Effects of hydrogen addition on structure and NO formation of highly CO-Rich syngas counterflow nonpremixed flames under MILD combustion regime

The present study has numerically investigated the Moderate or Intense Low oxygen Dilution (MILD) combustion regime, combustion processes and NO formation characteristics of the highly CO-rich syngas counterflow nonpremixed flames. To realistically predict the flame properties of the highly CO-rich syngas, the chemistry is represented by the modified GRI 3.0 mechanism. Computations are performed to precisely analyze the flame structure, NO formation rate, and EINO of each NO sub-mechanism. Numerical results reveal that the hydrogen enrichment and oxygen augmentation substantially influence the NO emission characteristics and the dominant NO production route in the CO-rich syngas nonpremixed flames under MILD and high temperature combustion regimes. It is found that the most dominant NO production routes are the NNH path for the lowest oxygen level (3%) and the thermal mechanism for the highest O₂ condition (21%). For the intermediate oxygen level (9%), the most dominant NO production routes are the NNH route for the hydrogen fraction up to 5%, the CO₂ path for the hydrogen fraction range from 5% to 10% and the thermal mechanism for the hydrogen fraction higher than 10%, respectively. To evaluate the contribution of the specific reaction on EINO the sensitivity coefficients are precisely analyzed for NO formation processes with the dominance of NNH/CO₂/Thermal mechanism under the highly CO-rich syngas flames.     

Studies on properties of laminar premixed hydrogen-added ammonia/air flames for hydrogen production

In order to evaluate the potential of burning and reforming ammonia as a carbon-free fuel in production of hydrogen, fundamental unstretched laminar burning velocities, and flame response to stretch (represented by the Markstein number) for laminar premixed hydrogen-added ammonia/air flames were studied both experimentally and computationally. Freely (outwardly)-propagating spherical laminar premixed flames at normal temperature and pressure were considered for a wide range of global fuel-equivalence ratios, flame stretch rates (represented by the Karlovitz number) and the extent of hydrogen substitution. Results show the substantial increase of laminar burning velocities with hydrogen substitution, particularly under fuel-rich conditions. Also, predicted flame structures show that the hydrogen substitution enhances nitrogen oxide (NO_x) and nitrous oxide (N₂O) formation. At fuel-rich conditions, however, the amount of NO_x and N₂O emissions and the extent of the increase with the hydrogen substitution are much lower than those under fuel-lean conditions. These observations support the potential of hydrogen as an additive for improving the burning performance with low NO_x and N₂O emissions in fuel-rich ammonia/air flames and hence the potential of using ammonia as a clean fuel. Increasing the amount of added hydrogen tends to enhance flame sensitivity to stretch.     

Study on stretch extinction limits of CH4/CO2 versus high temperature O2/CO2 counterflow non-premixed flames

Extinction limits of counterflow non-premixed flames with normal and high temperature oxidizers were studied experimentally and numerically for development of new-type oxygen-enriched mild combustion furnace. Extinction stretch rates of CH₄/CO₂ (at 300 K) versus O₂/CO₂ flames at oxygen mole fractions of 0.35 and 0.40 and oxidizer temperatures of 300 K, 500 K, 700 K and 1000 K were obtained. Investigation was also conducted for CH₄/N₂ (at 300 K) versus air (O₂/N₂) flames at the same oxidizer temperatures. An effect of radiative heat loss on stretch extinction limits of oxygen-enriched flames and air flames was investigated by computations with optical thin model (OTM) and adiabatic flame model (ADI). The results show influence of radiative heat loss on stretch extinction limits was not significant in relative high fuel mole fraction regions. The extinction curve of the oxygen-enriched flames with oxygen mole fraction of 0.35 was close to that of the air flames at the oxidizer temperature of 300 K. However, the extinction curve of air flames with high temperature oxidizer was comparable with that of oxygen-enriched flames with oxygen mole fraction of 0.40. Scaling analysis based on asymptotic solution of stretch extinction was applied and it was found that stretch extinction limits can be expressed by two terms. The first term is total enthalpy flux of fuel stream based on thermo-physical parameters. The second term is a kinetic term which reflects an effect of the chemical reaction rate on stretch extinction limits. OH radicals which play important roles in chain propagating and main endothermic reactions were used to represent the kinetic term of both oxygen-enriched and air flames. The global rates of OH formation in these two cases were compared to understand the contribution of kinetic term to stretch extinction limits. Variation of extinction curves of oxygen-enriched flames and air flames was well explained by the present scaling analysis. This offers an effective approach to estimate stretch extinction limits of oxygen-enriched flames based on those of air flames at the same oxidizer temperature.     

