Function Of Mixture Fraction Research Articles

Modelling heat loss effects in high temperature oxy-fuel flames with an efficient and robust non-premixed flamelet approach

The non-premixed steady flamelet model is extended by two simple, robust and effective heat loss modelling approaches. The heat release damping (HRD) approach decreases the chemical source term in the energy equation by a constant factor, while the artificial radiation (AR) approach introduces an augmented temperature dependent radiative source term. The models are tested in a simulation of the 0.78 MWth IFRF (International Flame Research Foundation) pilot scale, non-premixed, natural gas/oxygen flame. Both approaches are applied in steady laminar flamelet calculations with detailed chemistry, tabulating the thermo-chemical state as a function of mixture fraction and normalised heat loss. The turbulence-chemistry interaction is modelled using the β-PDF approach. An enthalpy transport equation is solved to keep track of the heat loss, while radiative heat transfer is calculated by the P-1 model. We observe that the major species, temperature, velocities and velocity fluctuations show a good agreement with the available experimental data. The heat loss modelling yields a significant improvement over the adiabatic model. Interestingly, both heat loss models (HRD and AR) show negligible differences in the simulations of the turbulent flame and permit to apply the steady laminar flamelet model to oxy-fuel processes in a simple, robust and user friendly manner.

Mathematical Modelling of Pool Fire Burning Rates in a Full- Scale Ventilated Tunnel

A computational fluid dynamic model with full coupling between gaseous and liquid phases is developed to predict buring rates of liquid pool fires in ventilated full-scale tunnel. Rates of fuel release are calculated using predictions of flame feedback to the surface of the pool. A pool fire in tunnel is modelled as an unsteady process, from the time of ignition until convergence to a quasi-steady burning rate. This feedback supports sustained flame above the pool surface and controls the burning rate of the fuel. The numerical model solves three dimensional, time-dependent Navier-Stokes equations, coupled with submodels for soot formation and thermal radiation transfer. Turbulent combustion process is modelled by an Eddy Dissipation Concept (EDC) by using two chemical reaction steps to CO prediction. The numerical model is shown to possess the ability to predict the effect of ventilation on burning rate and the initial growth period in a fullscale tunnel fire. The current study indicates that CO generation is relatively independent of position in the overfire region, and correlated solely as a function of mixture fraction. While no correlation of soot concentrations in terms of the mixture fraction is found. Abundant CO and soot are formed around the fire base, which is later deflected near the tunnel ceiling, and the backflow brings about the toxic products with a noticeable smoke stratification as the airflow velocity is below a critical value.

Evaluation of an Unsteady Flamelet Progress Variable Model for Autoignition and Flame Lift-Off in Diesel Jets

An unsteady flamelet progress variable (UFPV) model is evaluated for modeling autoignition and flame lift-off in diesel jets. Changes in injection pressure, orifice diameter, ambient temperature, density, and O2 concentration are considered. In implementing the model in a Reynolds-averaged Navier–Stokes (RANS) code, a look-up table of reaction source terms is generated as a function of mixture fraction Z, stoichiometric scalar dissipation rate χst and progress variable Cst by solving the unsteady flamelet equations. It is assumed that the probability density functions (pdfs) of Z, χst, and Cst are statistically independent, and presumed functions are employed for the pdfs. Comparisons with experimental results show that the model is able to predict ignition delay and flame lift-off with reasonable accuracy in the RANS simulations. The quantitative agreement between computed and measured results depends on the definitions employed to quantify autoignition time and lift-off height, but, in general, the agreement is within 25%.

Spatial structure and NO formation of a laminar methane–nitrogen jet in hot coflow under MILD conditions: A spontaneous Raman and LIF study

