Turbulent Burning Velocity Research Articles

Effects of laminar burning velocity to friction velocity ratio on turbulent premixed flame-wall interaction within turbulent boundary layers

Direct numerical simulation of flame-wall interaction (FWI) for two flame configurations under different laminar burning velocity to nonreacting wall friction velocity ratio, SL/uτNR, have been performed. The first configuration considered is a V-flame in a turbulent channel flow with isothermal inert walls and represents oblique wall interaction. The second configuration is representative of head-on interaction (HOI) of a planar flame interacting with a wall in a fully developed turbulent boundary layer. In the case of the V-flame with SL/uτNR=0.4, a smaller flame angle is obtained when compared with that of the V-flame with SL/uτNR=0.7. This is a consequence of the differences in the turbulent burning velocities between the two V-flame cases, where the case with SL/uτNR=0.4 has a lower turbulent burning velocity when compared with that of the case with SL/uτNR=0.7. By contrast, the ratio of turbulent to laminar burning velocity is higher for the SL/uτNR=0.4 HOI case when compared to the corresponding HOI case with SL/uτNR=0.7. The flame orientations with respect to the streamwise component of velocity and wall-normal direction in addition to the SL/uτNR values have been found to have a significant impact on the variations of wall heat flux, wall shear stress, and wall friction velocity in premixed FWI within turbulent boundary layers. The behaviors of nondimensional streamwise velocity, u+, and nondimensional temperature using wall units, T+, have also been investigated for different SL/uτNR ratios and it is found that the standard log-law profiles in the case of u+ and T+ are not valid for the two configurations and the two SL/uτNR ratios considered. Published by the American Physical Society 2024

Fuel blend combustion for decarbonization

The utilization of fossil fuels is currently transforming to low-carbon or zero-carbon fuels, which is one of the solutions to global warming. Hydrogen and ammonia are regarded as promising zero-carbon fuels in power supply and transportation scenarios but the availability of hydrogen and their distinctly different chemical activity constrain their large-scale direct utilizations. Fuel blends with physical and chemical complementary are considered as the effective approaches in the utilization of hydrogen and ammonia because no significant modification to the existing end-user infrastructures is needed. This paper reports recent progress in the fundamental combustion behaviors of fuel blends, focusing on hydrogen-hydrocarbon blends and ammonia-hydrocarbon blends. Firstly, laminar flame behaviors, auto- and forced-ignition characteristics, and pollutant emissions of binary fuels containing hydrogen are reviewed, all of which are supplemented with a discussion on the governing hydrogen-enriched combustion chemistry. Subsequently, the hydrogen-enriched flame responses to the flow conditions are discussed, including the turbulent burning velocity and statistical structures, the flashback swirl flames, thermoacoustic instabilities, and the jet ignition characteristics; Furthermore, with the increasing concern over ammonia as a zero carbon fuel and its extremely weak reactivity, recent progress on combustion of fuel blends containing ammonia are also reviewed. The fundamental combustion chemistry studies including laminar burning velocity, the ignition delay times data collection, as well as the attempts for chemical kinetic modeling development for fuel blend with ammonia are presented. The literature reported ammonia containing blends of turbulent flame characteristics are presented. Finally, from an engineering point of view, examples using hydrogen blends in practical internal combustion engines and in gas turbines are introduced, including the topic of engine efficiency performance and pollutant emissions and different combustors for gas turbines. It is suggested that fuel blends with hydrogen or ammonia that potentially monitors the overall reactivity will be one realistic solution to de-carbonization, on the basis of current transportation and power generation systems.

Turbulent Burning Velocity of High Hydrogen Flames

Abstract The turbulent burning velocity (ST) is one of the most important combustion properties controlling combustor operability limits, directly influencing blowoff, flashback, and combustion instabilities. Hydrogen has particularly significant influences on the turbulent flame speed. This paper presents new H2/CH4 data of high pressure, high hydrogen turbulent burning velocities. The datasets were designed to address fundamental questions as well as provide engineering/design relevant insights. This paper presents new scaling analysis of fuel composition, pressure, and preheat temperature effects on turbulent burning velocity. We also discuss the importance of considering what is being held constant (temperature, flame speed, Reynolds number, etc.) when one is analyzing these sensitivities. Data show that hydrogen fraction and pressure cause an increase in turbulent flame speed; whether quantified as raw ST,GC or normalized as ST,GC/SL,0 or ST,GC/SL,max (where SL,0 and SL,max are the unstretched and stretched laminar flame speed, respectively). We also propose that observed increases in ST,GC with pressure are due to increases in Reynolds number and not a kinetics/stretch sensitivity effect. With increasing preheat temperature, ST,GC increases while its normalized value (ST,GC/SL,0 and ST,GC/SL,max) can either increase or decrease, depending upon fuel composition. We also show how these sensitivities vary, depending on whether these comparisons are made at constant raw turbulence intensity urms or at constant normalized urms/SL,0 or urms/SL,max.