The effects of hydrogen addition on soot formation in counterflow diffusion n-heptane flames

The effects of H₂ addition on soot formation are investigated in counterflow diffusion n-heptane flames. Three effects including chemical, thermal, and dilution are fully isolated and characterized by additions of H₂, He, and Ar. Soot volume fractions are measured using LE-calibrated LII technique, and flame temperatures are measured using OH-TLAF method along with a thermocouple. Numerical simulations are conducted with a detailed mechanism with soot model. The simulated soot volume fractions and flame temperatures are in good agreement with experimental data. The experimental results show that H₂ addition can greatly reduce the soot formation. It is also found that the chemical and dilution effects suppress soot formation, while the thermal effect with increasing flame temperature promotes soot formation. Kinetic analysis suggests that HACA growth rate could be the dominant factor that controls the final soot formation through the three effects due to H₂ addition.     

Effects of ammonia substitution on hydrogen/air flame propagation and emissions

In order to evaluate the potential of partial ammonia substitution to improve the safety of hydrogen use and the effects on the performance of internal combustion engines, the propagation, development of surface cellular instability and nitrogen oxide (NO_x) and nitrous oxide (N₂O) emissions of spark-ignited spherical laminar premixed ammonia/hydrogen/air flames were studied experimentally and computationally. With ammonia being the substituent, the fundamental unstretched laminar burning velocities and Markstein numbers, the propensity of cell formation and the associated flame structure were determined. Results show substantial reduction of laminar burning velocities with ammonia substitution in hydrogen/air flames, similar to hydrocarbon (e.g., methane with a similar molecular weight to ammonia) substitution. In all cases, ammonia substitution enhances the NO_x and N₂O formation. At fuel-rich conditions, however, the amount of NO_x emissions increases and then decreases with ammonia substitution and the increased amount of NO_x and N₂O emissions with ammonia substitution is much lower than that under fuel-lean conditions. These observations support the potential of ammonia as a carbon-free, clean additive for improving the safety of hydrogen use with low NO_x and N₂O emissions in fuel-rich hydrogen/air flames. The potential of ammonia as a suppressant of both preferential-diffusional and hydrodynamic cellular instabilities in hydrogen/air flames was also found particularly for fuel-lean conditions, different from methane substitution. However, it should be noted that the use of ammonia also imposes considerable technological challenges and public concerns, particularly those associated with toxicity and the specific properties such as high reactivity with container materials and water, which should be completely resolved.     

Effect of sodium bicarbonate particle size on the extinction condition of non-premixed counterflow flames

The effect of chemically active sodium bicarbonate (NaHCO₃) particles and inert silica particles on suppression of laminar, non-premixed counterflow methane-air flames is investigated. In experiments, the NaHCO₃ particles are separated into size ranges of <10, 10-20, 20-30, and 40-60 μm and are introduced with the air stream using two types of particle seeders. To distinguish physical effects from chemical effects of particles on flame extinction condition, inert silica particles of similar size ranges are also used as control experiments. Counterflow flame extinction results suggest that NaHCO₃ particles below 10 μm are equally effective as the 10-20 μm particles, while 20-30 μm particles are only half as effective. Unlike previously reported non-monotonic variation in effectiveness with particle size, the present results do not indicate a reversal in effectiveness, for the particle size range investigated. The observed experimental trends on NaHCO₃ particle size are analyzed using a numerical model that includes interactions between the particles and the gas-phase flame. In the present numerical model, a global particle decomposition step is assumed and the need for a comprehensive particle decomposition model is identified.     

