Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Effects of preferential and differential diffusion on the mutual annihilation of two premixed hydrogen–air flames

The unsteady process of upstream head-on quenching of two laminar premixed hydrogen–air flames at different equivalence ratios in one dimension is investigated numerically in the presence of preferential and differential diffusion effects. Important chemical and transport characteristics of the mutual annihilation process are studied during the two primary stages of upstream mutual annihilation, preheat layers' and reaction layers' interactions. Because of the diffusive mobility of the fuel, hydrogen, relative to heat and the oxidizer, preferential and differential diffusion effects result in a shift in the equivalence ratio in the reaction zone to leaner conditions. This shift, in turn, affects the subsequent reaction layers' interactions through qualitative and quantitative changes in the rates of reactants' consumption and radicals' production. Another consequence of this shift is the presence of excess and ‘unburnt’ fuel or oxidizer at the end of the mutual annihilation process. The process of mutual annihilation occurs over time scales that are significantly shorter than characteristic residence times associated with flames.     

Analytic prediction of unconfined boundary layer flashback limits in premixed hydrogen–air flames

Flame flashback is a major challenge in premixed combustion. Hence, the prediction of the minimum flow velocity to prevent boundary layer flashback is of high technical interest. This paper presents an analytic approach to predicting boundary layer flashback limits for channel and tube burners. The model reflects the experimentally observed flashback mechanism and consists of a local and global analysis. Based on the local analysis, the flow velocity at flashback initiation is obtained depending on flame angle and local turbulent burning velocity. The local turbulent burning velocity is calculated in accordance with a predictive model for boundary layer flashback limits of duct-confined flames presented by the authors in an earlier publication. This ensures consistency of both models. The flame angle of the stable flame near flashback conditions can be obtained by various methods. In this study, an approach based on global mass conservation is applied and is validated using Mie-scattering images from a channel burner test rig at ambient conditions. The predicted flashback limits are compared to experimental results and to literature data from preheated tube burner experiments. Finally, a method for including the effect of burner exit temperature is demonstrated and used to explain the discrepancies in flashback limits obtained from different burner configurations reported in the literature.     

Laminar burning velocity and ignition delay time for premixed isooctane–air flames with syngas addition

The effects of blending syngas in different proportions to isooctane on the laminar burning velocity and ignition delay time of the fuel–air mixture have been studied in SI engine relevant conditions. The syngas is assumed to be composed of 50% H₂ and 50% CO. Simulations have been carried out using a skeletal mechanism containing 143 species and 643 reaction steps. It has been found that the blending of syngas augments the laminar burning velocity of isooctane due to increase of the thermal diffusivity of the reactant mixture and alteration in the chemistry of the flame reactions. For the mixture of 30% isooctane/70% syngas, the laminar burning velocity and the ignition delay time values are very close to those corresponding to pure isooctane. Additionally, the effects of exhaust gas recirculation have been explored for the 30% isooctane/70% syngas–air flame. It is seen that the reduction in laminar burning velocity due to the dilution by the recirculated exhaust gas can be compensated by an increase in the unburnt gas temperature. The effect of the exhaust gas dilution on the ignition delay time of 30% isooctane/70% syngas–air mixture has been found to be negligible.     

Diffusive–thermal oscillations of rich premixed hydrogen–air flames in a microflow reactor

In this paper the dynamics of rich hydrogen–air flames in a microflow reactor with controlled temperature of the walls is investigated numerically using the thermal-diffusion model with two-step kinetics in one spatial dimension. It is found that as the parameters of the system are varied the sequence of bifurcation occurs leading to the formation of complex spatio-temporal patterns. These include pulsating, chaotic, mixed-mode and FREI (Flames with Repetitive Extinction and Ignition) oscillations. The critical parameter values for the existence of different dynamical regimes are found in terms of equivalence ratio and flow velocity.     

Characterizing localization properties of two spinless electrons in a one-dimensional Harper model with concurrence

By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with on-site interaction U moving in the one-dimensional Harper model. Generally speaking, for electrons in extended regimes （potential parameter λ 〈 2）, the spectrum-averaged concurrence N（C） first decreases slowly as A increases until its local minimum, then increases with λ until its peak at λ = 2, while for electrons in localized regimes （λ 〉 2）, N（C） decreases drastically as λ increases. The functions of N（C） versus λ are different for electrons in extended and localized regimes. The maximum of N（C） occurs at the point λ= 2, which is the critical value in the one-dimensional singleparticle Harper model. From these studies it can distinguish extended, localized and critical regimes for the two-particle system. It is also found for the same λ that the interaction U always induce the decreases of concurrence, i.e., the concurrence can reflect the localization effect due to the interaction. All these provide us a new quantity to understand the localization properties of eigenstates of two interacting particles.     

A priori investigation of subgrid correlation of mixture fraction and progress variable in partially premixed flames

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z–c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z–c correlation effect is included.     