Turbulent flame acceleration and deflagration-to-detonation transitions in ethane–air mixture

The deflagration-to-detonation transition (DDT) poses significant risks in the oil, gas, and nuclear industries, capable of causing catastrophic explosions and extensive damage. This study addresses a critical knowledge gap in understanding the DDT of ethane–air mixtures on a large scale, amid increasing industrial utilization and production of ethane. A novel computational framework is introduced, utilizing the finite-volume code named Morris Garages, which incorporates reactive compressible Navier–Stokes equations, adaptive mesh refinement, and correlations of turbulent burning velocities. This model integrates the most recent data on laminar and turbulent burning velocities for premixed ethane–air mixtures, simulating flame acceleration and DDT within a two-dimensional large-scale setting, measuring 21 m in length and 3 m in height, with obstacles mimicking pipe congestion. Two mixture scenarios, lean and near-stoichiometric, are analyzed to evaluate the effects of equivalence ratios on flame propagation and DDT. The simulations, validated against large-scale experimental data from Shell, show reasonable agreement and provide critical insights into the onset conditions of DDT, such as temperature, pressure, flame speed, and turbulent kinetic energy. Furthermore, the ξ–ε detonation peninsula diagram is utilized to explore autoignition and detonation behaviors in ethane–air mixtures.

Implications of Using Scalar Forcing to Sustain Reactant Mixture Stratification in Direct Numerical Simulations of Turbulent Combustion

A recently proposed scalar forcing scheme that maintains the mixture fraction mean, root-mean-square and probability density function in the unburned gas can lead to a statistically quasi-stationary state in direct numerical simulations of turbulent stratified combustion when combined with velocity forcing. Scalar forcing alongside turbulence forcing leads to greater values of turbulent burning velocity and flame surface area in comparison to unforced simulations for globally fuel-lean mixtures. The sustained unburned gas mixture inhomogeneity changes the percentage shares of back- and front-supported flame elements in comparison to unforced simulations, and this effect is particularly apparent for high turbulence intensities. Scalar forcing does not significantly affect the heat release rates due to different modes of combustion and the micro-mixing rate within the flame characterised by scalar dissipation rate of the reaction progress variable. Thus, scalar forcing has a significant potential for enabling detailed parametric studies as well as providing well-converged time-averaged statistics for stratified-mixture combustion using Direct Numerical Simulations in canonical configurations.

Turbulent partially cracked ammonia/air premixed spherical flames

The combustion of ammonia requires, for most energy conversion systems, a combustion promoter such as hydrogen to guarantee the start-up, stability and combustion efficiency. Partially cracked ammonia (PCA) can provide sufficient hydrogen concentrations to enhance the burning velocity in comparison with pure ammonia. However, little work exists on the use of PCA blends operating under relevant turbulent conditions. To that end the outwardly propagating spherical flame configuration was employed to determine the laminar and turbulent flame propagation characteristics of PCA (NH3/(H2+N2)) and corresponding binary (NH3/H2) mixtures across various turbulent combustion regimes. First, PCA and ammonia-hydrogen blends exhibit similar flame propagation rates under various turbulent intensities, even for the laminar case. The highest turbulent burning velocity was observed at leanest conditions, as opposed to laminar flames which exhibited highest flame speed at conditions above stoichiometry. Under rich conditions, no substantial flame enhancement due to turbulence was measured irrespective of the hydrogen content. This lack of flame enhancement under turbulent conditions is attributed to the effect of preferential diffusion with good agreement observed with trends in measured Markstein numbers. The normalized turbulent flame speed is dominated by the enhanced molecular diffusivity afforded by the presence of hydrogen up to 15 % enrichment, prior to decreasing upon further hydrogen addition under lean and stoichiometric conditions. This ‘bending’ phenomenon may be the contribution of several factors including; the transitioning between combustion regimes associated with low Damköhler numbers (Da) and flame thickening; merging of flamelets due to the presence of ammonia enhancing wrinkling; and combined changes in laminar burning velocity and preferential diffusional behavior. Furthermore, good agreement for turbulent flame speed is observed with a correlation that includes the influence of turbulent stretch (Ka) and non-equidiffusion (Le), with the agreement reducing with decreasing chemical to turbulent time scale ratios (Da << 1).

