Flame propagation in the turbulent flow of a burning mixture

The propagation of a flame in the turbulent flow of a burning mixture is analyzed theoretically. An equation is derived for the gas temperature and velocity probability distributions. The solutions of this equation are analyzed and the rate of flame propagation is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–15, September–October, 1976.The author wishes to thank V. A. Sabel'nikova for critical comments.     

爆炸压力积聚工况下石松子粉尘爆炸火焰传播特性

搭建了一套兼具承压和可视性能粉尘爆炸实验平台,在压力积聚工况下实验研究了石松子粉尘爆炸火焰传播特性。实验结果表明:压力积聚工况下的石松子粉尘爆炸火焰呈现空间离散的束状结构,火焰锋面呈齿状。随着粉尘浓度的提升,火焰连续性增强,锋面趋于平滑,亮度增加,并在750g/m^3达到最佳。不同浓度条件下的石松子粉尘爆炸火焰在传播过程中均呈现明显的速度脉动特征,但脉动频率随粉尘浓度的增大而减小。爆炸火焰平均传播速度随粉尘浓度的增大先增大后减小,并在750g/m^3达到最高。不同浓度条件下的石松子粉尘爆炸火焰前期传播速度均高于后期传播速度。     

基于RGB颜色模型的玉米淀粉爆燃火焰传播速度

采用小尺度粉尘爆炸实验装置对不同质量浓度的玉米淀粉爆燃火焰传播过程进行了实验研究,建立了基于RGB颜色模型的火焰重构及形态学重建的粉尘火焰传播速度计算方法,计算了不同质量浓度下的玉米淀粉爆燃火焰传播速度。结果表明:采用基于RGB颜色模型的速度计算方法能够快速准确地计算出玉米淀粉爆燃火焰传播速度,火焰像素范围的确定是火焰速度计算的关键;管道内火焰传播速度受粉尘云质量浓度的影响,最大火焰传播速度随粉尘云质量浓度的增大先增大后减小,到达速度峰值的时间先缩短后增长,当质量浓度为0.63 kg/m3时,出现该实验条件下火焰传播速度最大值7.03 m/s。     

Relaxation,propagation of sound,and transfer processes in molecular gases

Taking account of rotational and vibrational degrees of freedom of the molecules, a system of equations has been obtained for a molecular gas which describes slightly nonequilibrium states with a length and time on the order of magnitude of the length and time of the rotational and vibrational relaxation. By solving this system, which describes the propagation of sound and the transfer process, the absorption coefficient, the dispersion of the velocity of sound, the transfer coefficients (in particular, the thermal conductivity coefficient), and an expression for the total tensor of the pressures have been found and analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 53–67, September–October, 1970.The author thanks V. M. Zhdanov for his valuable advice and remarks, and also Yu, Ya. Polyak and B. M. Chistoserdov for their useful evaluations.     

Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes

Advances in computing as well as measurement instrumentation have recently allowed for the investigation of a wider spectrum of physical phenomena in dynamic failure than previously possible. With increasing demand for specialized lightweight, high strength structures, failure of inhomogeneous solids has been receiving increased attention. Such inhomogeneous solids include structural composites such as bonded and sandwich structures, layered and composite materials as well as functionally graded solids. Many of such solids are composed of brittle constituents possessing substantial mismatch in wave speeds, and are bonded together with weak interfaces, which may serve as sites for catastrophic failure (Rosakis and Ravichandran (2000)).In the present study numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes is presented. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) softening generated by microdamage mechanisms; (iii) thermomechanical coupling (thermal plastic softening and thermal expansion); (iv) rate sensitivity.To describe suitably the time and temperature dependent effects observed experimentally during dynamic loading processes the kinetics of microdamage has been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elastic–plastic response can be obtained. The identification procedure is developed basing on the experimental observations. The finite difference method for regularized elasto-viscoplastic model is used. The edge-cracked bimaterial specimen is considered. In the initial configuration, the height of the specimen is equal to 30 cm, width is 12.5 cm and the length of the initial crack is equal to 2.5 cm. The length of the boundary over which impact is applied is equal to 5 cm, the rise time is fixed at 0.1 μs and the impact velocity is varied. The impact area is localized symmetrically or asymmetrically to the shorter axis of the specimen (symmetry axis of the cohesive band). Basing on the available data of recent experimental observation Rosakis et al. (1999) that have been carried out for relatively thin specimens both the plane stress and plane strain conditions are considered. The material of the specimen is AISI 4340 steel, while PMMA is the cohesive band, both modelled by thermo-elasto-viscoplastic constitutive equations with effects of isotropic hardening and softening generated by microdamage mechanisms and thermomechanical coupling. Fracture criterion based on the evolution of microdamage is assumed. Both, isothermal and adiabatic processes are considered.Particular attention is focused on the investigation of the interactions and reflections of stress waves and the influence of these waves on the propagation of macrocrack within the interface band. The propagation of the macroscopic crack within the material of the interface band for both symmetrical and asymmetrical impact cases has been investigated. It has been found that macrocrack-tip speeds vary from the shear wave speed to the dilatational wave speed of the material and is higher than the Rayleigh surface wave speed. This result is in accord with the experimental observations performed by Rosakis et al. (1999).     

Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type

A number of problems for the interaction of laser radiation with a heat-conducting half-space and a layer are considered. The obtained solutions are compared with each other and with the solutions of the classic heat equation and the wave equation. A laser impulse is modelled by defining the heat flux at the boundary for the opaque medium, or by defining the distribution of heat sources in the volume for the semitransparent medium. The power of the laser pulse depends on time as the Dirac delta function or as the Heaviside function do. It allows for the simulation of instant and continuous laser exposure on the medium. Temperature distributions are obtained by using Green’s functions for a half-space and a layer with the Dirichlet and Neumann boundary conditions.     

Turbulent Flame Speeds of Premixed Supersonic Flame Kernels

It is unclear whether turbulent flame speed scalings established in low speed regimes are applicable to supersonic flames. To investigate this question, the canonical flame kernel is investigated in a scramjet-like channel having a one degree wall divergence. The growth, shape and internal kernel dynamics are investigated. Results are presented for three Mach numbers, four equivalence ratios, and three turbulence generators. Schlieren photography provides flame images for growth rate statistics and particle image velocimetry (PIV) provides turbulence statistics and investigation of internal kernel dynamics. Supersonic flame kernels are self-propagating and respond to the equivalence ratio in a fashion that is similar to low speed flames. However, supersonic flame kernels have features that are not present in subsonic flame kernels. Baroclinicity, resulting from pressure-density misalignment, creates a reacting vortex ring structure. Further, the mean kernel shape has a Mach number dependence and the vortex ring enhances the turbulent flame speed through entrainment of reactants and augmented flame surface growth. Hence, the previously established (low speed) flame speed scalings are inappropriate for supersonic flame kernels. Drawing motivation from vortex ring literature, the ring propagation velocity is used as the characteristic velocity and a new flame speed scaling is proposed.     

Crack propagation resistance of Zeron 100 weld metal fabricated using the GTA and SMA welding processes

It is envisaged that super duplex stainless steels, as currently used in the offshore oil and gas industries, will find application in the emergent renewable energy sector in areas such as offshore wind, wave and tidal electricity/hydrogen generation. Such applications typically involve engineering components experiencing fluctuating loads. Sub-critical flaws inherent in welded joints are ideal sites for crack initiation and subsequent propagation leading to fast fracture. The current paper investigates the fatigue performance of two Zeron 100 weld metals in a benign environment (laboratory air). The effects of residual stresses and misalignment inherent from the welding process are also considered. The crack propagation threshold and the intrinsic crack propagation resistance of both weld metals was found to be similar to that of the base metal. However, the fracture toughness of the base metal was superior to the GTA weld metal, which was in turn better than the SMA weld metal.     

Self-Turbulent Flame Speeds

This paper reports an experimental investigation of premixed propane and methane-air flames propagating freely in tubes 1.5?m long and with diameters ranging from 26 to 141?mm. The thermo-acoustic instability was eliminated by means of a novel acoustic absorber placed at the closed end of the tube. We first remark that the flame can adopt different shapes either quasi-axisymmetric and normal to the mean direction of propagation, or inclined with a larger propagation speed because of the increase in flame surface area. The minima of the propagation speeds, corresponding to non-tilted flame propagation, are then analyzed using analytical models for the self-turbulent flame propagation. The concept of a cut-off wavelength appears to be relevant to explain the different behaviors observed on the rich side of methane-air and propane-air flames.     

