H2-air Flames Research Articles

Anisotropy of Reynolds Stresses and Their Dissipation Rates in Lean H2-Air Premixed Flames in Different Combustion Regimes

The interrelation between Reynolds stresses and their dissipation rate tensors for different Karlovitz number values was analysed using a direct numerical simulation (DNS) database of turbulent statistically planar premixed H2-air flames with an equivalence ratio of 0.7. It was found that a significant enhancement of Reynolds stresses and dissipation rates takes place as a result of turbulence generation due to thermal expansion for small and moderate Karlovitz number values. However, both Reynolds stresses and dissipation rates decrease monotonically within the flame brush for large Karlovitz number values, as the flame-generated turbulence becomes overridden by the strong isotropic turbulence. Although there are similarities between the anisotropies of Reynolds stress and its dissipation rate tensors within the flame brush, the anisotropy tensors of these quantities are found to be non-linearly related. The predictions of three different models for the dissipation rate tensor were compared to the results computed from DNS data. It was found that the model relying upon isotropy and a linear dependence between the Reynolds stress and its dissipation rates does not correctly capture the turbulence characteristics within the flame brush for small and moderate Karlovitz number values. In contrast, the models that incorporate the dependence of the invariants of the anisotropy tensor of Reynolds stresses were found to capture the components of dissipation rate tensor for all Karlovitz number conditions.

Spatiotemporal Surface Temperature Measurements Resolving Flame-Wall Interactions of Lean H2-Air and CH4-Air Flames Using Phosphor Thermometry

AbstractSpatiotemporal wall temperature (Twall) distributions resulting from flame-wall interactions of lean H2-air and CH4-air flames are measured using phosphor thermometry. Such measurements are important to understand transient heat transfer and wall heat flux associated with various flame features. This is particularly true for hydrogen, which can exhibit a range of unique flame features associated with combustion instabilities. Experiments are performed within a two-wall passage, in an optically accessible chamber. The phosphor ScVO4:Bi3+ is used to measure Twall in a 22 × 22 mm2 region with 180 µm/pixel resolution and repetition rate of 1 kHz. Chemiluminescence imaging is combined with phosphor thermometry to correlate the spatiotemporal dynamics of the flame with the heat signatures imposed on the wall. Measurements are performed for lean H2-air flames with equivalence ratio Φ = 0.56 and compared to CH4-air flames with Φ = 1. Twall signatures for H2-air Φ = 0.56 exhibit alternating high and low-temperature vertical streaks associated with finger-like flame structures, while CH4-air flames exhibit larger scale wrinkling with identifiable crest/cusp regions that exhibit higher/lower wall temperatures, respectively. The underlying differences in flame morphology and Twall distributions observed between the CH4-air and lean H2-air mixtures are attributed to the differences in their Lewis number (CH4-air Φ = 1: Le = 0.94; H2-air Φ = 0.56: Le = 0.39). Findings are presented at two different passage spacings to study the increased wall heat loss with larger surface-area-to-volume ratios. Additional experiments are conducted for H2-air mixtures with Φ = 0.45, where flame propagation was slower and was more suitable to resolve the wall heat signatures associated with thermodiffusive instabilities. These unstable flame features impose similar wall heat fluxes as flames with 2–3 times greater flame power. In this study, these flame instabilities occur within a small space/time domain, but demonstrate the capability to impose appreciable heat fluxes on surfaces.