Characteristics of turbulent nonpremixed jet flames under normal- and low-gravity conditions

An experimental study was performed with the aim of investigating the structure of transitional and turbulent nonpremixed jet flames under different gravity conditions. Experiments were conducted under three gravity levels, viz., 1 g, 20 mg, and 100 μg. The milligravity and microgravity conditions were achieved by dropping a jet-flame rig in the University of Texas at Austin 1.25-s and NASA-Glenn Research Center 2.2-s drop towers, respectively. The flames studied were piloted nonpremixed propane, ethylene, and methane jet flames at source Reynolds numbers ranging from 2000 to 10,500. The principal diagnostic employed was time-resolved cinematographic imaging of the visible soot luminosity. Mean and root-mean-square (RMS) images were computed, and volume rendering of the image sequences was used to investigate the large-scale structure evolution and flame tip dynamics. The relative importance of buoyancy was quantified with the parameter, ξL, as defined by Becker and Yamazaki (Combust. Flame 33 (1978) 123-149). The results showed, in contrast to some previous microgravity studies, that the high-Reynolds-number flames have the same flame length irrespective of the gravity level. The mean and RMS luminosity images and the volume renderings indicate that the large-scale structure and flame tip dynamics are essentially identical to those of purely momentum-driven flames provided ξL is less than approximately 2-3. The volume renderings show that the luminous structure velocities (i.e., celerities) normalized by the jet exit velocity are approximately constant for ξL<6, but scale as for ξL>8. The flame length fluctuation measurements and volume renderings also indicate that the luminous structures are more organized in low gravity than in normal gravity. Finally, taken as a whole, this study shows that ξL is a sufficient parameter for quantifying the effects of buoyancy on the fluctuating and mean characteristics of turbulent jet flames.     

Suppression limits of low strain rate non-premixed methane flames

The suppression of low strain rate non-premixed flames was investigated experimentally in a counterflow configuration for laminar flames with minimal conductive heat losses. This was accomplished by varying the velocity ratio of fuel to oxidizer to adjust the flame position such that conductive losses to the burner were reduced and was confirmed by temperature measurements using thermocouples near the reactant ducts. Thin filament pyrometry was used to measure the flame temperature field for a curved diluted methane-air flame near extinction at a global strain rate of 20 s⁻¹. The maximum flame temperature did not change as a function of position along the curved flame surface, suggesting that the local agent concentration required for suppression will not differ significantly along the flame sheet. The concentration of N₂, CO_2, and CF₃Br added to the fuel and the oxidizer streams required to obtain extinction was measured as a function of the global strain rate. In agreement with previous measurements performed under microgravity conditions, limiting non-premixed flame extinction behavior in which the agent concentration obtained a value that insures suppression for all global strain rates was observed. A series of extinction measurements varying the air:fuel velocity ratio showed that the critical N₂ concentration was invariant with this ratio, unless conductive losses were present. In terms of fire safety, the measurements demonstrate the existence of a fundamental limit for suppressant requirements in normal gravity flames, analogous to agent flammability limits in premixed flames. The critical agent volume fraction in the methane fuel stream assuring suppression for all global strain rates was measured to be 0.841 ± 0.01 for N₂, 0.773 ± 0.009 for CO₂, and 0.437 ± 0.005 for CF₃Br. The critical agent volume fraction in the oxidizer stream assuring suppression for all global strain rates was measured as 0.299 ± 0.004 for N₂, 0.187 ± 0.002 for CO₂, and 0.043 ± 0.001 for CF₃Br.     

Experimental investigation of premixed combustion limits of hydrogen and methane additives in ammonia

In this study, a specially designed premixed combustion chamber system for ammonia-hydrogen and methane-air laminar premixed flames is introduced and the combustion limits of ammonia-hydrogen and methane-air flames are explored. The measurements obtained the blow-out limits (mixed methane: 400–700 mL/min, mixed hydrogen: 200–700 mL/min), mixing gas lean limit characteristics (mixed methane: 0–82%, mixed hydrogen: 0–37%) and lean/rich combustion characteristics (mixed methane: ? = 0.6–1.9, mixed hydrogen: ? = 0.9–3.2) of the flames. The results show that the ammonia-hydrogen-air flame has a smaller lower blow-out limit, mixing gas ratio, lean combustion limit and higher rich combustion limit, thereby proving the advantages of hydrogen as an effective additive in the combustion performance of ammonia fuel. In addition, the experiments show that increasing the initial temperature of the premixed gas can expand the lean/rich combustion limits of both the ammonia-hydrogen and ammonia-methane flames.     

