Mixture Fraction Pdf Research Articles

Modeling the presumed joint probability density function of conditioning variables in stratified turbulent flames

Experimental data from the Cambridge-Sandia burner are used to calculate the conditional average of temperature and the mass fractions of H2O, CO, and CO2 in the context of the Uniform Conditional State (UCS) model. The performance of various presumed joint PDF models are examined for this burner working with different swirl and stratification levels. All of the presented PDF models are based on a few statistical moments of the conditioning variables which are extracted from the data at each measuring point. Primarily, only mixture fraction and reaction progress variable are employed as the conditioning variables. The β function is employed for modeling the marginal PDF of mixture fraction in all cases. For the progress variable, the β function and Modified Laminar Flamelet (MLF)-PDF are tested for modeling the marginal PDF. It is shown that even though the MLF-PDF results in more accurate predictions overall for most of the cases, its superiority with respect to the β-PDF is relatively small in the stratified flames. The performance of the product, Plackett, and Gaussian copulas are also investigated for employing the cross-correlation of mixture fraction and progress variable in building their joint PDF. It is found that the Gaussian copula shows a superior performance over the other two. Next, normalized total enthalpy is employed as a third conditioning variable, and different PDF models are examined for the three-condition version of UCS. It is found that even though adding the third conditioning variable can improve the predictions by considering the effect of heat transfer on the chemistry manifold, such improvements depend on having a proper 3D PDF model for the conditioning variables. In the vicinity of the flame brush, the models employed for the 3D PDFs represent an inferior performance compared to the two-condition version with the use of a Gaussian copula due to complications in the marginal PDF of normalized total enthalpy in these regions. To benefit from considering the impact of heat transfer on chemistry while also avoiding complexities in modeling the 3D joint PDF near the reaction zone, a switch between the two- and three-conditional models which is triggered by the variance of progress variable is proposed. It is shown that the predictions obtained by the use of this switch are almost always superior to all other PDF models investigated in this study.

Solution of the first-order conditional moment closure for multiphase reacting flows using quadrature-based moment methods

The quadrature-based semi-analytical solution for the conditional moment closure (SA-CMC) given in (A. D. Ilgun, A. Passalacqua, and R. O. Fox, “A quadrature-based conditional moment closure for mixing-sensitive reactions,” Chem. Eng. Sci., 226, 2020) eliminates the additional conditioning-space discretization in CMC applications by assuming that the mixture-fraction PDF is well represented by a β-PDF. A Gaussian quadrature provides the mixture-fraction abscissae, and the conditional scalar mean is expressed in terms of Jacobi polynomials. Here, by preserving the computational efficiency of SA-CMC, a novel quadrature-based moment method (QBMM-CMC) is developed for CMC applications, which does not assume the form of the mixture-fraction PDF. Remarkably, by solving the closed forms for the micromixing terms from CMC, exact expressions result for the mixture-fraction moments of any order. Thus, QBMM-CMC covers cases where the mixture-fraction PDF cannot be well represented by a β-PDF and can be applied to disperse multiphase flows with mass transfer (e.g., droplet evaporation). For single-phase and multiphase pure-mixing problems, the QBMM-CMC mixture-fraction moments are observed to deviate from the β-PDF. For single-phase mixing with and without dispersed-phase mass transfer, QBMM-CMC predictions for mixing-sensitive competitive-consecutive and parallel reactions are investigated parametrically.

Injection Type Effects on Pulverized Biomass (solid olive waste) Combustion in a 50 kW Combustor

The paper describes a 3D numerical simulation of pulverized solid olive waste (OW) combustion in a vertical combustor. This study is developed, in order to design a new efficient burner which operates with olive waste as a biomass fuel. Two types of injection modes are studied. The first named (R) where the biomass particles is perpendicularly injected to symmetric axis close to the co-flow entry by four injection square shape tubes and the second named (P) where particles are injected in parallel to the furnace central axis. The mean diameter of the pulverized particles is about 70 µm. The designed system is a vertical cylindrical furnace with swirling co-flow burner entry. The k-Iµ, mixture fraction PDF and discrete phase DPM models are used for turbulence closure, turbulence-chemistry interactions and tracking the particle motion respectively. Results show that the flame is more stabilized in the recirculation zones and achieved the higher temperature at 1560 K for (R) case. The particles residence time inside to the combustor is very important for the (R) case in comparison to (P) case. The analyses and comparison of the formed species for CO, CO 2 and NOx formation profiles at several longitudinal locations between (R) and (P) cases are performed.