Lagrangian, game theoretic, and PDE methods for averaging G-equations in turbulent combustion: existence and beyond

G-equations are popular level set Hamilton–Jacobi nonlinear partial differential equations (PDEs) of first or second order arising in turbulent combustion. Characterizing the effective burning velocity (also known as the turbulent burning velocity) is a fundamental problem there. We review relevant studies of the G-equation models with a focus on both the existence of effective burning velocity (homogenization), and its dependence on physical and geometric parameters (flow intensity and curvature effect) through representative examples. The corresponding physical background is also presented to provide motivations for mathematical problems of interest. The lack of coercivity of Hamiltonian is a hallmark of G-equations. When either the curvature of the level set or the strain effect of fluid flows is accounted for, the Hamiltonian becomes highly nonconvex and nonlinear. In the absence of coercivity and convexity, the PDE (Eulerian) approach suffers from insufficient compactness to establish averaging (homogenization). We review and illustrate a suite of Lagrangian tools, most notably min-max (max-min) game representations of curvature and strain G-equations, working in tandem with analysis of streamline structures of fluid flows and PDEs. We discuss open problems for future development in this emerging area of dynamic game analysis for averaging noncoercive, nonconvex, and nonlinear PDEs such as geometric (curvature-dependent) PDEs with advection.

On turbulent burning velocities of V-shaped turbulent premixed flames with circular fractal turbulence generators

The characteristics of turbulent burning velocities of V-shaped turbulent flames are experimentally investigated by varying the shape parameters of cross- and square-type circular fractal turbulence generators (FTG). For both type FTGs, the thickness reduction ratio, Rt, of 0.4, 0.6, 0.8, and 1.0, and the blockage ratios, σ, of 30 and 50% are used. The characteristics of non-reacting turbulent flows such as the mean flow velocity, U¯, velocity fluctuation, u′, and integral length scale, L, are measured using a hot-wire anemometer while the progress variable of reacting flows is evaluated using OH-PLIF images. The turbulent premixed flames are distributed in the Borghi-Peters diagram from the wrinkled flamelet regime to the thin reaction zone regime, depending on the shape parameters of the FTG. The local displacement speed, ST,LD, and the local consumption speed, ST,LC, are evaluated using the measured data of turbulent reacting and non-reacting flows. ST,LD and ST,LC are found to increase with increasing σ and decreasing Rt, and hence, the averaged ST,LD, and ST,LC can be expressed as a function of u′/SL and/or L/δL. Correlations between ST or u′ and the FTG shape parameters (Rt and σ) are also proposed, which can be used to control and predict ST and u′ for fundamental studies and industrial applications.

Measuring dust burning velocity for deflagration vent design

Deflagration vent design should be based on the burning velocity in the pressure range below 3 bara, where vent relief devices normally operate, rather than the KSt deflagration index, which is typically measured at pressures >50% of the maximum deflagration pressure, Pmax. Tests using a standardized 1000-L vessel showed that in the pressure range below about 3 bara, niacin and lycopodium burned faster than cornstarch, despite its larger KSt index. We attribute this behavior to the endothermic dehydration of cornstarch during the early stages of deflagration. Deflagration vents for cornstarch and other milled grains may have been oversized while vents for some other dusts may have been undersized. Burning velocities are most relevant in the region of the 2-bara midpoint overpressure and can theoretically be found from the “isothermal pressure rate gradient”, or IPRG, which we define as the gradient of (dP/dt) plotted against P (1-1/P)2/3. However, owing to irregular combustion caused primarily by two 5 kJ igniters, the IPRG is found indirectly from the “pressure rate gradient” or PRG, which we define as the gradient of (dP/dt) plotted against P. The PRG was found to be adequately linear for measurement at 2 bara and the experimental curves passed through the "origin". It was shown mathematically that at 2 bara the PRG is 1.05 times larger than IPRG, permitting the IPRG and turbulent burning velocity to be calculated. Since the calculation of burning velocity from the IPRG requires Pmax, a general extrapolation technique was developed for correcting Pmax values obtained in vessels smaller than 1000-L. We propose that, owing to the greater turbulence in the 20-L vessel, a calibration be made using methane. This would establish the turbulence factors for each vessel at 2 bara, allowing the underlying “reference” burning velocities to be calculated and compared. However, to measure turbulent dust burning velocities in 20-L vessels a smaller and more efficient igniter must be used. Two 5 kJ igniters not only obscure the pressure history but wastefully expend energy far from the vessel core, depleting the unburned mixture and depressing the subsequent pressure rate. An observed “double sigmoid” dependence of dust deflagration rate on particle diameter suggests that routine explosibility testing of organic dusts is usually carried out in a region where pressure rates are relatively insensitive to particle size.

