Thermochemical Variables Research Articles

A three mixture fraction flamelet model for multi-stream laminar pulverized coal combustion

A three mixture fraction flamelet model is proposed for multi-stream laminar pulverized coal combustion. The technique of coordinate transformation is utilized to map the flamelet solutions from a unit pyramid space into a unit cubic space to improve the stability of the simulation. The validity of the three mixture fraction flamelet model was assessed on different configurations, including a laminar counterflow pulverized coal/methane flame and a laminar piloted pulverized coal jet flame. The flamelet predictions were compared to the reference results of the detailed chemistry solutions. For the counterflow flame, it was found that the flame temperature and major species mass fractions are correctly predicted by the three mixture fraction flamelet model. However, discrepancies are observed for combustion-mode-sensitive species such as CO and H2 in the premixed combustion region. The thermo-chemical quantities in the char surface reaction zone cannot be correctly predicted if the mixing between the char off-gas stream and other streams is neglected. For the piloted jet flame, it was shown that the stable thermo-chemical variables can be correctly predicted at the upper and middle stream locations. However, at the downstream location, discrepancies can be observed in certain regions. Overall, the validity of the three mixture fraction flamelet model for multi-stream pulverized coal combustion is confirmed and its performance in turbulent pulverized coal combustion will be tested in future work.

The role of tangential diffusion in evaluating the performance of flamelet models

For non-premixed combustion, the steady laminar flamelet model (SLFM) and flamelet/progress variable approach (FPVA) are two popular methods for tabulating flamelet manifolds. Even if the two methods are used to tabulate and parameterize the same flamelet database, their results sometimes differ in the subsequent simulation. In this work, a novel perspective is provided to assess the performance of the SLFM and FPVA. Both approaches are compared with respect to their capabilities to capture tangential diffusion (TD) of the thermochemical state variables along iso-surfaces of mixture fraction. The relevance of TD effects is identified using generalized flamelet equations and regimes by comparing flamelet solutions with and without TD terms to a FTC (full transport and chemistry) solution of a well-known non-premixed coflow flame. It is found that TD effects can play an important role in entire mixture fraction space, even in the classical flamelet regime. This suggests that the ability to characterize TD effects is an important performance indicator for tabulation strategies. Thereafter, an a priori analysis is conducted comparing the results from the FPVA and SLFM (using the same flamelet database) with the FTC results. The results show that the FPVA is able to more accurately describe the thermochemical state and the flame structure than the SLFM. For a more detailed assessment of the two tabulation strategies, the TD terms reconstructed from the FPVA and SLFM are compared to those from the FTC results. It is found that the FPVA can capture a significant portion of TD effects, while the SLFM can hardly characterize TD effects. This particular capability allows the FPVA to describe chemistry-transport interaction and flame structure more accurately than the SLFM.

Feasibility of the Constrained Free Energy Method for Modeling NO Formation in Combustion

AbstractEmissions of nitrogen oxide (NO) from combustion are modeled based on the constrained free energy method (CFE). The CFE method is an extension of the Gibbs' free energy minimization technique, using additional immaterial constraints which allow for the calculation of local thermodynamic equilibria. Chemical reactions, enthalpic effect, and thermochemical state variables are calculated concurrently. Various kinetic constraints were applied in this study for modeling thermal and fuel‐based NO emissions for a number of combustion problems. The results were validated against data obtained from detailed kinetic models. The results indicate that the CFE method can be used for modeling post‐flame thermal and fuel‐based NO emissions. Where more specific estimation of radical buildup, radical overshoot, and ignition delay is needed, however, the accuracy of the applied CFE method was deemed insufficient.

Numerical exploration of dissimilar supersonic coaxial jets mixing

Mixing of two coaxial supersonic dissimilar gases in free jet environment is numerically explored. Three dimensional RANS equations with a k–ε turbulence model are solved using commercial CFD software. Two important experimental cases (RELIEF experiments) representing compressible mixing flow phenomenon under scramjet operating conditions for which detail profiles of thermochemical variables are available are taken as validation cases. Two different convective Mach numbers 0.16 and 0.70 are considered for simulations. The computed growth rate, pitot pressure and mass fraction profiles for both these cases match extremely well with experimental values and results of other high fidelity numerical results both in far field and near field regions. For higher convective Mach number predicted growth rate matches nicely with empirical Dimotakis curve; whereas for lower convective Mach number, predicted growth rate is higher. It is shown that well resolved RANS calculation can capture the mixing of two supersonic dissimilar gases better than high fidelity LES calculations.

