Turbulent Premixed Jet Flames Research Articles

Direct numerical simulations of pure and partially cracked ammonia/air turbulent premixed jet flames

Ammonia has been identified as a promising fuel to diminish greenhouse gas emission. However, ammonia combustion presents certain challenges including low reactivity and high NO emission. In the present study, three-dimensional direct numerical simulations (DNS) of ammonia/air premixed slot jet flames with varying Karlovitz numbers (Ka) and cracking ratios were performed. Three cases were considered, including two pure ammonia/air flames with different turbulence intensities and one partially cracked ammonia/air flame with high turbulence intensity. The effects of turbulence intensity and partial ammonia cracking on turbulence–flame interactions and NO emission characteristics of the flames were investigated. It was shown that the turbulent flame speed is higher for the flames with high turbulence intensity. In general, the flame displacement speed is negatively correlated with curvature in negative curvature regions, while the correlation is weak in the positive curvature regions for highly turbulent flames. Most flame area is consumed in negatively curved regions and produced in positively curved regions. It was found that the NO mass fraction is higher in the flame with partial ammonia cracking compared to the pure ammonia/air flames. The NO pathway analysis shows that the NH → NO pathway is enhanced, while the NO consumption pathway is suppressed in the partially cracked ammonia/air flame. The NO mass fraction is higher in regions of negative curvature than positive curvature. Interestingly, the NO mass fraction is found to be negatively correlated with the local equivalence ratio, which is consistent in both the DNS and the corresponding laminar premixed flames.

Augmenting filtered flame front displacement models for LES using machine learning with a posteriori simulations

The Flame Surface Density (FSD) model is an affordable combustion model that has been widely used in simulating turbulent premixed flames. In Large Eddy Simulations (LES) with FSD, the combined effect of reaction and diffusion is governed by the Filtered Flame Front Displacement (FFFD) term. While the existing modelling approaches for this term are computationally cost-effective, their predictions still show inconsistencies in certain cases. This study aims to address these inconsistencies by generating Machine Learning (ML) models for the FFFD and FSD terms using the DNS data of a turbulent premixed jet flame. With this approach, the relevance of certain input parameters as well as certain modelling assumptions used for the FFFD term are assessed. Overall, it is found that the resolved curvature term is the most important input parameter to consider and that the resolved progress variable should also be considered in the models. It is shown that the ML models perform significantly better than legacy, algebraic formulations using a priori testing. To further assess the performance of ML, one of the ML models is employed in a a posteriori LES and compared against simulations with the algebraic model. The ML simulation is stable and yields encouraging improvements on key physical parameters regarding the flame length and the FFFD distribution.Novelty and Significance Statement: This research is of importance because it answers fundamental and practical questions related to the use of combustion modelling approaches, specifically the Flame Surface Density (FSD) and the Filtered Flame Front Displacement (FFFD) models, by means of Machine Learning (ML) algorithms. From a fundamental aspect, we show that two features which are typically not considered as inputs in combustion models, i.e., the progress variable and the resolved curvature, are key to consider for improved predictions of the model, more so than features which are typically used in FSD modelling, i.e., uΔ′,Δ, and |∇c¯|. From a practical standpoint, we demonstrate a framework to use the developed ML combustion model a posteriori in a LES, without any stability issues. Overall, these findings are key to guide further traditional and ML improvement efforts on combustion models.

Data-based instantaneous conditional progress variable dissipation rate modeling for turbulent premixed combustion

