Darrieus–Landau instability and Markstein numbers of premixed flames in a Hele-Shaw cell

Hydrodynamic flame instabilities are studied in a Hele-Shaw burner. By studying the development of perturbations, starting from a 2D Bunsen flame at the top of the burner, growth rates are measured for propane and methane–air mixtures, and compared to theoretical predictions. It is found that the dispersion relation in a Hele-Shaw cell has the same dependence with wavenumber $\sigma =k?k^2$ as the one predicted in tubes. Markstein numbers relative to fresh gases are obtained for propane and methane flames and compared to the literature.     

Detailed simulation of laser-induced ignition,spherical-flame acceleration,and the origins of hydrodynamic instability

Ignition of a lean hydrogen–oxygen premixture by focused-laser-induced breakdown and subsequent three-dimensional expanding-flame instabilities are simulated in high detail. Both diffusive–thermal and hydrodynamic (Darrieus–Landau) instabilities are active and accelerate the flame expansion. The fluid is a partially-ionized gas in local thermodynamic equilibrium with detailed kinetics and transport models, starting from initial conditions from an auxiliary simulation based on a two-temperature local thermodynamic non-equilibrium model. After the decay of the initial laser-induced plasma, the r ～ t^1.5 growth in time of the flame radius matches theory and experimental observations. Based on hydrodynamic theory for spherical-flame propagation, a global Karlovitz number is defined as the ratio of the hydrodynamic to flame-distortion time scales. It initially increases during the diffusive–thermal instability stage, then with the onset of significant baroclinic torque, this trend reverses, with vorticity production becoming the dominant mechanism of instability.     

Scaling and instability analyses on flame spread over liquids

Stability and scaling analyses were applied to experimental data obtained by this group and other researchers on pulsating flame spread over liquids. Data to be analyzed include recent findings of cyclic appearance of a cold temperature valley at the liquid surface-created surface-wave ahead of the spreading flame, and main-pulsation of 0.5–2 Hz and sub-pulsation of 5–10 Hz. Our stability analysis is performed to understand the mechanism of instability on the liquid surface ahead of a flame’s leading edge, which is thought of as the major cause for pulsating flame spread. The scaling analysis is performed to explore the role of four independent (gravity, surface-tension, viscose, and inertia) forces on the mechanisms of flame spread. These four forces form three independent pi-numbers: Marangoni (Ma) number, Weber (We) number, and Froude (Fr) number, all of which include the critical length scale ratio: (height of sub-surface circulation)/(horizontal length of preheated liquid surface). We combined the wave equation obtained from the stability analysis, the three pi-numbers, and the critical length scale ratio, and used them as a universal formula to describe flame spread over liquids. Using this formula, flame spread mechanism over four different types of alcohols was divided into two separate regimes: the thin liquid pool and the thick-liquid pool. For the thin liquid pool, the flame spread rate was correlated with (Fr/Ma^0.5)^−1.0, while for the thick-liquid pool it was correlated with (Fr/Ma^0.5)^−1.5. Change of flame spread pattern from the uniform to the pulsating can be described with temperature difference between the flash point and bulk liquid temperature. For the thin liquid pool this temperature difference is correlated with Ma^−0.5, while for the thick-liquid pool it is correlated with Ma⁻¹. The frequency of pulsation is correlated with We^−1.0 for the thin liquid pool, while it is correlated with We^−1.5 for the thick-liquid pool.     

Strong flame acceleration and detonation limit of hydrogen-oxygen mixture at cryogenic temperature

A series of experiments were carried out in a closed tube at cryogenic temperature (77 K) for hydrogen-oxygen mixtures. Flame propagation speed and overpressure were measured by optical fibers and pressure sensors, respectively. The first and second shock waves were captured in the cryogenic experiments, although the shock waves always precede the flames in all cases indicating the absence of stable detonation. However, strong flame acceleration was observed for all situations, which is consistent with the prediction by expansion ratio and Zeldovich number. Besides, the tube diameter and length are also critical for flame acceleration to supersonic. All the flames in this work accelerate drastically reaching the C-J deflagration state. But at 0.4 atm, only fast flame is formed, while at higher initial pressures, the flame further accelerates to a galloping mode manifesting a near-limit detonation, which could be indicated by the stability parameter $\chi$.     

