Hydrogen-air deflagrations in open atmosphere: Large eddy simulation analysis of experimental data

The largest known experiment on hydrogen-air deflagration in the open atmosphere has been analysed by means of the large eddy simulation (LES). The combustion model is based on the progress variable equation to simulate a premixed flame front propagation and the gradient method to decouple the physical combustion rate from numerical peculiarities. The hydrodynamic instability has been partially resolved by LES and unresolved effects have been modelled by Yakhot's turbulent premixed combustion model. The main contributor to high flame propagation velocity is the additional turbulence generated by the flame front itself. It has been modelled based on the maximum flame wrinkling factor predicted by Karlovitz et al. theory and the transitional distance reported by Gostintsev with colleagues. Simulations are in a good agreement with experimental data on flame propagation dynamics, flame shape, and outgoing pressure wave peaks and structure. The model is built from the first principles and no adjustable parameters were applied to get agreement with the experiment.     

Experimental and numerical investigation of premixed flame propagation with distorted tulip shape in a closed duct

High-speed schlieren photography, pressure records and large eddy simulation (LES) model are used to study the shape changes, dynamics of premixed flame propagation and pressure build up in a closed duct. The study provides further understanding of the interaction between flame front, pressure wave and combustion-generated flow, especially when the flame acquires a “distorted tulip” shape. The Ulster multi-phenomena LES premixed combustion model is applied to gain an insight into the phenomenon of “distorted tulip” flame and explain the experimental observations. The model accounts for the effects of flow turbulence, turbulence generated by flame front itself, selective diffusion, and transient pressure and temperature on the turbulent burning velocity. The schlieren images show that the flame exhibits a salient “distorted tulip” shape with two secondary cusps superimposed onto the two original tulip lips. This curious flame shape appears after a well-pronounced classical tulip flame is formed. The dynamics of “distorted tulip” flame observed in the experiment is well reproduced by LES. The numerical simulations show that large-scale vortices are generated in the burnt gas after the formation of a classical tulip flame. The vortices remain in the proximity of the flame front and modify the flow field around the flame front. As a result, the flame front in the original cusp and near the sidewalls propagates faster than that close to the centre of the original tulip lips. The discrepancy in the flame propagation rate finally leads to the formation of the “distorted tulip” flame. The LES model validated previously against large-scale hydrogen/air deflagrations is successfully applied in this study to reproduce the dynamics of flame propagation and pressure build up in the small-scale duct. It is confirmed that grid resolution has an influence to a certain extent on the simulated combustion dynamics after the flame inversion.     

A consistent level set formulation for large-eddy simulation of premixed turbulent combustion

A consistent formulation of the G-equation approach for LES is developed. The unfiltered G equation is valid only at the instantaneous flame front location. Hence, in a filtering procedure applied to derive the appropriate LES equation, only the instantaneous unfiltered flame surface can be considered. A new filter kernel is provided, which averages along the flame surface. The filter kernel is used to derive the G equation for the filtered flame front location. This equation has two unclosed terms, involving a flame front conditional averaged flow velocity, and a filtered propagation term. A model for the conditional velocity is derived, expressing this quantity in terms of the Favre-filtered flow velocity, which is typically known from a flow solver. This model leads to the appearance of a density ratio in the propagation term of the G equation. LES of combustion in the thin reaction zones regime is discussed in the LES regime diagram. A new line is identified separating the thin reaction zones regime into two parts, where the broadened flame thickness is larger and smaller than the filter size, respectively. A model for the propagation term is provided. This leads to a term including the subfilter turbulent burning velocity and an additional term proportional to the resolved flame front curvature. For the former, an algebraic model is provided from an equation for the subfilter flame front wrinkling. The latter term depends on the inverse of the subfilter Damköhler number and disappears in the corrugated flamelets regime.     