Manifold-based turbulent combustion modeling reduces computational cost considerably by projecting the thermochemical state onto a lower-dimensional space of a few manifold variables and reconstructing the state from a set of manifold equations. In turbulent premixed combustion, a one-dimensional space is defined by the progress variable, and the progress variable dissipation rate appears as a parameter in the resulting one-dimensional manifold equations. Closure of the manifold equations requires a model for the dependence of this dissipation rate on the progress variable. Existing models for these profiles are often ad hoc, derived analytically with crude assumptions, and assumed to be spatially and temporally ‘universal’ — yet the resulting thermochemical state can be sensitive to these profiles. To evaluate the assumptions in traditional models, instantaneous conditional progress variable dissipation rate profiles are extracted from DNS databases of turbulent premixed jet flames. At low Karlovitz number, the instantaneous conditional progress variable dissipation rate profiles exhibit some variance but are relatively well-characterized by a ‘universal’ model. However, a large variance in the instantaneous conditional progress variable dissipation rate profiles is observed at high Karlovitz number, indicating the form of the conditional dissipation rate is certainly not ‘universal’. To capture this variation at high Karlovitz number, a data-based model for the instantaneous conditional progress variable dissipation rate profiles is generated, and the resulting model predictions demonstrate excellent agreement with profiles extracted from DNS and far less error than ‘universal’ models. The sensitivity of the solutions of the one-dimensional premixed manifold equations to the dissipation rate profile is demonstrated a priori, and the error associated with the observed variance in the instantaneous conditional progress variable dissipation rate profiles (i.e., relative to the DNS mean) indicates that an instantaneous modeling approach is necessary. A variable importance study is conducted, and the conditional velocity gradient is identified as the critical quantity that characterizes the observed variance in the instantaneous conditional progress variable dissipation rate profiles, providing further motivation for a data-based modeling approach.

Flame structure and broadening in turbulent premixed jet flames

High-resolution and high signal-to-noise (SNR) planar Rayleigh scattering thermometry measurements are performed to investigate preheat and reaction zone broadening, turbulent transport of high-temperature gases, and the internal flame structure in a series of highly turbulent, lean (ϕ = 0.75), premixed methane-air turbulent jet flames. These flames are characterized by turbulence intensities ranging from u′/SL of 35 to 150 and turbulent Reynolds numbers approaching 104, as determined from separate particle image velocimetry (PIV) measurements. Average flame profiles obtained using a gradient-based flame reconstruction method and probability density functions (PDFs) of the preheat, reaction, and thermal layer thicknesses show substantial broadening of the preheat and thermal layers. Instantaneous preheat zones are broadened by as much as a factor of 30 compared to laminar flames, with an average broadening approaching a factor of 14 for the most turbulent case. Moderate broadening of the reaction layer is observed with up to a factor of eight times that of a laminar premixed flame for instantaneous realizations and an average broadening of four times that of a laminar flame for the most turbulent case. Conditional statistics of temperature obtained at isodistance contours within and upstream of the preheat zone show large shifts towards significantly higher temperatures compared to laminar flame values. In addition, broad temperature distributions and reduced thermal gradients at each position provide strong evidence of persistent turbulent transport of high-temperature gases ahead of the preheat zone. Finally, a detailed analysis of scalar dissipation rate statistics and dissipation layer topology was conducted. The conditional mean scalar dissipation rates for the turbulent flames show significant reductions compared to calculated laminar flame values and a shift towards higher values of the reaction progress variable (CT) for increasing turbulence levels. PDFs show a transition from near-Gaussian to highly negatively skewed with increasing turbulence levels, where the most probable values of the scalar dissipation rate shift towards higher values of CT, indicating that the primary reaction zone and flame front are subjected to increased strain. In terms of structure, no significant broadening of the small-scale dissipation layers was observed with increasing turbulence intensity. However, as turbulence intensity increases, there is a transition from a sparse number of continuous layers to a large number of shorter, ”broken”, nearly straight segments. The reduction of individual layer lengths (i.e., ”breaking”) is favored over increases in dissipation layer wrinkling, where the sharp decreases in the local dissipation rate values are highly correlated with regions of high curvature. A final notable outcome of this work is that there were negligible differences in all statistical and topological results when moving between the two highest turbulent cases, even though the turbulence intensity, turbulent Reynolds number, and the turbulence Karlovitz number increased substantially (70 - 120%). This implies that there may be an asymptotic limit in which turbulence affects flame behavior for the current configuration.