Fluid age-based analysis of a lifted turbulent DME jet flame DNS

The link between the distribution of fluid residence time and the distribution of reactive scalars is analysed using Direct Numerical Simulation data. Information about the reactive scalar distribution is needed in order to model the reaction terms that appear in Large Eddy and Reynolds-Averaged simulations of turbulent reacting flows. The lifted flame is simulated taking account of multi-step chemistry for dimethyl-ether fuel. Due to autoignition and flame propagation, the reaction progress increases with residence time. The variation of fluid residence time is evaluated by solving an Eulerian transport equation for the fluid age. The fluid age is a passive scalar with a spatially-uniform source term, meaning that its moments and dissipation rates in turbulent flows can be modelled using closures already established for conserved scalars such as mixture fraction. In combination with the mixture fraction, the fluid age serves as a useful mapping variable to distinguish younger less-reacted fluid near the inlet from older more-reacted fluid downstream. The local fluctuations of mixture fraction and fluid age have strong negative correlation and, building upon established presumed-pdf models for mixture fraction, this feature can be used to construct an accurate presumed-pdf model for the joint mixture fraction/fluid age pdf. It is demonstrated that the double-conditional first-order moment closure combined with the proposed presumed model for the joint pdf of mixture fraction and fluid age gives accurate predictions for unconditional reaction rates – both for pre-ignition radical species produced by low-temperature processes upstream of the flame base, and for major species that are produced at the flame front.

An analytic model for the effects of nitrogen dilution and premixing characteristics on NOx formation in turbulent premixed hydrogen flames

Advanced hydrogen gas turbine is a promising technology to achieve near-zero emission of carbon dioxide and higher cycle efficiency. With the increased firing temperature and pressure ratio, nitrogen reinjection combined with dry premixed combustion is promising to achieve the challenging low NOx emission. In this study, the effects of nitrogen dilution and fuel/air premixing characteristics on the flame characteristics and NOx emission are investigated first through simulating one-dimensional premixed flames with a 13-species and 39-reaction mechanism at the elevated engine operation conditions. The variation of flame thicknesses and laminar flame speeds with nitrogen dilution is investigated. The NOx formation is characterized by the flame-front NOx and the constant NOx formation rates in the post-flame region. It is shown that the flame-front NOx is an order of 1 ppm and does not change significantly (within 20%) with nitrogen dilution. In contrast, the NOx formation rates in the post-flame region decrease monotonically with nitrogen dilution due to the decrease of oxygen concentration. A detailed analysis of NOx formation reveals that the N2O pathway is significant and it can account for at least 20% of the NOx formation in the post-flame region. Then an analytic model considering both the extended Zeldovich mechanism and the N2O pathway is constructed by assuming the involved radicals being in chemical equilibrium. The model can be employed to efficiently estimate the NOx formation in fully premixed hydrogen gas turbines. Next, the effects of fuel/air premixing characteristics on the mean NOx formation rate in the post-flame region are quantified by reconstructing the PDF of mixture fraction. It is shown that without the nitrogen dilution, the NOx formation rate increases dramatically with fuel/air unmixedness due to the existence of local hot spots. Nitrogen dilution can dramatically reduce the NOx formation rate at the same level of unmixedness through reducing the local hot spots. Moreover, nitrogen dilution reduces the sensitivity of the NOx formation rate to fuel/air unmixedness, which greatly alleviates the mixing requirement for the premixing nozzles in gas turbines. Finally, a model for the estimation of NOx emission is constructed, which builds the connection between NOx emission, nitrogen dilution, unmixedness and flow residence time in combustors.

Direct numerical simulation of a supersonic lifted hydrogen jet flame: A priori study on combustion models

In this study, a systematic assessment of turbulent combustion submodels of conditional moment closure (CMC) has been conducted using DNS data of a three-dimensional spatially-developing supersonic lifted hydrogen flame with a Mach number of 1.2 at the jet injection. It has been found that Beta pdf of mixture fraction can well capture the mixing space of the high speed reacting flow. The linear model exhibits a good performance for the axial velocity predictions. Girimaji׳s model for scalar dissipation rate performs well at upstream, while the AMC model presents better further downstream. The first order closure for the conditional reaction rate deviates a lot from the DNS extracted results. Second-order corrections made to temperature only or to the two rate-limiting reaction steps induce improvement, still with much discrepancy. Second order closure considering fluctuations of all the reacting species and temperature can accurately reproduce the DNS results.