Modeling of heat transfer and differential diffusion in transported PDF methods

In order to model the conditional diffusive heat and mass fluxes in the joint probability density function (PDF) transport equation of the thermochemical variables, the diffusive fluxes are decomposed into their Favre mean and fluctuation. While the mean flux appears to be closed, the contributions of fluctuating fluxes are modeled with the interaction by exchange with the mean (IEM) model. Usually, the contribution of the Favre averaged diffusive fluxes is neglected at high Reynolds numbers. Here, however, this term is included to account for molecular mixing in regions, where turbulent mixing is negligible. This model approach is applied in steady state Reynolds Averaged Navier–Stokes (RANS)/transported PDF calculations to simulate the heat transfer of wall bounded flows as well as the stabilization of a hydrogen–air flame at the burner tip. For both flow problems it is demonstrated that molecular transport is recovered in regions where turbulent mixing vanishes. In wall bounded flows this is the case in the viscous sublayer. Heat transfer studies show, that “mixing models” based on the high Reynolds number assumption fail to compute correctly the temperature field and the heat flux close to the wall. A similar situation occurs at the flame root of the investigated turbulent hydrogen-air jet flame, where turbulent mixing is still too weak to achieve a fast mixing of reactants. In this area differential diffusion effects are observed in the experiment, i.e. superequilibrium temperatures and nonlinear relations between the elemental mixture fractions of hydrogen and oxygen. It will be shown, that the presented model can successfully reproduce these effects, which underlines the necessity to include Favre averaged molecular diffusive fluxes in transported PDF methods.

Development and Application of a Transported Probability Density Function Method on Unstructured Three-Dimensional Grids for the Prediction of Nitric Oxides

The present work explores the capability of the transported probability density function (PDF) method to predict nitric oxide (NO) formation in turbulent combustion. To this end a hybrid finite-volume/Lagrangian Monte Carlo method is implemented into the THETA code of the German Aerospace Center (DLR). In this hybrid approach the transported PDF method governs the evolution of the thermochemical variables, whereas the flow field evolution is computed with a Reynolds-averaged Navier–Stokes (RANS) method. The method is used to compute a turbulent hydrogen-air flame and a methane-air flame and computational results are compared to experimental data. In order to assess the advantages of the transported PDF method, the flame computations are repeated with the “laminar chemistry” approach as well as with an “assumed PDF” method, which are both computationally less expensive. The present study reveals that the transported PDF method provides the highest accuracy in predicting the overall flame structure and nitric oxide formation.

Numerical investigation of a helicopter combustion chamber using LES and tabulated chemistry

This article presents Large Eddy Simulations (LES) of a realistic aeronautical combustor device: the chamber CTA1 designed by TURBOMECA. Under nominal operating conditions, experiments show hot spots observed on the combustor walls, in the vicinity of the injectors. These high temperature regions disappear when modifying the fuel stream equivalence ratio.In order to account for detailed chemistry effects within LES, the numerical simulation uses the recently developed turbulent combustion model F-TACLES (Filtered TAbulated Chemistry for LES). The principle of this model is first to generate a lookup table where thermochemical variables are computed from a set of filtered laminar unstrained premixed flamelets. To model the interactions between the flame and the turbulence at the subgrid scale, a flame wrinkling analytical model is introduced and the Filtered Density Function (FDF) of the mixture fraction is modeled by a β function. Filtered thermochemical quantities are stored as a function of three coordinates: the filtered progress variable, the filtered mixture fraction and the mixture fraction subgrid scale variance. The chemical lookup table is then coupled with the LES using a mathematical formalism that ensures an accurate prediction of the flame dynamics. The numerical simulation of the CTA1 chamber with the F-TACLES turbulent combustion model reproduces fairly the temperature fields observed in experiments. In particular the influence of the fuel stream equivalence ratio on the flame position is well captured.