A filtered-laminar-flame PDF sub-grid-scale closure for LES of premixed turbulent flames: II. Application to a stratified bluff-body burner

Large eddy simulation of the two stratified nonswirling configurations of the Cambridge burner studied by Sweeney et al. (2012) is presented. The sub-grid-scale combustion closure relies on a physical space filtering operation with a filter size determined locally depending on the resolved and sub-grid-scale flame properties, which is discussed in a companion paper. Similarly to the premixed configuration of the same burner, the modeling reproduces the differential diffusion effects leading to accumulation of carbon and an enhancement of mixture fraction in the recirculation zone, an effect that is less pronounced than in the fully lean premixed case, because of the modification of the topology of the reaction zone that is induced by the mixture stratification. The study of the LES combustion regimes shows that the reaction zones develop under a quite large range of flame topologies, from wrinkled flamelets up to thin reaction zones. Instantaneous and time-averaged LES data were analyzed to extract information concerning the degree of stratification and the orientation of flame and mixing vectors. A decomposition of the flame response into premixed, diffusion, and partially premixed flamelets is performed, to conclude that the premixed mode dominates close to the burner, with a partially premixed burning regime further downstream. Overall, the length scales associated with stratification were found to be much larger than that of the reaction zone and flame, resulting in a quasi-homogeneous propagation, predominantly in a back supported stratified combustion regime. Overall good agreement between simulation and measurements was obtained for either configurations.     

A filtered tabulated chemistry model for LES of premixed combustion

A new modeling strategy called F-TACLES (Filtered Tabulated Chemistry for Large Eddy Simulation) is developed to introduce tabulated chemistry methods in Large Eddy Simulation (LES) of turbulent premixed combustion. The objective is to recover the correct laminar flame propagation speed of the filtered flame front when subgrid scale turbulence vanishes as LES should tend toward Direct Numerical Simulation (DNS). The filtered flame structure is mapped using 1-D filtered laminar premixed flames. Closure of the filtered progress variable and the energy balance equations are carefully addressed in a fully compressible formulation. The methodology is first applied to 1-D filtered laminar flames, showing the ability of the model to recover the laminar flame speed and the correct chemical structure when the flame wrinkling is completely resolved. The model is then extended to turbulent combustion regimes by including subgrid scale wrinkling effects in the flame front propagation. Finally, preliminary tests of LES in a 3-D turbulent premixed flame are performed.     

LES of a premixed jet flame DNS using a strained flamelet model

Turbulent premixed flames in the thin and broken reaction zones regimes are difficult to model with Large Eddy Simulation (LES) because turbulence strongly perturbs subfilter scale flame structures. This study addresses the difficulty by proposing a strained flamelet model for LES of high Karlovitz number flames. The proposed model extends a previously developed premixed flamelet approach to account for turbulence’s perturbation of subfilter premixed flame structures. The model describes combustion processes by solving strained premixed flamelets, tabulating the results in terms of a progress variable and a hydrogen radical, and invoking a presumed PDF framework to account for subfilter physics. The model is validated using two dimensional laminar flame studies, and is then tested by performing an LES of a premixed slot-jet direct numerical simulation (DNS). In the premixed regime diagram this slot-jet is found at the edge of the broken reaction zones regime. Comparisons of the DNS, the strained flamelet model LES, and an unstrained flamelet model LES confirm that turbulence perturbs flame structure to leading order effect, and that the use of an unstrained flamelet LES model under-predicts flame height. It is shown that the strained flamelet model captures the physics characterizing interactions of mixing and chemistry in highly turbulent regimes.     

A filtered-laminar-flame PDF sub-grid scale closure for LES of premixed turbulent flames. Part I: Formalism and application to a bluff-body burner with differential diffusion

A sub-grid scale closure for Large Eddy Simulation (LES) of turbulent combustion based on physical-space filtering of laminar flames is discussed. Applied to an unstructured grid, the combustion LES filter size is not fixed in this novel approach devoted to LES with refined meshes, but calibrated depending on the local level of unresolved scalar fluctuations. The context is premixed or stratified flames, the derived model relies on four balance equations for mixture fraction and its variance, and a progress variable and its variance. The proposed formalism is based on a presumed probability density function (PDF) derived from the filtered flames. Closures for the terms of the equations that are unresolved over LES grids are achieved through the PDF. The method uses flamelet tabulated detailed chemistry and is first applied to the simulation of laminar flames (1D and 2D) over various grids for validation, before simulating a turbulent burner studied experimentally by Sweeney et al. (2012). Since this burner also features differential diffusion effects, the numerical model is modified to account for accumulation of carbon in the recirculation zone behind the bluff-body. A differential diffusion number based on the gradient of residence times is proposed, in an attempt to globally quantify differential diffusion effects in burners.     

