Laminar Flamelet Approach Research Articles

A mixing model providing joint statistics of scalar and scalar dissipation rate

For the simulation of turbulent nonpremixed flames the joint statistics of mixture fraction and scalar dissipation rate are of major importance. If thin reaction zones are present, these quantities determine essentially the composition and thermal state in the flow domain. It has been argued that in the transported probability density function (PDF) context the commonly used mixing models do not provide such statistics even though PDF methods are applied with some success for the simulation of flames involving local extinction. In this work, we propose an extension of the parameterized scalar profile (PSP) mixing model, which is able to provide the joint scalar–scalar dissipation rate PDF. The model predictions are compared with direct numerical simulation (DNS) data, where the influence of different initial scalar lengthscales on the mixing dynamics was investigated. In a small study involving a partially stirred reactor (PaSR), the suggested mixing model is combined with a laminar flamelet approach forming a closure for the reaction/diffusion dynamics.

Extended flamelet model and improved interaction of chemistry and turbulence for modeling partially premixed combustion with a joint PDF method

AbstractTurbulent combustion is commonly categorized into premixed, non‐premixed and partially premixed combustion. For nonpremixed combustion simulations the laminar flamelet concept proved to be very valuable while for the more complex case of partially premixed combustion this model shows considerable deficiencies. Here, the classical laminar flamelet approach is extended to the partially premixed combustion regime. For that, the joint statistics of mixture fraction, scalar dissipation rate and a progress variable, calculated with a joint probability density function (PDF) method, is used to get the statistics of the compositions and of the chemical energy source term from pre‐processed flame tables. This approach can be compared with the unsteady flamelet concept; the main differences consists of the way the progress variable evolution is computed and in the pre‐computed flame tables. The progress variable describes the point of time a fluid parcel is consumed by a flame front. The fluid parcels are represented by computational particles, which are used for PDF methods. The pre‐computed flame tables are computed from steady solutions 2D stabilized flames propagating into an unburnt mixture with varying mixture fraction. The corresponding position of a fluid particle in such a 2D laminar flame is determined by its mixture fraction and a burning time; both to be modeled for each computational particle in the PDF simulation. Numerical experiments of turbulent diffusion jet flames demonstrate that this approach can be employed for challenging test cases. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Validation of FDS for the prediction of medium-scale pool fires

Fire dynamics simulator (FDS) has been applied to simulate a medium-scale methanol pool fire. The simulation used predominantly the existing features in FDS except that an additional sub-grid-scale combustion model based on the laminar flamelet approach of Cook AW and Riley JJ [Combust and Flame 1998;112:593–606] was used alongside the default mixture fraction combustion model for comparison. The predictions of the two different combustion models for temperature and axial velocity distributions were found to be in reasonably good agreement with each other and the experimental data. The pulsating nature of air entrainment was demonstrated by the air entrainment velocity fluctuations and the instantaneous velocity vectors, which revealed formation and shedding of vortices and the well-known “neck-in” at a distance of approximately one diameter from the pool surface. The predicted variations of air entrainment at different heights agreed well with some published data and correlation. Although the limitation of the code in predicting the puffing frequency was noticed as the spectra of temperature fluctuations failed to demonstrate any dominant frequency, the present study has demonstrated the capability of FDS to deliver reliable predictions on most important parameters of pool fires.

