We propose a predictive model of the turbulent burning velocity over a wide range of conditions. The model consists of sub models of the stretch factor and the turbulent flame area. The stretch factor characterizes the flame response of turbulence stretch and incorporates effects of detailed chemistry and transport with a lookup table of laminar counterflow flames. The flame area model captures the area growth based on Lagrangian statistics of propagating surfaces, and considers effects of turbulence length scales and fuel characteristics. The present model predicts the turbulent burning velocity via an algebraic expression without free parameters. It is validated against 285 cases of the direct numerical simulation or experiment reported from various research groups on planar and Bunsen flames over a wide range of conditions, covering fuels from hydrogen to n-dodecane, pressures from 1 to 20 atm, lean and rich mixtures, turbulence intensity ratios from 0.35 to 110, and turbulence length ratios from 0.5 to 80. The comprehensive comparison shows that the proposed turbulent burning velocity model has an overall good agreement over the wide range of conditions, with the averaged modeling error of 25.3%. Furthermore, the model prediction involves the uncertainty quantification for model parameters and chemical kinetics to extend the model applicability.
This paper demonstrates the ability of neural networks to reliably learn the nonlinear flame response of a laminar premixed flame, while carrying out only one unsteady CFD simulation. The system is excited with a broadband, low-pass filtered velocity signal that exhibits a uniform distribution of amplitudes within a predetermined range. The obtained time series of flow velocity upstream of the flame and heat release rate fluctuations are used to train the nonlinear model using a multi-layer perceptron. Several models with varying hyperparameters are trained and the dropout strategy is used as …
A modified Thickened Flame (TF) model based on Large Eddy Simulation methodology is used to investigate premixed combustion and the model predictions are evaluated by comparing with the piloted premixed stoichiometric methane-air flame data (Chen et al., 1996) for Reynolds numbers Re = 24,000 (flame F3) and Re=52,000 (flame F1). The basic idea of Thickened-Flame approach is that the flame front is artificially thickened to resolve on the computational LES grid while keeping the laminar flame speed ( ) constant. The artificially thickening of the flame front is obtained by enhancing the molecul…
Influences of reaction zone thickening and local extinctions on the burning rate of extremely turbulent hydrogen-enriched methane-air flames are investigated using simultaneous planar laser-induced fluorescence of formaldehyde molecule and hydroxyl radical as well as separate stereoscopic particle image velocimetry techniques. Karlovitz numbers upto 76 are examined. It is shown that, by increasing the turbulence intensity, the preheat and reaction zone thicknesses can increase to values that are, respectively, 6.3 and 4.9 of the corresponding laminar flames. Broadening of these zones for inten…
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 thermo-diffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λn 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 v…
We investigate and model pressure effects on the turbulent burning velocity over a wide range of pressures and turbulence intensities with the direct numerical simulation (DNS) of statistically planar turbulent premixed flames for lean hydrogen/air mixture. DNS results indicate that the stretch factor has an impact on the turbulent burning velocity and flame surface area at elevated pressures. In particular, the enhanced stretch factor at high pressures increases the ratio of turbulent and laminar burning velocities, diminishing the "bending" effect. Based on a good consistency between turbule…
The mechanism of finger flame acceleration at the early stage of burning in tubes was studied experimentally by Clanet and Searby [Combust. Flame 105: 225 (1996)] for slow propane-air flames, and elucidated analytically and computationally by Bychkov et al. [Combust. Flame 150: 263 (2007)] in the limit of incompressible flow. We have now analytically, experimentally and computationally studied the finger flame acceleration for fast burning flames, when the gas compressibility assumes an important role. Specifically, we have first developed a theory through small Mach number expansion up to the…
Three-dimensional numerical simulations of canonical statistically-steady statistically-planar turbulent flames have been used in an attempt to produce distributed burning in lean methane and hydrogen flames. Dilatation across the flame means that extremely large Karlovitz numbers are required; even at the extreme levels of turbulence studied (up to a Karlovitz number of 8767) distributed burning was only achieved in the hydrogen case. In this case, turbulence was found to broaden the reaction zone visually by around an order of magnitude, and thermodiffusive effects (typically present for lea…