Direct numerical simulation of turbulent premixed ammonia and ammonia-hydrogen combustion under engine-relevant conditions

The combustion characteristics of ammonia and ammonia-hydrogen fuel blends under spark-ignited turbulent premixed engine-relevant conditions were investigated by means of direct numerical simulation and detailed chemistry. Several test cases were investigated for an outwardly expanding turbulent premixed flame configuration covering pure ammonia and ammonia-hydrogen fuel blends with 10% and 15% hydrogen content by volume for different equivalence ratio values of 0.9, 1.0 and 1.1. The results showed that the fuel-lean flames exhibit strong wrinkled structures at flame front compared to stoichiometric and fuel-rich flames. The heat release rate plots indicate that adding hydrogen into ammonia improves the reactivity of the flame and enhances the combustion process. The scatter plots of heat release rate versus local curvature coloured by NO formation, show that high heat release rate values occur in the concave structures and low heat release rate values occur in the convex structure, which is consistent with NO distribution. The highest turbulent burning velocity values were found for the fuel-lean cases due to more wrinkled flame front with lower effective Lewis number compared to fuel-rich cases. The results show a bending effect for the ratio between turbulent to laminar burning velocities with respect to hydrogen addition at all equivalence ratios with 10% hydrogen addition into ammonia exhibiting a highest value for the burning velocity ratio. Two distinct flame structures (concave and convex) were analysed in terms of local equivalence ratio based on the elements of N and O as well as H and O. They revealed an opposite distribution of NO formation normal to the flame front within concave and convex structures. Elementary chemical reactions involved in NO formation have shown that hydrogen addition into ammonia influences the reactivity of certain specific chemical reactions.     

A computational study and correlation of premixed isooctane–air laminar reaction front properties under spark ignited and spark assisted compression ignition engine conditions

To address the need for reliable premixed laminar burning velocity and thickness information within the spark assisted compression ignition (SACI) combustion regime, a large dataset of simulated reaction fronts has been generated in this work. A transient one dimensional premixed laminar flame simulation was applied to isooctane–air mixtures using a 215 species chemical kinetic mechanism. The simulation was exercised over fuel–air equivalence ratios, unburned gas temperatures and pressures ranging from 0.1 to 1.0, 298 to 1000 K and 1 to 250 bar, respectively, a range that extends beyond that of previous researchers. Steady reaction fronts with burning velocities in excess of 5 cm/s could not be established under all of these conditions, especially when burned gas temperatures were below 1500 K and/or when characteristic reaction front times were on the order of the unburned gas ignition delay. Steady premixed laminar burning velocities were correlated using a modified two-equation form based upon the asymptotic structure of a laminar flame, which produced an average error of 2.5% between the simulated and correlated laminar burning velocities, with a standard deviation of 3.0%. Additional correlations were constructed for reaction front thickness and adiabatic flame temperature. The resulting premixed laminar burning velocity correlation showed good agreement with experiments and existing correlations within the spark-ignited (SI) regime. Analysis of the simulated characteristic reaction front times and ignition delays suggests that homogeneous SACI combustion is most useful under medium and high load operating conditions.     

LES–ODT study of turbulent premixed interacting flames

The LES–ODT model is implemented for the study of twin turbulent premixed flames in decaying isotropic turbulence. The approach is based on the coupling of large-eddy simulation (LES) for mass and momentum with a fixed 3D lattice of 1D fine-grained solutions based on the one-dimensional turbulence (ODT) model. The ODT solutions for momentum and reactive scalars are designed to capture subgrid scale physics that is not captured by LES. The LES–ODT formulation is capable of capturing important fine-scale processes, such as flame–flame interactions, which play an important role in flame shortening in turbulent premixed flames, and the role of preferential diffusion on curved flames’ structures.     