A COMPARATIVE STUDY OF TURBULENCE MODELLING IN HYDROGEN-AIR NONPREMIXED TURBULENT FLAMES

Hydrogen-hydrocarbon blend flames have recently received increased attention as alternative fuels for terrestrial and aerospace power generation applications. The combustion modelling of these composite fuels flames is complex. Turbulence modelling as well is difficult because in the near field region of the jet exit, high density gradients at high inlet velocity cause difficulties. In order to correctly predict turbulent flames if blend fuels, it is necessary to validate the model's capability for hydrogen flames and hydrocarbon flames separately. In this study, pure hydrogen-air turbulent nonpremixed flames are numerically investigated. The configuration used is a co-flowing axisymetric turbulent non-premixed hydrogen flame, which is experimentally investigated by Barlow and Carter (1994) and Flury and Schlatter (1997). The model uses two turbulence closures that are the k-ε model and the Reynolds Stress Model (RSM) coupled with the steady strained laminar flamelet model. The performance of the k-ε and the RSM models are particularly discussed in the locations close to the nozzle exit. The results obtained demonstrate that the strained steady laminar flamelet approach based on the k-ε and the Reynolds stress turbulence models is, in general, capable of predicting this hydrogen-air flame at atmospheric pressure. Comparisons with measurements indicate that the predictions are sensitive to turbulence modelling and differential diffusion in the near-field region whereas the far-field region is influenced only by turbulence modelling. The RSM model gives better results than the k-ε model predictions close to the nozzle exit due to its corresponding turbulence parameters that are modelled more accurately. However, because of unity Lewis number assumption in the flamelet library generation, air entrainment is found to be not well predicted by the two turbulence models. Downstream, the k-ε model performs better and the predictions are very close to experimental data.

Investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations

Acoustically forced lean premixed turbulent bluff-body stabilized flames are investigated using turbulent combustion CFD. The calculations simulate aspects of the experimental investigation by Balachandran et al. [R. Balachandran, B. Ayoola, C. Kaminski, A. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37–55] and focus on the amplitude dependence of the flame response. For the frequencies of interest in this investigation an unsteady Reynolds-averaged Navier–Stokes (URANS) approach is appropriate. The combustion is represented using a modified laminar flamelet approach with an algebraic representation of the flame surface density. The predictions are compared with flame surface density (FSD) and OH ∗ chemiluminescence measurements. In the experiments the response of the flame has been quantified by means of a number of single-frequency, amplitude-dependent transfer functions. The predicted flame shape and position are in good agreement with the experiment. The dynamic response of the flame to inlet velocity forcing is also well captured by the calculations. At moderate frequencies nonlinear behavior of the transfer functions is observed as the forcing amplitude is increased. In the experiments this nonlinearity was attributed in part to the rollup of the reacting shear layer into vortices and in part to the collision of the inner and outer flame sheets. This transition to nonlinearity is also observed in the transfer functions obtained from the predictions. Furthermore, the vortex shedding and flame-sheet collapse may be seen in snapshots of the predicted flow field taken throughout the forcing cycle. The URANS methodology successfully predicts the behavior of the forced premixed turbulent flames and captures the effects of saturation in the transfer function of the response of the heat release to velocity fluctuations.

A hybrid scalar model for sooting turbulent flames

A Lagrangian Monte Carlo solution of the joint scalar pdf transport equation for mixture fraction and representative soot properties, coupled with an Eulerian solution for the turbulent flow field and here described as a “hybrid model,” has been developed. The modeling of soot formation and destruction employs an existing description of the key processes based on two soot variables—the soot volume fraction (or mass concentration) and the particle number density. The gas-phase chemistry is introduced through flamelet-state relationships. The simulation strategy is based on tracing the evolution of reactive stochastic particles within the computational domain. The ensemble of these particles at a fixed location and time then describes the joint scalar pdf. Soot rate equations, represented as functions of mixture fraction, soot mass concentration, and number density, are solved exactly in terms of the scalar values of each individual stochastic particle and the associated gas-phase properties derived from laminar flamelet-state relationships. The solution for the turbulent flow field provides the mean velocity and mixing frequency required for the transport of the stochastic particles in both physical and compositional space, while the Monte Carlo simulation returns the computed mean density field to the CFD code. Density-weighted mean values are approximated by ensemble averages over the scalar values of the stochastic particles in individual computational cells. The principal objective of the hybrid model is the improved treatment of nonlinear soot formation and oxidation, in particular, the capture of the intermittency in the oxidation process associated with the noncoexistence of soot and the principal oxidizing species. Significant computational economies accompany the adoption of the laminar flamelet approach for the source terms in the soot rate equations and the reduced number of scalars computed stochastically.