Suppression of the turbulent kinetic energy and enhancement of the flame-normal Reynolds stress in premixed jet flames at small Lewis numbers

We report the effects of the Lewis number on the turbulent kinetic energy, Reynolds stresses, and scalar fluxes in premixed jet flames with strong mean shear. The direct numerical simulation (DNS) of piloted turbulent premixed jet flames is performed under the same condition except for different Lewis numbers to isolate the Lewis number effects. The turbulence intensity within the mean flame brush is found to decay more rapidly along the axial distance with a smaller Lewis number. This Lewis number dependence results from the coupling of the mean shear and the combustion heat release, where the mean shear is the primary source of turbulence production. We show that, under the strain imposed by the mean shear and turbulence fluctuation, the heat release of premixed jet flames is significantly enhanced at the Lewis number smaller than unity, which is represented by the rising flamelet consumption speed and flame surface area. As a consequence, the mean shear within the flame brush is suppressed at small Lewis numbers via the dilatation effect, and the weakened mean shear production causes the fast turbulence suppression along the axial direction. The enhanced heat release at small Lewis numbers also increases the flame-normal Reynolds stress, and leads to the counter-Boussinesq behavior of the shear Reynolds stress and the counter-gradient transport of scalar fluxes. We model the Lewis number effects on local turbulence and scalar transport using the stretched laminar flame speed and thickness, and achieve overall good estimations of the flame-normal Reynolds stress and scalar transport at small Lewis numbers.

Large eddy simulation of premixed turbulent combustion using a non-adiabatic, strain-sensitive flamelet approach

In this study, a novel strained, non-adiabatic flamelet generated manifold (FGM) model is developed based on a counterflow premixed flame. The different levels of strain and heat loss are introduced into the flamelets by varying the stagnation point strain rate and burnt temperature of the counterflow configuration. The strain rate response of these flamelets is found to exhibit different extinction patterns for different ranges of burnt temperature. A priori studies are performed to compare the phase-space flame structures of the strained and unstrained flamelets. It is found that the strained flamelet degenerates towards the unstrained flamelet with burnt temperature decreasing. A bifurcation burnt temperature is further defined that separates the two types of flamelet quenching that are driven by strain and heat loss. An appropriate set of tabulation parameters is chosen that preserves the uniqueness of mapping between the manifold and the populated flamelets. The external boundaries of the tabulations are defined, where the proposed model degenerates into the conventional unstrained/non-adiabatic FGM manifold. Internal tabulation boundaries are defined to distinguish different combustion modes among stable combustion, strain-induced quenching, and heat-loss-induced quenching. The model is validated using large eddy simulation (LES) of a confined turbulent premixed jet flame. The proposed FGM model vastly increases accuracy of predictions when both strain and heat loss effects are included. Without accounting for these effects, there are discrepancies in the prediction of flame height and temperature as compared with experimental data. An analysis of the dominant physical process (strain, heat loss) that contributes to the evolution of the turbulent flame is performed.

Damköhler number scaling of active cascade effects in turbulent premixed combustion

Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damköhler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames. At low Karlovitz numbers, where heat-release effects dominate turbulent kinetic energy budgets, their relative significance scales with the integral Damköhler number in a priori Reynolds-Averaged Navier–Stokes (RANS) statistics and the filter Damköhler number in Large Eddy Simulation (LES). The Damköhler-number scaling of counter-gradient transport in this regime follows theoretical arguments underpinning linear-algebraic turbulence models, which explains their efficacy at low Karlovitz numbers. Conversely, at moderate Karlovitz numbers, LES subfilter turbulence is more strongly influenced by heat-release effects than the analogous large-scale RANS turbulence. This is consistent with the notion of an “active cascade,” which postulates that heat-release-induced volumetric expansion competes on intermediate scales with classical forward-cascade energy transfer. LES exposes these dynamics as dominant subfilter-scale physics, unlike in RANS, where they are secondary to the effects of mean-shear production at the large scales. The significance of subfilter-scale interactions is promoted by the LES filter itself, which modifies the RANS spectral basis by incorporating local flame-normal averaging. This is highlighted by comparing LES fields obtained using a 3D filter to those using a modified 2D filter, excluding the flame-normal direction, which significantly reduces the apparent influence of heat-release effects but is not representative of LES in practice. The subfilter modeling challenges posed by these distinctions at moderate Karlovitz numbers and order-unity Damköhler numbers remain to be understood.