Flame propagation through a non-volatile solid-fuel suspension is studied using a simplified, time-dependent numerical model that considers the influence of both diffusional and kinetic rates on the particle combustion process. It is assumed that particles react via a single-step, first-order Arrhenius surface reaction with an oxidizer delivered to the particle surface through gas diffusion. Unlike the majority of models previously developed for flames in suspensions, no external parameters are imposed, such as particle ignition temperature, combustion time, or the assumption of either kinetic…
The present paper seeks to determine the mechanism of flame acceleration and transition to detonation when a turbulent flame preceded by a shock interacts with a single obstruction in its path, taken as a cylindrical obstacle or a wall in the present study. The problem is addressed experimentally in a mixture of propane-oxygen at sub-atmospheric conditions. The turbulent flame was generated by passing a detonation wave through a perforated plate, yielding flames with turbulent burning velocities 10 to 20 larger than the laminar values and incident shock Mach numbers ranging between 2 and 2.5. …
The effects of initial pressure and temperature on the laminar burning speed of n-hexane-air mixtures were investigated experimentally and numerically. The spherically expanding flame technique with a nonlinear extrapolation procedure was employed to measure the laminar burning speed at atmospheric and sub-atmospheric pressures and at nominal temperatures ranging from 296 to 422 K. The results indicated that the laminar burning speed increases as pressure decreases and as temperature increases. The predictions of three reaction models taken from the literature were compared with the experiment…
Shock flame interactions are fundamental problems in many combustion applications ranging from flame acceleration to flame control in supersonic propulsion applications. The present paper seeks to quantify the rate of deformation of the flame surface and burning velocity caused by the interaction and to clarify the underlying mechanisms. The interaction of a single shock wave with a cellular flame in a Hele-Shaw shock tube configuration was studied experimentally, numerically, and theoretically. A mixture of stoichiometric hydrogen-air at sub-atmospheric pressure was chosen such that large cel…
Data from a three-dimensional Direct Numerical Simulation of a turbulent premixed Bunsen flame at a low global Lewis number are analyzed to address the effects of the curvature on the local flame front. For this purpose, the chemical kinetics is modeled according to a reduced scheme, involving 5 reactions and 7 species, to mimic a H$_{2}$/Air flame at equivalence ratio $ϕ=0.5$. An increase of the local temperature and reaction rate is found for fronts elongated into the fresh gases (concave), while local quenching is observed for fronts elongated in the opposite direction (convex), i.e. toward…
We propose a predictive model of the turbulent burning velocity $S_T$ in homogeneous isotropic turbulence (HIT) based on Lagrangian statistics of propagating surfaces. The propagating surfaces with a constant displacement speed are initially arranged on a plane, and they evolve in non-reacting HIT, behaving like the propagation of a planar premixed flame front. The universal constants in the model of $S_T$ characterize the enhancement of area growth of premixed flames by turbulence, and they are determined by Lagrangian statistics of propagating surfaces. The flame area is then modelled by the…
Although experimental evidence for the correlation between early flame kernel development and cycle-to-cycle variations (CCV) in spark ignition (SI) engines was provided long ago, there is still a lack of fundamental understanding of early flame/turbulence interactions, and accurate models for full engine simulations do not exist. Since the flame kernel is initiated with small size, i.e. with large positive curvature, differential diffusion is expected to severely alter early flame growth in non-unity-Lewis-number (${\mathrm{Le}\neq1}$) mixtures as typically used in engines. In this work, a DN…
Recent complex-chemistry direct numerical simulations of lean hydrogen-air flames propagating in forced turbulence in a box were continued by switching-off the turbulence forcing. Results show that a decrease in burning velocity U_T(t), caused by the turbulence decay, is reversed when the turbulence becomes weak and a peak of U_T(t) appears, with the peak magnitudes and associated Karlovitz numbers being similar in two different cases. These results (i) are attributed to activation of laminar flame instabilities, which have been suppressed by intense turbulence, and (ii) are argued to indicate…
Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocity
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA（机械与工业工程系，东北大学，波士顿，马萨诸塞州，02115，美国）；School of Mechanical Engineering, University of Leeds, Leeds, UK（机械工程学院，利兹大学，利兹，英国）
A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent combustion experiment. In contrast to the power law decay of a standard turbulence grid, the downstream turbulence intensity of the fractal grid increases until it reaches a peak at some distance from the grid before it finally decays. The effective mesh size and the solidity are the same as those of a standard square mesh grid with which it is compared. It is found that, for the same flow rate and stoichiometry, the fractal generated turbulence enhances the burning rate and causes the fl…
The paper discusses the peculiarities of flame propagation in the ultra-lean hydrogen-air mixture. Numerical analysis of the problem shows the possibility of the stable self-sustained flame ball existence in unconfined space on sufficiently large spatial scales. The structure of the flame ball is determined by the convection processes related to the hot products rising in the terrestrial gravity field. It is shown that the structure of the flame ball corresponds to the axisymmetric structures of the gaseous bubble in the liquid. In addition to the stable flame core, there are satellite burning…
Large hydrocarbon fuels are used for ground and air transportation and will be for the foreseeable future. Despite their extensive use, turbulent combustion of large hydrocarbon fuels, remains relatively poorly understood and difficult to predict. A key parameter when burning these fuels is the turbulent consumption speed; the velocity at which fuel and air are consumed through a turbulent flame front. Such information can be useful as a model input parameter and for validation of modeled results. In this study, turbulent consumption speeds were measured for three jet-like fuels using a premix…
The problem of non-perturbative description of unsteady premixed flames with arbitrary gas expansion is solved in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas velocity jumps given on it, we show that the front dynamics can be determined without having to solve the flow equations in the bulk. On the basis of the Thomson circulation theorem, an implicit integral representation of the gas velocity downstream is constructed. It is then simplified by a successive stripping of the potential contributions to obtain an explicit…
Despite the high technical relevance of early flame kernel development for the reduction of cycle-to-cycle variations in spark ignition engines, there is still a need for a better fundamental understanding of the governing in-cylinder phenomena in order to enable resilient early flame growth. To isolate the effects of small- and large-scale turbulent flow motion on the young flame kernel, a three-dimensional DNS database has been designed to be representative for engine part load conditions. The analysis is focussed on flame displacement speed and flame area in order to investigate effects of …
Synergy of turbulence and thermo-diffusive effects on the intermittent boundary-layer flashback of swirling flames
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University（北京大学工学院湍流与复杂系统国家重点实验室）；HEDPS-CAPT, Peking University（北京大学高能量密度物理研究所）
A series of Direct Numerical Simulations (DNS) of lean methane/air flames was conducted in order to investigate the enhancement of the turbulent flame speed and modifications to the reaction layer structure associated with the systematic increase of the integral scale of turbulence $l$ while the Karlovitz number and the Kolmogorov scale are kept constant. Four turbulent slot jet flames are simulated at increasing Reynolds number and up to $Re \approx 22000$, defined based on the bulk velocity, slot width, and the reactants' properties. The turbulent flame speed $S_T$ is evaluated locally at se…
The problem of burning of high-velocity gas streams in channels is revisited. Previous treatments of this issue are found to be incomplete. It is shown that despite relative smallness of the transversal gas velocity, it plays crucial role in determining flame structure. In particular, it is necessary in formulating boundary conditions near the flame anchor, and for the proper account of the flame propagation law. Using the on-shell description of steady anchored flames, a consistent solution of the problem is given. Equations for the flame front position and gas-velocity at the front are obtai…
The complete set of hydrodynamic equations for a corrugated flame front is reduced to a system of coordinate-free equations at the front using the fact that vorticity effects remain relatively weak even for corrugated flames. It is demonstrated how small but finite flame thickness may be taken into account in the equations. Similar equations are obtained for turbulent burning in the flamelet regime. The equations for a turbulent corrugated flame are consistent with the Taylor hypothesis of stationary external turbulence.