Application of the tomographic BOS technique to a H2-air premixed flame

Application of the tomographic BOS technique to a H2-air premixed flame

Acceleration of premixed H[formula omitted]-Air-Steam flames when accounting for thermal radiation

Diluting hydrogen flames with steam can increase flame stability and reduce nitrogen oxide emissions. While the effects of dilution on the flame characteristics due to variations in chemistry or transport properties have been well investigated, this is not the case for those related to thermal radiation. Thermal radiation is indeed often neglected in free flame simulations. However, it can be critical in diluted flames in which participating species are present in the fresh gases. This study explores thermal radiation’s impact on H2-Air flames diluted with steam through 1D laminar flame computations. To this end, a reactive fluid solver is coupled with a semi-analytical thermal radiation code. Both the grey gas approximation, for a preliminary understanding, and the more accurate CK narrow-band model, for detailed simulations that account for spectral-dependent gas properties, are used. The combustion numerical setup is validated against literature results. Three main thermal radiation effects are highlighted: a preheating of the fresh gases, an increased laminar flame speed, and a decreased temperature in the burnt gases. It is found that domain length considerably affects this preheating and flame speed, which can then affects laminar burning velocity measurements. It is shown that thermal radiation and combustion can often be decoupled and that a preheated adiabatic flame can recover the main characteristics of the corresponding radiative flame. The increase of the laminar flame speed by thermal radiation is reported for a wide range of equivalence ratios, dilution levels, and pressures. The observed acceleration is especially significant for lean and very lean flames which can be up to 500% faster when considering thermal radiation.

On flame speed enhancement in turbulent premixed hydrogen-air flames during local flame-flame interaction

Local flame displacement speed Sd of a turbulent premixed flame is of fundamental and practical interest. For H2-air flames, the interest is further accentuated given the recent drive towards the development of zero-carbon combustors for both power and aircraft engine applications. The present study investigates several three-dimensional Direct Numerical Simulation (3D DNS) cases of premixed H2-air turbulent flames to theoretically model the Sd at negative curvatures, building upon recent works. Two of the four DNS cases presented are simulated at atmospheric pressure and two at elevated pressure. The DNS cases at different turbulence Reynolds numbers (Ret) and Karlovitz numbers (Ka) are generated using detailed chemistry. It has been shown in the previous studies that at atmospheric pressure, the density-weighted flame displacement speed Sd˜ is enhanced significantly over its laminar value (SL) at large negative curvature κ due to flame-flame interactions. The current work justifiably employs an imploding cylindrical laminar flame configuration to represent the local flame surfaces undergoing flame-flame interaction in a 3D turbulent flame. Therefore, to acquire a deep understanding of the interacting flame dynamics at large negative curvatures, one-dimensional (1D) simulations of an inwardly propagating cylindrical H2-air laminar premixed flame, with detailed chemistry at the corresponding atmospheric and elevated pressure conditions are performed. In particular, the 1D simulations emphasized the transient nature of the flame structure during these interactions. Based on the insights from the 1D simulations, we utilize an analytical approach to model the Sd˜ at these regions of extreme negative κ of the 3D DNS. The analytical approach is formulated to include the effect of variable density, convection and the inner reaction zone motion. The joint probability density function (JPDF) of Sd˜ and κ and the corresponding conditional averages obtained from 3D DNS showed clear negative correlation between Sd˜ and κ at all pressures. The obtained model successfully predicts the variation of 〈Sd˜|κ〉 with κ for the regions on the flame surface with large negative curvature (κδL≪−1) at atmospheric as well as at elevated pressure, with good accuracy. This showed that the 1D cylindrical, interacting flame model is a fruitful representation of a local flame-flame interaction that persists in a 3D turbulent flame, and is able to capture the intrinsically transient dynamics of the local flame-flame interaction. The 3D DNS cases further showed that even in the non-interacting state at κ=0, on average Sd˜ can deviate from SL. Sd˜ at κ=0 is a manifestation of the internal flame structure, controlled by turbulence transport in the large Ka regime. Therefore, the correlation of 〈Sd˜〉/SL with the the normalized gradient of the progress variable, 〈|∇c^|c0〉 at κ=0 is explored.