Neck propagation

Propagation of a neck along the length of a tensile specimen as occurs in certain polymeric materials and in a few metals is studied. Two material models are considered: a nonlinear elastic solid, and an inelastic flow theory solid with both rate-dependent and rate-independent behaviors. For the elastic solid the states ahead and behind the neck transition can be obtained fairly simply from just the jump conditions governing continuity of mass, momentum and energy. For the inelastic solid a full three-dimensional analysis must be performed to obtain the same information, and an analysis of axisymmetric neck propagation is carried out.     

Cellular and Tulip Flame Configurations

Flame propagation in a plane channel with the formation of tulip and cellular configurations of the combustion front is simulated. The near-flame flow structure and the thermal flow structure are determined. An analogy is found between the tulip configuration and flame inflections at cell interfaces.     

Modelling of a Premixed Swirl-stabilized Flame Using a Turbulent Flame Speed Closure Model in LES

This paper proposes a combustion model based on a turbulent flame speed closure (TFC) technique for large eddy simulation (LES) of premixed flames. The model was originally developed for the RANS (Reynolds Averaged Navier Stokes equations) approach and was extended here to LES. The turbulent quantities needed for calculation of the turbulent flame speed are obtained at the sub grid level. This model was at first experienced via an test case and then applied to a typical industrial combustor with a swirl stabilized flame. The paper shows that the model is easy to apply and that the results are promising. Even typical frequencies of arising combustion instabilities can be captured. But, the use of compressible LES may also lead to unphysical pressure waves which have their origin in the numerical treatment of the boundary conditions.     

Lifted Diffusion Flame Stabilisation: Conditional Analysis of Multi-Parameter High-Repetition Rate Diagnostics at the Flame Base

Data from simultaneous 5?kHz OH-PLIF and Stereo-PIV at the stabilisation region of a propane/ argon lifted diffusion jet flame are presented for jet-exit Reynolds numbers of 10,000 and 15,000. The time history leading to the upstream appearance of flame islands is investigated for both flames. These flame islands are found to be preceded, on average, by a increased out-of-plane fluid velocity. Conditioning local flame statistics on the instantaneous flame base, as indicated by the OH image, permits analysis of upstream and downstream flame motions (in laboratory co-ordinates). The relative velocity is investigated by conditioning out the data with significant out-of-plane fluid velocity. This has introduced greater accuracy over previous attempts at estimating this quantity. No evidence is found for a correlation between increased turbulence intensity or the passage of large scale eddies with increased flame propagation speeds. Furthermore, divergence at the flame base is not found to correlate with upstream flame motion (as a combination of propagation and convection). The volume of the data investigated has led to the development of robust statistics for all quantities presented here.     

Flame Stabilization Mechanisms in Lifted Flames

Flame stabilization and the mechanisms that govern the dynamics at the flame base of lifted flames have been subject to numerous studies in recent years. A combined Large Eddy Simulation-Conditional Moment Closure (LES-CMC) approach has been successful in predicting flame ignition and stabilization by auto-ignition, but accurate modelling of the competition between turbulent quenching and laminar and turbulent flame propagation at the anchor point had not been demonstrated. This paper will consolidate LES-CMC results by analysing a wide range of lifted flame geometries with different prevailing stabilization mechanisms. The simulations allow a clear distinction of these mechanisms. It is corroborated that LES-CMC accurately predicts the competition between turbulence and chemistry during the auto-ignition process, the dynamics of turbulent flame propagation can be captured, however, the dynamics of the extinction process are not approximated well under certain conditions. The averaging process inherent in the CMC methods does not allow for an instant response of the transported conditionally averaged reactive species to the changes in the flow conditions and any response of the scalars will therefore be delayed. The dimensionality of the CMC implementation affects the solution and higher dimensionality does no necessarily improve results. Stationary or quasi-stationary conditions, however, can be well predicted for all flame configurations.     

Fatigue-crack propagation in metals

Cyclic-tension tests between constant limits of stress-intensity factor and at constant speed have been conducted on aluminum alloy RR 58 and mild steel BS 15. The resulting crack propagation was monitored against the number of cycles. The results, together with those obtained by other workers on similar metals, have been examined in the light of linear elastic fracture-mechanics concepts and two simple crack-propagation laws assessed. A typical linear relationship between crack length and number of cycles was observed, the relationship between crack growth and stress intensity was found to exhibit three separate regions and a law based on mean levels of the stress intensity found to adequately describe the results. There was evidence of a threshold value of stress intensity below which fatigue cracks may not grow.     

