Mixture Fraction Gradient Research Articles

An iterative methodology for REDIM reduced chemistry generation and its validation for partially-premixed combustion

Partially-premixed flames (PPFs) incorporate effects of both premixed and non-premixed types of reaction zones. The modelling of PPFs using manifold-based model reduction methods faces some inherent difficulties due to the underlying assumptions of a-priori identification of the type of combustion system. In this work, the reaction–diffusion manifold (REDIM) model reduction method is applied to study PPFs. The REDIM method requires minimal prior knowledge about the type of combustion system, which makes it a suitable method for studying PPFs. It allows incorporating system-specific diffusion (gradients) terms in a generic way so that the manifold can evolve according to the diffusion related information provided by the combustion system. In this way, a prior identification of the type of combustion system is no longer needed. This work utilises an iterative methodology to generate REDIM chemistry tables so that the reduced manifold can be iteratively converged very close to the detailed manifold according to the gradients of the reduced coordinates provided by the physical combustion system in each iteration step. In addition, a new method is proposed to provide the gradient estimates of the reduced coordinates during the generation of REDIM from the scattered gradient data in REDIM reduced CFD calculations. Laminar triple flames, a special case of PPFs, with two types of mixture fraction gradients are selected as the target cases to assess the presented iterative methodology. REDIM reduced calculations are compared with simulations based on detailed finite-rate kinetics. It is found that in the final iteration steps, temperature and all considered major and minor species mass fraction profiles are very well predicted by the REDIM reduced calculations.

A comparative analysis of the evolution of compositional and entropy waves in turbulent channel flows

Indirect combustion noise, as an important source of noise in gas turbines, was traditionally attributed solely to entropy waves. In recent years, compositional waves were introduced as another contributor to indirect combustion noise. Nonetheless, unlike that of entropy waves, the annihilation of compositional waves by the mean flow has remained largely unexplored. Hence, the current numerical study analyzes the spatiotemporal evolution of different components of compositional waves and compares them with the decay of entropy waves. A convecting wave, including a mixture of combustion products at elevated temperature, is introduced at the inlet of a simple channel. This allows simultaneous analysis of entropy and compositional waves. The passage of these along the channel is modeled using a large eddy simulation, and the annihilation of the waves' components is examined in the frequency domain. It is shown that the turbulence level of the mean flow and convective heat transfer on the walls can both result in a considerable wave deterioration. However, the effects of heat losses from the channel walls are found to be stronger than that of turbulence intensity. Importantly, as the wave is convected, the chemical potential function remains coherent for most of the channel length, and deterioration of the compositional wave majorly ensues from the mixture fraction gradient. The results indicate that, overall, the compositional sources feature 10%–20% more dissipation in comparison with the entropic sources. Therefore, compositional waves are less likely to survive the flow and generate noise.

Scalar gradient and flame propagation statistics of a flame-resolved laboratory-scale turbulent stratified burner simulation

A bluff-body stabilised turbulent jet flame burning in a stratified mode of combustion for fuel-lean methane/air mixtures is investigated by a flame-resolved simulation. A tabulated chemistry approach based on premixed flamelet generated manifolds (PFGM) accounts for thermochemistry. The computations are performed for a grid-resolution of 100 µm, sufficient to resolve the thermal flame thickness. The look-up table is generated with a mixture-averaged diffusivity assumption and the preferential diffusion fluxes are included in the simulation, using an efficient method without increasing the dimensionality of the manifold. The predicted mean and RMS quantities are found to be in good agreement with the experiment. The investigation focuses on the comparison of the combustion behaviour of the upstream locations close to the inlet with weak mixture fraction gradients to the downstream locations away from the inlet with strong mixture fraction gradients. Statistical analysis of the diffusion terms within the flame revealed that the preferential diffusion remains significant near the inlet, in the recirculation zone over the bluff-body. The structure of the stratified flame in downstream locations is statistically analysed in terms of displacement speed and scalar gradients by comparing against the corresponding quantities in upstream locations with weak mixture fraction gradients. It is shown that the displacement speed is statistically different between the flames under weak or strong mixture fraction gradients due to the influence of molecular diffusion and reaction rate components. However, increased curvature effects and cross-dissipation component also play a role. Finally, scalar dissipation and cross-dissipation rates of the mixture fraction fluctuation and the reaction progress variable fluctuation within the flame-brush are investigated, and their closure approaches are discussed.