Morphology and turbulent burning velocity of n-decane/air expanding flames at constant turbulent Reynolds numbers

In this work we experimentally investigated the propagation and the turbulent burning velocity of n-decane/air turbulent expanding flames at 423 K and 0.5-3.0 atm, with constant turbulent Reynold number, ReT,flow = (urmsLI)/ν, ranging from 174 to 4712, using a medium-scale, fan-stirred combustion chamber, where urms and LI are respectively the turbulence intensity and the integral length scale, and ν is the kinematic viscosity of a fresh mixture. It was found that the n-decane/air turbulent expanding flame is self-similar, and the normalized turbulent flame propagation speed scales with the turbulent flame Reynold number, ReT,flame = (urms/SL)(〈r〉/δL), to the one-half power for mixtures characterized by non-unity Lewis numbers, where the mean flame radius (〈r〉) is the length scale, and the thermal diffusivity (α = SLδL) is the transport property. The turbulent burning velocity (ST,c=0.5) at the mean progress variable (〈c〉) of 0.5 decreases with the pressure at a constant ReT,flow, following the similar pressure dependence of the laminar burning velocity (SL). The ST,c=0.5/SL of the fuel-rich n-decane/air flame (ϕ = 1.4) is twice larger than that of the fuel-lean mixture (ϕ = 0.8), which would be attributed to the promotion of local burning rates by coupling between the differential diffusion and the turbulent flame stretch on the local flame fronts. In addition, five useful modified correlations for the turbulent burning velocity with the experimental Lewis number (LeBM) consideration were obtained based on the present experimental data of n-decane/air turbulent expanding flames. Particularly, the successful scaling of the modified correlation based on Damköhler's second hypothesis, ST,c=0.5/SL = 1 + 0.115(ReT,flowLeBM−2)0.5, suggesting that the ST,c=0.5/SL is inversely proportional to the LeBM. The importance of using experimental determined values of the Lewis number in the scaling of turbulent burning velocity with the differential diffusion consideration should be emphasized.

Crankcase Explosions in Marine Diesel Engines: A Computational Study of Unvented and Vented Explosions of Lubricating Oil Mist

Accidental crankcase explosions in marine diesel engines are presumably caused by the inflammation of lubricating oil in air followed by flame propagation and pressure buildup. This manuscript deals with the numerical simulation of internal unvented and vented crankcase explosions of lubricating oil mist using the 3D CFD approach for two-phase turbulent reactive flow with finite-rate turbulent/molecular mixing and chemistry. The lubricating oil mist was treated as either monodispersed with a droplet size of 60 μm or polydispersed with a trimodal droplet size distribution (10 μm (10 wt%), 250 μm (10 wt%), and 500 μm (80 wt%)). The mist was partly pre-evaporated with pre-evaporation degrees of 60%, 70%, and 80%. As an example, a typical low-speed two-stroke six-cylinder marine diesel engine was considered. Four possible accidental ignition sites were considered in different linked segments of the crankcase, namely the leakage of hot blow-by gases through the faulty stuffing box, a hot spot on the crankpin bearing, electrostatic discharge in the open space at the A-frame, and a hot spot on the main bearing. Calculations show that the most important parameter affecting the dynamics of crankcase explosion is the pre-evaporation degree of the oil mist, whereas the oil droplet size distribution plays a minor role. The most severe unvented explosion was caused by the hot spot ignition of the oil mist on the main bearing and flame breaking through the windows connecting the crankcase segments. The predicted maximum rate of pressure rise in the crankcase attained 0.6–0.7 bar/s, whereas the apparent turbulent burning velocity attained 7–8 m/s. The rate of heat release attained a value of 13 MW. Explosion venting caused the rate of pressure rise to decrease and become negative. However, vent opening does not lead to an immediate pressure drop in the crankcase: the pressure keeps growing for a certain time and attains a maximum value that can be a factor of 2 higher than the vent opening pressure.