Large-eddy simulation of a bluff-body stabilized nonpremixed flame

Large-eddy simulations have been performed for a turbulent nonpremixed bluff-body stabilized CH 4:H 2 (50:50 vol.) flame at a Reynolds number of 15,800. The corresponding isothermal flow has also been computed. The Sydney bluff-body burner under consideration has been investigated experimentally by Masri and co-workers, who obtained velocity and scalar statistics. The focus of the current work is on flow and mixing effects with the thermochemistry evaluated using a steady-state laminar flamelet approach. The incompressible (low-Mach-number) governing equations for mass, momentum, and mixture-fraction have been solved on a structured cylindrical grid and resolution effects investigated using up to 3.643 × 10 6 nodes. The corresponding nonreactive case was resolved by 5.76 × 10 5 nodes, resulting in a resolution of more than 80% of the turbulence kinetic energy. The reacting case yields a resolution in excess of 75% on the finest grid—arguably sufficient to permit conclusions regarding the accuracy of submodels. Comparisons with experimental data show that for high resolutions comparatively good agreement is obtained for the flow field and for species other than nitric oxide. However, resolution effects are important and results obtained with 4.51 × 10 5 nodes show that a resolution of less than 70% of the turbulent kinetic energy is insufficient in the context of the Smagorinsky subgrid model combined with the dynamic procedure of Germano. The latter result is consistent with the analysis of Pope.

OPTIMIZATION OF SOOT MODELING IN TURBULENT NONPREMIXED ETHYLENE/AIR JET FLAMES

ABSTRACT Two-equation soot models, which solve conservation equations for soot number density and mass concentration, have been extensively used to study soot formation in laboratorial turbulent flame and practical gas-turbine combustors. This study investigates the effects of different inception, growth coagulation, and oxidation source terms in a two-equation semi-empirical soot model that has been implemented to model two turbulent ethylene/air jet flames. The gas-phase chemistry is modeled using the laminar flamelet approach. A new soot inception submodel is proposed that is based on the naphthalene formation rate calculated by the detailed chemical kinetics. The expected value of the formation rate is stored in the flamelet library. Model predictions were compared with the measurements of Young and Moss. The predictions of the soot volume fraction are very sensitive to the soot surface growth rate. The soot predictions agree well with measurements when the surface growth rate is assumed to be proportional to the square root of the surface area. The result also indicate that the naphthalene inception route exhibits better performance. Finally a new soot model with an optimal combination of rates was developed. The model predictions provided good agreement with the experimental temperature, mixture fraction, and soot volume fraction distributions along both the axial and radial directions. The optimal soot model was also successfully validated on another turbulent ethylene/air jet flame.

Modeling soot formation in turbulent kerosene/air jet diffusion flames

Soot volume fraction and number density in a turbulent diffusion flame burning kerosene/air were predicted using two approaches. The first used a conventional soot inception model based on the acetylene concentration and is referred to as the acetylene model. The second used a soot inception model based on the formation rate of three and two ring aromatics [1] and is referred to as the PAH inception model. The soot models account for inception, coagulation, surface growth, and oxidation processes. The Favre-averaged governing equations of mass, momentum, and energy in the turbulent field were solved in conjunction with the k − ε turbulence model. A recently developed detailed reaction mechanism for kerosene/air [2] was coupled to the turbulent flow field by the stretched laminar flamelet approach. A radiation heat transfer model that considered the soot, water and CO 2 levels is included. Models are validated by comparing the numerical results to the experimental results of Young et al. [3] for a turbulent jet-flame burning pre-vaporized aviation kerosene. Significant improvements in the prediction of soot volume fraction are obtained using the PAH inception model for soot inception compared to the conventional acetylene approach.