An extended flame index partitioning for partially premixed combustion

Compared to partially premixed combustion (or combustion of non-homogeneous reactants in general), fully premixed and diffusion flames represent only two asymptotic limits of combustion modes. However, the deep knowledge accumulated over the years on these two elementary and archetypal flame prototypes is such that they remain the cornerstone and reference building blocks of most combustion modelling proposals. Therefore, from a general point of view, being able to distinguish between premixed and non-premixed modes of combustion thanks to a flame index appears as a quite appealing but challenging task that still concentrates many research efforts. Indeed, the availability of such an index is not only appealing to proceed with the analysis of either experimental or computational data issued from DNS (or highly resolved LES) databases. It is also an essential ingredient to elaborate advanced flamelet-based multiregime combustion models on the basis of single regime tabulated flamelet databases. In the present study, a new definition of the premixedness index is proposed for partially premixed combustion. It is based on a weighted form of the cross-scalar dissipation rate of the mixture fraction and progress variable , i.e. quantities that have been previously identified as relevant parameters to describe partially premixed combustion regimes. The relevance of the corresponding index is assessed through a detailed computational procedure that includes three successive validation subsets: counterflow flames (including premixed, rich partially-premixed, and diffusion flames), (ii) stabilised triple flames for three distinct values of the inlet mixture fraction gradient, and finally (iii) unsteady flame kernel developments in non-homogeneous mixtures of fresh reactants, which are characterised by various initial levels of the segregation rate between the fuel and oxidiser. The proposed premixedness index and its counterpart are used as the weighting coefficients between tabulated premixed flamelets (TPF) and tabulated diffusion flamelets (TDF) data, which have been parameterised as functions of and . It is noteworthy that, in contrast to some previous proposals of the literature, the present flame index does not require the consideration of any other quantities in addition to those already used to parameterise the flamelets databases, i.e. and . The validation procedure makes use of steady and unsteady processes with a priori and a posteriori analyses. In both cases, the comparisons between the results obtained with the proposed flame partitioning and detailed chemistry (DC) computations lead to a satisfactory level of agreement and, from a general viewpoint, the level of agreement is better than the one obtained with either premixed or diffusion flamelet-based models.

Nonlinear Flame Dynamics for Laminar Flame in a Co-flow Mixing Layer with Widely Varying Premixedness: Preferential Diffusion and Stoichiometry Effects

ABSTRACT Intrinsic oscillations arising due to thermo-diffusive mechanism have been studied numerically in the literature for laminar flames having Lewis number greater than unity. In the previous work, the Lewis numbers of fuel and oxidizer are assumed to be equal and the unburnt mixture to be in stoichiometric in proportion. Here, the study is extended to relax these assumptions. In the first part of the present work, the Lewis numbers of fuel and oxidizer are varied individually keeping the overall mixture stoichiometric. The simulations are run for laminar flames stabilized near to a cold burner in a co-flow mixing layer generated by a fuel rich stream and oxidizer rich stream. The premixedness of the unburnt mixture is varied using a premixedness parameter defined in the previous work. This parameter characterizes upstream mixture-fraction gradients such that it approaches unity for zero mixture-fraction gradient and zero when the mixture-fraction gradient is infinite. Thus, upon ignition, different flame structures like, planar premixed flame, triple flames and an edge flame can be observed, as this parameter is varied from zero to unity. Simulations are run to study large time behavior for various values in this range of premixedness. Intrinsic oscillations in the total reaction rate (integrated over the domain) are observed for a combination of values of Lewis numbers of fuel and oxidizer. These are presented as series of contour plots of amplitude of total reaction rate onto a 2D plane with Lewis number of fuel on x-axis and Lewis number of oxidizer on y-axis for various values of premixedness. It is found that the contours of constant amplitude are nearly linear for diffusion flame and partially premixed flames, thus validating the effective Lewis number definition hitherto defined for diffusion flames. Hence, this effective Lewis number can determine the onset of oscillations and also their magnitude. But for weakly curved triple flames, there is significant variation, where the constant amplitude lines are curved. Also, the amplitude of oscillations observed for weakly curved triple flames is much higher than that for other flames. Apart from intrinsic oscillations the shape and structure of triple flame is also studied. It is found that premixed flame branches of a triple flame are highly asymmetric about the trailing edge diffusion flame. The change in the location of triple point is also observed. In the second part of the work, the assumption of the overall stoichiometric ratio being unity is relaxed to understand the effect of the off-stoichiometric mixture on the shape and stability of flame. However, the Lewis numbers of the fuel and oxidizer are maintained to be equal. The maximum intensity of oscillations is observed at an equivalence ratio of 0.3 for partially premixed flames and at around unity for premixed flames.