10 kHz 2D thermometry in turbulent reacting flows using two-color OH planar laser-induced fluorescence.

10 kHz two-color OH planar laser-induced fluorescence (PLIF) thermometry was demonstrated in both laminar Hencken flames and turbulent premixed jet flames using two injection-seeded optical parametric oscillators (OPOs) pumped by a high-speed three-legged burst-mode laser. The two burst-mode OPOs generate ∼5mJ/pulse at 282 nm and 286 nm to excite the Q1(5) and Q1(14) transitions of the A2Σ+←X2Π (1,0) system of OH, respectively. PLIF images were collected simultaneously from each of the two transitions and ratios of intensities from the two images were used to determine local temperatures. Analyses of flame curvature, temperature, and the correlation in time of these two quantities are also discussed. The results from this work are promising for the use of this technique in more complex flow environments and at, potentially, even higher repetition rate.

A comparison of the blow-out behavior of turbulent premixed ammonia/hydrogen/nitrogen-air and methane–air flames

Ammonia has been identified as a promising energy carrier that produces zero carbon dioxide emissions when used as a fuel in gas turbines. Although the combustion properties of pure ammonia are poorly suited for firing of gas turbine combustors, blends of ammonia, hydrogen, and nitrogen can be optimized to exhibit premixed, unstretched laminar flame properties very similar to those of methane. There is limited data available on the turbulent combustion characteristics of such blends and important uncertainties exist related to their blow-out behavior. The present work reports experimental measurements of the blow-out limits in an axisymmetric unconfined bluff-body stabilized burner geometry of NH3/H2/N2-air flame, comprised of 40% NH3, 45% H2, and 15% N2 by volume in the “fuel” blend. Blow-out limits for the NH3/H2/N2-air flames are compared to those of methane–air flames. OH PLIF and OH chemiluminescence images of the flames just prior to blow-out are presented. Furthermore, two large-scale Direct Numerical Simulations (DNS) of temporally evolving turbulent premixed jet flames are performed to investigate differences in the turbulence-chemistry interaction and extinction behavior between the NH3/H2/N2-air and methane–air mixtures. The experiments reveal that the blow-out velocity of NH3/H2/N2-air flames is an order of magnitude higher than that of methane–air flames characterized by nearly identical unstretched laminar flame speed, thermal thickness and adiabatic flame temperature. Results from the DNS support the experimental observation and clearly illustrate that a methane–air mixture exhibits a stronger tendency towards extinction compared to the NH3/H2/N2-air blend for identical strain rates. Furthermore, the DNS results reveal that, even in the presence of intense sheared turbulence, fast hydrogen diffusion into the spatially distributed preheat layers of the fragmented and highly turbulent flame front plays a crucial role in the enhancement of the local heat release rate and, ultimately, in preventing the occurrence of extinction.

Closure modeling for the conditional Reynolds stresses in turbulent premixed combustion

Turbulence is significantly affected by combustion-induced dilatation in low Karlovitz number premixed flames. Conventional turbulence modeling approaches based on traditional unconditional averaging are limited in accurately capturing combustion heat release effects since they must capture both the direct influence of combustion heat release on turbulence and the flame dynamics. Solving momentum transport equations conditionally averaged with respect to a flame structure variable (progress variable for premixed combustion) could provide a superior framework for modeling combustion-affected turbulence since the flame dynamics are embedded into the flame structure variable conditioning. However, the conditional momentum equations contain numerous unclosed terms that evolve in both physical and phase spaces. Of the many unclosed terms, the conditional Reynolds stresses (conditional analog of the Reynolds stresses) represent the influence of turbulent transport on the conditional velocities. In this work, a new model consisting of two components for the conditional Reynolds stresses in turbulent premixed flames is developed to capture heat release effects on turbulence. The first component is the conditional analog of the Boussinesq model that characterizes turbulent shear effects in physical space. The second component depends on the conditional velocity gradient not in physical space but in phase space and captures the anisotropy in the conditional Reynolds stresses driven by thermal expansion effects that vary within the flame structure. The model is validated a priori using DNS databases of turbulent premixed jet flames at low and high Karlovitz numbers. At low Karlovitz number, the phase space term enables the model to capture direct heat release effects on all conditional Reynolds stress components, specifically the correct anisotropy of the normal components and the sign of the shear component. At high Karlovitz number where heat release effects on turbulence are insignificant, turbulent shear effects are dominant, and the phase space term has a nearly negligible effect.

