Premixed flame oscillations in obstructed channels with both ends open

An initially laminar premixed flame front accelerates extremely fast and may even trigger a detonation when propagating in a semi-open obstructed channel (one end of the channel is closed; the flame is ignited at the closed end and moves towards the open one). However, industrial and laboratory conduits oftentimes have both ends open, or vented, with a flame ignited at one of these ends. The latter constitutes the focus of the present work. Specifically, premixed flame propagation through a comb-shaped array of obstacles, in-built in a channel with both ends open, is studied by means of computational simulation of the reacting flow equations with fully-compressible hydrodynamics and an Arrhenius chemical kinetics. The parametric study includes various blockage ratios and spacing as well as the thermal expansion ratios, with oscillations of the burning rate observed in the majority of the cases, which conceptually differs from fast flame acceleration in semi-open channels. Such a difference is devoted to the fact that while the entire flame-generated jet-flow is pushed towards a single exit in a semi-open channel, in a channel with two ends open, this jet-flow is distributed between the upstream and downstream flows, thereby moderating flame propagation. The flame oscillations are nonlinear in all cases where they are observed. The oscillation period grows with the blockage ratio but decreases with the thermal expansion. The present results also support the recent experiments, modeling and theory of flames in obstructed channels with both ends open, which all yielded steady or quasi-steady flame propagation prior to the onset of flame acceleration. Indeed, the present oscillations can be treated as the fluctuations around a quasi-steady solution.     

Effects of gas compressibility on the dynamics of premixed flames in long narrow adiabatic channels

We examine the dynamics of premixed flames in long, narrow, adiabatic channels focusing, in particular, on the effects of gas compressibility on the propagation. Recognising the importance of the boundary conditions, we examine and compare three cases: flame propagation in channels open at both ends, where the pressure must adjust to the ambient pressure at both ends and the expanding gas is allowed to leave the channel freely, and flame propagation in channels that remain closed at one of the two ends, where the burned/unburned gas remains trapped between the flame and one of the two walls. Earlier studies have shown that a flame accelerates when travelling down a narrow channel as a result of the combined effects of wall friction and thermal expansion. In the present work we show that compressibility effects enhance the transition to fast accelerating flames in channels open at both ends and in channels closed at the ignition end. In both situations, the accelerating flames could reach values that, depending on the effective Mach number, are as large as fifty times the laminar flame speed. In contrast, when the channel is closed at the far end, the acceleration is limited and the propagation speed is damped as the flame approaches the far boundary. Moreover, we show that, in channels closed at their ignition end, the flame in sufficiently long channels evolves into a steadily propagating compression-driven flame. The propagation speed of these flames depends exponentially on the constant-volume equilibrium temperature, which is higher than the (constant pressure) adiabatic flame temperature, and is therefore larger than for ordinary isobaric flames. Fast propagating compression waves cannot emerge in channels that remain open at their ignition end because of the reduced pressure forced by the open boundary.     

Controlled detonation initiation in hypersonic flow

Experimental evidence of controlled detonation initiation and propagation in a hypersonic flow of premixed hydrogen-air is presented. This controlled detonation initiation is created in a hypersonic facility capable of producing a Mach 5 flow of hydrogen-air. Flow diagnostics such as high-speed schlieren and OH* chemiluminescence results show that a flame deflagration-to-detonation transition occurs as a combined result of turbulent flame acceleration and shock-focusing. The experimental results define three new distinct regimes in a Mach 5 premixed flow: deflagration-to-detonation transition (DDT), unsteady compressible turbulent flames, and shock-induced combustion. A two-dimensional implicit-LES (ILES) simulation, which solves the compressible, reactive Navier-Stokes equations on an adapting grid is conducted to provide additional insight into the local physical mechanism of detonation transition and propagation.     