Turbulent burning velocity of hydrogen/n-heptane/air propagating spherical flames: Effects of hydrogen content

This study investigated the flame propagation and turbulent burning velocity of hydrogen/n-heptane/air mixtures subjected to differential diffusion and flame stretch induced by turbulence at different hydrogen molar fractions (XH2 = 0–100%), equivalence ratios (ϕ = 0.5–1.0) and turbulence intensities (u’ = 0–3.62 m/s). The experiments were carried out on a medium-scale, fan-stirred cylindrical combustion chamber generating near-isotropic turbulence. Results show that as hydrogen content increases, the turbulent flame propagation speed tends to be affected by stronger differential diffusion and weakened turbulence, characterized by decreasing Lewis number (Le) and Karlovitz number (Ka) within a similar range of turbulence intensity. Among them, the effect of differential diffusion on the normalized turbulent propagation speed (d<r>/dtσSL) appears to be well correlated with ReT,flameLe-2, where ReT,flame represents the turbulent flame Reynolds number. However, inconsistencies in the fitting parameters for this scale are observed at different XH2, highlighting the impact of substantial variations in flame stretch induced by turbulence. Therefore, the normalized turbulent flame propagation velocity under varying hydrogen contents is proposed to be accurately predicted by d<r>/dtσSL-1 = 0.07Ka0.32(ReT,flameLe−2)0.5. The synergistic effects of Le and Ka can also account for the peak phenomenon in the normalized turbulent burning velocity (ST/SL) observed at 85% hydrogen content. Furthermore, the quantitative characterization of turbulence and differential diffusion under extensive experimental data (Ka = 0.03–90) is studied. As evidenced by the Damköhler theoretical hypothesis, the two-stage trend between ST/SL and (u’/SL)Le-1 is identified with a transition near unity Ka. The modified correlations for turbulent burning velocity in terms of (u’/SL)Le-1 and Ka0.2 are obtained with consideration of the differential diffusion and flame stretch rate induced by turbulence, which show good predictive performance for data at different turbulence regime diagrams regardless of fuel type and equipment size.

Transition from turbulence-dominated to instability-dominated combustion regime in lean hydrogen-air flames

To explore the importance of thermodiffusive and hydrodynamic instabilities of laminar flames in turbulent flows, previously generated direct numerical simulations of statistically one-dimensional complex-chemistry lean hydrogen-air flames in forced turbulence were continued by switching-off turbulence forcing. Three sets of flames characterized by different ratios of initial root-mean-square velocity to laminar flame speed, i.e., (A) u′/SL=2.2, (B) u′/SL=4.0, and (C) u′/SL=8.3, were addressed. Moreover, new complementary simulations of unstable laminar flames were performed. Analyses from the obtained numerical results indicate (but do not prove) that laminar flame instabilities play a minor role at sufficiently high Karlovitz numbers Ka. This supposition is supported, first, in cases B and C, where the initial value of turbulent burning velocity UT is significantly higher than burning velocity evaluated during non-linear stage of laminar flame instability development in the same computational domain. Second, regular large-scale perturbations of instantaneous flame surface are prominent in the unstable laminar flame but are not observed at high Ka. Third, Karlovitz numbers associated with appearance of such perturbations as the turbulence decays are scattered between 4 and 10 and are consistent within an order of magnitude to a recently proposed criterion (Chomiak and Lipatnikov, Phys. Rev. E 107: 015102, 2023) of importance for laminar flame instabilities in turbulent flows. Fourth, at such transition instants, a ratio of potential and solenoidal turbulent kinetic energies, averaged over the flame-brush leading edge, is close to 2.0 in 11 studied cases and a ratio of UT/SL varies between 3.0 and 3.5. Fifth, the maximum fuel consumption rate (over the computational domain) decreases as the turbulence decays. Thus, the initial maximum rates are significantly higher than the counterpart rate in the unstable laminar flame. Together these results show that the hypothesis that laminar flame instabilities play only a minor role at high Ka deserves further study.