Experimental and simulation study of NH3–H2-Air flame dynamics at elevated temperature in a closed duct

Ammonia allows for long-distance and large-scale storage transport of renewable energy sources. The reactivity of NH3-Air flame can be enhanced by doping with hydrogen and by increasing the initial temperature. The flame combustion characteristics of NH3–H2-Air are studied in a rectangular closed pipe with a mole fraction of 45% H2, an equivalence ratio (φ) of 0.8–1.2 and 0.1 MPa. The initial temperatures (Tu) of the mixture are 300 K, 375 K and 450 K. Experimental studies of flame front speed, flame tip structure evolution, and overpressure dynamics are performed. Laminar burning velocity (SL), peak mole fraction of key radicals, and flame instability of NH3–H2-Air flames are simulated in Chemkin Pro-software using the Mathieu and Petersen mechanism. The results show that the relatively low equivalence ratio and initial temperature promote the structural changes of the flame tip, forming a “tulip” flame and a distorted “tulip”. As the equivalence ratio increases, the flame front speed and overpressure increase and the flame oscillates slightly. The distortion in the lip of the “tulip” is more pronounced. The increase in temperature promotes flame propagation in the early stages and the pressure decreases. Reactive activity increases with increasing temperature, the peak mole fraction of NH2 and H radicals increases, and SL increases. At normal temperature, the flame is affected by thermo-diffusive instability only when lean mixture. The Darrieus-Landau instability increases as the equivalence ratio increases. Conversely, the Darrieus-Landau instability decreases with increasing temperature. Therefore, the current experimental and simulation results help to understand the laminar combustion characteristics of NH3–H2-Air at high temperatures.

Combustion Characteristics of Hydrogen/Air Mixtures in a Plasma-Assisted Micro Combustor

This work performs an analysis of plasma-assisted non-premixed H2-air flames in Y-shaped micro combustors in the presence of field emission dielectric barrier discharge (FE-DBD) plasma actuators. The combustion, flow, and heat transfer characteristics are numerically investigated, and the effect of sinusoidal plasma discharges on combustion performance is examined at various equivalence ratios (φ). A coupled plasma and chemical kinetic model is implemented, using a zero-dimensional model based on the solution of the Boltzmann equation and the ZDPlasKin toolbox to compute net charges and radical generation rates. The estimated body forces, radical production rates, and power densities in the plasma regions are then coupled with hydrogen combustion in the microchannel. Plasma-assisted combustion reveals improvements in flame length and maximum gas temperature. The results demonstrate that FE-DBDs can enhance mixing and complete the combustion of unreacted fuel, preventing flame extinction. It is shown that even in cases of radical and thermal quenching, these plasma actuators are essential for stabilizing the flame.

Flame–Solid Interaction: Thermomechanical Analysis for a Steady Laminar Stagnation Flow Stoichiometric NH3–H2 Flame at a Plane Wall

While thermomechanical analyses in solid and combustion processes in the gas phase are intensively studied separately, their interaction is less investigated. On one hand, the combustion system can be affected by the solid as a result of, for example, the heat conduction. On the other hand, the high-temperature flame can induce the thermal load in the solid, which significantly affects the mechanical stress field in the material. This work focuses on the coupling between the solid and flame and the combustion-induced mechanical stress in the material. The influence of the solid on the flame structures and properties and also the influence of the flame on the thermomechanical behavior in the solid are investigated. A stagnation flow NH3–H2–air flame to a plane wall is considered as a representative model, which is simple but also realistic in many engineering conditions. It is mainly found that an increase of the flame strain rate leads to an increase of thermomechanical stress in the wall, and the system pressure improves the flame stability against extinction but enlarges the induced thermomechanical stress at the same time. Furthermore, it is observed that the hydrogen content in the gas mixture does not affect the thermomechanical stress in the wall if the flames with different hydrogen additions are imposed with the same strain rate. On the basis of various flame parameters, it is also shown that the solid would also flow plastically under certain conditions, such as high pressures. From the viewpoint of the wall, it is mainly shown that the flame stability against extinction can be improved using wall materials with larger heat conductivities.