The role of spontaneous waves in the deflagration-to-detonation transition in submillimetre channels

Flame acceleration and transition to detonation in submillimetre two-dimensional planar and three-dimensional square channels were simulated by solving the compressible reactive Navier–Stokes equations. A simplified chemical–diffusive model was used to describe the diffusive transport and chemical reaction of a highly reactive mixture, such as stoichiometric ethylene and oxygen in 2D and 3D channels. The walls of the channels were modelled as no-slip and adiabatic. The initial flame acceleration and precursor shock formation were consistent with earlier results. Viscous dissipation in the boundary layer heats the reactants, which have been compressed by the precursor shock. The strength of the precursor shock and the amount of viscous dissipation increase until the temperature of the boundary layer is high enough to ignite the reactants. This produces a spontaneous wave, which, in most of the cases considered, initiates the detonation. The spontaneous wave first forms where the flame attaches to the wall in the planar channels, and forms at the corner where two walls meet in the square channels. In a separate study, the boundary layer also ignited in a computation for a circular tube containing a mixture hydrogen and oxygen represented by a detailed chemical reaction mechanism. The formation of spontaneous waves to the extent studied appears to be robust, and is relatively insensitive to channel geometry, fuel and oxidiser mixture, and the level of detail in the chemical–diffusive models used.     

Numerical simulation of turbulence transition and sound radiation for flow through a rigid glottal model

Large eddy simulation (LES)-based computational aeroacoustics techniques were applied to a static model of the human glottis, idealized here as a planar channel with an orifice, to study flow-acoustic interactions related to speech. Rigid models of both converging and diverging glottal passages, each featuring a 20 deg included angle and a minimal glottal diameter of 0.04 cm, with an imposed transglottal pressure of 15 cm H2O, were studied. The Favre-filtered compressible Navier-Stokes equations were integrated for this low-Mach-number flow using an additive semi-implicit Runge-Kutta method and a high-order compact finite-difference scheme with characteristic-based nonreflecting boundary conditions and a multiblock approach. Flow asymmetries related to the Coanda effect and transition to turbulence, as well as the far-field sound, were captured. Acoustic-analogy-based far-field sound predictions were compared with direct simulations and showed that dipole sources, arising from unsteady flow forces exerted on the glottal walls, are primarily responsible for the tonal sound observed in the divergent glottis case.     

Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture

We study flame acceleration and deflagration-to-detonation transition (DDT) in channels with obstacles using 2D and 3D reactive Navier–Stokes numerical simulations. The energy release rate for the stoichiometric H₂–air mixture is modeled by a one-step Arrhenius kinetics. Computations show that at initial stages, the flame and flow acceleration is caused by thermal expansion of hot combustion products. At later stages, shock–flame interactions, Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities, and flame–vortex interactions in obstacle wakes become responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. Computations performed for different channel widths d with the distance between obstacles d and the constant blockage ratio 0.5 reproduce the main regimes observed in experiments: choking flames, quasi-detonations, and detonations. For quasi-detonations, both the initial DDT and succeeding detonation reignitions occur when the Mach stem, created by the reflection of the leading shock from the bottom wall, collides with an obstacle. As the size of the system increases, the time to DDT and the distance to DDT increase linearly with d². We also observe an intermediate regime of fast flame propagation in which local detonations periodically appear behind the leading shock, but do not reach it.     

Explicit algebraic Reynolds stress model for compressible flow turbulence

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a new ARSM model is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for ARSM for compressible flow can hardly be obtained due to dilatation terms. We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.     

Numerical simulation of flames as gas-dynamic discontinuities

The dynamics of thin premixed flames is computationally studied within the context of a hydrodynamic theory. A level-set method is used to track down the flame, which is treated as a free-boundary interface. The flow field is described by the incompressible Navier–Stokes equations, with different densities for the burnt and unburnt gases, supplemented by singular source terms that properly account for thermal expansion effects. The numerical scheme has been tested on several benchmark problems and was shown to be stable and accurate. In particular, the propagation of a planar flame front and the dynamics of hydrodynamically unstable flames were successfully simulated. This includes recovering the planar front in narrow domains, the Darrieus–Landau linear growth rate for long waves of small amplitude, and the nonlinear development of cusp-like structures predicted by the Michelson–Sivashinsky equation for a small density change. The stationary flame of a Bunsen burner with uniform and parabolic outlet flows were also simulated, showing in particular a careful mapping of the flow field. Finally, the evolution of a hydrodynamically unstable flame was studied for finite amplitude disturbances and realistic values of thermal expansion. These results, which constitute one of the main objectives of this study, elucidate the effect of thermal expansion on flame dynamics.     