On numerical comparison of enclosure fire in a multi-compartment building

This paper reports a validation study of a CFD simulation for an enclosure fire in a single level multi-room building. Model predictions are compared against measured data of Luo and Beck (Fire Safety J 23 (1994) 413). The CFD-based fire model focuses on the use of laminar flamelet approach to account for the combustion of fire. Global radiation in the multi-compartment building is evaluated though the discrete ordinates method (Combust. Sci. Technol. 59 (1988) 321). Soot model proposed by Syed et al. (Proceedings of the 23rd Symposium on Combustion, The Combustion Institute, 1990. p. 1533) that accounts for the essential physical processes of nucleation, coagulation, surface growth and oxidation is utilised to predict the soot formation and burnout. The presence of soot augmenting the global radiative heat exchange was considered. Overall, our results are in good agreement with the experimental data of Luo and Beck's and also consistent with their numerical results.

Prediction of lifted, non-premixed turbulent flames using a mixedness-reactedness flamelet model with radiation heat loss

The laminar flamelet approach is frequently applied to model turbulent non-premixed flames based on the assumption of adiabatic combustion. This generally results in the significant overprediction of temperatures for flames where thermal radiation is important. In the present study, an adiabatic, mixedness-reactedness flamelet combustion model has been extended to incorporate the effect of radiation heat transfer using the concept of enthalpy defect. This requires the generation of flamelet data sets using a detailed chemical kinetic mechanism and introduction of enthalpy defect as an additional flamelet parameter. The methodology developed has been applied to simulate lifted, free, turbulent non-premixed natural gas flames for which measurements are reported in the literature. A non-adiabatic flamelet data library for methane-air flames has been generated with the GRI reaction mechanism using the modified CHEMKIN code for the modeling of turbulent radiating flames. The turbulent flame computational results, with and without radiation heat transfer, are compared with experimental data for mean gas temperatures, species concentrations and flame lift-off heights for a number of laboratory- and large-scale lifted turbulent jet flames. Predictions obtained using the non-adiabatic flamelet model are found to be in good agreement with temperature measurements, whereas the original adiabatic model significantly overestimates temperatures in the downstream regions of flames where significant heat loss occurs. Species concentration and lift-off height results show small differences between predictions with and without radiation losses in regions close to the base of the flame, although both methodologies provide satisfactory agreement with the available data.

COMBUSTION-RADIATION-TURBULENCE INTERACTION MODELING IN ABSORBING/EMITTING NONPREMIXED FLAMES

A model is presented lo account for the interaction among combustion. radiation, and turbulence in nonpremixed turbulent flames with gas-phase radiation, based on the stretched laminar flamelet (slf) approach. In particular, the effect of heat transfer on combustion is accounted for by introducing the enthalpy defect as an additional fundamental state quantity. The radiative transfer equation (RTE) is solved via the discrete-transfer method, and the effect of fluctuations is accounted for by a suitable averaging procedure, intended to overcome the inherent shortcomings of the "mean-property" method. A lest case is discussed, and the effect of fluctuations along a typical ray is quantified. The turbulent combustion regime is also ascertained, by an appropriate extension of Peters’ phase-diagram. Possible further extensions of the model are outlined.

The effect of microscopic and global radiative heat exchange on the field predictions of compartment fires

This paper reports on some further results of the CFD simulations of large-scale compartment fires previously reported in Wen et al. (Proceedings of the Combustion Institute , vol. 27, 1998) and Wen and Huang (Fire Safety J 2000;34(1)). It focuses on the use of the laminar flamelet approach and highlights the effect of microscopic radiation on the field predictions of temperature and species concentrations in compartment fires. The flamelet calculations with and without microscopic radiation are performed using RUN-1DL (Rogg. RUN-1DL Manual, 1099) . Radiative properties in the flamelet are calculated by a modified exponential wide band model. Global radiation is coupled with the field calculation through the discrete transfer radiation method (Shah. Ph.D. thesis, Imperial College of Science and Technology, 1979) and Hubbard and Tien's (ASME J Heat Transfer 1978;100:235–9) mean emission and absorption coefficient concept. The soot model of Leung et al. (Combust Flame 1991;87;289–305) is used for soot predictions. Improved agreement with experimental data on temperature distributions has been achieved by including the microscopic radiation in the flamelet calculation. Microscopic radiation is also found to have significant effect on the predictions of soot and OH radical but its effect on the predictions of CO 2, CO and H 2O are found to be marginal. The present study recommends that radiative heat exchange at microscopic level (within the laminar flamelet) should be included when using the laminar flamelet approach to compute turbulent reacting flows.