Large eddy simulation of premixed hydrogen/methane/air flame propagation in a closed duct

In this paper, large eddy simulation (LES) is performed to investigate the propagation characteristics of premixed hydrogen/methane/air flames in a closed duct. In LES, three stoichiometric hydrogen/methane/air mixtures with hydrogen fractions (volume fractions) of 0, 50% and 100% are used. The numerical results have been verified by comparison with experimental data. All stages of flame propagation that occurred in the experiment are reproduced qualitatively in LES. For fuel/air mixtures with hydrogen fractions of 0 and 50%, only four stages of “tulip” flame formation are observed, but when the hydrogen fraction is 100%, the distorted “tulip” flame appears after flame front inversion. In the acceleration stage, the LES and experimental flame speed and pressure dynamic coincide with each other, except for a hydrogen fraction of 0. After “tulip” flame formation, all LES and experimental flame propagation speeds and pressure dynamics exhibit the same trends for hydrogen fractions of 0 and 100%. However, when the hydrogen fraction is 50%, a slight periodic oscillation appears only in the experiment. In general, the different structures displayed in the flame front during flame propagation can be attributed to the interaction between the flame front, the vortex and the reverse flow formed in the unburned and burned zones.     

A general flamelet transformation useful for distinguishing between premixed and non-premixed modes of combustion

The flame index was originally proposed by Yamashita et al. as a method of locally distinguishing between premixed and non-premixed combustion. Although this index has been applied both passively in the analysis of direct numerical simulation data, and actively using single step combustion models, certain limitations restrict its use in more detailed combustion models. In this work a general flamelet transformation that holds in the limits of both premixed and non-premixed combustion is developed. This transformation makes use of two statistically independent variables: a mixture fraction and a reaction progress parameter. The transformation is used to produce a model for distinguishing between premixed and non-premixed combustion regimes. The new model locally examines the term budget of the general flamelet transformation. The magnitudes of each of the terms in the budget are calculated and compared to the chemical source term. Determining whether a flame burns in a premixed or a non-premixed regime then amounts to determining which sets of these terms most significantly contribute to balancing the source term. The model is tested in a numerical simulation of a laminar triple flame, and is compared to a recent manifestation of the flame index approach. Additionally, the model is applied in a presumed probability density function (PDF) large eddy simulation (LES) of a lean premixed swirl burner. The model is used to locally select whether tabulated premixed or tabulated non-premixed chemistry should be referenced in the LES. Results from the LES are compared to experiments.     

A DNS study of hydrogen/air swirling premixed flames with different equivalence ratios

Hydrogen/air swirling premixed flames with different equivalence ratios are studied using direct numerical simulation. A fourth-order explicit Runge–Kutta method for time integration and an eighth-order central differencing scheme for spatial discretization are used to solve the full Navier–Stokes (N–S) equation system. A 9 species 19-step reduced mechanism for hydrogen/air combustion is adopted. The flames are stabilized with the help of a recirculation zone characterizing a high swirling flow. The vortex structures of the swirling premixed flames are presented. The flame structures are investigated in terms of the flame front curvature and tangential strain rate probability density functions (pdfs). The local flamelet temperature profiles are also extracted randomly along the flame front and compared with the corresponding laminar flame temperature profile. In order to study preferential diffusion effects, direct numerical simulation of two additional freely propagating planar flames in isotropic turbulence is conducted. Preferential diffusion effects observed in the planar flames are suppressed in the swirling flames. Further analysis confirms that the coherent small-scale eddies play important roles in the interactions between turbulence and the flame front. They are able to change the dynamic properties of the flame font and lead to enhanced burning intensity in the flame front with negative curvature for both stoichiometric and fuel-lean flames.     