Visualization of shock-vortex interaction radiating acoustic waves

Unsteady compressible flow fields past a wedge and a cone, evolved by propagation and interaction of shock waves, slip lines, and vortices, are studied by shadowgraphs and holographic interferograms taken during the shock tube experiment. The supplementary numerical calculation also presented time-accurate solution of the shock wave physics which was essential to recognize the similarity and dissimilarity between the wedge and the conical flows. The decelerated shock detained by the vortex interacts with the small vortexlets along the slip layer, producing diverging acoustics: this phenomenon is more distinct in the case of wedge flow for a given shock Mach number. The decelerated shock penetrated through the vortex core constitutes a transmitted shock, which eventually merges with the diaphragm shock that bridges the vortex pair/vortex ring. This phenomenon became remarkably salient in the case of conical flow.     

A pressure-based algorithm for multi-phase flow at all speeds

A new finite volume-based numerical algorithm for predicting incompressible and compressible multi-phase flow phenomena is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regimes. The method is formulated on a non-orthogonal coordinate system in collocated primitive variables. Pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density, which become very small at low Mach numbers. The pressure equation is derived from overall mass conservation. The performance of the new method is assessed by solving the following two-dimensional two-phase flow problems: (i) incompressible turbulent bubbly flow in a pipe, (ii) incompressible turbulent air–particle flow in a pipe, (iii) compressible dilute gas–solid flow over a flat plate, and (iv) compressible dusty flow in a converging diverging nozzle. Predictions are shown to be in excellent agreement with published numerical and/or experimental data.     

连续激光内通道传输的弱可压缩流模型

 分析了激光在气体中传输时采用等压近似线性方程求解流场密度分布的优缺点，在高低速流场统一计算模型的基础上提出了基于压力原变量的分步求解的弱可压缩流计算模型，并分析了该模型的特点。采用该模型结合标量衍射理论对连续激光在封闭充气管道中受到的气体热效应影响进行了数值仿真。仿真结果与实验结果的对比表明，弱可压缩流计算模型能更精确地反映非自由边界热对流对气体密度分布的影响，进而反映流场对光束的影响。这说明弱可压缩流计算模型能较好地适应内通道光传输问题的仿真研究。     

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.     

Flame acceleration in long narrow open channels

We study the propagation of premixed flames in long but finite channels, when the mixture is ignited at one end and both ends remain open and exposed to atmospheric pressure. Thermal expansion produces a continuous flow of burned gas directed away from the flame and towards the end of the channel where ignition took place. Owing to viscous drag, the flow is retarded at the walls and accelerated in the center, producing a pressure gradient that pushes the unburned gas ahead of the flame towards the other end of the channel. As a result the flame accelerates when it travels from end to end of the channel. The total travel time depends on the length of the channel and is proportional to γ^?1ln(1 + γ), where γ is the heat release parameter.     

Transition in the propagation mechanism during flame acceleration in porous media

The combustion of stoichiometric hydrogen-air at various initial pressures was investigated in a 7.62 cm square cross-section channel filled with 1.27 cm diameter beads. The flame time-of-arrival and pressure time history along the channel were obtained by ionization probes and piezoelectric pressure transducers. Flame acceleration was found to be very rapid, e.g. at an initial pressure of 45 kPa the flame achieves a velocity of over 600 m/s in roughly 0.3 m. It was determined that at this high speed a well defined planar shock wave precedes a thick reaction zone. It was also shown that there is a transition in the flame propagation mechanism, similar to that observed in an obstacle laden channel [G. Ciccarelli and C. Johansen, The role of shock-flame interactions on flame acceleration in an obstacle laden channel, Proc. 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems, Minsk, 2009]. By varying the initial pressure of the mixture, changes in the axial location of the transition between combustion propagation regimes was also observed. A soot foil technique was used to identify the transition in the propagation mechanism, as well as to provide information concerning the local flow field around the beads and the overall average flow direction.     

