A DNS study of the physical mechanisms associated with density ratio influence on turbulent burning velocity in premixed flames

Data obtained in 3D direct numerical simulations of statistically planar, 1D weakly turbulent flames characterised by different density ratios σ are analysed to study the influence of thermal expansion on flame surface area and burning rate. Results show that, on the one hand, the pressure gradient induced within a flame brush owing to heat release in flamelets significantly accelerates the unburned gas that deeply intrudes into the combustion products in the form of an unburned mixture finger, thus causing large-scale oscillations of the burning rate and flame brush thickness. Under the conditions of the present simulations, the contribution of this mechanism to the creation of the flame surface area is substantial and is increased by σ, thus implying an increase in the burning rate by σ. On the other hand, the total flame surface areas simulated at σ = 7.53 and 2.5 are approximately equal. The apparent inconsistency between these results implies the existence of another thermal expansion effect that reduces the influence of σ on the flame surface area and burning rate. Investigation of the issue shows that the flow acceleration by the combustion-induced pressure gradient not only creates the flame surface area by pushing the finger tip into the products, but also mitigates wrinkling of the flame surface (the side surface of the finger) by turbulent eddies. The latter effect is attributed to the high-speed (at σ = 7.53) axial flow of the unburned gas, which is induced by the axial pressure gradient within the flame brush (and the finger). This axial flow acceleration reduces the residence time of a turbulent eddy in an unburned zone of the flame brush (e.g. within the finger). Therefore, the capability of the eddy for wrinkling the flamelet surface (e.g. the side finger surface) is weakened owing to a shorter residence time.     

Zone conditional analysis of a freely propagating one-dimensional turbulent premixed flame

The zone conditional conservation equations are derived and validated against the DNS data of a freely propagating one-dimensional turbulent premixed flame. Conditional flow velocities are calculated by the conditional continuity and momentum equations, and a modeled transport equation for the Reynolds average reaction progress variable. An asymptotic formula for turbulent burning velocity is obtained with the effects of a finite Damköhler number accounted for as an additional factor. It is shown that flame generated turbulence is primarily due to correlations between fluctuating gas velocities and fluctuating unit normal vector on a flame surface. More investigation is required to validate general predictive capability of the derived conditional conservation equations and the relationships modeled for closure.     

Measurements of three-dimensional mean flame surface area ratio in turbulent premixed Bunsen flames

A data processing scheme with particular emphasis on proper flame contour smoothing is developed and applied to measure the three-dimensional mean flame surface area ratio in turbulent premixed flames. The scheme is based on the two-sheet imaging technique such that the mean flame surface area ratio is an average within a window covering a finite section of the turbulent flame brush. This is in contrast to the crossed-plane tomograph technique which applies only to a line. Two sets of Bunsen flames have been investigated in this work with the turbulent Reynolds number up to 4000 and the Damköhler number ranging from less than unity to close to 10. The results show that three-dimensional effects are substantial. The measured three-dimensional mean flame surface area ratio correlates well with a formula similar to the Zimont model for turbulent burning velocity but with different model constants. Also, the mean flame surface area ratio displays a weak dependency on turbulence intensity but a strong positive dependency on the turbulence integral length scale.     

Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature

Turbulent burning velocities for methane/air mixtures at pressures ranging from atmospheric pressure up to 1.0 MPa and mixture temperatures of 300 and 573 K were measured, which covers the typical operating conditions of premixed-type gas-turbine combustors. A bunsen-type flame stabilized in a high-pressure chamber was used, and OH-PLIF visualization was performed with the pressure and mixture temperature being kept constant. In addition to a burner with an outlet diameter of 20 mm for the high-pressure experiments, a large-scale burner with an outlet diameter of 60 mm was used at atmospheric pressure to extend the turbulence Reynolds number based on the Taylor microscale, R_λ, as a common parameter to compare the pressure and temperature effects. It was confirmed that R_λ over 100 could be attained and that u′/S_L could be extended even at atmospheric pressure. Based on the contours of the mean progress variable c = 0.1 determined using OH-PLIF images, turbulent burning velocity was measured. S_T/S_L was also found to be greatly affected by pressure for preheated mixtures at 573 K. The bending tendency of the S_T/S_L curves with u′/S_L was seen regardless of pressure and mixture temperature and the R_λ region where the bending occurs corresponded well to the region where the smallest scale of flame wrinkling measured as a fractal inner-cutoff approaches the characteristic flame instability scale and becomes almost constant. A power law of S_T/S_L with (P/P₀)(u′/S_L) was clearly seen when S_T was determined using c = 0.1 contours, and the exponent was close to 0.4, indicating agreement with the previous results using the mean flame cone method and the significant pressure effects on turbulent burning velocity.     

Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data

The interaction between turbulence and reactive scalar fields is discussed for the wrinkled flamelets regime of turbulent premixed combustion. Emphasis is placed on the effects associated with the turbulent straining term. In the regime of turbulent combustion under consideration, which corresponds to Karlovitz and Damköhler numbers such that Ka < 1 and Da > 1, a clear and simple formulation is proposed to explain and to model the influence of the correlation between velocity and reactive scalar gradients. This formulation is based on the conservative variables budget across one-dimensional premixed laminar flamelets. The analysis firmly confirms the dependence on both the Damköhler number and the expansion factor, a feature already foreseen in recent studies. Nevertheless, in contrast with previous work, (i) the scaling arguments used in the present contribution are different from those used in other recent proposals, and (ii) the proposed closures are not only deduced from dimensional arguments but also from the consideration of conservative variable budgets across laminar flamelets. The resulting functional dependence on the expansion factor is found to be influenced by the underlying one-dimensional flamelet representation and two possible closures are put forward to take this dependence into account. (iii) The two closures do not exhibit a proportionality to the mean scalar dissipation rate as suggested in previous studies but to the square of this quantity. This results in the presence of a second contribution proportional to in the modelled transport equation for the mean scalar dissipation rate, in addition to the modelled molecular dissipation term. (iv) Since previous Direct Numerical Simulation (DNS) studies have been essentially devoted to the influence of the Damköhler number, the present DNS validation step is focused on the effects of the expansion rate. To this purpose, the proposed models are validated against three available DNS databases obtained for turbulent premixed flames with different values of the density ratio between unburned and fully burned gases.     

Strain rates,flow patterns and flame surface densities in hydrodynamically unstable,weakly turbulent premixed flames

Recent numerical and experimental studies have unveiled a potentially marked difference between the laminar as well as turbulent propagation of premixed flames exhibiting Darrieus–Landau (DL) (or hydrodynamic) instabilities from flames for which instabilities are inhibited. In this study we utilize two-dimensional numerical simulations of slot burner flames as well as experimental Propane–Air Bunsen flames to analyse differences in turbulent propagation, strain rate and induced flow patterns of hydrodynamically stable and unstable flames. We also investigate the effects of hydrodynamic instability on quantities which are directly related to reaction rate closure models, such as flame surface density and stretch factor. A clear enhancement of turbulent flame speed can be observed for unstable flames, generally mitigated at higher turbulence intensity, which is attributed to a flame area increase induced by the characteristic cusp-like DL-induced corrugation, absent in stable flames, which occurs concurrently and in synergy with turbulent wrinkling. Unstable flames also exhibit, both numerically and experimentally, a different correlation between strain rate and flame curvature and are observed to give rise to a channeling of the induced flow in the fresh mixture. Conditionally averaged flame surface density is also observed to attain smaller values in unstable flames, as a result of the thicker turbulent flame brush, indicating that closure models should incorporate instability-related parameters in addition to turbulence-related parameters.     

The impact of dilatation,scrambling, and pressure transport in turbulent premixed flames

Premixed turbulent flames feature strong interactions between chemical reactions and turbulence that affect scalar and turbulence statistics. The focus of the present work is on clarifying the impact of pressure dilatation/flamelet scrambling effects with a comprehensive second-moment closure used for evaluation purposes. Model extensions that take into account flamelet orientation and molecular diffusion are derived. Isothermal pressure transport is included with an additional variable density contribution derived for the flamelet regime of combustion. Full closure is assessed by comparisons with Direct Numerical Simulations (DNSs) of statistically ‘steady’ fully developed premixed turbulent planar flames at different expansion ratios. Subsequently, the prediction of lean premixed turbulent methane–air flames featuring fractal grid generated turbulence in an opposed jet geometry is considered. The overall agreement shows that ‘dilatation’ effects contribute to counter-gradient transport and can also increase the turbulent kinetic energy significantly. Levels of anisotropy are broadly consistent with the DNS data and key aspects of opposed jet flames are well predicted. However, it is also shown that complications arise due to interactions between the imposed pressure gradient and combustion and that redistribution is affected along with the scalar flux at the leading edge. The latter is strongly affected by the reaction rate closure and, potentially, by pressure transport. Overall, the derived models offer significant improvements and can readily be applied to the modelling of premixed turbulent flames at practical rates of heat release.     

Influences of initial velocity, diameter and Reynolds number on a circular turbulent air/air jet

This paper assesses the suitability of the inflow Reynolds number defined by Re_o ≡ U_oD/ν (here U_o and D are respectively the initial jet velocity and diameter while ν is kinematic viscosity) for a round air/air jet. Specifically an experimental investigation is performed for the influences of U_o, D and Re_o on the mean-velocity decay and spread coefficients (K_u, K_r) in the far field of a circular air jet into air from a smoothly contracting nozzle. Present measurements agree well with those previously obtained under similar inflow conditions. The relations K_u ∝ U_o and K_r ∝ 1/U_o for U_o < 5 m/s appear to work, while each coefficient approaches asymptotically to a constant for U_o > 6 m/s, regardless of the magnitudes of Re_o and D. It is revealed that Re_o may not be an appropriate dimensionless parameter to characterize the entire flow of a free air/air jet. This paper is the first paper that has challenged the suitability of Re_o for turbulent free jets.     