Experimental observations of flame acceleration and transition to detonation following shock-flame interaction

Observations are presented from experiments where laminar flame bubbles were perturbed successively by incident and reflected shock waves. Significant flame acceleration was observed in many instances, with the flame closely coupled to the reflected shock wave. The coupled waves are interpreted using a generalized Hugoniot analysis. As the incident shock velocity increased, detonation emerged near the highly convolved reaction zone. Prior to detonation the external visual attributes of the combustion fronts appear identical to turbulent combustion. However, they cannot be due to classical isotropic turbulence. The overall conclusion is that the observed enhancement of combustion is driven by chemi-acoustic interactions and related gas-dynamic effects. An analysis of the prevailing thermodynamic states suggests that thermal auto-ignition chemistry could also play a significant role prior to the onset of detonation.     

Chemical-diffusive models for flame acceleration and transition-to-detonation: genetic algorithm and optimisation procedure

This paper presents a general approach for developing an automated, fast and flexible procedure to determine the reaction parameters for a simplified chemical-diffusive model to simulate flame acceleration and deflagration-to-detonation transition (DDT) in a stoichiometric methane–air mixture. The procedure uses a combination of a genetic algorithm and Nelder-Mead optimisation scheme to find the optimal reaction parameters for a reaction rate based on an Arrhenius form for conversion of reactants to products. The model finds six optimal reaction parameters that reproduce six flame and detonation properties. Results show that the reaction parameters closely reproduce their intended flame and detonation properties. The laminar flame profile computed using the reaction parameters in a 1D Navier-Stokes code matches the profile obtained when using a detailed chemical reaction mechanism. The optimal reaction parameters are then used in a 2D simulation of flame acceleration and DDT in an obstacle-laden channel containing stoichiometric methane–air, and the results show that the computation closely follows the transition-to-detonation observed in experiments. This automated procedure for finding parameters for a proposed reaction model makes it possible to simulate the behaviour of flames and detonations in large, complex scenarios, which would otherwise be an incalculable problem.     

Temporal evolution of flame stretch due to turbulence and the hydrodynamic instability

The temporal evolution of the strain rate on a turbulent premixed flame was measured experimentally using cinema-stereoscopic particle image velocimetry. Turbulence strains a flame due to velocity gradients associated both directly with the turbulence and those caused by the hydrodynamic instability, which are initiated by the turbulence. The development of flame wrinkles caused by both of these mechanisms was observed. Wrinkles generated by the turbulence formed around vortical structures, which passed through the flame and were attenuated. After the turbulent structures had passed, the hydrodynamic instability flow pattern developed and caused additional strain. The hydrodynamic instability also caused the growth of small flame front perturbations into large wrinkles. In the moderately turbulent flame investigated, it was found that the evolution of the strain rate caused by turbulence–flame interactions followed a common pattern involving three temporal regimes. In the first, the turbulence exerted extensive (positive) strain on the flame, creating a wrinkle that had negative curvature (concave towards the reactants). This was followed by a transition period, leading into the third regime in which the flow pattern and strain rate were dominated by the hydrodynamic instability mechanism. It was also found that the magnitudes of the strain rate in the first and third regimes were similar. Hence, the hydrodynamic instability mechanism caused significant strain on a flame and should be included in turbulent combustion models.     

Caldeira-Leggett model, Landau damping, and the Vlasov-Poisson system

The Caldeira-Leggett Hamiltonian describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between the Caldeira-Leggett model and the linearized Vlasov-Poisson equation are analyzed, and it is shown that the damping in the Caldeira-Leggett model is analogous to that of Landau damping in plasmas (Landau, 1946 [1]). An invertible linear transformation (Morrison and Pfirsch, 1992 [18]; Morrison, 2000 [19]) is presented that converts solutions of the Caldeira-Leggett model into solutions of the linearized Vlasov-Poisson system.     