Sensitivity of calculated extinction strain rate to molecular transport formulation in nonpremixed counterflow flames

The counterflow flame is a commonly used geometry for experimental and chemical kinetic modeling studies of nonpremixed combustion. Because the flame structure is quasi-one-dimensional and more computationally tractable than inherently multidimensional flame geometries [1], detailed chemical kinetic modeling codes for counterflow flames have come into widespread use. An important characteristic of counterflow flames is the extinction strain rate, the maximum velocity gradient which a flame can support and still burn. At strain rates below the extinction value, there exist three solutions to the governing equations which determine the flame structure. Two of the solutions correspond to a stable flame and an essentially non-reacting cold flow, while the third branch is an unstable solution which cannot be physically realized [2]. Various computational approaches have been used to extend stable solutions onto the unstable branch, and thus determine the limits of bistability corresponding to flame extinction and autoignition [2, 3]. The extinction strain rate is important for modeling turbulent combustion using the laminar flamelet approach [4], and is a figure of merit for the effectiveness of fire suppressants in nonpremixed flames [5]. It is desirable for calculations to accurately predict extinction strain rates. Substantial variations in predicted extinction strain rates of nonpremixed methane/ air counterflow flames have been noted between different chemical kinetic mechanisms [6]. Here, the predicted extinction strain rate is found to also be sensitive to the treatment of molecular transport in the computational model. The effect of transport on premixed flame structure and extinction has been recently investigated by Paul and Warnatz [7], and by Ern and Giovangigli [8, 9]. To our knowledge, the effect of transport formalism on extinction of nonpremixed counterflow flames has not been previously reported in the literature. Furthermore, earlier studies reporting computational predictions of extinction strain rates have not always specified the manner in which the calculation handled species transport. In the present study, we employ two computer programs developed for counterflow flames incorporating the CHEMKIN program packages developed at Sandia National Laboratories. Initially, the chemical kinetics [10] and molecular transport [11] routines were applied

Numerical predictions of a turbulent diffusion flame in a cylindrical combustor using eddy dissipation and flamelet combustion models

A mathematical model has been applied to simulate a confined, turbulent natural gas diffusion flame for which measurements were reported in the literature [7]. The combustion is modelled using both eddy dissipation [2] and non-equilibrium, mixedness—reactedness flamelet [6, 20] models. The latter model is based on a laminar flamelet approach originally developed for premixed combustion. The turbulence is represented by a Reynolds stress model based on the differential transport equations for stresses. The computational results are compared with experimental data for gas temperature and species concentrations. The predictions obtained using the flamelet model are found to be in good agreement with measurements, whereas the eddy dissipation combustion model fails to capture the measured trends in the near-burner region. Efforts have been made to improve the quality of the predictions of the latter model by incorporating an extinction criterion [25] and by adjusting the value of the model parameter. Both actions generate predictions similar to that of the flamelet model.

Flamelet-based smoke properties for the field modelling of fires

Abstract Simplified soot formation models are developed for two fuels—propylene and methylmethacrylate—representative of the pyrolysates derived from burning polymeric materials in compartment fires. The models incorporate descriptions of the key processes of soot particle nucleation, coagulation and surface growth and introduce fuel-dependent model coefficients which are established through detailed comparisons between laminar diffusion flame experiment and computational prediction. A laminar flamelet approach is employed to simplify the computation of the scalar fields for composition and temperature. For purposes of model evaluation and calibration, detailed property maps are constructed in the two flames for mixture fraction, using probe sampling and mass spectrometric analysis, temperature by fine wire thermocouple and soot volume fraction by laser extinction. The level of complexity introduced reflects the compromise between the physical mechanisms described and the computational demands of the target application to the improved field modelling of fires.