A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence

A new set of petascale direct numerical simulations (DNS) modelling lean hydrogen combustion with detailed chemistry in a temporally evolving slot-jet configuration is presented as a database for the development and validation of models for premixed turbulent combustion. The jet Reynolds number is 10,000, requiring grid numbers up to nearly seven billion, which was achieved by computation on 120,000 processor cores. In contrast to many prior DNS studies, a mean shear exists that drives strong turbulent mixing within the flame structure. Three cases are simulated with different Damköhler numbers, while Reynolds number is held fixed. Basic statistics are presented showing that integrated burning rates up to approximately six times the laminar burning rate are obtained. It is shown that increased flame surface area accounts for most of the enhanced burning while increases in the burning rate per unit area also play an important contribution.The database is then used to assess a new model of flame wrinkling intended for large-eddy simulations (LES). The approach draws on concepts from fractal geometry, requiring the modelling of an inner cut-off scale representing the smallest scale of flame wrinkling, and the fractal dimension controlling the resolution dependence of the unresolved flame surface area. In contrast to previous modelling, it is argued that the inner cut-off should be filter-size invariant in an inertial range. Then, dimensional and physical reasoning together with Damköhler’s limiting scaling laws for the turbulent flame speed are used to infer the cut-off and fractal dimension in limiting regimes. Two methods of determining the fractal dimension are proposed: a static, algebraic expression or a dynamic approach exploiting a Germano-type identity. Finally the model is compared against the DNS in a priori tests and is found to give excellent results, quantitatively capturing the trends with time, space, filter size and Damköhler number.     

A computational study and correlation of premixed isooctane air laminar reaction fronts diluted with EGR

The current work investigates the propagation of premixed laminar reaction fronts for mixtures of isooctane–air and recirculated combustion products (or EGR) under high pressure and temperature conditions. The work uses a transient one-dimensional flame simulation with a skeletal 215 species chemical kinetic mechanism to generate laminar burning velocity and front thickness predictions. The simulation was exercised over fuel–air equivalence ratios, unburned gas temperatures, pressures and EGR levels ranging from 0.1 to 1.0, 400 to 1000 K, 1 to 250 bar, and 0% to 60% (by mass) respectively, a range extending beyond that of previous researchers. Steady reaction fronts with burning velocities in excess of 5 cm/s could not be established under all of these conditions, especially when burned gas temperatures were below 1450 K and/or when characteristic reaction front propagation times were on the order of the unburned gas ignition delay. For a given pressure, T_u and T_b, the burning velocity of an EGR dilute mixture was found to be lower than that of an air dilute mixture, with the decrease in burning velocity attributed primarily to the reduced oxygen concentration’s effect on chemistry. Steady premixed laminar burning velocities were correlated using a modified two-equation form based on the asymptotic structure of a laminar flame, which produced an average error of 3.4% between the simulated and correlated laminar burning velocities, with a standard deviation of 4.3%, while additional correlations were constructed for reaction front thickness and adiabatic flame temperature. Correlations are presented based on a non-product equivalence ratio φ and a fraction of stoichiometric combustion products X_SCP. Conversion factors are provided to facilitate application to modern direct injection internal combustion engines with inherent charge stratification where the local global Φ is different from the global Φ of the residual gas.     

Effects of CO addition on the characteristics of laminar premixed CH4/air opposed-jet flames