Inverse analysis and regularisation in conditional source-term estimation modelling

Conditional Source-term Estimation (CSE) obtains the conditional species mass fractions by inverting a Fredholm integral equation of the first kind. In the present work, a Bayesian framework is used to compare two different regularisation methods: zeroth-order temporal Tikhonov regulatisation and first-order spatial Tikhonov regularisation. The objectives of the current study are: (i) to elucidate the ill-posedness of the inverse problem; (ii) to understand the origin of the perturbations in the data and quantify their magnitude; (iii) to quantify the uncertainty in the solution using different priors; and (iv) to determine the regularisation method best suited to this problem. A singular value decomposition shows that the current inverse problem is ill-posed. Perturbations to the data may be caused by the use of a discrete mixture fraction grid for calculating the mixture fraction PDF. The magnitude of the perturbations is estimated using a box filter and the uncertainty in the solution is determined based on the width of the credible intervals. The width of the credible intervals is significantly reduced with the inclusion of a smoothing prior and the recovered solution is in better agreement with the exact solution. The credible intervals for temporal and spatial smoothing are shown to be similar. Credible intervals for temporal smoothing depend on the solution from the previous time step and a smooth solution is not guaranteed. For spatial smoothing, the credible intervals are not dependent upon a previous solution and better predict characteristics for higher mixture fraction values. These characteristics make spatial smoothing a promising alternative method for recovering a solution from the CSE inversion process.

Experimental and Numerical Study of the Scalar Turbulent/Non-Turbulent Interface Layer in a Jet Flow

Based on two large-eddy simulations (LES) of a non-reacting turbulent round jet with a nozzle based Reynolds number of 8,610 with the same configuration as the one that has recently been investigated experimentally (Gampert et al., 2012; J Fluid Mech, 2012; J Fluid Mech 724:337, 2013), we examine the scalar turbulent/non-turbulent (T/NT) interface layer in the mixture fraction field of the jet flow between ten and thirty nozzle diameters downstream. To this end, the LES—one with a coarse grid and one with a fine grid—are in a first step validated against the experimental data using the axial decay of the mean velocity and the mean mixture fraction as well as based on radial self-similar profiles of mean and root mean square values of these two quantities. Then, probability density functions (pdf) of the mixture fraction at various axial and radial positions are compared and the quality of the LES is discussed. In general, the LES results are consistent with the experimental data. However, in the flow region where the imprint of the T/NT interface layer is dominant in the mixture fraction pdf, discrepancies are observed. In a next step, statistics of the T/NT interface layer are studied, where a satisfactory agreement for the pdf of the location of the interface layer from the higher resolved LES with the experimental data is observed, while the one with the coarse grid exhibits considerable deviations. Finally, the mixture fraction profile across the interface is investigated where the same trend as for the pdf of the location is present. In particular, it is found that the sharp interface that is present in experimental studies (Gampert et al., J Fluid Mech, 2013; Westerweel et al., J Fluid Mech 631:199, 2009) is less distinct in the LES results and rather diffused in radial direction outside of the T/NT interface layer.

The role of turbulent fluctuations on radiative emission in hydrogen and hydrogen-enriched methane flames

A theoretical analysis is reported in the present work to quantify the increase of radiative emission due to turbulence for hydrogen and hydrogen-enriched methane diffusion flames burning in air. The instantaneous thermochemical state of the reactive mixture is described by a flamelet model along with a detailed chemical mechanism. The shape of the probability density function (pdf) of mixture fraction is assumed. The results show that turbulent fluctuations generally contribute to reduce the Planck mean absorption coefficient of the medium, in contrast with the blackbody emissive power, which is significantly increased by turbulence. If the turbulence level is relatively small, the influence of turbulence on the absorption coefficient is marginal. Otherwise, fluctuations of the absorption coefficient of the medium should be taken into account. The scalar dissipation rate and the fraction of radiative heat loss have a much lower importance than the turbulence intensity on the mean radiative emission.