Time-series analysis and measurements of intermendiate-species concentration spectra in turbulent non-premixed flames

The ability to make frequency-resolved measurements of minor-species concentrations in turbulent flames has recently been demonstrated by picosecond time-resolved laser-induced fluorescence (PITLIF). However, few previous studies have focused on the power spectral density (PSD) of minor species in reacting flows. What little information is available suggests that strong interactions between velocity fluctuations and scalar distributions complicate the PSD, making interpretation of flame data difficult. In this work, time-series analysis, previously applied in flame-radiation studies, is extended to the study of temporal fluctuations in minor-species concentrations. In particular, an assumed PSD model for mixture fraction (Z) is used to simulate its time series. State relationships for narrowly distributed minor species as a function of mixture fraction are applied to develop concentration time series. Extension of this laminar-flamelet approach to minor species requires additional consideration of the effect of flame strain rate on the width of a minor-species profile in Z space as well as its peak concentration. The resulting minor-species concentration PSDs are computed and studied as a function of profile width (in Z) and fluctuation intensity (Z′ RMS ). These simulations compare favorably to previously reported CH and OH PSDs in a low-Reynolds-number, methane diffusion flame. Similarly, new PITLIF measurements of OH time series in a hydrogen diffusion flame at several Reynolds numbers also demonstrate favorable comparisons to the PSD simulations.

Radiation Modelling in Non-Luminous Nonpremixed Turbulent Flames

A finite-rate chemistry model for nonpremixed turbulent combustion, based on the stretched laminar flamelet (slf) approach, is extended to account for radiative heat transfer in non-luminous flames, in the optically thin limit. The model is applied to a methane/air flame, and results in greatly improved predictions of mean temperature, and of its probability density function. Mean carbon monoxide concentration predictions are instead shown to be somewhat deteriorated. The model is further tested to reproduce radiative heat flux levels; solutions obtained by determining the average heat flux divergence by full convolution with the pdT, and by the simpler but less fundamentally correct ‘mean-property’ method, are compared, and show a significant gap. A formulation to deal with non-unity Lewis number flames is proposed; the model holds potential for further extension.

A laminar flamelet approach to subgrid-scale chemistry in turbulent flows

A method is presented whereby filtered chemical species may be modeled in large eddy simulations (LES) of nonpremixed, turbulent combustion. The model is based on the concept of laminar flamelets, and assumes that a filtered mixture-fraction, as well as its subgrid-scale variance and filtered dissipation rate, are known at each grid cell of an LES. The model makes use of the subgrid-scale or “large-eddy” probability density function of the mixture-fraction, which is assumed to follow a beta-distribution. Also, an assumed functional form for the scalar dissipation rate is employed. The model is evaluated by filtering data from direct numerical simulations (DNS) of homogeneous, isotropic, decaying turbulence. Results show that the model, termed the large-eddy, laminar flamelet model (LELFM), is reasonably accurate and that the accuracy improves with increasing Damköhler number.

Modeling of soot formation and oxidation in turbulent diffusion flames

Soot concentration in a turbulent diffusion flame burning propane was predicted using several formation and oxidation models. The Favre-averaged equations governing conservation of mass, momentum, and energy and transport equations for turbulent quantities, mixture fraction and its variance were solved using the k-t model and the laminar flamelet approach. Calculation of soot concentration was performed using the results of the flame field model as input data. The soot formation models of Khan and Greeves, and Moss and co-workers were used together with the soot oxidation models of Magnussen and Hjertager, Lee et al., and Nagle and Strickland-Constable. Comparison of the results with available measurements, and with the predictions obtained by Fairweather et al. using their own soot formation model, shows that reasonable predictions of soot concentration requires an adjustment of the constants of the model of Moss and co-workers. The soot formation model of Fairweather et al. appears to be less sensitive to the constants. The model of Khan and Greeves yields correct orders of magnitude, but fails to predict some important features of the data. Hence, there is a need to improve presently available soot formation and oxidation models to achieve a satisfactory predictive capability.