Effects of Biogas Composition on the Edge Flame Propagation in Igniting Turbulent Mixing Layers

Three-dimensional compressible Direct Numerical Simulations have been used to investigate the localised forced ignition of statistically planar biogas/air mixing layers for different levels of turbulence intensity and biogas composition. The biogas is represented by a hbox {CH}_4/hbox {CO}_2 mixture and a two-step mechanism capturing the variation of the unstrained laminar flame speed with equivalence ratio and hbox {CO}_2 dilution was used. The mixture composition was found to significantly affect the flame kernel development which was reflected in the diminished growth rate of the burned gas volume with increasing hbox {CO}_2 dilution. A successful ignition of hbox {CH}_4/hbox {CO}_2/air mixing layer gives rise to a tribrachial flame structure involving fuel-rich and lean premixed branches on either side of the diffusion flame stabilised on the stoichiometric mixture fraction iso-surface. The most probable edge flame speed decreases in time and converges to a value that is at most equal to its laminar theoretical limit, and can even locally become negative for large values of the dilution and/or turbulence intensity. The decomposition of the edge flame speed showed a negligible or negative contribution of the mixture fraction surface displacement speed, while the displacement speed of the fuel mass fraction surface appeared as the dominant contributor. Finally, the edge flame speed dependences to the fuel mass fraction and mixture fraction gradients, fuel mass fraction iso-surface curvature and tangential strain rate have been analysed and found, within the dilution values considered, qualitatively similar to those of undiluted mixtures regardless of the amount of hbox {CO}_2, although quantitative differences were observed.

Heat-release dynamics in a doubly-transcritical LO2/LCH4 cryogenic coaxial jet flame subjected to fuel inflow acoustic modulation

Large Eddy Simulations are used to study the heat-release response to fuel inflow acoustic harmonic oscillations, in a coaxial jet flame where both reactants (O2 and CH4) are injected in a dense cryogenic state. The geometry is that of the academic test rig Mascotte, operated by ONERA (France), which high pressure operating conditions are relevant for the characterization of flame dynamics in Liquid Rocket Engines (LREs). The simulations, which are carried out with a real-gas fluid solver using a detailed kinetic scheme for CH4 high-pressure oxycombustion, provide a thorough insight into the flame response for a wide range of forcing frequencies, spanning from approximately 1kHz to 20kHz. Local Flame Transfer Functions (FTF) are computed and analyzed: regions of preferential heat-release response are observed to be highly dependent on the forcing frequency. An analysis based on a flame sheet assumption is conducted to distinguish the main sources of heat release fluctuations: the primary contribution comes from the species diffusivity oscillations, while the density variations have a negligible effect. The second largest contributor is either the mixture fraction gradient or the flame surface area, depending on the forcing frequency. The FTFs are expected to be useful for thermoacoustic Low-Order Models or Helmholtz solvers, and the subsequent analysis has the potential to guide future development of analytical models for flame dynamics in LREs.

Derivation and analysis of two-dimensional composition space equations for multi-regime combustion using orthogonal coordinates