Large eddy simulation of fuel variability and flame dynamics of hydrogen-enriched nonpremixed flames

In this study large eddy simulation (LES) technique has been used to predict the fuel variability effects and flame dynamics of four hydrogen-enriched turbulent nonpremixed flames. The LES governing equations are solved on a structured non-uniform Cartesian grid with the finite volume method, where the Smagorinsky eddy viscosity model with the localised dynamic procedure is used to model the subgrid scale turbulence. The conserved scalar mixture fraction based thermo-chemical variables are described using the steady laminar flamelet model. The Favre filtered scalars are obtained from the presumed beta probability density function approach. Results are discussed for the instantaneous flame structure, time-averaged flame temperature and combustion product mass fractions. In the LES results, significant differences in flame temperature and species mass fractions have been observed, depending on the amount of H2, N2and CO in the fuel mixture. Detailed comparison of LES results with experimental measurements showed that the predicted mean temperature and mass fraction of species agree well with the experimental data. The high diffusivity and reactivity of H2 largely affect the flame temperature and formation of combustion products in syngas flames. The study demonstrates that LES together with the laminar flamelet model is capable of predicting the fuel variability effects and flame dynamics of turbulent nonpremixed hydrogen-enriched combustion including syngas flames.

Hybrid simulations of metal particle nucleation: A priori and a posteriori analyses of the effects of unresolved scalar interactions on nanoparticle nucleation

The effects of turbulence on nanoparticle nucleation are studied using a combination of fully resolved and large-scale quantities from direct numerical simulations. Growth of these particles is considered by Brownian coagulation. Three simulations are performed using a single Reynolds number and vapor mass fraction. In addition to the direct numerical simulation, we perform hybrid simulations in which fluid, thermal, and scalar transport are fully resolved, while the thermo-chemical variables used in predicting nanoparticle nucleation are filtered. This allows us to elucidate the effects of the unresolved or sub-grid scale (SGS) scalars on the formation of metal particles. The results show that the saturation ratio—representative of the driving force towards particle nucleation—is over-predicted when the SGS interactions are neglected. This results in increased nucleation—particle formation occurs both further upstream and at greater rates. While the SGS interactions act to both increase and decrease particle formation, the tendency to decrease nucleation is dominant.

A Filtered Tabulated Chemistry model for LES of stratified flames

The model called Filtered Tabulated Chemistry for LES (F-TACLES), recently developed for turbulent premixed combustion [1], is extended in the present article to stratified flames where the equivalence ratio is not spatially uniform. The principle is to generate a look-up table where thermo-chemical variables, computed from a set of filtered laminar unstrained premixed flamelets, are stored as a function of the filtered progress variable Y˜c, the filtered mixture fraction c˜, and the mixture fraction subgrid scale variance z″2∼ for a given value of the LES filter size Δ. From this database and using a classical subgrid scale flame surface wrinkling model, a closure model for the filtered progress variable balance equation is then proposed. As only three balance equations (respectively for Y˜c, z˜ and z″2∼) are added to the Navier–Stokes system, this turbulent combustion model is straightforward to implement and is not expensive in terms of CPU time. After preliminary tests on 1-D planar flames, the proposed strategy is applied to a 3-D simulation of a swirled turbulent stratified flame. The agreements observed between numerical and measured data validate the modeling strategy. Finally, it is observed that the flame position cannot be captured without accounting for the subgrid scale mixture fraction heterogeneities that impact on the flame propagation. This result highlights the importance of the mixture fraction filtered density function on the filtered chemical reaction rate.

Laminar flamelet modeling of a turbulent CH 4/H 2/N 2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH 4/H 2/N 2 flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence–chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.

Mixing time-history effects in Large Eddy Simulation of non-premixed turbulent flames: Flow-Controlled Chemistry Tabulation

The time history of mixing is known to play a crucial and non-trivial role in non-premixed turbulent combustion. In a first part, Eulerian balance equations are derived for both a flow residence time and a characteristic time of the mixing which the particles gathered in a fluid element have been subjected to in their flow histories. These equations are analyzed and solved in a Large Eddy Simulation (LES) context for a fuel jet mixing with an oxidizer co-flow. Typical responses of filtered mixture fraction versus flow residence time are highlighted. In a second part, a Flow-Controlled Chemistry Tabulation (FCCT) is devised in which the effects of unresolved fluctuations of thermochemical variables in LES are simulated, combining partially stirred reactors with tabulated chemistry. The reactor evolutions are organized to mimick flow engulfment and micro-mixing, so as to reproduce the observed filtered mixture fraction versus residence time response. This allows for dynamically building subgrid scale joint probability density functions, and thereby the subfilter response of the non-premixed flames, according to four control parameters: the filtered mixture fraction, the progress of reaction, the flow residence time, and a mixing time. Finally, LES of the Cabra et al. [Combust. Flame 143 (2005) 491–506] fuel-jet lifted-flame developing in a vitiated oxidizer environment is performed and results are compared against measurements.