Large eddy simulation of fire plumes

FireFOAM, a new fire modeling code based on the OpenFOAM platform ( www.openfoam.org), is developed and applied to model a series of purely buoyant fire plumes with heat release rates from 14 to 58 kW. The calculations are compared with McCaffrey’s (1979) experiments. The simulation results demonstrate good quantitative agreement with experimental measurements, and show the scaling relations of mean temperature and velocity in the continuous flame, intermittent and plume regions. The numerical simulations are shown to be strictly conservative in energy. Predicted flame heights and entrainment rates also compare well with experimental correlations. The good agreements in all aspects examined show that the current CFD model performs well for small-scale fire plumes. Turbulent fluctuation intensities and PDF of mixture fraction are presented to gain more insights into the structure of fire plumes.

LES of intermittency in a turbulent round jet with different inlet conditions

Large eddy simulation (LES) is a promising technique for accurate prediction of turbulent free shear flows in a wide range of applications. Here the LES technique has been applied to study the intermittency in a high Reynolds number turbulent jet with and without a bluff body. The objective of this work is to study the turbulence intermittency of velocity and scalar fields and its variation with respect to different inlet conditions. Probability density function distributions (pdf) of instantaneous mixture fraction and velocity have been created from which the intermittency has been calculated. The time averaged statistical results for a round jet are first discussed and comparisons of velocity and passive scalar fields between LES calculations and experimental measurements are seen to be good. The calculated probability density distributions show changes from a Gaussian to a delta function with increased radial distance from the jet centreline. The effect of introducing a bluff body into the core flow at the inlet changes the structure of pdfs, but the variation from Gaussian to delta distribution is similar to the jet case. However, the radial variation of the intermittency indicates differences between the results with and without a bluff body at axial locations due the recirculation zone created by the bluff body.

Large eddy simulation of forced ignition of an annular bluff-body burner

The optimization of the ignition process is a crucial issue in the design of many combustion systems. Large eddy simulation (LES) of a conical shaped bluff-body turbulent nonpremixed burner has been performed to study the impact of spark location on ignition success. This burner was experimentally investigated by Ahmed et al. [Combust. Flame 151 (2007) 366–385]. The present work focuses on the case without swirl, for which detailed measurements are available. First, cold-flow measurements of velocities and mixture fractions are compared with their LES counterparts, to assess the prediction capabilities of simulations in terms of flow and turbulent mixing. Time histories of velocities and mixture fractions are recorded at selected spots, to probe the resolved probability density function (pdf) of flow variables, in an attempt to reproduce, from the knowledge of LES-resolved instantaneous flow conditions, the experimentally observed reasons for success or failure of spark ignition. A flammability map is also constructed from the resolved mixture fraction pdf and compared with its experimental counterpart. LES of forced ignition is then performed using flamelet fully detailed tabulated chemistry combined with presumed pdfs. Various scenarios of flame kernel development are analyzed and correlated with typical flow conditions observed in this burner. The correlations between, velocities and mixture fraction values at the sparking time and the success or failure of ignition, are then further discussed and analyzed.

Multiple mapping conditioning for flames with partial premixing

Fully closed multiple mapping conditioning (MMC) is used to model partially premixed flames in homogeneous, isotropic decaying turbulence where the partial premixing is caused by local extinction and reignition phenomena. Two reference variables that represent mixing and reaction progress, such as mixture fraction and sensible enthalpy, are used to emulate turbulent scalar fluctuations. Local extinction is achieved by a priori coupling between scalar dissipation and temperature fluctuations via a correlation function that is based on the conditionally averaged sensible enthalpy at stoichiometric composition. The proposed model provides closures for the joint PDF of mixture fraction and sensible enthalpy, for the conditional variance equation of a reactive scalar, and for the doubly conditioned dissipation terms. Model results are compared with DNS in three flame cases with varying levels of local extinction, up to global extinction. The joint PDF predicted by MMC is in fair agreement with DNS. It constitutes, however, a clear improvement over conventional models using preassumed distribution functions for the PDFs. The doubly conditioned dissipation terms are modeled well and the results for all major chemical species are in good agreement with DNS. Predictions for intermediate species are also satisfactory.