Effects of blending 2,5-dimethylfuran on the laminar burning velocity and ignition delay time of isooctane/air mixture

The prospects of 2,5-dimethylfuran (DMF) as a bio-derived fuel that can be blended with gasoline are believed to be impressive. However, the effects of blending DMF on the key combustion parameters like the laminar burning velocity and ignition delay time of gasoline/air mixture need to be studied extensively for the successful implementation of the fuel mixture in spark ignition engines. Therefore, a skeletal chemical kinetic mechanism, comprising of 999 reactions among 218 species, has been developed in the present work for this purpose. The proposed chemical kinetic model has been validated against a wide range of experimental data for the laminar burning velocity and ignition delay time of isooctane (representing gasoline), DMF and their blends. It has been found from the present study that the thermal diffusivity of the unburnt gas mixture changes by a very small amount from the corresponding value for the pure isooctane/air mixture when DMF is added. Unlike isooctane, the DMF molecule does not consume H radicals during its primary breakup. Therefore, the maximum laminar burning velocity increases marginally when 50% DMF is blended with isooctane due to the increased presence of H radicals in the flame. The negative temperature coefficient behaviour in the ignition delay time of the isooctane fuel vanishes when 30% DMF (v/v) is blended to it.     

Effects of combined dimension reduction and tabulation on the simulations of a turbulent premixed flame using a large-eddy simulation/probability density function method

A turbulent lean-premixed propane–air flame stabilised by a triangular cylinder as a flame-holder is simulated to assess the accuracy and computational efficiency of combined dimension reduction and tabulation of chemistry. The computational condition matches the Volvo rig experiments. For the reactive simulation, the Lagrangian Large-Eddy Simulation/Probability Density Function (LES/PDF) formulation is used. A novel two-way coupling approach between LES and PDF is applied to obtain resolved density to reduce its statistical fluctuations. Composition mixing is evaluated by the modified Interaction-by-Exchange with the Mean (IEM) model. A baseline case uses In Situ Adaptive Tabulation (ISAT) to calculate chemical reactions efficiently. Its results demonstrate good agreement with the experimental measurements in turbulence statistics, temperature, and minor species mass fractions. For dimension reduction, 11 and 16 represented species are chosen and a variant of Rate Controlled Constrained Equilibrium (RCCE) is applied in conjunction with ISAT to each case. All the quantities in the comparison are indistinguishable from the baseline results using ISAT only. The combined use of RCCE/ISAT reduces the computational time for chemical reaction by more than 50%. However, for the current turbulent premixed flame, chemical reaction takes only a minor portion of the overall computational cost, in contrast to non-premixed flame simulations using LES/PDF, presumably due to the restricted manifold of purely premixed flame in the composition space. Instead, composition mixing is the major contributor to cost reduction since the mean-drift term, which is computationally expensive, is computed for the reduced representation. Overall, a reduction of more than 15% in the computational cost is obtained.     

A DNS assessment of linear relations between filtered reaction rate,flame surface density,and scalar dissipation rate in a weakly turbulent premixed flame

Linear relations between (i) filtered reaction rate and filtered flame surface density (FSD) and (ii) filtered reaction rate and filtered scalar dissipation rate (SDR), which are widely used in Large Eddy Simulation (LES) research into premixed turbulent combustion, are examined by processing DNS data obtained from a statistically 1D planar flame under weakly turbulent conditions that are most favourable for the two approaches (flamelet combustion regime, single-step chemistry, equidiffusive mixture, adiabatic burner, and low Mach number). The analysis well supports the former approach provided that the filtered reaction rate is combined with filtered molecular transport term. In such a case, both the RANS and LES FSD approaches are based on local relations valid within weakly perturbed flamelets. Accordingly, simply recasting RANS expressions to a filtered form works well. On the contrary, while the FSD and SDR approaches appear to be basically similar at first glance, the analysis does not support the latter one, but shows that a ratio of the filtered reaction rate to the filtered SDR is strongly scattered within the studied flame brush, with its conditionally mean value varying significantly with Favre-filtered combustion progress variable. As argued in the paper, these limitations of the LES SDR approach stem from the fact that it is based on a relation valid after integration over weakly perturbed flamelets, but this relation does not hold locally within such flamelets. Consequently, when a sufficiently small filter is applied to instantaneous fields, the filter may contain only a part of the local flamelet, whereas the linear relation holds solely for the entire flamelet and may not hold within the filtered flamelet volume. Thus, the present study implies that straightforwardly recasting well-established RANS equations to a filtered form is a flawed approach if the equations are based on integral features of local burning.