Interactions between premixed and non-premixed reaction zones can lead to complex mixed combustion regimes, here denoted as multi-regime combustion, which pose challenges to many conventional combustion modeling approaches. Such conditions occur in most practical combustors and can originate from partial premixing, mixture inhomogeneities/stratification, hot product recirculation, or local flame extinction and re-ignition. Therefore, novel equations are derived for modeling multi-regime combustion which are formulated with respect to a two-dimensional composition space spanned by mixture fraction and reaction progress variable. Contrary to previous works, the dependency of the progress variable on the mixture fraction is considered in the new model. This is achieved by splitting the progress variable gradient into an aligned and an orthogonal component with respect to the mixture fraction gradient and the latter is used to define the second coordinate. In the theory that follows, a balance equation for the progress variable on mixture fraction iso-surfaces is formulated. Using this balance equation together with the orthogonal coordinate system, the transformation of species and temperature equations to the 2D composition space yields a novel set of equation without so-called cross-terms. This is advantageous since cross-terms obtained with previous approaches lack a general closure and it is uncertain if it exists at all. Furthermore, the approach allows to naturally distinguish between non-premixed and premixed combustion regimes, auto ignition, and it covers multi-regime combustion characteristics. The theory is validated and discussed by means of a fully resolved solution of a laminar triple flame using detailed chemistry. At first, regions which exhibit premixed, non-premixed or multi-regime combustion characteristics are identified. The triple flame solution then serves as a database from which all relevant theoretical relations are post-processed and validated. In comparison to budgets of conventional 1D flamelet equations for premixed and non-premixed combustion it is shown that only the full set of transport terms considered in the 2D equations accurately balances chemical source terms everywhere in the triple flame, especially in regions where multi-regime combustion prevails.

The Speed and Temperature of an Edge Flame Stabilized in a Mixing Layer: Dependence on Fuel Properties and Local Mixture Fraction Gradient

ABSTRACT Edge flames are of fundamental importance to the attachment and stabilization of diffusion flames in many practical devices, and serve as transient structures for establishing combustion in locally-quenched regions of turbulent diffusion flames. In this study, we consider an edge flame sustained in the mixing layer of two streams, one containing fuel and the other oxidizer, and examine its structure and its thermal and dynamic properties over a wide range of flow conditions, using a diffusive-thermal (constant-density) model. In addition, we allow for the fuel Lewis number to vary from sub- to super-unity values, corresponding to light and moderately heavy fuels, or fuels suitably diluted by inert species, with unity oxidizer Lewis number as appropriate for combustion in air. Two regimes have been identified and examined; a thermal-interaction regime where there is appreciable heat loss from the edge flame to the splitter plate, and a freely-standing regime where the edge flame lifts off considerably and the plate plays no role on its stabilization. The objective is to correlate important edge-flame properties, including standoff distance and edge speed and temperature, with global parameters such as overall flow rate and total heat conducted from the flame to the plate, and local parameters such as local mixture fraction gradient at the edge of the flame.

Liftoff and blowout of the Emmons flame: Analysis of the triple flame

The steady burning and stabilization of the boundary layer diffusion flame over a gasifying condensed fuel surface, commonly called the Emmons flame, is an important problem in the study of boundary layer combustion. We investigate herein, theoretically and numerically, the liftoff distance and blowout limit of the Emmons flame, through the corresponding response of the controlling triple flame in the leading edge of the bulk flame. An explicit solution of the flame liftoff distance and the critical blowout limit is derived, with the theoretical results agreeing well with the numerical simulation for an extensive range of the system parameters. In particular, it is shown that the transversal velocity gradient (TVG) ahead of the triple flame renders the flame harder to liftoff and blowout, with this effect increasing for increasing TVG and decreasing triple flame curvature, which is related to the mixture fraction gradient. Furthermore, the Spalding mass transfer number, Bv, for the surface segment ahead of the flame front affects the flame stabilization and blowout limit by modifying the similarity structure of the flow and the location of stoichiometry. Thermal expansion of the flow around the triple flame together with the surface viscous drag also significantly promotes flame stabilization.

Edge flame propagation statistics in igniting monodisperse droplet-laden mixtures