The effects of CO addition on the characteristics of premixed CH₄/air opposed-jet flames are investigated experimentally and numerically. Experimental measurements and numerical simulations of the flame front position, temperature, and velocity are performed in stoichiometric CH₄/CO/air opposed-jet flames with various CO contents in the fuel. Thermocouple is used for the determination of flame temperature, velocity measurement is made using particle image velocimetry (PIV), and the flame front position is measured by direct photograph as well as with laser-induced predissociative fluorescence (LIPF) of OH imaging techniques. The laminar burning velocity is calculated using the PREMIX code of Chemkin collection 3.5. The flame structures of the premixed stoichiometric CH₄/CO/air opposed-jet flames are simulated using the OPPDIF package with GRI-Mech 3.0 chemical kinetic mechanisms and detailed transport properties. The measured flame front position, temperature, and velocity of the stoichiometric CH₄/CO/air flames are closely predicted by the numerical calculations. Detailed analysis of the calculated chemical kinetic structures reveals that as the CO content in the fuel is increased from 0% to 80%, CO oxidation (R99) increases significantly and contributes to a significant level of heat-release rate. It is also shown that the laminar burning velocity reaches a maximum value (57.5 cm/s) at the condition of 80% of CO in the fuel. Based on the results of sensitivity analysis, the chemistry of CO consumption shifts to the dry oxidation kinetics when CO content is further increased over 80%. Comparison between the results of computed laminar burning velocity, flame temperature, CO consumption rate, and sensitivity analysis reveals that the effect of CO addition on the laminar burning velocity of the stoichiometric CH₄/CO/air flames is due mostly to the transition of the dominant chemical kinetic steps.     

A study of numerical hazard prediction method of gas explosion

A 3-dimensional computational fluid dynamics (CFD) simulation of a premixed hydrogen/air explosion in a large-scale domain is performed. The main feature of the numerical model is the solution of a transport equation for the reaction progress variable using a function for turbulent burning velocity that characterizes the turbulent regime of propagation of free flames derived by introducing the fractal theory. The model enables the calculation of premixed gaseous explosion without using fine mesh of the order of micrometer, which would be necessary to resolve the details of all instability mechanisms. The value of the empirical constant contained in the function for turbulent burning velocity is evaluated by analyzing the experimental data of hydrogen/air premixed explosion. The comparison of flame behavior between the experimental result and numerical simulation shows good agreement. The effect of mesh size on simulated flame propagation velocity is also tested, showing that the numerical result agrees reasonably well with experiment when the mesh size is less than about 20 cm.     

Development of a turbulent burning velocity model based on flame stretch concept for SI engines

According to the US Energy Information Administration, fossil fuels will remain the main source of energy for transportation over the next decades and thus the combustion of these fuels remains an important concern.This research studied the flame propagation under engine in-cylinder conditions and developed a correlation for turbulent burning velocity based on the global flame stretch concept. To study the impact of engine operation on flame stretch, two speeds, two loads, and three fuel-air mixtures were investigated. The flame front was determined by processing images of the flame natural luminosity.A turbulent burning velocity model was developed using dimensional analysis. The model showed that the turbulent burning velocity decreased due to flame stretching. Higher engine speeds increased the turbulent burning velocity by increasing the turbulent intensity, yet a tradeoff between the flame stretch and the turbulent burning velocity due to higher engine speed was observed. In cases where the flame distortion was very high, the flame stretch may cancel out any benefits of a large enflamed area.Incorporating the flame stretch into the burning velocity model and coupling the developed model with GT-Power simulation software revealed that the stretch may result in a 35% reduction in turbulent burning velocity.     

The propagation of a laminar reaction front during end-gas auto-ignition

A transient, one dimensional premixed laminar reaction front is used as a model problem to further understand the physical processes influencing reaction front propagation during the various stages of spark-assisted compression ignition (SACI) combustion for both constant and variable domain pressures. This approach is consistent with the wrinkled laminar flame representation of turbulent, spark ignited engine combustion. With the proper choice of timescales and pressure rise rate, it applies to the interaction of the flame with auto-igniting end-gas in a typical automotive engine. Under the conditions simulated by a transient flame code, the reaction front begins as a deflagration, propagating into an end-gas with an initially negligible level of reaction progress. The diffusive–reactive nature of the front is maintained until significant levels of end-gas reaction progress, where the burning velocity depends upon the degree of pre-reaction. At the time of the end-gas maximum chemical power, the maximum temperature gradient and peak rate of heat conduction within the front diminish to the point where combustion becomes chemically controlled. Although significant increases in burning velocity are observed at the onset of chemically controlled combustion within the front, the end-gas is within one front time from the completion of combustion. As a result, no more than one front thickness is consumed by the apparent propagation of the spontaneous ignition front.