Gradient Trajectory Analysis of the Burning Rate in Turbulent Premixed Jet Flames

ABSTRACT An analysis of the combustion process along gradient trajectories is presented for a set of Direct Numerical Simulations of turbulent premixed jet flames at different Reynolds numbers and approximately constant Karlovitz numbers. The variation of the jet Reynolds number, ranging from 5600 to 22400, is achieved by increasing the width of the jet and keeping the bulk velocity constant, which also implies approximately constant values of the turbulence intensities across the flames. The flames considered are nominally in the thin-reaction zone regime of the Borghi-Peters diagram of turbulent combustion. The thickening of the inner reaction layer and its enhancement with increasing Reynolds number, observed in previous works on the same database, is linked here to the presence of extremal points in the temperature field (local maxima in the low temperature side and minima in the high temperature side) in the vicinity or inside the inner reaction layer. Therefore, an enhancement of the turbulent flame speed is linked to the interruption of the flamelet structure by turbulence and not by the thickening of the entire flamelet itself. In addition to the expected large thickening of the formaldehyde layer, the layers of species which are characteristic of the inner reaction zone, such as OH and O, show a significant thickening and these species are observed several flame thicknesses ahead of the turbulent flame surface. Finally, it is shown that, in the regions where the inner reactive layer is thickened, the local fuel consumption rate is reduced in comparison to a laminar planar flame, but the total burning rate integrated over the entire flame structure is larger due to the increased volume of the reactive layer. These observations highlight the importance of assessing the balance between two competing phenomena related to high Karlovitz numbers. The first is the effect of turbulence strain and stirring on the chemistry, which usually decreases the local burning rate. The second is the effect on the species fields, which might experience modifications in their topology, such as the introduction of local extremal points, and significant thickening of the volumes between their isosurfaces.

Carbon oxidation in turbulent premixed jet flames: A comparative experimental and numerical study of ethylene, n-heptane, and toluene

An experimental and numerical investigation of the thermochemical structure of piloted premixed jet flames was conducted, encompassing laser absorption tomography measurements and large-eddy simulations (LES). The investigation was performed holding laminar flame speed, jet Reynolds number, and surrounding flow conditions constant while considering three different fuel types, namely an alkene, a normal alkane, and an aromatic fuel. Quantitative spatially-resolved thermochemical profiles of carbon monoxide (CO), carbon dioxide (CO2), and temperature obtained from laser absorption tomography were compared against profiles predicted by the simulations for premixed ethylene-, toluene-, and n-heptane-air flames. Variations in flow structure are observed for the different fuels, highlighting fuel-specific chemical effects on the spatial evolution of the flames. Quantitative agreement of laser absorption tomography and LES results is generally observed for all flames, with larger deviations observed in the nozzle-near region for the higher molecular-weight fuels, indicating potential deficiencies in the turbulent mixing models. To the authors’ knowledge, these measurements represent the largest molecular-weight fuels for which quantitative thermochemical data have been reported in a canonical piloted premixed jet-flame configuration. The spatially-resolved experimental measurements of CO, CO2, and gas temperature provide valuable data which can be used as validation targets for the development of turbulent combustion models.