The effects of droplet diameter, overall (i.e., liquid+gaseous phases) equivalence ratio, and turbulence intensity on the edge flame propagation statistics for localized forced ignition of uniformly dispersed n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on direct numerical simulations data. It has been found that the edge flame structure becomes increasingly prominent for large overall equivalence ratios and droplet diameters. Although the mean edge flame speed has been found to be positive and its most probable value remains comparable to the theoretical value for laminar edge flames in purely gaseous mixtures, the mean values have been found to decrease and the probabilities of finding locally negative edge flame speeds have been found to increase with increasing turbulence intensity. The marginal probability density function and curvature and strain rate dependences of the edge flame speed have been found to be principally governed by the displacement speed of the fuel mass fraction isosurface intersecting the stoichiometric mixture fraction isosurface. The displacement speed of the stoichiometric mixture fraction isosurface has also been found to influence the local scalar gradient dependences of the edge flame speed in this configuration, especially for large droplets. The displacement speed of the fuel mass fraction isosurface Sd has been found to be principally governed by leading order contributions of the reaction and molecular diffusion components and the evaporation contribution remains weak in comparison to these leading order contributors. The local edge flame speed exhibits nonlinear curvature and strain rate dependences and its variation with the magnitudes of both fuel mass fraction and mixture fraction gradients has been found to be nonmonotonic for all cases considered here. The correlations of the edge flame speed with curvature, strain rate, and scalar gradient have been found to be qualitatively similar to the corresponding statistics reported in the existing literature for edge flames in purely gaseous mixtures. Additionally, the curvature and tangential strain rate dependences of the edge flame speed have been found to be dependent on the droplet size and overall equivalence ratio, and these dependences become weak for cases with large droplets.

Scalar predictors of premixed gas ignition by a suddenly-starting hot jet

Hot-jet ignition is usually designed to reduce emissions in lean-burn combustion engines, and has potential in enabling novel pressure-gain combustion. Inspired by our experimental observations related to wave-rotor combustion chamber ignition, this work employs a numerical method to examine the sudden injection of a hot jet into a quiescent mixture of CH4–H2-air and the subsequent ignition. The goal is to provide the range of thermo-physical scalars that are supportive of successful ignition. The evolution of scalar fields is evaluated using large-eddy simulation (LES). The temporal evolution of mixture fraction, the squared gradient of mixture fraction (as indicative of scalar dissipation rate), strain rate, and intermediate species are investigated in order to find the appropriate physical conditions which support ignition. Independent distribution of stain rate and squared gradient of mixture fraction, especially in the leading head vortex, shows the necessity of correlated scalar analysis of the ignition process. Experimental and numerical methods are then employed to provide the qualitative and quantitative understanding of ignition process for fuels with two distinct hydrogen contents. Results show the meaningful difference in spatial distribution of local ignition as hydrogen content of the fuel increases.

Statistics of Scalar Dissipation and Strain/Vorticity/Scalar Gradient Alignment in Turbulent Nonpremixed Jet Flames

Turbulence and mixing statistics are investigated in a set of flames at a jet Reynolds number of 15000 achieving a Taylor’s scale Reynolds number in the range 100 ≤Reλ ≤ 150. In particular, the impact on small scale turbulence statistics of different levels of flame extinction, induced imposing different Damkohler numbers in the three simulated cases, is investigated. It is found that the non-dimensional scalar dissipation depends on the Damkohler number slightly. This deviation from self-similarity manifests itself as a decrease of the non-dimensional scalar dissipation with increasing occurrence of localized extinction events. This is caused by the decrease of molecular diffusion due to the lower flame temperatures in the low Damkohler number cases. Probability density functions of the scalar dissipation χ show important deviations from the log-normal distribution. The left tail of the pdf scales as χ1/2 while the right tail scales as $e^{-c\chi ^{\alpha }}$ , as shown for incompressible turbulence. In all flames, the vorticity vector displays a pronounced tendency to align with the direction of the intermediate strain and the gradient of mixture fraction aligns with the most compressive strain. Conditioning on the local values of mixture fraction and heat release does not affect the statistics. The alignment statistics of vorticity are in agreement with those in homogeneous isotropic turbulence while they show some difference compared to previous results in non premixed flames. The alignment between strain and mixture fraction gradient differs slightly from the homogeneous isotropic turbulent case but agree remarkably well with previous results observed in homogeneous shear incompressible flows.

Influence of flow topology and scalar structure on flame-tangential diffusion in turbulent non-premixed combustion