NO[formula omitted] pathways in lean partially premixed swirling H2‐air turbulent flame

Today’s climate and energy challenges are driving the use of decarbonised and renewable alternative fuels in power generation and transportation. Hydrogen as a fuel is a good candidate to meet these requirements, as it offers no carbon emissions and can play the role of an energy carrier to store excess energy produced by renewable energy. Nonetheless, the production of NOx needs to be assessed. For this reason, this study proposes high-fidelity Large Eddy Simulations (LES) with detailed NOx analyzes of a partially premixed lean swirling H2-air flame. The chosen configuration is the technically premix hydrogen injector measured at the Berlin Institute of Technology (TUB) in Germany. A novel kinetic scheme for H2-air comprising 15 species and 47 reactions is developed to take into account all NOx pathways. To accurately solve the combustion process and the NOx production level, static mesh refinement (SMR) and conjugate heat transfer (CHT) are applied to the LES modeling and their impact on the numerical predictions is evaluated. A detailed analysis of the preferential diffusion and formation of NO is presented, demonstrating that the proposed numerical model, combined with the novel chemical kinetic scheme, is able to correctly predict complex transport phenomena observed in lean turbulent hydrogen flames and to predict their NO dynamic formation accounting for both primary and secondary (N2O and NNH) NOx pathways.

Effects of thermal expansion on moderately intense turbulence in premixed flames

This study aims at analytically and numerically exploring the influence of combustion-induced thermal expansion on turbulence in premixed flames. In the theoretical part, contributions of solenoidal and potential velocity fluctuations to the unclosed component of the advection term in the Reynolds-averaged Navier–Stokes equations are compared, and a new criterion for assessing the importance of the thermal expansion effects is introduced. The criterion highlights a ratio of the dilatation in the laminar flame to the large-scale gradient of root mean square (rms) velocity in the turbulent flame brush. To support the theoretical study, direct numerical simulation (DNS) data obtained earlier from two complex-chemistry, lean H2–air flames are analyzed. In line with the new criterion, even at sufficiently high Karlovitz numbers, the results show significant influence of combustion-induced potential velocity fluctuations on the second moments of the turbulent velocity upstream of and within the flame brush. In particular, the DNS data demonstrate that (i) potential and solenoidal rms velocities are comparable in the unburnt gas close to the leading edge of the flame brush and (ii) potential and solenoidal rms velocities conditioned to unburnt gas are comparable within the entire flame brush. Moreover, combustion-induced thermal expansion affects not only the potential velocity but even the solenoidal one. The latter effects manifest themselves in a negative correlation between solenoidal velocity fluctuations and dilatation or in the counter-gradient behavior of the solenoidal scalar flux. Finally, a turbulence-in-premixed-flame diagram is sketched to discuss the influence of combustion-induced thermal expansion on various ranges of turbulence spectrum.

A novel flamelet manifold parametrization approach for lean CH4–H2-air flames

Hydrogen is a carbon-free energy carrier that can substantially support the decarbonization of the power generation and transportation sector in the near future. Blending H2 into natural gas represents a feasible option to continue using the current infrastructure, allowing a smooth transition to pure H2 combustion technologies. In the present study, a flamelet model is proposed to describe lean CH4–H2-air laminar Bunsen flames with inert gas as a coflow, simultaneously taking into account multiple complex physical phenomena such as differential diffusion, heat losses at the burner wall and mixing between the main flow and coflow. In most previous works based on manifold-based reduction methods, transport equations are solved for the progress variable, mixture fraction and enthalpy. In contrast, transport equations for several species and enthalpy are solved in the present study and species diffusivities are evaluated with a mixture-averaged diffusion model. The control variables of the manifold are then reconstructed with those transported variables. In order to consider the mixing between the main flow and the inert coflow, two different approaches based on a three-dimensional and a four-dimensional manifold, respectively, are formulated and assessed. Utilizing a “linear mixing” assumption, the three-dimensional manifold is parameterized by a progress variable, an approximate Bilger mixture fraction and enthalpy. The four-dimensional manifold relaxes this assumption and additionally includes the inert gas mass fraction as the fourth control variable. The accuracy of the two approaches is evaluated by comparison with detailed chemistry results and experimental measurements. Overall, results obtained with both approaches show good agreement with the reference data, both qualitatively and quantitatively, indicating that all the effects mentioned above are well captured. Slightly better agreement is achieved with the four-dimensional manifold, which shows superiority in the mixing layer between the main flow and the inert coflow.