Role of Coherent Structures in Turbulent Premixed Flame Acoustics

Spectral proper orthogonal decomposition (SPOD) is applied to direct numerical simulation datasets of a lean and a stoichiometric methane–air turbulent premixed jet flame. SPOD is used to extract the coherent structures that correlate with the radiated sound by using an inner product based on a linearized disturbance energy. Two types of structures are prominent in the data. The first type arises in the jet’s shear layer and is linked to the Kelvin–Helmholtz instability, which is an important mechanism of sound generation in nonreacting jets. These structures produce sound through deformation of the flame front in the shear layer. They contain most of the acoustic energy and are dominant at Strouhal numbers (defined based on the jet’s diameter and the inlet mean velocity) less than unity. The second type of structures is found near the jet centerline, where large fluctuations of the flame surface are observed. The structures are linked to small nonlinear flame dynamics and to the Orr mechanism. They travel at a speed close to the inlet mean velocity and are important at higher Strouhal numbers. Regardless of their energy content, both types of structures have important contributions to the broadband nature of combustion noise.

Heat release effects on the Reynolds stress budgets in turbulent premixed jet flames at low and high Karlovitz numbers

In turbulent premixed flames at low Karlovitz number, combustion heat release can have a significant impact on turbulence. Thermal expansion in flame induces dilatation, and the corresponding pressure–dilatation correlation acts as a primary source of turbulent kinetic energy (TKE). As a consequence, the flame-normal component of the normal Reynolds stresses significantly increases. Additionally, for sheared flames, typical of jet flames, the shear component of the Reynolds stresses exhibits counter-Boussinesq behavior. For flames at low Karlovitz number, where these effects dominate, no models have successfully predicted all Reynolds stress components. To develop more complete turbulence models, heat release effects on the evolution of all Reynolds stress components need to be analyzed. In this work, Reynolds stress budgets are evaluated from Direct Numerical Simulation (DNS) databases of spatially-evolving turbulent premixed planar jet flames at low and high Karlovitz numbers. In the Reynolds stress budgets, the velocity–pressure gradient correlation term is important at both Karlovitz numbers but serves fundamentally different roles in each case. In the budgets for the normal components, the velocity–pressure gradient correlation term is decomposed into a redistribution term and an isotropic term, where the redistribution term acts to redistribute energy between the Reynolds stress components and the isotropic term is the pressure–dilatation source term of turbulent kinetic energy. At high Karlovitz number, the isotropic term is negligible, and the redistribution term acts to isotropize the turbulence as in non-reacting flows. Conversely, at low Karlovitz number, the isotropic term acts as a large source, and the redistribution term preferentially injects energy into the flame-normal component at the expense of other components which acts to make the turbulence less isotropic. In the budget for the shear component, the shear production term dominates the velocity–pressure gradient correlation term at high Karlovitz number, but the opposite is observed at low Karlovitz number. The dominance of the velocity–pressure gradient correlation term at low Karlovitz number is primarily induced by the flame-generated mean pressure gradient and ultimately leads to the counter-Boussinesq behavior of the shear component. The overall analysis indicates that any turbulence model that relies on small-scale isotropy and/or rapid isotropization will fail to capture the heat release effects on turbulence at low Karlovitz number.

Direct numerical simulation of turbulent premixed jet flames: Influence of inflow boundary conditions

Direct Numerical Simulations (DNS)s of a low Karlovitz number turbulent premixed round jet flame are performed to determine the impact of the turbulence inflow conditions on the flame characteristics. This is accomplished by providing the first flame with a fully developed turbulent inflow via simulation of the upstream pipe and the coflow region, while the inflow boundary condition in the second flame is generated with a digital filter-based method without including the upstream region. The two databases are then thoroughly compared to reveal any differences resulting from the different inflow boundary conditions. The turbulence kinetic energy is observed to drop shortly downstream of the synthetic inflow, which results in a higher jet momentum and a longer flame compared to the flame with the fully developed turbulent inflow. The distributions of the flame front orientation in the near field are observed to differ between the two flames but differences decrease quickly downstream as distributions tend towards isotropy. The flame structure is largely affected by tangential straining close to the inflow while further downstream, the flame structure is similar to that in an unstrained laminar flame. While the difference between the inflow boundaries had a significant effect on global parameters such as flame length, the influence of the inflow conditions on local statistics related to turbulence-flame interaction appear to be limited to the near inflow region.