Measurements and simulations of mixing and autoignition of an n-heptane plume in a turbulent flow of heated air

The autoignition of a gaseous n-heptane plume in heated turbulent air has been investigated experimentally and numerically with the conditional moment closure and a CFD code. It has been demonstrated that, consistent with previous experimental results for hydrogen and acetylene, the increased scalar dissipation rate created by faster co-flowing air delays autoignition, as revealed by a disproportionate increase of ignition length with air velocity. The predicted mean and variance of the mixture fraction, the mixture fraction PDF and the conditional scalar dissipation rate are in good agreement with experimental results obtained with acetone-tracer PLIF. The first-order, spatially averaged CMC model reproduces the experimental trends quite well, despite the neglect of conditional fluctuations and spatial dependence of the conditional averages. This is attributed to the fact that for a significant period of time before autoignition the conditional scalar dissipation rate at the most reactive mixture fraction is much smaller than the critical value above which autoignition is precluded.

Assumed PDF Modeling of Turbulent Spray Combustion

The present study is a new step in the attempt to extend an approach used in the modeling of gaseous turbulent combustion to spray turbulent combustion. Our attention is focused on the new random fluctuations created by the presence of the spray. The ideas developed here are based on the discussion presented by Borghi (1995). A local study of the equations allows us to find a closure for the new correlation term induced by spray evaporation in the equation for the variance of the mixture fraction. This was done without new assumptions, just by using the stochastic approach already developed in the KIVA II code to describe spray vaporization. We also show the importance of a new variable, Z,, which describes the initial state of an evaporated fluid particle. An equation for the PDF of this variable and for its mean value is also written in closed form. For the moment, its contribution to the mixture fraction PDF is taken into account through its average value. Finally we have tested our model with an experiment where one set of experimental conditions is close to the infinitely fast chemistry and another set of conditions demonstrates the effect of finite chemical kinetics. We have found a qualitative agreement between the measured data and our computational results. Further development should be done, for instance coupling this model with an atomization model to avoid any assumption about the first stages of the evaporation and combustion process.

Experiments on the scalar structure of turbulent CO/H 2/N 2 jet flames

Scalar and velocity measurements are reported for two turbulent jet flames of CO/H 2/N 2 (40/30/30 volume percent) having the same jet Reynolds number of 16,700 but different nozzle diameters (4.58 mm and 7.72 mm). Simultaneous measurements of temperature, the major species, OH, and NO are obtained using the combination of Rayleigh scattering, Raman scattering, and laser-induced fluorescence. Three-component laser-Doppler velocimetry measurements on the same flames were performed at ETH Zurich and are reported separately. This paper focuses on the scalar results but includes some limited velocity data. Axial profiles of mixture fraction, major species mole fractions, and velocity in these two flames are in close agreement when streamwise distance is scaled by nozzle diameter. However, OH mole fractions are lower and NO mole fractions are higher near the stoichiometric flame length in the larger flame due to the lower scalar dissipation rates and longer residence times. Turbulent flame measurements are compared with steady strained laminar flame calculations. Laminar calculations show remarkably close agreement with measured conditional means of the major species when all diffusivities are set equal to the thermal diffusivity. In contrast, laminar flame calculations that include the normal Chemkin treatment of molecular transport are clearly inconsistent with the measurements. These results suggest that turbulent stirring has a greater influence than molecular diffusion in determining major species concentrations at the flow conditions and locations considered in the present experiments, which begin at an axial distance of 20 nozzle diameters. Analysis of the conditional statistics of the differential diffusion parameter supports this conclusion, though some evidence of differential diffusion is observed. With regard to validation of turbulent combustion models, this data set provides a target that retains the geometric simplicity of the unpiloted jet flame in coflow, while including a chemical kinetic system of intermediate complexity between hydrogen flames and the simplest hydrocarbon flames. Aspects of the measurements, including Favre-averaged profiles, conditional statistics, mixture fraction pdf’s, and departures from partial equilibrium, are presented and discussed in terms or their relevance to the testing of turbulent combustion submodels. The complete data are available on the World Wide Web for use in model validation studies.