Effect of Injection Angle in Mixing and Combustion Characteristics of Scramjet Combustor

Effect of injection angle in mixing and combustion in a scramjet combustor is numerically simulated. Three dimensional Navier Stokes equations alongwith k-e turbulence model are solved using commercial CFD software. Both infinitely fast rate kinetics and single step finite rate kinetics are used to model chemical kinetics. Turbulence chemistry interaction is modeled by Eddy Dissipation Concept (EDC). Good agreement between the computed and experimental results for angular injection (30°) and perpendicular injection forms the basis of further analysis. More flow blockage has caused significant upstream interaction for perpendicular injection and terminal shock is seen to anchor upstream of combustor step; while for angular injection, the flow field is predominantly supersonic. Single step finite rate chemistry show comparatively low pressure and lesser upstream interaction because of the presence of backward reaction. Thermochemical variables are analysed to study the effect of angle of injection on nature...

Molecular diffusion effects in LES of a piloted methane–air flame

Molecular diffusion effects in LES of a piloted methane–air (Sandia D) flame are investigated on a series of grids with progressively increased resolution. The reacting density, temperature and chemical composition are modeled based on the mixture fraction approach combined with a steady flamelet model. With a rationale to minimize interpolation uncertainties that are routinely introduced by a flamelet table look-up, quadratic splines relationships are employed to represent thermochemical variables. The role of molecular diffusivity in effecting spatial transport is studied by drawing a comparison with the turbulent diffusivity and analyzing their statistics conditioned on temperature. Statistical results demonstrate that the molecular diffusivity in the near-field almost always exceeds the turbulent diffusivity, except at low temperatures (less than 500 K). Thus, by altering the jet near-field, molecular transport plays an important role in the further downstream jet development. Molecular diffusivity continues to dominate in the centerline region throughout the flow field. Overall, the results suggest the strong necessity to represent molecular transport accurately in LES studies of turbulent reacting flows.

English

Thermochemical exploration of mixing and combustion of parallel hydrogen injection into supersonic vitiated air stream in a divergent duct is presented. Three-dimensional Navier Stokes equations along with twoequation turbulence models and Eddy dissipation concept (EDC)-based combustion models are solved using commercial CFD software. Chemical reaction for H2-air system is modelled by two different simple chemical kinetic schemes namely; infinitely fast rate kinetics as well as the single-step finite rate kinetics. Grid convergence of the solution is demonstrated and a grid convergence index-based error estimate has been provided. Insight into the mixing and combustion of high-speed turbulent reacting flow is obtained through the analysis of various thermochemical variables. Very good comparisons are obtained for the exit profiles for various fluid dynamical and chemical variables for the mixing case. For reacting case, the comparison between the experimental and the numerical values are reasonable. Parametric studies were carried out to study the effect of different turbulence models and turbulent Schmidt numbers. It is seen that Wilcox k-w turbulence model performed better than the other two-equation turbulence models in its class. Strong dependence of flow behaviour on turbulent Schmidt number was observed. The results indicate that simple chemical kinetics is adequate to describe the H2-air reaction in the scramjet combustor. Defence Science Journal, 2010, 60(5), pp.465-475 , DOI:http://dx.doi.org/10.14429/dsj.60.57

Numerical Simulation of Liquid Fueled SCRAMJET Combustor Flow Fields

Numerical simulations were carried out for various reacting flow fields related to scramjet propulsion system using commercial CFD Software. Three-dimensional Navier stokes equations were solved along with the K-e turbulence model. Modeling of the turbulence chemistry interaction is done through infinitely fast rate chemical kinetics. The software was validated extensively by comparing different experimental conditions for scramjet combustor to find its error band and range of application. Good agreement between the experimental and computational values were obtained for the scramjet combustor flow field with strut, pylon and cavity injection system with both hydrogen and hydrocarbon fuel. The validated CFD tool was applied in the design exercise of flight-sized kerosene fuel scramjet combustor of a hypersonic airbreathing mission. Significant improvement of combustion efficiency and thrust could be achieved by relocating the fuel injection system through the analysis of various thermochemical variables i...