Effects of heat release and fuel type on highly turbulent premixed jet flames

An experimental study on the fuel type and attendant heat release effects on piloted turbulent premixed jet flames was carried out. The investigation focused on four fuels, namely methane, ethylene, n-heptane, and toluene, five lean to stoichiometric equivalence ratios, and two jet Reynolds numbers. The average flame height and the global turbulent consumption speed were scaled against the laminar flame speed, the maximum heat release rate, and the laminar flame thickness for all fuels and conditions. Results showed that for the different fuel types and for the lower equivalence ratios, the average flame height does not scale well with any of the aforementioned parameters, while the global consumption speed was determined to scale well with laminar flame speed and maximum heat release rate. The thickness of the shear layer was also characterized through detailed particle image velocimetry measurements and was found to decrease with increasing heat release when the jet diameter is used to scale the axial distance. However, when a density-based momentum diameter is used as the scaling parameter of the axial distance, the effect of heat release is suppressed. Additionally, the growth rates of the shear layer thickness could not be scaled between the different fuels using either the laminar flame speed or the maximum heat release rate. Finally, the turbulent kinetic energy and turbulent shear stress development in the shear layer was determined also to be different between the fuels despite keeping either the laminar flame speed or maximum heat release rate constant, with methane flames most notably showing a sharper decay in intensity with axial distance. The fuel effects on the turbulent kinetic energy and the turbulent shear stress were more pronounced at the higher Reynolds number conditions.

Evolution of flame-conditioned velocity statistics in turbulent premixed jet flames at low and high Karlovitz numbers

Turbulence in low Karlovitz number premixed flames is strongly affected by small-scale combustion heat release. At low Karlovitz number conditions, flame-normal thermal expansion leads to increased anisotropy of the velocity field, and pressure-dilatation becomes the most significant source of turbulent kinetic energy (TKE). These effects are balanced in TKE budgets by the phenomenon of “negative production,” which leads to changes to the Reynolds stress tensor that are independent of the mean strain-rate tensor. The resulting statistical misalignment contributes to the failure of Boussinesq-type turbulence models in low Karlovitz number turbulent premixed combustion. Attempts have been made to develop turbulence models for premixed combustion, but these models depend on theoretical frameworks that are valid only in the zero- and infinite-Karlovitz number limits. In this work, a new statistical framework is introduced that could provide a foundation for turbulence models in flames of arbitrary Karlovitz number. In this framework, velocity statistics conditioned on a reaction progress variable are capable of distinguishing between actual turbulent fluctuations and fluctuations due to the motion of the flame. This capability is evaluated using data from Direct Numerical Simulations (DNS) of spatially-evolving turbulent premixed jet flames at low and high Karlovitz numbers. The evolution equation of the conditional mean velocity is derived, and budgets of the cross-stream, that is, essentially flame-normal, conditional mean velocity are compared in the two Karlovitz number regimes. At low Karlovitz number, the pressure gradient source is found to be balanced by the terms associated with the progress variable source term, indicating a dominance of flame effects on the turbulence dynamics. Conversely, at high Karlovitz number, physical-space transport terms are found to become leading-order, indicating a reduced effect of the flame on the turbulence dynamics.

On the statistics of flame stretch in turbulent premixed jet flames in the thin reaction zone regime at varying Reynolds number

Direct Numerical Simulations (DNS) are conducted to study the statistics of flame surface stretch in turbulent jet premixed flames. Emphasis is placed on the rates of surface production and destruction and their scaling with the Reynolds number. Four lean methane/air turbulent slot jet flames are simulated at increasing Reynolds number and up to Re ≈ 22 × 103, based on the bulk velocity, slot width, and the reactants’ properties. The Karlovitz number is held approximately constant and the flames fall in the thin reaction zone regime. The simulations feature finite rate chemistry and mixture-average transport. Our data indicate that the area of the flame surface increases up to the streamwise position corresponding to 80% of the average flame length and decreases afterwards as surface destruction overtakes production. It is observed that the tangential rate of strain is responsible for the production of flame surface in the mean and surface destruction is due to the curvature term. In addition, it is found that these two terms are both significantly larger than their difference, i.e., the net surface stretch.The statistics of the tangential strain rate are in good agreement with those for infinitesimal material surfaces in homogeneous isotropic turbulence. Once scaled by the Kolmogorov time scale, the means of both contributions to stretch are largely independent of location and equal across flames with different values of the Reynolds number. Surface destruction is due mostly to propagation into the reactants where the surface is folded into a cylindrical shape with the center of curvature on the side of the reactants. The joint statistics of the displacement speed and curvature of the reactive surface are nuanced, with the most probable occurrence being that of a negative displacement speed of a flat surface, while the surface averaged displacement speed is positive as expected.