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.     

Tunable optical transmission through gold hole arrays with converging and diverging shaped channels

We investigate the extraordinary light transmission through gold hole arrays with converging–diverging, diverging–converging, and converging shaped channels by using finite-difference time-domain (FDTD) method. We find that the resonance wavelength and intensity of each type of hole array are sensitive to the aperture size and unit number of the converging or diverging shape unit in the channels. We show that transmission behaviors are noticeably different for the gold hole arrays with such three different types of channel shapes. The resonant characteristics of the gold hole arrays with shaped channels have a number of important device applications, including filters, modulators and sensors.     

The Zero-Mach Limit of Compressible Flows

We prove that compressible Navier-Stokes flows in two and three space dimensions converge to incompressible Navier-Stokes flows in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the external force, the initial velocity, or the time interval. We assume instead that the incompressible flow exists and is reasonably smooth on a given time interval, and prove that compressible flows with compatible initial data converge uniformly on that time interval. Our analysis shows that the essential mechanism in this process is a hyperbolic effect which becomes stronger with smaller Mach number and which ultimately drives the density to a constant. Received: 10 June 1997 / Accepted: 15 July 1997     

Numerical study of strongly-nonlinear regimes of steady premixed flame propagation. The effect of thermal gas expansion and finite-front-thickness effects

Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based on fixed-point iterations and uses simple (Picard) iterations or the Anderson acceleration method that facilitates separation of different solutions. Using these techniques, we scan the parameter space of the problem so as to study various effects governing formation of curved flames. These include the thermal gas expansion and the finite-front-thickness effects, namely flame stretch, curvature, and compression. In particular, flame compression is demonstrated to have a profound influence on the flame, strongly affecting the dependence of its propagation speed on the channel width b. Specifically, the solutions found exhibit a sharp increase of flame speed with channel width. Under weak flame compression, this increase commences at b/λ_c ≈ 2 ～ 3, where λ_c is the cutoff wavelength, but this ratio becomes significantly larger as the flame compression grows. The results obtained are also used to identify limitations of the analytical approach based on the weak-nonlinearity assumption, and to revise the role of noise in flame evolution.     

Application of the Wiener–Hopf method for describing the propagation of sound in cylindrical and rectangular channels with an impedance jump in the presence of a flow

Exact solutions to problems of the propagation of acoustic modes in lined channels with an impedance jump in the presence of a uniform flow are constructed. Two problems that can be solved by the Wiener- Hopf method—the propagation of acoustic modes in an infinite cylindrical channel with a transverse impedance jump and the propagation of acoustic modes in a rectangular channel with an impedance jump on one of its walls—are considered. On the channel walls, the Ingard–Myers boundary conditions are imposed and, as an additional boundary condition in the vicinity of the junction of the linings, the condition expressing the finiteness of the acoustic energy. Analytical expressions for the amplitudes of the transmitted and reflected fields are obtained.     

微细光滑管内气体的流动与传热特性研究

在评述当前微细管内流动和换热特性研究的基础上提出了需考虑流体压缩性对速度剖面的影响。可压缩流动守恒方程组的数值解结果表明：运动流体的压缩性不仅使管内平均流速增加，而且使速度剖面更加饱满，从而使局域阻力系数和换热系数增加。与此同时，尽管管道的长细比很大，亦不可能出现充分发展的速度和温度剖面。这是由于微细管道中由于阻力引起的压力降可以很大，它所引起的流动加速达较大马赫数时，压缩性对阻力系数和传热系数的影响就不能忽略。