navier–Stokes formulation. The tabulated premixed conditional moment closure model is a table lookup combustion model that tabulates species, reaction rates, and thermodynamic data for use by the computational-fluid-dynamics code during run time. In this work, the tabulated premixed conditional moment closure model is extended to unsteady Reynolds-averaged Navier–Stokes. The new model is validated against particle image velocimetry and laser Raman measurements of an enclosed turbulent reacting methane jet from the German Aerospace Center. The flame’s reaction progress variable, its variance, and the scalar dissipation rate are calculated by the computational fluid dynamics in three dimensions. These three parameters are used to index detailed species information from the table for use by the computational-fluid-dynamics code. The scalar dissipation is used to account for the effects of the small-scale mixing, whereas a presumed shape beta function probability density function is used to account for the effects of large-scale turbulence on the reaction rates. Velocity, temperature, and major species are compared to the experimental data. Accurate predictions of the velocity fields were obtained, but accurate predictions of scalar quantities were limited by the adiabatic assumption of the tabulated premixed conditional moment closure model.

Lagrangian conditional moment closure model with flame group interaction for lifted turbulent spray jet flames

A new Lagrangian conditional moment closure (CMC) model is developed for multiple Lagrangian groups of sequentially evaporating fuel in turbulent spray combustion. Flame group interaction is taken into account as premixed combustion by the eddy breakup (EBU) model in terms of the probability of finding flame groups in the burned and the unburned state. Evaporation source terms are included in the two phase conditional transport equations, although they turn out to have negligible influence on the mean temperature field during combustion. The Lagrangian CMC model is implemented in OpenFOAM [1] and validated for test cases in the Engine Combustion Network (ECN) [2,3]. Similar ignition delays and lift-off lengths are predicted by the incompletely stirred reactor (ISR) and the Eulerian CMC models due to relatively uniform conditional flame structure in the domain. The improved Lagrangian CMC model shows no abrupt reaction or oscillatory behaviour with an appropriate model constant K and gives results in better agreement with measurements lying between the predictions by ISR and Lagrangian CMC without flame group interaction.

Doubly conditional moment closure modelling for HCCI with temperature inhomogeneities

This paper presents a doubly conditional moment closure (DCMC) as an a posteriori predictive modelling tool for ignition of mixtures with large thermal stratification in homogeneous charge compression ignition (HCCI) conditions. Double conditioning is applied on enthalpy and its dissipation rate. The performance of the DCMC model is evaluated using a number of previously reported direct numerical simulations (DNSs) with various fuels. The DNSs modelled ignition of various lean homogeneous mixtures with a high level of temperature inhomogeneities. The selected cases exhibit a prevalence of deflagration mode of combustion as opposed to a spontaneous ignition-front mode, which has proven challenging for previous singly CMC. In all simulations, DCMC solver is run in a stand-alone mode with certain terms, such as the probability density functions of enthalpy and dissipation rate, being provided using the DNS input. The DCMC results are in a very good agreement with the DNS data, and are significantly improved compared with a singly conditional moment closure. A set of a posteriori DNS-DCMC tests is also performed to demonstrate importance of various terms in the doubly CMC equations. These tests first reveal that the effects of the cross dissipation and sources of enthalpy and dissipation rate (which lead to convective terms in conditional space) are insignificant and these terms can be safely neglected from the DCMC equations. The significance of this result is that the main unclosed models that would be needed for satisfactory results in a practical simulation of an engine would be the joint probably density function of enthalpy and its dissipation rate and the dissipation rate of dissipation rate.

LES-CMC simulations of a turbulent hydrogen jet in oxy-combustion regimes

The paper presents the results of numerical simulations of a combustion process for a pure hydrogen jet in the atmosphere of oxygen and water vapor. The research was performed using Large Eddy Simulations (LES) combined with Conditional Moment Closure (CMC) model and included the analysis of auto- and forced (spark) ignition, flame development and flame propagation. In the configuration analyzed in the study, the fuel jet issues into a hot co-flowing oxidizer stream (O2/H2O). We considered two different co-flow temperatures, 1030 K and 1045 K, and various oxidizer compositions with H2O mass fraction over the range of Y H2O=0.1−0.9 and with YO2=1−YH2O. The analyses were carried out with assuming constant 30% excess of the mass flow rate of oxygen relative to the hydrogen. It was found that: (i) the auto-ignition process occurs only for a low content of H2O in the co-flow (YH2O≤0.5), (ii) and is additionally determined by its temperature; (iii) depending on O2/H2O proportion the flames stabilizes as attached or lifted. By alteration of YH2O in the oxidizer, the maximum flame temperature and the lift-off height (LH) can be changed in the range of 1500K→3000K and LH=0→11 jet diameters, respectively.

Prediction of Global Extinction Conditions and Dynamics in Swirling Non-premixed Flames Using LES/CMC Modelling

The Large Eddy Simulation (LES)/three-dimensional Conditional Moment Closure (CMC) model with detailed chemistry is applied to predict the operating condition and dynamics of complete extinction (blow-off) in swirling non-premixed methane flames. Using model constants previously selected to provide relatively accurate predictions of the degree of local extinction in the piloted jet flames Sandia D −F, the error in the blow-off air velocity predicted by LES/3D-CMC in short, recirculating flames with strong swirl for a range of fuel flow rates is within 25 % of the experimental value, which is considered a new and promising result for combustion LES that has not been applied before for the prediction of the whole blow-off curve in complex geometries. The results also show that during the blow-off transient, the total heat release gradually decreases over a duration that agrees well with experiment. The evolution of localized extinction, reactive scalars and scalar dissipation rate is analyzed. It has been observed that a consistent symptom for flames approaching blow-off is the appearance of high-frequency and high-magnitude fluctuations of the conditionally filtered stoichiometric scalar dissipation rate, resulting in an increased fraction of local extinction over the stoichiometric mixture fraction iso-surfaces. It is also shown that the blow-off time changes with the different blow-off conditions.

Modelling of methanol and H2/CO bluff-body flames using RANS based turbulence models with conditional moment closure model

In this article, conditional moment closure model (CMC) along with four variants of RANS turbulence models has been used for investigating methanol and H2/CO bluff-body flames. This work was attempted to establish the accuracy of turbulence models in predicting the mixing fields. Accurate mixing field ensured an accurate prediction of probability density function (PDF) of the mixture fraction field which was used to obtain unconditional quantities from the conditional quantities calculated from the CMC closure. The flow and mixing field were calculated using ANSYS Fluent software by incorporating four different turbulence models viz. standard k–ε (SKE), modified k–ε (MKE), re-normalization group (RNG) k–ε and Reynolds stress turbulence models. Flow field simulations have been coupled with an in-house CMC solver to obtain the mean flame structure. Predicted mixture fraction profile, obtained using Reynolds stress turbulence model showed an excellent agreement against the experimental data. The unconditional mean temperature and species mass fraction obtained from the CMC model showed improved predictions when coupled with the Reynolds stress turbulence models for both the flames. However, conditional quantities were almost independent of the turbulence models tested.