Effects of combustion heat release on velocity and scalar statistics in turbulent premixed jet flames at low and high Karlovitz numbers

Theoretical scaling arguments for turbulent premixed combustion indicate that the pressure-dilatation source of turbulent kinetic energy becomes significant at low Karlovitz numbers, leading to potential invalidation of commonly-used turbulence models developed for non-reacting flow. Based on these arguments, a critical Karlovitz number is defined, below which dilatation effects are expected to become significant. Velocity and scalar statistics are obtained from Direct Numerical Simulation (DNS) calculations of low Mach number spatially-evolving turbulent premixed planar jet flames. At fixed bulk Reynolds number and stoichiometric equivalence ratio, two simulations are performed at Karlovitz numbers above and below the critical Karlovitz number. Hydrogen combustion with detailed transport is modeled using a detailed nine-species chemical kinetic mechanism, and coflows of combustion products are used to ensure flame stability at uniform equivalence ratio. The analysis of these statistics focuses on three key areas. First, the influence of the velocity-pressure gradient source of turbulent kinetic energy is confirmed at a low Karlovitz number, and the unimportance of these effects is confirmed at a high Karlovitz number. Similar effects are observed for the chemical source term in the scalar variance budgets. Second, the degree of alignment between the Reynolds stress tensor (scalar flux) and the strain-rate tensor (scalar gradient), the foundation of a majority of the turbulence models used in reacting flows, is assessed with the DNS databases. Additionally, consistency of anisotropic Reynolds stress and strain-rate tensor invariants is assessed using invariant maps. While good alignment and consistency are obtained for statistics and invariants at a high Karlovitz number, both alignment and consistency degrade at a low Karlovitz number. Third, turbulence models formulated for non-reacting flow are modified algebraically in the Bray–Moss–Libby (BML) formalism for turbulent premixed combustion. A variable efficiency function is defined to capture the regime dependence of heat release effects in these models. Model performance is evaluated at Karlovitz numbers above and below the critical Karlovitz number using the DNS databases, and satisfactory prediction of counter-gradient transport in the flame-normal direction is obtained. However, heat release effects are also observed in the flame-parallel directions in the low-Karlovitz number simulation, and the models developed in the formalism for statistically planar flames fail to capture these effects. Furthermore, in the low-Karlovitz number case, redistributive effects are active on the shear components of the Reynolds stress, which are not considered in the BML formalism. More advanced turbulence models are therefore necessary for turbulent premixed jet flames below the critical Karlovitz number.

Visualization of the heat release zone of highly turbulent premixed jet flames

Visualization of the heat release zone (HRZ) of highly turbulent flames is significantly important to understand the interaction between turbulence and chemical reactions, which is the foundation to design and optimize engines. Simultaneous measurements of OH and CH2O using planar laser-induced fluorescence (PLIF) were performed to characterize the HRZ. A well-designed piloted premixed jet burner was employed to generate four turbulent premixed CH4/air jet flames, with different jet Reynolds numbers (Rejet) ranging from 4900 to 39200. The HRZ was visualized by both the gradient of OH and the pixel-by-pixel product of OH and CH2O. It is shown that turbulence has an increasing effect on the spatial structure of the flame front with an increasing height above the jet exit for the premixed jet flames, which results in the broadening of the HRZ and the increase of the wrinkling. The HRZ remains thin as the Rejet increases, whereas the preheat zone is significantly broadened and thickened. This indicates that the smallest turbulent eddies can only be able to enter the flame front rather than the HRZ in the present flame conditions. The flame quenching is observed with Rejet = 39200, which may be due to the strong entrainment of the cold air from outside of the burned gas region.