A computational study of oscillatory extinction of spherical diffusion flames

The transient behavior of burner-supported spherical diffusion flames was studied in the transport-induced limit of low mass flow rate and the radiation-induced limit of high mass flow rate which characterize the isola response of flame extinction. Oscillatory instability was observed near both steady-state extinction limits. The oscillation typically grows in amplitude until it becomes large enough to extinguish the flame. The oscillatory behavior was numerically observed using detailed chemistry and transport for methane (50%CH₄/50%He into 21%O₂/79%He) and hydrogen (100% H₂ into 21%O₂/79%He) diffusion flames where the fuel was issued from a point source, and helium was selected as an inert to increase the Lewis number, facilitating the onset of oscillation. In both methane and hydrogen flames, the oscillation always leads to extinction, and no limit cycle behavior was found. The growth rate of the oscillation was found to be slow enough under certain conditions to allow the flame to oscillate for over 450 s, suggesting that such oscillations can possibly be observed experimentally. For the hydrogen flames, however, the frequency of oscillation near the transport-induced limit is much larger, approximately 60 Hz as compared to 0.35 Hz for the methane flame, and the maximum amplitude of temperature oscillations was about 5 K. The distinctively different structures of the hydrogen and methane flames suggest that while both instabilities are thermal-diffusive in origin, oscillations in the hydrogen flames resemble those of premixed flames, while oscillations in the methane flames are non-premixed in character.     

Combustion performances of premixed ammonia/hydrogen/air laminar and swirling flames for a wide range of equivalence ratios

Ammonia, a carbon-free source of hydrogen has recently gained considerable attention as energy solution towards a green future. Previous works have shown that adding 30_VOL.% hydrogen with ammonia can eradicate the drawbacks of pure ammonia combustion but no study in the literature has investigated this blend across a wide range of equivalence ratios. The present work investigates 70/30_VOL.% NH₃/H₂ blend from 0.55 ≤ Φ ≤ 1.4 for both premixed laminar spherically expanding flames and turbulent swirling flames at atmospheric conditions. A detailed chemistry analysis has been conducted in Ansys CHEMKIN-PRO platform using a chemical reactor network (CRN) model to simulate the swirling turbulent flames. NO and NO₂ emissions have followed similar bell-shaped trends, peaking at around Φ = 0.8, while N₂O emission rises at lean conditions (Φ ≤ 0.7). The results indicate that Φ = 1.2 is the optimum equivalence ratio with reduced NO_X emissions and some ammonia slip.     

Kinetic incentive of hydrogen addition on nonpremixed laminar methane/air flames

In order to find out the respective influences of chemical reactivity and physical transport of hydrogen additive on nonpremixed flame, two fabricated hydrogen additions were introduced into nonpremixed methane/air flame modeling. Hydrogen addition was assumed as inert gas or partial reactivity fuel to respectively explore the kinetic reasons by the three aspects: the elementary reaction route, heat release, and physical diffusion of hydrogen addition. The analyses were implemented in terms of OH and H production. Results showed that, hydrogen addition can enhance OH and H production via elementary reactions, and causes flame reaction zone migration through the coupling interaction between the low-temperature heat enthalpy release and diffusion behavior of hydrogen addition. R84 (OH + H₂=H + H₂O) and R38 (H + O₂=O + OH) are the most important elementary reactions related to OH and H production. The physical incentive of hydrogen addition can hardly work without the chemical effects of hydrogen addition.     

Premixed ammonia/hydrogen swirl combustion under rich fuel conditions for gas turbines operation

Energy storage is one of the highest priority challenges in transitioning to a low-carbon economy. Fluctuating, intermittent primary renewable sources such as wind and solar require low-carbon storage options to enable effective load matching, ensuring security of supply. Chemical storage is one such option, with low or zero carbon fuels such as hydrogen, alcohols and ammonia having been proposed. Ammonia provides zero-carbon hydrogen storage whilst offering liquefaction at relatively low pressures and atmospheric temperatures, enabling ease of transportation in a pre-existing infrastructure. Ammonia can also be used directly as a fuel in power plants such as gas turbines to avoid complete conversion back to hydrogen. It is a relatively unreactive fuel, and so it is of interest to explore the potential utilisation of ammonia/hydrogen mixtures. Hence, the goal of this paper is to provide a first assessment of the suitability of a chosen 70%NH₃30%H₂ (%vol) blend for utilisation within a gas turbine environment, based on primary combustion diagnostics including combustion stability – via OH chemiluminescence - and emissions (NO_x and NH₃). An established optical generic swirl-burner enabled studies of the influence of equivalence ratio (φ > 1), ambient temperature (<484 ± 10 K) and bypass air, with a focus on NO_x reduction, one of the main challenges for ammonia combustion. A numerical GT cycle model is developed alongside the experimental investigation. The results demonstrate that the blend has considerable potential as a fuel substitute with reasonable combustion stability and significant reduction of emissions for the cases without bypass air, due to increased chemical reactivity of unburned ammonia. However, emissions are still above those recommended for gas turbine cycles, with a theoretical cycle that still produces low efficiencies compared to DLN methane, highlighting the requirement for new injection techniques to reduce NO_x/unburned NH₃ in the flue gases whilst ensuring increased power outputs.     