Mixing and reaction in curved liquid shear layers

The concentration field of mixing layers subject to stabilizing and destabilizing streamwise curvature was investigated at post-mixing-transition conditions. A set of operating conditions was implemented, identical to those at which straight layers were previously investigated in the same facility, in order to compare the effects of hydrodynamic instabilities upon scalar mixing. Quantitative imaging of planar laser-induced fluorescence was used for (i) passive scalar measurements, and (ii) chemical product measurements. Similar to the straight mixing layer, the results for the curved layers show that beyond the mixing transition the layer continues to evolve, and undergoes a small change in its scalar structure. At conditions just past the mixing transition both stable and unstable layers have average mixed-fluid compositions which are uniform across the layer, and average chemical product concentration profiles which are symmetric. At more fully developed conditions, the scalar field evolved: the average mixed-fluid concentration developed a small lateral variation, while the chemical product concentration profiles became asymmetric. Similar to the straight layer, the mixture-fraction PDF is believed to be of the tilted type for the most fully developed layer examined, with the marching PDF being a poor representation. Consistent with previous investigations, the growth rate of the unstable layer was found to be higher than that of straight or stable layers. The most important result is that the measured mixing efficiency of all the layers (curved and straight) was found to be the same: both the total mixed-fluid composition, and the volume fraction of mixed fluid were the same for all unstable, stable, and straight layers. The amount of mixed fluid (and of chemical product formed) was larger for the unstable layer, but always in a fixed proportion to the layer's thickness. The lack of increase in the mixing efficiency for the unstable layer is surprising, given that previous hydrodynamic measurements had shown enhanced turbulent transport for the unstable case. Thus, for all liquid shear layers studied, the rate of scalar mixing appears to be directly proportional to the entrainment rate (which essentially determines the layer's growth rate), and not to any hydrodynamic measures.

Interaction of turbulence and radiation in confined diffusion flames

A new approach for modeling turbulence-radiation interaction in confined diffusion flames is proposed. In addition to the balance equations of velocity and mixture fraction f, equations of mean, variance, and covariance of the heat-release rate g and mixture fraction are solved. Coupling with the chemistry model is achieved by means of a two-dimensional PDF of mixture fraction and heat-release rate. The proposed approach is open for improvement by more sophisticated submodels. Validity of this approach is illustrated by simulation of a 20-kW axisymmetric confined swirling combustion system. The results are compared to experimental data from LDV and Raman/Rayleigh measurements obtained from the same combustion system. Particularly, investigations of the influence of different coupling models on the local source terms of the radiation and of the nitrogen oxide production are discussed. The main results of this study are (1) the thin eddy assumption is valid for this system; (2) there are considerable fluctuations of the heat-release rate g with constant mixture fraction f at all locations because of the individual history of the burned gas eddies; (3) the coupling model has only negligible influence on the spatial temperature- velocity- and mixture-fraction fields and on the overall integrated radiation-transfer power; (4) the coupling model has strong influence on the local nitrogen oxide production and on the total nitrogen oxide emission. The present study demonstrates that for middle-sized enclosed diffusion flames, the complex phenomenon of turbulence-radiation interaction can be simulated efficiently without use of tedious stochastic approaches.

On the eddy break-up coefficient

Advanced combustion models for turbulent reactive flow are still not at a stage where they are useful for engineering calculations of practical systems such as gas turbine combustors. State-of-the-art methods still use the Eddy Break-Up (EBU) model to give the fast chemistry limit to the reaction rate with a global kinetics formula being used to estimate the kinetically limited rates. While there must continue to be basic reservations about the general correctness of the EBU approach, it has recently been shown that the EBU limit does have a basis in theory for the nonpremixed case. The theoretical result of Bilger for the mixing-limited reaction rate shows that it is proportional to the probability density of the mixture being at stoichiometric. The EBU model, however, takes it as being proportional to the mass fraction of the deficient reactant, but this is in turn a property of the mixture fraction pdf (probability density function) under fast chemistry conditions. The theoretical result can be used to evaluate the correct value of the EBU coefficient, which is usually taken as a constant but with quite widely varying values. In this paper the authors evaluate this theoretical value for the EBU coefficient using two commonlymore » adopted forms of the pdf. Recommendations are made with regard to the best values to use in practice.« less

Turbulence-radiation interaction in confined combustion systems

A new approach for modeling turbulence-radiation interaction is proposed. The formulation is based upon equations for statistical moments. Additional to the balance equations for the velocity and mixture fraction, equations for the mean, variance, covariance of heat release rate, and mixture fraction is solved. The coupling with the chemistry model is formulated by means of a two dimensional pdf of mixture fraction and heat release rate. The proposed approach is open for improvement by more sophisticated submodels. A natural gas fired combustion chamber is designed and constructed, and the temperature field measured by CARS spectroscopy. The main features of the modified combustion system are discussed. The comparison of experimental temperatures with the numerical simulation of the combustion system shows the good quality of our approach. The modeling of the two dimensional pdf is found to be most suitable for the hot region near the burner, where most radiation effects take place.