Quasi-kinematic flood wave propagation

Summary In the flood waves of natural streams, the plot of discharge versus simultaneous water level values at a river station usually show a little shift from the socalled steady rating curve. In other terms, natural flood waves normally have small loops and may be considered to be quasi-kinematic. Very often, on the basis of the steady rating curve and of the observed hydrograph at an upstream gage station, we can quickly and easily forecast the values and time of flood peaks at one or more downstream channel sections. This article describes a set of very simple formulas first to check whether the flood wave may be considered to be quasi-kinematic, and then to estimate the speed and the attenuation with which it moves downstream. For a number of prismatic channels, the results were compared with those obtained with equally simple, currently used formulas (Jones, Henderson) and with the exact solutions. The comparisons showed that the formulas proposed in this article are more general and accurate than the other known simple formulas and that, for flood loops of less than 10%, give results that are very near to being exact.

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Sommario Nei fenomeni di piena dei corsi d'acqua naturali la successions nel tempo dei valori di portata e livello idrometrico in una sezione d'alveo presenta, nella gran parte dei casi, modesti scostamenti dalla cosiddetta scala di deflusso di moto permanente: in altri termini normalmente le onde naturali di piena hanno cappi modesti e possono ritenersi quasi cinematiche. Molto spesso, data una stazione di monte in cui sia nota la scala di deflusso el'drogrammadei livelli, occorre prevedere semplicemente e rapidamente i valori e gli istanti dei colmi di portata e livello in una o più sezioni a valle. In questo articolo vengono presentate formule molto semplici per verificare dapprima che l'onda di piena possa ritenersi quasi cinematica, e stimare quindi la velocità e l'attenuazione con cui i colmi si propagano verso valle. I confronti fatti, per alcuni alvei cilindrici, con la soluzione esatta e con i risultati ottenibili con formule altrettanto semplici e di uso corrente (Jones, Henderson), mostrano che le formule proposte sono più generali e corrette di queste ultime, e danno risultati quasi esatti finchè i cappi di piena relativi sono inferiori al 10%.

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List of symbols P(x, z) steady rating curve - Q volumetric rate of discharge - q=Q-P flood loop - g gravitational acceleration - I water surface slope - c=dP/dA kinematic wave velocity - y water depth - p, s time and space steps - x, t channel distance starting upstream; time - z water surface height above datum - A, B channel cross section area and surface width - F=B Q ²/gA ³ Froude number - L,L ₀,L ₁,L ₂,L ₃ characteristic lengths of the channel - T=L/c characteristic time of the channel - f _x =f/x, f _f =f/t etc for the partial derivatives - Df/Dt,Df/Dx for the derivatives of functionf following the discharge peak     

Influence of Co-flow on Flickering Diffusion Flame

The influence of air co-flow on flickering methane diffusion flame was studied experimentally using the image processing technique and the proper orthogonal decomposition (POD) analysis. The flickering of the flame is characterized by the mean height, the oscillation amplitude and the Strouhal number, which are measured by the digital image analysis of the diffusion flame. The experiments are carried out for various combinations of burner diameters, fuel velocities and co-flow velocities. With increasing the velocity ratio of the co-flow to the fuel flow, the oscillation amplitude is decreased and the Strouhal number is increased slightly in proportional to the inverse Froude number, while the frequency jump occurs in the low co-flow velocity ratio. These results are commonly observed in all the burners of different diameters, while the critical co-flow velocity ratio to suppress the flickering is found to be increased with increasing the burner diameters due to the influence of Froude number. The POD analysis of the flickering flame shows that the flickering energy is dominant in the first two POD modes and they are axisymmetric except for the zero co-flow velocity case and fully suppressed case. The correlation of POD coefficients in the first two fluctuating POD modes suggests the suppression of large-scale structure of flickering due to the influence of co-flow.     

Flame computations by a Chebyshev multidomain method

A Chebyshev collocation method is proposed for the computation of laminar flame propagation in a two-dimensional gaseous medium. The method is based on a domain decomposition technique associated with co-ordinate transforms to map the infinite physical subdomains into finite computational ones. The influence matrix method is used to handle the patching conditions at the interfaces. This technique is particularly efficient since at each time step only matrix products have to be performed. The method is tested first on an elliptic model problem; it is then applied to laminar flame computations, including calculations of cellular instabilities of flame fronts.