Chemical structure and laminar burning velocity of atmospheric pressure premixed ammonia/hydrogen flames

This paper presents experimental data on the flame structure of laminar premixed ammonia and ammonia/hydrogen flames at different equivalence ratios (φ = 0.8, 1.0 and 1.2) and the laminar flame speed of ammonia/hydrogen flames (φ = 0.7–1.5) at 1 atm. Experimental data were compared with modeling results obtained using four detailed chemical-kinetic mechanisms of ammonia oxidation. In general, all models adequately predict the flame structure. However, for the laminar burning velocity, this is not so. The main nitrogen-containing species present in the post-flame zone in significant concentrations are N₂ and NO. Experimental data and numerical simulations show that the transition to slightly rich conditions enables to reduce NO concentration. Numerical simulation indicate that increasing the pressure rise also results into reduction of NO formation. However, when using ammonia as a fuel, additional technologies should be employed to reduce NO formation.     

NTC-affected ignition and low-temperature flames in nonpremixed DME/air counterflow

An experimental study, supported by computation, was conducted on the coupling of NTC-chemistry and transport in the low-temperature ignition and the associated steady burning in nonpremixed DME/air counterflow. In particular, the presence of low-temperature chemical reactivity was detected nonintrusively by using a photomultiplier tube combined with a filter to capture the chemiluminescence of HCHO, which is a characteristic intermediate species formed in low-temperature chemistry. Furthermore, the ignition temperature was determined through high-sensitivity infrared imaging with proper discrimination of the background signal. Experimental results show that the transport-coupled low-temperature, NTC chemical reactivity is enhanced with smaller strain rate, higher air boundary temperature, and is insensitive to the fuel concentration. These findings agree well with those obtained from computation using detailed chemistry, leading to further identification of the controlling chemistry.     

Effects of turbulence on nonpremixed ignition of hydrogen in heated counterflow

Experiments were conducted to determine the effects of turbulence on the temperature of a heated air jet required to ignite a counterflowing cold hydrogen/nitrogen jet. In contrast to pseudo-turbulent flows, where turbulence was generated by only a perforated plate on the fuel side, resulting in little effect on ignition in a hydrogen system, fully turbulent flows with perforated plates on both sides of the flow were found to produce noticeable effects. The difference was attributed to the fact that in fully turbulent flows, a significantly larger range of turbulent eddies extend to smaller scales than in pseudo-turbulent flows. At atmospheric pressure, the lowest turbulence intensity studied had ignition temperatures notably lower than laminar ones, while further increases in turbulence intensity resulted in rising ignition temperatures. As a result, optimal conditions for nonpremixed hydrogen ignition exist in weakly turbulent flows where the ignition temperature is lower than can be obtained in other laminar or turbulent flows at the same pressure. Similar trends were seen for all fuel concentrations and at all pressures in the second ignition limit (below 3-4 atm). At higher pressures, turbulent flows caused the ignition temperatures to continue to follow the second limit resulting in ignition temperatures higher than the laminar values. The extension of the second limit ends at the highest pressures (7 to 8 atm) where evidence of third limit behavior appears. Three mechanisms were noted to explain the experimental results. First, turbulent eddies similar in size to the ignition kernel can promote discrete mixing of otherwise isolated pockets of gas. Second, this mixing can promote HO₂ chain branching pathways, which can account for the enhanced ignition noted in the second limit where reaction is governed by crossover temperature chemistry. Third, turbulence limits the excursion times available for reaction, inordinately affecting the slower HO₂ reactions. This is responsible for the increasing ignition temperature with turbulence intensity and pressure.     