We report the spatial structure of the reaction zone from a diluted, preheated fuel jet in hot coflowing oxidizer in laminar flow, using an axisymmetric laminar-jet-in-hot-coflow (LJHC) burner. In the experiments, a preheated CH4/N2 (20/80) mixture at ∼1100K flows into the 1500K products of a flat, premixed burner-stabilized flame, having 3mol% residual oxygen. Measurements of major species and temperature profiles using spontaneous Raman scattering show a temperature rise in the reaction zone of less than 300K, indicating that the reaction zone was in the MILD combustion regime. Analysis of the data shows that the spatial development of the combustion has the characteristics of an “ordinary” coflow diffusion flame, but with changes in temperature and species fractions due to combustion that are nearly an order of magnitude smaller than when using undiluted reactants. Measurements of profiles of NO mole fraction using Laser Induced Fluorescence (LIF) show that the contribution of the MILD combustion to the NO fraction is less than 2ppm, in agreement with other studies on MILD combustion in turbulent flows. Analysis of the NO fraction as a function of mixture fraction indicates that the NO field is dominated by mixing of the NO formed in the coflow with the reaction products of the diluted fuel, with negligible NO formation from the fuel. Replacement of the nitrogen in the hot coflow with argon resulted in NO fractions below the detection limit of the measurement system.

Evaluation of an unsteady flamelet progress variable model for autoignition and flame development in compositionally stratified mixtures

The unsteady flamelet progress variable (UFPV) model has been proposed by Pitsch and Ihme [“An unsteady/flamelet progress variable method for LES of nonpremixed turbulent combustion,” AIAA Paper No. 2005-557, 2005] for modeling the averaged/filtered chemistry source terms in Reynolds averaged simulations and large eddy simulations of reacting non-premixed combustion. In the UFPV model, a look-up table of source terms is generated as a function of mixture fraction Z, scalar dissipation rate χ, and progress variable C by solving the unsteady flamelet equations. The assumption is that the unsteady flamelet represents the evolution of the reacting mixing layer in the non-premixed flame. We assess the accuracy of the model in predicting autoignition and flame development in compositionally stratified n-heptane/air mixtures using direct numerical simulations (DNS). The focus in this work is primarily on the assessment of accuracy of the probability density functions (PDFs) employed for obtaining averaged source terms. The performance of commonly employed presumed functions, such as the dirac-delta distribution function, the β distribution function, and statistically most likely distribution (SMLD) approach in approximating the shapes of the PDFs of the reactive and the conserved scalars is evaluated. For unimodal distributions, it is observed that functions that need two-moment information, e.g., the β distribution function and the SMLD approach with two-moment closure, are able to reasonably approximate the actual PDF. As the distribution becomes multimodal, higher moment information is required. Differences are observed between the ignition trends obtained from DNS and those predicted by the look-up table, especially for smaller gradients where the flamelet assumption becomes less applicable. The formulation assumes that the shape of the χ(Z) profile can be modeled by an error function which remains unchanged in the presence of heat release. We show that this assumption is not accurate.

Large Eddy Simulation of Autoignition in a Turbulent Hydrogen Jet Flame Using a Progress Variable Approach

The potential of a progress variable formulation for predicting autoignition and subsequent kernel development in a nonpremixed jet flame is explored in the LES (Large Eddy Simulation) context. The chemistry is tabulated as a function of mixture fraction and a composite progress variable, which is defined as a combination of an intermediate and a product species. Transport equations are solved for mixture fraction and progress variable. The filtered mean source term for the progress variable is closed using a probability density function of presumed shape for the mixture fraction. Subgrid fluctuations of the progress variable conditioned on the mixture fraction are neglected. A diluted hydrogen jet issuing into a turbulent coflow of preheated air is chosen as a test case. The model predicts ignition lengths and subsequent kernel growth in good agreement with experiment without any adjustment of model parameters. The autoignition length predicted by the model depends noticeably on the chemical mechanism which the tabulated chemistry is based on. Compared to models using detailed chemistry, significant reduction in computational costs can be realized with the progress variable formulation.

Radiation of noise in turbulent non-premixed flames

A model for the prediction of combustion-generated noise in non-premixed flames has been developed. This model is based on Lighthill’s acoustic analogy and employs the flamelet/progress variable model to express the excess density as function of mixture fraction and reaction progress variable. In this model, three major sources of sound have been identified, and their individual contribution to the acoustic spectra and overall sound pressure level are analyzed for a nitrogen-diluted methane–hydrogen/air flame. The hybrid approach, combining a large-eddy simulation and a computational aeroacoustic method, introduces spurious noise which can pollute the acoustic results. All relevant sources of spurious noise are analyzed, and a physics-based low-pass filter is proposed which eliminates spurious noise due to the convection of acoustic sources. The numerical predictions for both statistical flow field quantities and acoustic results have been validated with experimental data. The good agreement between experiments and simulation highlights the potential of the method for applications to more complex flow configurations and to provide further understanding of combustion noise mechanisms.