Impact of chamber back pressure on the ignition dynamics of hydrogen enriched premixed flames

The impact of chamber back pressure and H2-enrichment on flashback of premixed CH4−H2-Air flames triggered by ignition dynamics is investigated. Different back pressures are imposed by varying the exhaust flow blockage with perforated plates of different porosities. Experiments measuring the ignition transient, from kernel formation to stable flames and flashback, with increasing levels of H2-enrichment covering a wide range of operating conditions are conducted. Time-series of pressure, velocity and heat release rate are examined to characterise the ignition process. It is shown that the final state of the flame is highly modified by the over pressure caused by the volumetric expansion of the hot gases. Three different scenarios are identified: Soft ignition with direct stabilisation, transient flashback and permanent flashback. The magnitude of the over pressure generated at ignition is significantly amplified by small increases in mean back pressure which, in turn, modifies the flowrate through the injector thereby promoting flashback. In addition to its role as a pressure amplifier, increasing the combustor back pressure also affects the time lag between the over pressure and the peak in heat release rate just after ignition. The impact of H2-enrichment on flashback is investigated by keeping both the bulk injection velocity Ub and laminar burning velocity Sl0 constant for flames with 0% to 100%H2-content. It is shown that the magnitude of the over pressure approximately scales with Ub/Sl0 and is independent of the total thermal power and H2 enrichment. Although the mean flow conditions and over pressures are kept constant, the stabilisation mode directly depends on H2-content. This shows that flashback triggered by the ignition dynamics cannot be fully described by classical kinematic arguments and a new mechanism is presented.

Flamelet modeling of thermo-diffusively unstable hydrogen-air flames

In order to reduce CO2 emissions, hydrogen combustion has become increasingly relevant for technical applications. In this context, lean H2-air flames show promising features but, among other characteristics, they tend to exhibit thermo-diffusive instabilities. The formation of cellular structures associated with these instabilities leads to an increased flame surface area which further promotes the flame propagation speed, an important reference quantity for design, control, and safe operation of technical combustors. While many studies have addressed the physical phenomena of intrinsic flame instabilities in the past, there is also a demand to predict such flame characteristics with reduced-order models to allow computationally efficient simulations. In this work, a H2-air spherical expanding flame, which exhibits thermo-diffusive instabilities, is studied with flamelet-based modeling approaches both in a-priori and a-posteriori manner. A recently proposed Flamelet/Progress Variable (FPV) model, with a manifold based on unstretched planar flames, and a novel FPV approach, which takes into account a large curvature variation in the tabulated manifold, are compared to detailed chemistry (DC) calculations. Both flamelet approaches account for differential diffusion utilizing a coupling strategy which is based on the transport of major species instead of transporting the control variables of the manifold. First, both FPV approaches are assessed in terms of an a-priori test with the DC reference dataset. Thereafter, the a-posteriori assessment contains two parts: a linear stability analysis of perturbed planar flames and the simulation of the spherical expanding flame. Both FPV models are systematically analyzed considering global and local flame properties in comparison to the DC reference data. It is shown that the new FPV model, incorporating large curvature variations in the manifold, leads to improved predictions for the microstructure of the corrugated flame front and the formation of cellular structures, while global flame properties are reasonably well reproduced by both models.