Conditional moment closure prediction of soot formation in turbulent, nonpremixed ethylene flames

Results obtained from incorporating a semiempirical soot model into a first-order conditional moment closure (CMC) approach to modeling turbulent nonpremixed flames of ethylene and air are presented. Soot formation is determined via the solution of two transport equations for soot mass fraction and particle number density, with acetylene and benzene employed as the incipient species responsible for soot nucleation, and the concentrations of these species calculated using a detailed gas-phase kinetic scheme involving 463 reactions and 70 species. The study focuses on the influence of differential diffusion of soot particles on soot volume fraction predictions. The results of calculations are compared with experimental data for three sooting ethylene flames and, in general, predictions of mixing and temperature fields within the three flames show good agreement with data. Soot volume fraction predictions are found to be in significantly better accord with data when differential diffusion is accounted for in the CMC-based soot model, supporting the importance of such effects in sooting flames, as previously noted by Kronenburg et al. in relation to methane combustion. Overall, the study demonstrates that the CMC-based soot model, when used in conjunction with a model of differential diffusion effects, is capable of accurately predicting soot formation in turbulent nonpremixed ethylene-air flames.     

Effects of strain rate on high-pressure nonpremixed n-heptane autoignition in counterflow

The effect of steady strain on the transient autoignition of n-heptane at high pressures is studied numerically with detailed chemistry and transport in a counterflow configuration. Skeletal and reduced n-heptane mechanisms are developed and validated against experiments over a range of pressure and stoichiometries. Two configurations are investigated using the skeletal mechanism. First, the effect of strain rate on multistage n-heptane ignition is studied by imposing a uniform temperature for both the fuel and the oxidizer streams. Second, a temperature gradient between the fuel and the oxidizer streams is imposed. The global effect of strain on ignition is captured by a Damköhler number based on either the heat-release rate or the characteristic chain-branching rate. Results show that for low to moderate strain rates, both the low- and intermediate-temperature chemistries evolve in a manner comparable to that in homogeneous systems, including the negative temperature coefficient regime, but with somewhat slower evolution attributable to diffusive losses. At high strain rates diffusive losses inhibit ignition; for two-stage ignition, it is found that ignition is inhibited during the second, intermediate-temperature stage. The imposition of an overall temperature gradient further inhibits ignition because reaction zones for key branching reactions with large activation energies are narrowed. For a fixed oxidizer stream temperature that is not sufficiently high, a higher fuel temperature results in a shorter ignition delay provided that the heptyl radicals are mainly oxidized by low-temperature chemistry. As expected, an increase in pressure significantly increases reaction rates and reduces ignition delay time. However, with increasing pressure there is a shift toward single-stage low-temperature-dominated ignition which serves to delay ignition.     

Prediction of the liftoff,blowout and blowoff stability limits of pure hydrogen and hydrogen/hydrocarbon mixture jet flames

The paper presents experimental studies of the liftoff and blowout stability parameters of pure hydrogen, hydrogen/propane and hydrogen/methane jet flames using a 2 mm burner. Carbon dioxide and Argon gas were also used in the study for the comparison with hydrocarbon fuel. Comparisons of the stability of H₂/C₃H₈, H₂/CH₄ and H₂/CO₂ flames showed that H₂/C₃H₈ produced the highest liftoff height and H₂/CH₄ required highest liftoff, blowoff and blowout velocities. The non-dimensional analysis of liftoff height was used to correlate liftoff data of H₂, H₂/C₃H₈, H₂/CO₂, C₃H₈ and H₂/Ar jet flames tested in the 2 mm burner. The suitability of extending the empirical correlations based on hydrocarbon flames to both hydrogen and hydrogen/hydrocarbon flames was examined.     

Modeling extinction and reignition in turbulent flames

The conditional moment closure method (CMC) has been extended to improve reactive species predictions in flames with significant local extinction and reignition. Simple first-order closure of the conditionally averaged reaction rate term does not give satisfactory results due to large fluctuations around the conditional mean and an alternative closure is suggested here. The new closure is based on a precomputed parameterized reference field that maps reactive species mass fractions as functions of mixture fraction and sensible enthalpy. During the computations, the reference field is continuously adjusted to ensure consistency with the CMC solution and doubly conditioned chemical source terms that are functions of time, space, mixture fraction, and sensible enthalpy can thus be obtained. Integration over sensible enthalpy space yields the improved singly conditioned chemical source term that can be used for the solution of the CMC equations. Full closure can be achieved by assuming a β-PDF for the probability distribution in sensible enthalpy space and an additional conditional variance equation needs to be solved. The overall agreement between the measured and the computed variance is satisfactory and the extended CMC model is applied to Sandia Flames D, E, and F. Excellent predictions of temperature, major species, intermediates, and NO are obtained in Flames D and E while temperature predictions can be significantly improved in Sandia Flame F.