Measurements in Standard Room Scale Fires

In this paper the results of a continuing effort to develop a comprehensive compartment fire database for validation of numerical fire modeling is presented. Natural gas fires were conducted inside a full-scale ISO 9705 room and are compared with previous results obtained in a 2/5 scale, reduced-scale enclosure. In these experiments, fires with heat release rates as large as 2.7 MW were used in the full-scale room. Gas species and temperature measurements were made inside the room at several locations in the upper layer and the doorway. Oxygen, CO/CO2, and total hydrocarbon gas analyzers were used in addition to gas chromatography to make gas species measurements. Temperature measurements were made in the upper layer of the room using aspirated thermocouples. Fires as large as 2.7 MW were observed not to produce underventilated compartment fire conditions in the full-scale enclosure despite the large heat release rate and temperatures observed in excess of 1200 °C. A comparison of the gas species in the upper layer of the reduced-scale and full-scale results showed similarities in terms of the gas species volume fractions when plotted as a function of mixture fraction, but the temperature results showed that the full-scale enclosure was reaching higher temperatures than the reduced-scale enclosure.

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.

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.

Modeling of Mixing and Reaction in Turbulent Multi-Phase Flows with Distribution Functions

Numerical simulation of turbulent reacting or multiphase flows is gaining popularity as a tool for the analysis and optimization of many complex applications in process engineering. To make possible the accurate modeling of relevant reaction and transport processes, the respective distribution functions of mixture fraction or particle size must be considered in an adequate manner. In the present paper, novel approaches to make possible a more detailed yet efficient representation of distribution functions in turbulent, reacting multiphase flows are introduced. The application of the methods to the example of a system with mixing and reaction among three species is discussed.

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.

Strategy for the simplification of nitric oxide chemistry in a laminar methane/air diffusion flamelet

A reduction of two detailed kinetic mechanisms for nitrogen oxidation, GRI-Mech 2.11 and Drake & Blint, is presented which uses the conserved scalar description of species transport. Profiles of C/H/O species, temperature, and scalar dissipation rate as functions of mixture fraction are required as model inputs. Reaction rate analysis of the nitrogen chemistry is used to identify steady state relationships and pare insignificant reactions. The resultant skeletal mechanism for nitrogen chemistry can be recast as a closed set of five linear species conservation equations for NH 3, HNCO, HCNO, HCN, and NO. The concentrations of nine other intermediates (HOCN, CN, NCO, NH, NH 2, HNO, N, NO 2, and N 2O) may be obtained through steady-state relationships. Validation of the reduced mechanisms is accomplished through comparison with the parent detailed mechanisms. Of particular significance is the dominance of the reaction HCCO + NO → HCNO + CO in NO reburn chemistry in one of the detailed mechanisms investigated (GRI-Mech 2.11) and its derived reduced mechanism.

A Comparison of CMC and PDF Modelling Predictions with Experimental Nitric Oxide LIF/Raman Measurements in a Turbulent H2Jet Flame

Abstract The prediction of nitric oxide (NO) formation in turbulent flames requires a modelling approach that takes into account the coupled nature of local turbulent mixing and chemical reaction. The Conditional Moment Closure (CMC) and Probability Density Function (PDF) methods have been developed to include these interactions, and have been applied in this case to predict NO formation in a turbulent nonpremixed hydrogen jet flame with a Reynolds number of 10000. Instantaneous point measurements of NO concentrations have been made by the simultaneous use of Laser Induced Fluorescence of NO, Rayleigh scattering and Raman scattering. These point measurements provide quantitative information regarding NO formation as a function of mixture fraction within the flame itself. It has been found that the CMC and PDF modelling methods predict NO concentrations to within 30% of the levels measured at each location. Results show that the effects of differential diffusion and flame radiation are significant in a turbulent flame of this type, the former in upstream regions of the flame and the later in downstream regions of the flame

Single-shot temperature and mixture fraction profiles by Rayleigh scattering in the development zone of a turbulent diffusion flame