Are differential diffusion effects of importance when burning hydrogen under elevated pressures and temperatures?

A ratio of turbulent burning velocity to laminar flame speed is well known to be abnormally high in lean hydrogen-air mixtures, with this phenomenon being commonly attributed to differential diffusion effects. Magnitude of such effects is known to be increased by pressure, but a few recent studies have indicated that the effects are mitigated when reactants are preheated. It is not yet known, however, which of these two counteracting trends is of more importance under elevated pressures and temperatures associated with combustion in engines. Accordingly, it is not yet clear whether or not models of differential diffusion effects are required for research and development of future ultra-clean and highly efficient engines that burn hydrogen (the emphasized effects are typically ignored in engineering computations). To clarify the issue, numerical simulations of lean complex-chemistry hydrogen-air strained laminar flames are performed by varying strain rate, pressure 1≤P≤50 bar, temperature 300≤Tu≤900 K, and equivalence ratio (Φ=0.4, 0.55, and 0.7). This simple problem is selected because maximal consumption speeds reached in critically strained (close to extinction) lean hydrogen-air laminar flames are considered to characterize the influence of differential diffusion on turbulent burning rates within the framework of Zel'dovich's leading point concept, which was well supported in recent studies. Computed results show that, even at Tu=900 K, the aforementioned consumption speeds are significantly larger than the unperturbed laminar flame speeds if the mixture is sufficiently lean (the equivalence ratio Φ=0.55 or lower) and pressure is sufficiently high (P≥30 bar). Therefore, differential diffusion effects are expected to be of importance when burning so lean hydrogen-air mixtures in engines and should be properly modeled.

Overall lift-off characteristics of CH4/H2 non-premixed jet flames in laminar/turbulent transition

The effects of adding hydrogen to methane were investigated through the transition between laminar and turbulent regimes based on the characteristics of non-premixed lifted flames. Lift-off heights can show complex trends depending on the fuel tube diameter, jet velocity, and hydrogen ratio. In the laminar regime, the lift-off heights were smaller than the laminar mixing core and decreased with hydrogen addition. In the turbulent regime, the lift-off heights could be much smaller or larger than the turbulent core when the jet velocities were smaller or larger than specific criteria, respectively. Such transitional phenomena were discussed based on the theories related to flow development, premixed flame, and edge flame structures. These included the mixing layer, quenching distance, flow re-direction, Damköhler number, turbulent flame speed, etc. Meanwhile, existing relationships between the lift-off heights and the flow velocities showed significant deviations when the hydrogen ratio was large. An improved relationship between the lift-off heights and the fuel jet velocities was proposed, considering the influence of the virtual origin and the flammable mixing layer. This relationship will apply to various fuel compositions such as propane, methane, hydrogen, and their mixtures. In addition, the blow-off mechanism was explained based on the turbulent burning velocity. Finally, the overall stabilization modes and mechanisms of the lifted flames were explained.

Experimental study on turbulent burning velocities of premixed flames for natural gas/air mixtures

Experiments on the spherical expanding flame of turbulent premixed natural gas/air mixtures were conducted in a fan-stirred turbulent combustor for the first time. As the belief that the methane burning velocity data can be obtained for natural gas is not justified, natural gas constitutes of 90% CH4, 7% C2H6 and 3% C3H8 by volume fraction was used. The operation conditions are equivalence ratio of 0.7–1.3, initial temperature of 300–400 K, initial pressure of 0.1–0.3 MPa, turbulence intensity of 1.0–2.7 m/s, oxygen volume fraction of 15–21% and carbon dioxide volume fraction of 0–20%. A self-developed program and post-processing procedure was developed to highly restore the real information of flame front without ignoring small local information. It was concluded that methane cannot be taken as a representative of natural gas for studying turbulent burning velocities. The increase of flame propagation speed with initial pressure is not as significant as that with initial temperature and turbulence intensity under low-intermediate pressure range. Dispersions exists for previous correlations relating to turbulent flame Reynolds number, Karlovitz number, Damköhler number, respectively, and a new correlation were proposed based on the ratio of Karlovitz number and Damköhler number. The new correlation was validated by both current and previous experimental data and its advantage and applicability were summarized. It will be validated by turbulent flames of various kinds of fuels over a wide range of working conditions in the further study.