Flamelet-based combustion models have been extensively used in the modeling of turbulent non-premixed combustion due to their notable advantages in reducing computational cost. The classical one-dimensional flamelet equations are derived based on an assumption: flame-normal transport of thermochemical state variables in mixture fraction gradient direction dominates over flame-tangential transport along iso-surfaces of mixture fraction. The motivation of this work is to quantify the contribution of tangential diffusion (TD) and seek the source of TD, since several recent studies have shown that TD effects may play an important role in the regions with large curvature and finite-rate chemistry. In this work, the most probable cause and effect chain that elucidates the source of TD in a turbulent non-premixed jet flame is proposed for the first time from a flow topology perspective. To this end, local flow topology and its effects on scalar structure are first investigated. It is found that the local flow structures with unstable focus compressing (UFC) topology have the highest probability of large compressive strain and that the negative correlation between curvature and strain strongly depends on local flow topology, scalar structure and reaction. Then, the influence of flow topology and scalar structure on the relevance of TD is assessed with the angle between reactive scalars and mixture fraction. The results show that TD effects mainly exist in the regions with high curvatures and low strain rates or scalar dissipation rates. These findings suggest that the local flow structures with low probability of UFC topology tend to cause significant flame-tangential diffusion in the turbulent non-premixed flame.

Dynamics of triple-flames in ignition of turbulent dual fuel mixture: A direct numerical simulation study

Pilot-ignited dual fuel combustion involves a complex transition between the pilot fuel autoignition and the premixed-like phase of combustion, which is challenging for experimental measurement and numerical modelling, and not sufficiently explored. To further understand the fundamentals of the dual fuel ignition processes, the transient ignition and subsequent flame development in a turbulent dimethyl ether (DME)/methane-air mixing layer under diesel engine-relevant conditions are studied by direct numerical simulations (DNS). Results indicate that combustion is initiated by a two-stage autoignition that involves both low-temperature and high-temperature chemistry. The first stage autoignition is initiated at the stoichiometric mixture, and then the ignition front propagates against the mixture fraction gradient into rich mixtures and eventually forms a diffusively-supported cool flame. The second stage ignition kernels are spatially distributed around the most reactive mixture fraction with a low scalar dissipation rate. Multiple triple flames are established and propagate along the stoichiometric mixture, which is proven to play an essential role in the flame developing process. The edge flames gradually get close to each other with their branches eventually connected. It is the leading lean premixed branch that initiates the steady propagating methane-air flame. The time required for the initiation of steady flame is substantially shorter than the autoignition delay time of the methane-air mixture under the same thermochemical condition. Temporal evolution of the displacement speed at the flame front is also investigated to clarify the propagation characteristics of the combustion waves. Cool flame and propagation of triple flames are also identified in this study, which are novel features of the pilot-ignited dual fuel combustion.

A generalized flamelet tabulation method for partially premixed combustion

A flamelet tabulation method for partially premixed flames is proposed, in which partially premixed flamelets are incorporated as the archetypal flamelet elements. This method considers triple flame structures with both the partial premixing of fuel in the oxidizer side and the partial premixing of oxidizer in the fuel side, by replacing the pure-air and pure-fuel in the counterflow diffusion flame with a range of fuel-lean and -rich mixtures, respectively. The thermo-chemical quantities in the partially premixed flamelet are stored in a four-dimensional flamelet library as a function of the mixture fraction Z, describing the mixing process, the reaction progress variable YPV, describing the progress of reactions, and the trajectory variables YF and YO, characterizing the partial premixings of fuel and oxidizer, respectively. The performance of the proposed partially premixed flamelet tabulation (PPFT) method is evaluated through both a priori and a posteriori tests on laminar tribrachial flames with different mixture fraction gradients. The PPFT results are compared with those from a premixed flamelet tabulation (PFT) method and a diffusion flamelet tabulation (DFT) method. It is found that the combustion-mode-sensitive species such as CO and H2 can be accurately predicted by the PPFT method for both the low and high mixture fraction gradient flame cases, which cannot be well predicted by the PFT and DFT methods.

Evaluation of chemistry models on methane/air edge flame simulation

The integration of chemistry into a numerical fully compressible solver is carried out in this study using three models: detailed chemistry, fully tabulated chemistry (CTC) and a model coupling both approaches called HTTC, for hybrid transported-tabulated chemistry. With HTTC major species are transported while most minor species are tabulated. As minor species are no longer transported with the flow, the time step is close to the values usually encountered for non-reactive flows, far beyond what is found in detailed chemistry. The performance of HTTC for reproducing the dynamics of a methane/air edge flame featuring a very strong mixture fraction gradient is also investigated. The results agree favorably with the reference case simulated with detailed chemistry unlike the CTC model which is unable to predict the topology of the flame. Finally, the shape of the flame, the flame speed and the flame stabilization height are reasonably well captured with HTTC with a calculation cost divided by about 5 compared to the reference case.