Single-shot laser Rayleigh scattering profiles have been obtained in the development zone of a turbulent diffusion flame of a diluted hydrogen jet issuing into a coflowing air stream. The Rayleigh scattering cross section that depends on the local molecular composition is calculated at each laser shot as a function of mixture fraction ( Z) and the temperature profile by the use of an algorithm involving a strained flame library. This processing provides the instantaneous profiles of T and Z, so that the radial structure of the reaction zones can be statistically investigated, apart from the flame motion, in terms of the pdf and correlations for the scalars and their gradients. The main result is the large regular spreading of peak temperature distributions down to low values that are far less than the extinction limit. This is attributed to the occurrence of local and intermittent extinctions due to the action of turbulent stretch.

Li−SF 6 combustion in stored chemical energy propulsion systems

Appropriate thermodynamic models and thermo-chemical data for multicomponents and immiscible phases have been incorporated into a code for the computation of chemical equilibrium of the reactants used in a stored chemical energy propulsion system. The reactants considered are molten lithium fuel and gaseous sulfur hexafluoride oxidant. Extensive equilibrium state relationships as a function of mixture fraction have been presented over a temperature range of possible operating conditions. They were subsequently employed to predict the complex flow structure of a choked, turbulent, reacting SF6 gas jet submerged in a molten lithium bath. Detailed profiles of velocity, temperature, void fraction and mass fraction of all phases in the jet have been presented. The results show that the reaction is completed within a short distance from the injector but the plume jet penetrates farther beyond due to significant evaporation of lithium fuel in the hot temperature plume, and subsequent condensation of the evaporated fuel and reaction products in the later part of the plume. The effect of lithium subcooling on flow structure has also been examined. It is found that lowering the degree of subcooling by raising the fuel bath temperature increases fuel evaporation, decreases the entrainment rate, delays the completion of reaction and lengthens greatly the jet penetration distance. Finally, for practical use, a simple correlation of the jet penetration length as a function of subcooling has also been presented.

Transient combustion in a turbulent eddy

A mathematical model of a local transient diffusion flame generated by mixing in a turbulent eddy is presented. It is intended ultimately as a computational “molecule” to be imbedded in numerical simulations of large scale reacting flows. The specific objective of the present analysis is to account explicitly for the modification of the local velocity field induced by the heat generation process. An “idealized” single step irreversible reaction model and a model treating the effects of real chemistry within the laminar flamelet approximation are considered. The convection diffusion equation for the mixture fraction and the mass conservation equation are analyzed using the experimental observation that specific volume is a piecewise linear function of mixture fraction. A Cole-Hopf transformation is used to reduce this equation to an incompressible form in terms of a new “pseudo mixture fraction” which can be related to all scalar properties using measured or idealized state relationships. Seven different fuels have been studied. Sample results for two of these are presented.

Equilibrium computations of multiphase nonideal electrolytic systems and structure of turbulent reacting dissolving jets

The objectives of the paper are two-fold. First, a method has been presented and a computer program developed for the computation of chemical equilibrium of complex reacting, nonideal, multiphase and electrolytic mixtures Validity, of the program has been confirmed by comparing the calculated values with experimental solubility data of three binary systems. Applications have been made to hydrogen chloride gas and aqueous ammonia reacting dissolving systems. Extensive state relationships as a function of mixture fraction have been generated for ammonia solutions over a wide range of ammonia concentrations. The second objective is to investigate the structure of a turbulent, gaseous, reacting, dissolving hydrogen chloride jet submerged in an aqueous ammonia bath. The use of HCl(g) as oxidizer and NH 3(aq) as fuel has been of recent interest to simulate the tubulent combustion of a haogenegaseous oxidizer with an alkali liquid metal fuel. With the state relationships generated, the k -∈-g turbulent model, the local homogeneous two-phase flow approximation and a clipped Gaussian probability function for the square of the mixture fraction flucations, predictions have been made for the plume penetration length, temperature, voil fraction and concentration profiles of the plume. It is found that the total plume penetration length is controlled by the extent of vaporization of the bath liquid, which is governed by the concentration of the ammonia fuel. The theoretical calculations are found in good agreement with the recent experimental data, which include the maximum plume temperature, the plume penetration lengths and the void fraction profile.