The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted to determine the PDF of the shock distribution, a power-law with an exponent of -3, and the burning rate of unreacted pockets from their edges - through surface turbulent flames with a speed approximately 3-7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel Large Eddy Sim…
A joint experimental and numerical investigation of turbulent flame front anchoring at externally heated walls is presented. The phenomenon is examined for lean hydrogen/air mixtures in a novel burner design, which comprises a cylindrical burning chamber converging into a glass pipe as well as a wall heating assembly at their intersection. The transparent part allows for optical OH* chemiluminescence measurements serving as a basis for numerical validation. For a comprehensive numerical evaluation the effect of heat loss on different hydrogen/air chemical reaction mechanisms is reviewed in a p…
Soot formation in Delft flame III, a pilot stabilized turbulent diffusion flame burning natural gas/air, is investigated using ANSYS FLUENT by considering two different approaches for soot inception. In the first approach soot inception is based on the formation rate of acetylene, while the second approach considers the formation rate of two and three-ringed aromatics to describe the soot inception [1]. Transport equations are solved for soot mass fraction and radical nuclei concentration to describe inception, coagulation, surface growth, and oxidation processes. The turbulent-chemistry inter…
The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cut off wavelength of the instability. The developed theory is used to analyse recent experi…
Rayleigh-Taylor (RT) unstable flames play a key role in the explosions of Type Ia supernovae. However, the dynamics of these flames is still not well-understood. RT unstable flames are affected by both the RT instability of the flame front and by RT-generated turbulence. The coexistence of these factors complicates the choice of flame speed subgrid models for full-star Type Ia simulations. Both processes can stretch and wrinkle the flame surface, increasing its area and, therefore, the burning rate. In past research, subgrid models have been based on either the RT instability or turbulence set…
(Abridged) A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully-resolved premixed flame with a highly subsonic, statistically steady, homogeneous, isotropic turbulence. We consider a wide range of turbulent intensities and system sizes, corresponding to the Damköhler numbers Da = 0.1-6.0. These calculations show that turbulent flames in the regimes considered are intrinsically unstable. In particular, we find three effects. 1) Turbulent flame speed develops pulsations with the …
Rayleigh-Taylor (RT) unstable flames are a key component of Type Ia and Iax supernovae explosions, but their complex hydrodynamics is still not well understood. These flames are affected not only by the RT instability, but also by the turbulence it generates. Both processes can increase the flame speed by stretching and wrinkling the flame. This makes it hard to choose a subgrid model for the flame speed in full star Type Ia or Iax simulations. Commonly used subgrid models get around this difficulty by assuming that either the RT instability or turbulence is dominant and sets the flame speed. …
In the current study, the influence of turbulent mixing and local reaction rates on deflagration to detonation transition (DDT) was investigated using a state-of-the-art large eddy simulation (LES) strategy. Specifically, detonation attenuation by a porous medium, and the subsequent re-initiation for methane-oxygen, a moderately unstable mixture, was considered. The purpose of the investigation was to validate the numerical strategy with previous experimental observations, and to determine what specific roles turbulent mixing and shock compression have on flame acceleration during the final st…
Since detonation is the only established theory that allows rapid burning producing a high pressure that can be sustained in open areas, the generally accepted opinion was that the mechanism explaining the high rate of combustion in dust explosions is deflagration-to-detonation transition. We propose a theoretical substantiation of an alternative mechanism explaining the origin of the secondary explosion producing high speeds of combustion and high overpressures in unconfined dust explosions. We show that the clustering of dust particles in a turbulent flow ahead of the advancing flame gives r…
It is known that unconfined dust explosions consist of a relatively weak primary (turbulent) deflagrations followed by a devastating secondary explosion. The secondary explosion may propagate with a speed of up to 1000 m/s producing overpressures of over 8-10 atm. Since detonation is the only established theory that allows a rapid burning producing a high pressure that can be sustained in open areas, the generally accepted view was that the mechanism explaining the high rate of combustion in dust explosions is deflagration to detonation transition. In the present work we propose a theoretical …