Application of spray combustion simulation in DI diesel engine

This work presents the development and implementation of combustion model for DI diesel engines by using the PDF-Chemical Equilibrium combustion model. The key concept of this approach is to predict the thermochemical variables (e.g., temperature, species mass fractions) and then the average scalars of these variables are evaluated by a probability density function (PDF) averaging approach. To realize flame propagation, the reaction time scale is employed to relax the infinitely fast chemistry of chemical equilibrium. The PDF-Eddy Break Up ignition model is adopted in the auto-ignition calculation. With regard to the comparison results, the simulation results are in good agreement with the experimental results in both ignition and combustion modes. In addition, the predicted lift-off length also corresponds to a power-law scaling of Siebers et al.

Modelling of instabilities in turbulent swirling flames

A large eddy simulation-based data analysis procedure is used to explore the instabilities in turbulent non-premixed swirling flames. The selected flames known as SM flames are based on the Sydney swirl burner experimental database. The governing equations for continuity, momentum and mixture fraction are solved on a structured Cartesian grid and the Smagorinsky eddy viscosity model with dynamic procedure is used as the sub-grid scale turbulence model. The thermo-chemical variables are described using the steady laminar flamelet model. The results show that the LES successfully predicts the upstream first recirculation zone generated by the bluff body and the downstream second recirculation zone induced by swirl. Overall, LES comparisons with measurements are in good agreement. Generated power spectra and snapshots demonstrate oscillations of the centre jet and the recirculation zone. Snapshots of flame SM1 showed irregular precession of the centre jet and the power spectrum at a downstream axial location situated between the two recirculation zones showed distinct precession frequency. Mode II instability defined as cyclic expansion and collapse of the recirculation zone is also identified for the flame SM2. The coupling of swirl, chemical reactions and heat release exhibits Mode II instability. The presented simulations demonstrate the efficiency and applicability of the LES technique to swirl flames.

A Hybrid Large Eddy Simulation/Filtered Mass Density Function for the Calculation of Strongly Radiating Turbulent Flames

Due to the complex nonlinear coupling of turbulent flow, finite-rate combustion chemistry and thermal radiation from combustion products and soot, modeling, and/or simulation of practical combustors, or even laboratory flames undergoing strong soot formation, remain elusive. Methods based on the determination of the probability density function of the joint thermochemical scalar variables offer a promising approach for handling turbulence-chemistry-radiation interactions in flames. Over the past decade, the development and application of the filtered mass density function (FMDF) approach in the context of large eddy simulations (LES) of turbulent flames have gained considerable ground. The work described here represents the first application of the LES/FMDF approach to flames involving soot formation and luminous radiation. The initial focus here is on the use of a flamelet soot model in an idealized strongly radiating turbulent jet flame, which serves to detail the formulation, highlight the importance of turbulence-radiation interactions, and pave the way for the inclusion of a soot transport and finite-rate kinetics model allowing for quantitative comparisons to laboratory scale sooting flames in the near future.

LES of Recirculation and Vortex Breakdown in Swirling Flames

In this study large eddy simulation (LES) technique has been applied to predict a selected swirling flame from the Sydney swirl burner experiments. The selected flame is known as the SM1 flame operated with fuel CH 4 at a swirl number of 0.5. In the numerical method used, the governing equations for continuity, momentum and mixture fraction are solved on a structured Cartesian grid. The Smagorinsky eddy viscosity model with the localised dynamic procedure of Piomelli and Liu is used as the subgrid scale turbulence model. The conserved scalar mixture fraction-based thermo-chemical variables are described using the steady laminar flamelet model. The GRI 2.11 is used as the chemical mechanism. The Favre-filtered scalars are obtained from the presumed beta probability density function (β-PDF) approach. The results show that with appropriate inflow and outflow boundary conditions LES successfully predicts the upstream recirculation zone generated by the bluff body and the downstream vortex breakdown zone induced by swirl with a high level of accuracy. Detailed comparison of LES results with experimental measurements show that the mean velocity field and their rms fluctuations are predicted very well. The predictions for the mean mixture fraction, subgrid variance and temperature are also reasonably successful at most axial locations. The study demonstrates that LES together with the laminar flamelet model in general provides a good technique for predicting the structure of turbulent swirling flames.