Flame front tracking in turbulent lean premixed flames using?stereo PIV and time-sequenced planar LIF of OH

This paper describes the simultaneous application of time-sequenced laser-induced fluorescence imaging of OH radicals and stereoscopic particle image velocimetry for measurements of the flame front dynamics in lean and premixed LP turbulent flames. The studied flames could be acoustically driven, to simulate phenomena important in LP combustion technologies. In combination with novel image post processing techniques we show how the data obtained can be used to track the flame front contour in a plane defined by the illuminating laser sheets. We consider effects of chemistry and convective fluid motion on the dynamics of the observed displacements and analyse the influence of turbulence and acoustic forcing on the observed contour velocity, a quantity we term as s _d ^2D. We show that this quantity is a valuable and sensitive indicator of flame turbulence interactions, as (a) it is measurable with existing experimental methodologies, and (b) because computational data, e.g. from large eddy simulations, can be post processed in an identical fashion. s _d ^2D is related (to a two-dimensional projection) of the three-dimensional flame displacement speed s _d , but artifacts due to out of plane convective motion of the flame surface and the uncertainty in the angle of the flame surface normal have to be carefully considered. Monte Carlo simulations were performed to estimate such effects for several distributions of flame front angle distributions, and it is shown conclusively that s _d ^2D is a sensitive indicator of a quantity related to s _d in the flames we study. s _d ^2D was shown to increase linearly both with turbulent intensity and with the amplitude of acousting forcing for the range of conditions studied.     

k-quantum nonlinear Jaynes－Cummings model in two trapped ions

We have obtained a k-quantum nonlinear Jaynes－Cummings model for two trapped ions interacting with laser beams resonant to the kth red side-band of the centre-of-mass mode, far from the Lamb－Dicke regime. The exact analytic solution shows the existence of quantum collapses and revivals of the occupation of two atoms.     

Phase transitions in the generalized spin-one-half Falicov–Kimball model in two dimensions

The extrapolation of small-cluster exact-diagonalisation calculations and the Monte-Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U _ff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave (CDW) phase and the spin-density-wave (SDW) phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The critical temperature T _c for a transition from the low-temperature ordered phases to the high-temperature disordered phase is calculated numerically for various values of J and U _ff .     

Development of a numerical model for the electric current in burner-stabilised methane–air flames

This study presents a new model to simulate the electric behaviour of one-dimensional ionised flames and to predict the electric currents in these flames. The model utilises Poisson’s equation to compute the electric potential. A multi-component diffusion model, including the influence of an electric field, is used to model the diffusion of neutral and charged species. The model is incorporated into the existing CHEM1D flame simulation software. A comparison between the computed electric currents and experimental values from the literature shows good qualitative agreement for the voltage–current characteristic. Physical phenomena, such as saturation and the diodic effect, are captured by the model. The dependence of the saturation current on the equivalence ratio is also captured well for equivalence ratios between 0.6 and 1.2. Simulations show a clear relation between the saturation current and the total number of charged particles created. The model shows that the potential at which the electric field saturates is strongly dependent on the recombination rate and the diffusivity of the charged particles. The onset of saturation occurs because most created charged particles are withdrawn from the flame and because the electric field effects start dominating over mass based diffusion. It is shown that this knowledge can be used to optimise ionisation chemistry mechanisms. It is shown numerically that the so-called diodic effect is caused primarily by the distance the heavier cations have to travel to the cathode.     

An all-optical comparison scheme between two multi-bit data with optical nonlinear material

Over the last few decades,several all-optical circuits have been proposed to meet the need of high-speed data processing.In some information processing architectures,the role of various analog and digital data comparisons is very important.In this letter,we proposed a multi-bit data comparison scheme.The scheme is based on the switching property of optical nonlinear material.Ultrafast operational speed larger than gigahertz can be expected from this all-optical scheme.     

Stable exponential cosmological solutions with two factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$-term

We study D-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss–Bonnet term and the cosmological term \(\Lambda \). We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters \(H >0\) and h, corresponding to factor spaces of dimensions \(m >2\) and \(l > 2\), respectively. These solutions contain a fine-tuned \(\Lambda = \Lambda (x, m, l, \alpha )\), which depends upon the ratio \(h/H = x\), dimensions of factor spaces m and l, and the ratio \(\alpha = \alpha _2/\alpha _1\) of two constants (\(\alpha _2\) and \(\alpha _1\)) of the model. The master equation \(\Lambda (x, m, l,\alpha ) = \Lambda \) is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. The explicit solution for \(m = l\) is presented in “Appendix”. Imposing certain restrictions on x, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. We also consider a subclass of solutions with small enough variation of the effective gravitational constant G and show the stability of all solutions from this subclass.     

Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

Compositional change in human enamel irradiated with MIR free electron laser

The purpose of this study was to investigate compositional changes in human enamel irradiated with the free electron laser (FEL).The exposure on dental enamel at the wavelength of 9.64μm was observed with the Beijing free electron laser.The distribution of elements in the irradiated or non-irradiated enamel was measured by scanning electron microscope (SEM) with energy-dispersive spectroscopy and synchrotron radiation X-ray fluorescence(SRXRF) in Beijing Synchrotron Radiation Facility (BSRF).The results showed that the P/Ca ratio in the ablation region of enamel at the maximum wavelength of infrared absorption of enalmel at the maximum wavelength of infrared absorption was obviously smaller than that at the non-maximum wavelength.In the ablation region the ratios of P/Ca and Ca/Sr were smaller than those in the non-ablation region.The distribution of P,Ca and Sr in the ablation region were heterogeneous due to the element change caused by FEL irradiation.     

Squeezing in a three-level Jaynes-Cummings model with strong field

Squeezing in three-level Jaynes-Cummings model with the strong initial coherent state is studied numerically. The dependence of the squeezing on the field intensity and time is analysed. The cases that the light field is initially in a Fock state and in a squeezed vacuum state are also discussed.