Local flame displacement speeds of hydrogen-air premixed flames in moderate to intense turbulence

Comprehensive knowledge of local flame displacement speed, Sd, in turbulent premixed flames is crucial towards the design and development of hydrogen fuelled next-generation engines. Premixed hydrogen-air flames are characterized by significantly higher laminar flame speed compared to other conventional fuels. Furthermore, in the presence of turbulence, Sd is enhanced much beyond its corresponding unstretched, planar laminar value SL. In this study, the effect of high Karlovitz number (Ka) turbulence on density-weighted flame displacement speed, Sd˜, in a H2-air flame is investigated. Recently, it has been identified that flame-flame interactions in regions of large negative curvature govern large deviations of Sd˜ from SL, for moderately turbulent flames. An interaction model for the same has also been proposed. In this work, we seek to test the interaction model’s applicability to intensely turbulent flames characterized by large Ka. To that end, we investigate the local flame structures: thermal, chemical structure, the effect of curvature, along the direction that is normal to the chosen isothermal surfaces. Furthermore, relative contributions of the transport and chemistry terms to Sd˜ are also analyzed. It is found that, unlike the moderately turbulent premixed flames, where enhanced Sd˜ is driven by interactions among complete flame structures, Sd˜ enhancement in high Ret and high Ka flame is predominantly governed by local interactions of the isotherms. It is found that enhancement in Sd˜ in regions of large negative curvature occurs as a result of these interactions, evincing that the interaction model is useful for high Ka turbulent premixed flames as well.

Local entropy generation and entropy fluxes of a transient flame during head-on quenching towards solid and hydrogen-permeable porous walls

Premixed H2-air flames are studied in a one-dimensional wall-bounded configuration. The laminar flame propagates towards and quenches at a wall that is either solid or permeable. Entropy generation by each of 19 elementary reactions is evaluated. Their total contribution remains the most important up to the quenching instance. Close to quenching, the conduction entropy generation grows considerable. Mass diffusion has a modest contribution, which decreases towards quenching. Viscous forces are negligible as a source of entropy. Effects of unburnt-mixture temperature and fuel-air ratio are investigated, and also dilution with nitrogen (inert) and water vapour. The diffusive entropy flux changed direction away from the permeating wall compared that of the solid wall. A major finding is that fuel permeation through the wall tends to decrease the entropy generation per unit of converted fuel, in particular for initially lean mixtures.

Combustion enhancement and inhibition of hydrogen-doped methane flame by HFC-227ea

Hydrogen enriched with compressed natural gas is an efficient and environment-friendly gaseous fuel. However, the safety issues of mixture and the method to control or weaken their combustion are highly concerned. To explore the inhibition effect of halogenated fire suppressants on the mixture, the effect of HFC-227ea on the laminar premixed methane/air flames, with different fractions of H2, have been studied. Burning velocities have been measured with constant-volume combustion chamber and kinetically modelled a recently assembled kinetic mechanism. The fractions of H2 influence the enhancement and inhibition effect of HFC-227ea, and it is less effective with the lean mixture. In stoichiometric condition, HFC-227ea showed good inhibition effect on the mixture flames. The HFC-227ea increased the burning velocities of CH4-0% H2-air and CH4-10% H2-air flames at leanest condition, whereas the increased burning velocity arising from HFC-227ea not occurred as the addition of H2 above 20%. Experimental results coincided well with numerical results, however the agreement was poor for the leanest flames at low agent loading. Lastly, kinetic mechanism analysis was used to interpret the combustion enhancement and inhibition effect of hydrogen-doped methane flame by HFC-227ea.

Flame Stabilization and Blow-Off of Ultra-Lean H2-Air Premixed Flames

The manner in which an ultra-lean hydrogen flame stabilizes and blows off is crucial for the understanding and design of safe and efficient combustion devices. In this study, we use experiments and numerical simulations for pure H2-air flames stabilized behind a cylindrical bluff body to reveal the underlying physics that make such flames stable and eventually blow-off. Results from CFD simulations are used to investigate the role of stretch and preferential diffusion after a qualitative validation with experiments. It is found that the flame displacement speed of flames stabilized beyond the lean flammability limit of a flat stretchless flame (ϕ=0.3) can be scaled with a relevant tubular flame displacement speed. This result is crucial as no scaling reference is available for such flames. We also confirm our previous hypothesis regarding lean limit blow-off for flames with a neck formation that such flames are quenched due to excessive local stretching. After extinction at the flame neck, flames with closed flame fronts are found to be stabilized inside a recirculation zone.