Turbulent burning velocity and thermodiffusive instability of premixed flames.

Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermodiffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λ_{n} that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained, and (ii) simulations of turbulent flames are performed by varying the width from Λ<Λ_{n} (in this case, the instability is suppressed) to Λ>Λ_{n} (in this case, the instability may grow). Moreover, simulations are performed either using mixture-averaged transport properties (low Lewis number flames) or setting diffusivities of all species equal to heat diffusivity of the mixture (equidiffusive flames), with all other things being equal. Obtained results show a significant increase in turbulent burning velocity U_{T} when the boundary Λ=Λ_{n} is crossed in weak turbulence, but almost equal values of U_{T} are computed at Λ<Λ_{n} and Λ>Λ_{n} in moderately turbulent flames characterized by a Karlovitz number equal to 3.4 or larger. These results imply that thermodiffusive instability of laminar premixed flames substantially affects burning velocity in weak turbulence only, in line with a simple criterion proposed by Chomiak and Lipatnikov (Phys. Rev. E 107, 015102, (2023)10.1103/PhysRevE.107.015102).

A priori test of perfectly stirred reactor approach to evaluating mean fuel consumption and heat release rates in highly turbulent premixed flames

Unsteady three-dimensional Direct Numerical Simulation (DNS) data obtained earlier by Dave et al. ( J Fluid Mech 2020; 884: A46) from a statistically planar and one-dimensional, highly turbulent, moderately lean hydrogen-air flame propagating in a box are processed to perform a priori test of perfectly stirred reactor model. The test aims in particularly at estimating mesh resolution (or filter width within large eddy simulation framework) required to neglect variations in the temperature and mixture composition within a computational cell when evaluating mean (or filtered) fuel consumption and heat release rates. For this purpose, fuel consumption and heat release rates sampled directly from the DNS data and averaged over a cube of width [Formula: see text] are compared with fuel consumption and heat release rates calculated using the temperature and species concentrations averaged over the same cube. Moreover, turbulent burning velocities computed by integrating the former and latter rates are compared with one another. A ratio of [Formula: see text] to a laminar flame thickness [Formula: see text] is varied from 0.44 to 1.8. The obtained results indicate that the tested simple approach performs reasonably well (poor) if [Formula: see text] ([Formula: see text], respectively). This result is further supported by directly filtering fuel consumption rate in a laminar premixed flame. The values of the thickness [Formula: see text], calculated using detail chemical mechanisms for different fuels under elevated temperatures and pressures associated with combustion in piston engines, indicate that it is difficult to satisfy the constraint of [Formula: see text] in contemporary unsteady multidimensional numerical simulations of turbulent burning in such engines.

Turbulence Effects on the Statistical Behaviour and Modelling of Flame Surface Density and the Terms of Its Transport Equation in Turbulent Premixed Flames

The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.

Influence of initial temperature on laminar burning velocity in hydrogen-air mixtures as potential for green energy carrier

One of the most important parameters describing a combustible mixture is the laminar burning velocity. The determination of this value forms the basis for the calculation of backflow parameters, the flame cone angle in burners and the turbulent burning velocity. It is also an indispensable parameter in flame stabilization and quenching studies.In this regard, the present study compares the predictive performance of three relatively simple numerical models used to determine the laminar burning velocity of hydrogen-air mixtures: 1) Monton, Lewis et al., 2) Bradley and Mitcheson, and 3) Dahoe. Their performance was determined for three initial burning temperatures (298.15 K, 323.15 K, and 348.15 K), comparing the respective laminar burning rates of hydrogen with measurements made using the Cantera toolbox and the GRI-Mech 3.0 chemical reaction kinetics mechanism.The experimental results show that the models of Bradley and Mitcheson et al. and Dahoe, although relatively simple, have relatively satisfactory predictive power compared to the measurements of the Cantera toolkit. The difference between the two numerical models and Cantera was less than 0.05 m/s. On the other hand, due to the relative simplicity, Monton, Lewis et al. model showed the lowest accuracy compared to the Cantera toolkit, with an average error of the hydrogen burning rate of 0.3 m/s. The results presented in this study enrich the basic hydrogen combustion rate data, which is critical for further research related to the use of hydrogen as a renewable energy source.