Electron, positron, and photon wakefield acceleration: trapping, wake overtaking, and ponderomotive acceleration

The electron, positron, and photon acceleration in the first cycle of a laser-driven wakefield is investigated. Separatrices between different types of the particle motion (trapped, reflected by the wakefield and ponderomotive potential, and transient) are demonstrated. The ponderomotive acceleration of electrons can be largely compensated by the wakefield action, in contrast to positrons and positively charged mesons. The electron bunch energy spectrum is analyzed. The maximum upshift of an electromagnetic wave frequency during reflection from the wakefield is obtained.     

Effects of heat loss and viscosity friction at walls on flame acceleration and deflagration to detonation transition

The coupled effect of wall heat loss and viscosity friction on flame propagation and deflagration to detonation transition(DDT) in micro-scale channel is investigated by high-resolution numerical simulations.The results show that when the heat loss at walls is considered, the oscillating flame presents a reciprocating motion of the flame front.The channel width and Boit number are varied to understand the effect of heat loss on the oscillating flame and DDT.It is found that the oscillating propagation is determined by the competition between wall heat loss and viscous friction.The flame retreat is led by the adverse pressure gradient caused by thermal contraction, while it is inhibited by the viscous effects of wall friction and flame boundary layer.The adverse pressure gradient formed in front of a flame, caused by the heat loss and thermal contraction, is the main reason for the flame retreat.Furthermore, the oscillating flame can develop to a detonation due to the pressure rise by thermal expansion and wall friction.The transition to detonation depends non-monotonically on the channel width.     

Symmetry,Landau theory and polytope models of glass

Order in supercooled liquids and metallic glasses is related to a regular icosahedral “crystal” consisting of 120 particles inscribed on the surface of a sphere in four dimensions. Hyperspherical harmonics and the discrete symmetry group of this four-dimensional platonic solid can be used to construct an order parameter for glasses in three-dimensional flat space. A uniformly frustrated Landau expansion in this order parameter suggests a ground state with a regular array of wedge disclination lines. Homotopy theory is used to classify all topologically stable defects. A generalization of Bloch's theorem for electronic states in flat space solids allows explicit diagonalization of tight binding models defined on the curved-space icosahedral crystal.     

Momentum conservation,time dependent Ginzburg Landau equation and paraconductivity

Superconductors exhibit increasing electrical conductivity as the temperature approachesT _c from above, due to superconducting fluctuations. The functions σ_f1=σ(ω, ?)-σ _n (ω), ?=(T-T _c )/T _c , have been derived by Schmidt phenomenologically using the time dependent Ginzburg-Landau equation (TDGL). These functions fail to vanish in the absolute clean limit τ → ∞ as they must. We have therefore reinvestigated the derivation of the linearized TDGL-equation and the corresponding current expression in the presence of a time dependent vector potential. We find several new terms, which are important for the rather clean superconductor only and are easily interpreted physically in terms of momentum conservation. Applying these corrected equations to the paraconductivity problem, we derive σ_fl(ω, ?) which has an extra factor (1 —iωτ)^?2 compared to Schmidt's result. There is also an additional term, which is connected to the problem of the contribution calculated by Maki. By comparison with the linear response function belowT _c , we show that this term is valid in the limit ¦ω¦?¦Δ¦ only and may not be continued to ω=0. There remains, however, a problem connected with this term, which cannot be solved within the present phenomenological framework.     

Pulsating hydrodynamic instability and thermal coupling in an extended Landau/Levich model of liquid-propellant combustion: I. Inviscid analysis

Hydrodynamic (Landau) instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. In the context of liquid-propellant combustion, such instability has recently been shown to occur for critical values of the pressure sensitivity of the burning rate and the disturbance wavenumber, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. Additionally, however, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. In the present work, we consider the realistic influence of a non-zero temperature sensitivity in the local burning rate on both types of stability thresholds. It is found that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the (disturbance-wavenumber, pressure-sensitivity) plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values, that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a non-steady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.     

Computational investigations of the coupling between transient flame dynamics and thermo-acoustic instability in a self-excited resonance combustor

Combustion instability due to thermo-acoustic interactions is a critical combustion problem that requires a thorough understanding because of its adverse impact on stable and reliable operation of combustors in high-speed propulsion devices like gas turbines and rockets. This work conducts computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A 2D modelling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damköhler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localise the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor despite the fact that the results are obtained from 2D simulations. The same analysis is expected to be extensible to fully 3D simulations.