Role of cellular wavelengths in self-acceleration of lean hydrogen-air expanding flames under turbulent conditions

An investigation is done upon the lean H2-air flame under turbulent conditions to clarify the role of inherent instabilities and turbulence in self-acceleration of expanding flames. The result shows that, in weak turbulent flow fields, the two-stage self-acceleration feature still exists. As the turbulent intensity increases, the originally evident two-stage “transition-saturation” feature is weakened. When the Karlovitz number becomes greater than 1, the self-acceleration process no longer experiences the transition stage and performs a single-stage feature. These observations are correlated with the distribution and evolution of length scales in the cellular structure of the flamefront. A theoretical analysis is conducted to compare growth rates of disturbances induced by instability and turbulence, with consideration of their wavelength dependence. On this basis, interpretations are proposed on afore-mentioned phenomenal observations and response of quantitative parameters such as fractal excess and average cell wavelength.

Effect of hydrocarbon addition on tip opening of hydrogen-air bunsen flames

The effect of hydrocarbon addition on tip opening of lean and stoichiometric hydrogen-air flames is studied computationally by performing two-dimensional numerical simulations. The numerical study reveals that the flame tip of the H2-air burner stabilized flame is open at lean and stoichiometric mixture conditions. The flame tip closes upon hydrocarbon addition. The tip closing is mainly affected by preferential diffusion of the multi-component mixture and the stretch effects. In the addition of light hydrocarbon (CH4), the tip closing starts at a higher percentage of hydrocarbon addition in H2-air flames. Whereas, upon the addition of heavy hydrocarbons such as propane and butane in H2-air flames, tip closing starts with a lesser amount of hydrocarbon addition. Temperature, OH mole fraction and heat release rate have been investigated, focusing on the flame structure at the tip. The tip opening regime diagram for H2–CH4-air, H2–C3H8-air and H2–C4H10-air mixtures are presented.

A comparison of entrainment velocity and displacement speed statistics in different regimes of turbulent premixed combustion

The statistics of entrainment velocity, defined as the displacement speed of an enstrophy isosurface, which can be taken to be the interface between turbulent/non-turbulent regions, have been analysed using a Direct Numerical Simulation database of statistically planar H2-air flames with a range of different Karlovitz numbers. It has been found that the component of the entrainment velocity arising from molecular dissipation plays a leading order role for all values of Karlovitz number, whereas the relative importance of the baroclinic torque and dilatation rate weakens with increasing Karlovitz number. By contrast, the relative contribution of the entrainment velocity component arising from vortex-stretching strengthens with increasing Karlovitz number Ka. The mean entrainment velocity remains positive for the case representing the corrugated flamelets regime (i.e. Ka<1), whereas it assumes negative values in the cases with large values of Karlovitz number (i.e. Ka≫1). The magnitude of the ratio of the mean values of entrainment velocity to the mean values of flame displacement speed conditional upon non-dimensional temperature within the flame front remains of the order of unity irrespective of Karlovitz number. However, the probability density functions of entrainment velocity exhibit considerably higher probabilities of finding large magnitudes than in the case of flame displacement speed. The alignments between the normal vector on the enstrophy isosurface and local principal strain rates have been found to be qualitatively similar to the corresponding alignments between flame normal and local principal strain rates, and the same holds true for the distributions of curvature shape factor of reaction progress variable and enstrophy isosurfaces. These findings indicate that the isosurface topologies and the alignments of normal vectors with local principal strain rates for enstrophy and reaction progress variable exhibit qualitatively similar behaviours. Consequently, turbulence and combustion modelling strategies cannot be considered in isolation in premixed turbulent flames.