A modification to temperature-composition pdf method and its application to the simulation of a transitional bluff-body flame

This study proposes a modification to the temperature-composition pdf approach. Instead of equilibrium mass fractions, values of a time-varying homogeneous reacting system are used in the simplification of the joint-pdf into the multiplication of marginal pdfs. The approach takes into consideration of local time scales which are defined on the basis of energy balance with two competing transport mechanisms on the flame surface; these are the turbulent convective transport perpendicular to the flame and the diffusive flux tangent to the flame. The flame surface and flux directions are described by the gradient of mixture fraction and unitary tangent vector which is defined by the scalars. The new approach in combination with the ILDM chemistry is used in the numerical simulation of a transitional bluff-body flame. Despite the use of simple pdf models, the present formulation appears to be very successful in predicting the flow field, the temperature and progress variables and, except for the mixture fraction, show relatively good agreement with the experimental data. The profiles of the time scale show that the flame develops in relation to the distributions of progress variables in the T−ξ parameter space. Hence, the approach offers the possibility of local flame extinction. It also gives a rational explanation of the bimodal distributions of the reactive scalar pdfs in a turbulent flow with fluctuations of a wide spectrum of scales.

Scalar dissipation rates in a turbulent partially-premixed dimethyl ether/air jet flame

This paper presents the gradient structure of a turbulent partially premixed dimethyl ether (DME)/air jet flame operating at a jet Reynolds number of 29,300. Temperature and mixture fraction profiles from Raman/Rayleigh/CO-LIF line measurements are used to determine one-dimensional scalar dissipation rates at six axial locations. A major focus of the current work is to assess the effects of experimental artifacts, including spatial resolution, noise, and dimensionality, on the accuracy of the derived scalar dissipation rate. Two-dimensional probability density functions (PDFs) of the mixture fraction gradients are used to determine possible clipping effects due to insufficient spatial resolution. This resolution limit is compared to values determined from one-dimensional dissipation spectra and scaling laws. Spatial resolution also is investigated using laminar flame calculations in conjunction with optical-blur filters representing the experimental setup. The impact of noise is treated by error propagation methods. Monte Carlo simulations and experimental data from laminar flames are used to verify and validate the models used to predict noise propagation for the measurements of the absolute gradients, squared gradients, and scalar dissipation rates. Gradient and scalar dissipation rate detection limits and contribution from apparent dissipation (due to noise effects) are presented as functions of measurement signal-to-noise ratios. A noised lognormal function is introduced to investigate the impact of noise on derived PDFs and corresponding statistical moments of the measured scalar gradients and the scalar dissipation rate within the turbulent flame. Results from the turbulent flame measurements are presented in the form of scatter plots and conditional statistics to examine turbulence-chemistry interaction and develop a database for model assessment. Specifically, the results are compared to laminar flame calculations over a broad range of strain rates with multi-component and unity Lewis number transport assumptions. This comparison is used to assess the relevance of differential diffusion effects on scalar dissipation rates in the turbulent flame.

Dissipation element analysis of a turbulent non-premixed jet flame

The objective of the present work is to examine the interaction between turbulent mixing and chemistry by employing the method of dissipation elements in a non-premixed turbulent jet flame. The method of dissipation elements [L. Wang and N. Peters, J. Fluid Mech. 554, 457–475 (2006)] is used to perform a space-filling decomposition of the turbulent jet flow into different regimes conditioned on their location with respect to the reaction zone. Based on the non-local structure of dissipation elements, this decomposition allows us to discern whether points away from stoichiometry are connected through a diffusive layer with the reaction zone. In a next step, a regime based statistical analysis of dissipation elements is carried out by means of data obtained from a direct numerical simulation. Turbulent mixing and chemical reactions depend strongly on the mixture fraction gradient. From a budget between strain and dissipation, the mechanism for the formation and destruction of mean gradients along dissipation elements is inspected. This budget reveals that large gradients in the mixture fraction field occur at a small but finite length scale. Finally, the inner structure of dissipation elements is examined by computing statistics along gradient trajectories of the mixture fraction field. Thereby, the method of dissipation elements provides a statistical characterization of flamelets and novel insight into the interaction between chemistry and turbulence.